Hemodynamic forces play a critical role in vascular pathology. For example, areas of disturbed flow in bifurcations in arterial tree are atherogenic, while areas of laminar flow are atheroresistant. These observations led researchers to investigate the relationship between the vectorial forces such as shear stress created by frictional forces of blood flow or the circumferencial tension (hoop stretch) caused by periodic vessel expansion and the alterations in morphology and function of arterial cells. Situated at the interface between the flowing blood and the vessel wall, endothelial cells (EC) are directly exposed to these forces. Previous studies report that they respond to these stimuli by adapting their morphology in relation to the characteristics of the applied flow in a precise and predictable manner and this morphological adaptation is concomitant with a drastic reorganization at the cytoskeletal level [1]. How these external physical stimuli are converted into intracellular signals, how the cells detect cues such as the direction of stretch or flow, the flow pattern or its intensity still remains largely unknown.
Cytoskeletal actin filaments and transmembrane proteins providing the link between
these filaments and the extracellular milieu are of particular interest in this intracellular
reorganization process as a response to applied mechanical stresses. Several biochemical
and molecular events take place in EC's following the onset of pulsatile flow. Many
studies have been devoted to identify them, and certain stress activated ion channels,
signaling pathways, and cascades of gene activation and protein synthesis have been
identified so far [2]. However for the elucidation of the primary mechanosensor(s) or the
key switch(es) controlling how mechanical stresses applied on the cells mediate
cytoskeletal reorganization, it is necessary to consider and evaluate the mechanical effect
of these forces hand in hand with biochemical processes at cellular level in a single
framework. We develop a theoretical model of cytoskeletal dynamics relating the
quantitative features of the physical stimuli at microscopic scale (stress applied on cell
surface molecules) to cytoskeletal modifications at macroscopic scale (mechanical
properties and kinetics of cytoskeletal filaments and alignment).
LE11 3TU, Leicestershire, UK
The trains of action potentials that travel over single neuron
dendritic trees with active spines are discussed in terms of both
continuum and lattice models. In contrast to continuum models, waves
in models with physically separated spines are shown to travel with a
non-constant profile. The properties of these waves (speed,
dispersion curve, ...) are obtained numerically for detailed single
neuron models with active spines and analytically for
integrate-and-fire spine-head dynamics.
A kinematic formulation of the continuum models, in which ßpike
trainscapture the underlying biological process, allows the
analytical discussion of irregular waves. Making use of the
properties of the previously calculated dispersion curves we predict
the existence of period doubling wave bifurcations and the existence
of non-periodic waves with a smooth connection between interspike
intervals of differing period. We confirm these predictions with
numerical simulations.
Damage spreading and shape space strategies in the immune system
Nöthnitzer Str. 38, 01187 Dresden, Germany
A model describing possible mechanisms with which antibody producing cells cope with a mutating pathogen has been developed. The two species involved are, namely, concentrations of antigen (species ) and immune system cells involved in the recognition and elimination process (species ). The coevolution of this two competing species is embedded in a space accounting for the possible geometrical and physico-chemical properties involved in the recognition and eliminations of pathogens [1]. Pathogen mutations, which correspond to movement in this space, activate movements of the ``-cell population via a finite range recognition length. The possible elimination of the pathogen is triggered by another finite range, elimination range. The fact that the antigen is allowed to proliferate, mutate and be eliminated within a non vanishing elimination range implements the idea that fuzzy matching effectively intervenes in the elimination of the antigen, avoiding a rapid growth of newly appearing mutants. Depending on the virus mutation and replication rates the virus can be completely eliminated or take over and persist in the system.
CA-oscillations in a pump driven dynamical model
2) Institut für Neurophysiologie, Universität zu Köln, D-50931 Köln, Germany
Oscillatory changes of cytosolic -concentration occur in various cell types spontaneously or in response to agonist stimulation. Most models dealing with -oscillations take the source for this widespread phenomenon to be the dynamics of the -release process, e.g., the interplay between the -concentration inside the cytosol and the -channels, which are assumed to have very special, -dependent receptor kinetics. In contrast to this approach, we have constructed a model based on the dynamics of a hypothetic -pump that is independent of the concrete structure of the -release process. In our model, the pump-process is described both by the -ATPase itself and by an ATP-generating mechanism, leading to a system that controls the -concentration inside the cytosol more precisely than the -ATPase alone. The resulting system of differential equations shows a rich behaviour, ranging from simple periodic oscillations to more complex patterns such as bursting and spiking, which is investigated by means of stability analysis and bifurcation diagrams.
Marileen Dogterom
Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
The assembly and disassembly of cytoskeletal filaments such as actin and microtubules can generate forces that contribute to various forms of (intra-)cellular motility. Experiments will be presented that allow for the quantitative study of forces generated by single growing microtubules as well as the effect of an applied load on the polymerization dynamics of these microtubules. So-called force-velocity curves were measured at different initial growth velocities in vitro, which will be compared to theoretical predictions. Data suggesting that the catastrophe rate of microtubules is greatly enhanced near the stall force will also be presented.
based on local cell dynamics
Postfach 100131, 33501 Bielefeld
Nöthnitzer Str. 38, 01187 Dresden, Germany
Most mathematical models of avascular solid tumour growth are formulated as appropriately constructed (integro-)differential equations, which incorporate concepts of apoptosis, necrosis, growth (inhibitor) factors or pressure inside the tumour (e.g. [Adam],[Greenspan]). These models are in particular based on the assumptions (i) that the tumour is spherically symmetric at all times and (ii) that the tumour sphere has a multi-layered structure, as for example a central core of necrotic cells, surrounded by an outer ring of proliferating cells. The growth of the tumour is modelled by the growth of the outer radii of these layers.
Here, we present a two-dimensional hybrid-cellular automaton model, formulated in terms of lattice-gas terminology [Dormann]. Based purely on local cell dynamics the selforganised formation of a two-dimensional (multi-layered) tumour can be observed. All cells follow the same migration and interaction rules. Each cell can proliferate, be quiescent or die due to apoptosis or necrosis. These processes are influenced by nutrient and/or growth factor concentrations, which satisfy deterministic reaction-diffusion equations.
Other cellular automaton models of avascular tumour growth include also non-local rules (e.g. [Kansal], [Qi]). Furthermore, not all of them are capable of developing a multi-layered tumour structure (e.g. [Qi]).
A Survey of Models for Tumor-Immune System Dynamics.
Birkhäuser, Boston, 1997.
Pattern Formation in Cellular Automaton Models - Characterisation, Examples and Analysis.
Dissertation, Universität Osnabrück (Germany), Applied Systems Science, (http://www.usf.uos.de/sabine/), 2000.
Models for the growth of a solid tumor by diffusion.
Stud. Appl. Math., 51:317-340, 1972.
A cellular automaton model of cancerous growth.
J. theor. Biol., 161:1-12, 1993.
Simulated brain tumor growth dynamics using a three-dimensional cellular automaton.
J. theor. Biol., 203:367-382, 2000.
CP231 Boulevard du Triomphe, B-1050 Brussels, Belgium
The proper working of many cells depends on the fine tuning of their level of cytosolic , which acts as a widespread second messenger. Many of these signals are mediated by a rise in the level of inositol 1,4,5-trisphosphate which itself activates the release of from the endoplasmic reticulum. It is now well-known that in most cell types, the resulting increase in cytosolic is organized at the temporal and spatial level (oscillations and waves). Spontaneous organization alos holds on a larger (mm) and smaller () length-scale. Waves or/and oscillations can indeed also be observed in cell cultures, or even in entire organs. Finally, short-lived subcellular increases associated with the coordinated opening of a few channels have also been reported. Given the non-linear character of the regulations involved in the generation of such processes and the variety of time and length scales necessary to describe those phenomena, theoretical models have been largely used to gain a better understanding of the dynamics of intracellular . Here, we focus on some aspects of these dynamics for which the dual point of view provided by experiments and modeling can be particularly fruitful.
Glushcov prospect 2, 01327 Kiev, Ukraine
The method and computing algorithm of targets search in genomes is developed with the purpose of study of influence on these targets by antisemantic oligonucleotides. With the purpose of approbation of a prospective new precision method of targets search for series of known genomes of microorganisms the comparative computer researches are conducted. Method, algorithm and computer program, developed on their basis, allow the following:
- 1.
- To simulate "walksöf pi-electron exaltation of a molecula DNA, previous to usual reading anyone, genetic information, written down on it;
- 2.
- To find working vacancies as place of strongly linked atoms and ions of trace substances with nucleotides. As a rule, the vacancies are placed in a narrow or in wide groove DNA in regions öf defect of masses änd are a combination 9 nucleotides.
- 3.
- To forecaste probability and number of pieces of a gene, which can be used during a transcription;
- 4.
- To find main gene-corrector, which to control shift of a framework of reading in a genome.
Institut für Biologie/Theoretische Biophysik
Invalidenstraße 42, 10115 Berlin, Germany
The structural design of ATP and NADH producing pathways such as glycolysis and the citric acid (TCA) cycle is investigated using optimisation principles. It is assumed that these pathways, combined with oxidative phosphorylation, have reached, during their evolution, a high efficiency with respect to ATP production rates. On the basis of kinetic and thermodynamic principles conclusions are derived concerning the optimal stoichiometry of such pathways. Extending previous investigations, both the concentrations of adenine nucleotides as well as nicotinamid adenine dinucleotides are considered variable quantities. This implies the consideration of the interaction of an ATP and NADH producing system, an ATP consuming system, a system coupling NADH consumption with ATP production, and a system consuming NADH decoupled from ATP production. It is examined in what respect real metabolic pathways can be considered optimal by studying a large number of alternative pathways. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations. In this manner, the steady state ATP production rate can be calculated for any possible ATP and NADH producing pathway. It is shown that most of the possible pathways result in a very low ATP production rate and that the very efficient pathways share common structural properties. Optimisation with respect to the ATP production rate is performed by an evolutionary algorithm. The following results of our analysis are in close correspondence to the real design of glycolysis and the TCA cycle: (i) In all efficient pathways the ATP consuming reactions are located near the beginning. (ii) In all efficient pathways NADH producing reactions as well as ATP producing reactions are located near the end. (iii) The number of NADH molecules produced by the consumption of one energy-rich molecule (glucose) amounts to four in all efficient pathways.
The analysis of more complex metabolic systems with a branched network structure neccesitates the development of new methods and computational tools. The branching in network structures is represented by chemical reactions that split or recombine molecules with different numbers of carbon atoms. In order to apply optimisation principles on such pathways a method has been developed to construct alternative network structures. Presently a systematic approach is being followed to elucidate the design of possible alternative pathways. Statistical analyses have been performed on the stoichiometric properties of these networks. The frequency of networks able to perform certain conversions between molecules with a different number of carbon atoms is investigated as well as the statistical occurence of conservation rules.
Tetanus-induced Presynaptic Calcium Dynamics in Single Neurons
Institut für Theoretische Physik
Technische Universität Dresden
D-01062 Dresden, Germany
A model is presented, which describes the presynaptic calcium influx in single neurons
due to a tetanus. The model consists of a system of coupled differential equations, based on
existing models of reaction-diffusion systems. Induced by high or low frequency stimulation via
presynaptic incoming action potentials, specific voltage dependent calcium channels in the
presynaptic cell membrane open. The resulting calcium influx now opens specific intracellular calcium
channels, whereby there is a further calcium influx into the cell. The calcium surplus
is pumped out up to the initial concentration with the aid of specific calcium pumps and exchangers.
The presynaptic and postsynaptic calcium dynamics is involved in the formation of synaptic
plasticity. Thus it is directly related to the neural basis of the memory of mammals.
We applied a recently developed magnetic bead micro-rheometer (Magnetic Tweezers) to investigate the influence of actin on the properties of the cell membrane of endothelial cells (HUVEC). Superparamagnetic beads of a diameter of 4.5m are coated with different integrin-binding proteins (e.g. fibronectin, collagen IV, invasin) and thus linked to the actin cortex. Via an external magnetic coil we can apply forces of up to 5 nN to these beads. The displacement is measured in real time by a single particle trecking algorithm. To characterize the properties of the actin cortex we additionally analyzed the strain field, which we visualize by non-magnetic beads attached to the cell membrane and by fluorescence staining of the mitochondria inside the cell.
Am Mühlenberg 1, Golm, Germany
The central interest of our laboratory is to increase our understanding of carbohydrate metabolism within the potato tuber. To achieve this we have previously created numerous transgenic plants characterised by either antisense inhibition or ectopic overexpression of proteins mediating the major pathways of carbon metabolism. Whilst these plants have provided direct evidence of the regulation of these pathways they have also yielded new insights into both the flexibility of plant metabolism and the complexity of the regulatory circuits and signalling mechanisms within the plant cell (Trethewey et al., 1998). We therefore decided to broaden the scope of our studies by developing a method capable of simultaneously detecting a wide range of metabolites.
The method we developed is based on gas chromatography linked to mass spectrometry and allows the detection of a total of 150 compounds, 78 of which we identified with respect to their chemical nature. Analysis of transgenic potato tubers cytosolically expressing either a yeast invertase (both in combination with and independently of a bacterial glucokinase), or a bacterial sucrose phosphorylase revealed large scale differences in metabolite content with respect to wild type. We are in the process of analysing these data using contemporary bioinformatic methods in the hope of better understanding regulation of carbon metabolism within the potato tuber.
Trethewey, R.N., Geigenberger, P., Riedel, K., Hajirezaei, M.-R., Sonnewald, U., Stitt, M., Riesmeier, J.W., Willmitzer, L. (1998) The Plant Journal (15), 199-118
Nöthnitzer Str. 38, 01187 Dresden, Germany
During the course of an immune response, the affinity of antibodies acting against the pathogen or toxin which invaded the organism increases. This phenomenon of affinity maturation of the humoral immune response is interesting but not completely understood. The process of affinity increase takes place intensively in germinal centers, whose structure and dynamics have been experimentally investigated [Liu], [Berek].
In the germinal centers, B cells able to produce antibodies undergo intense proliferation associated to a high mutation rate (hypermutation). Cells which produce antibodies with high affinity against the antigen are selected to survive. Some theoretical models have been proposed where the phenomenon is described as an optimized evolutionary process [Kepler]. Still however, there is no definitive answer related to the mechanisms of selection. The most common proposal is that a local competition for antigen takes place. Only recently, however this aspect has been explored theoretically in detail [Kesmir].
In this work, we assume that such a local competition mechanism exists and propose a simple model for a global clone selection of the locally successful cell clones. We assume that the probability of selection depends on the affinity of the cells and also on some global quantity that regulates the threshold for selection. We let this global quantity depend on the number of selected cells and show that under specific conditions, our model can reproduce affinity maturation. The model is investigated considering the existence of accumulation of mutations (``recycling'') or not, and the results for the two scenarios are discussed.
University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
Prior to any immune response is the binding of antibody to antigen or T-cell receptor to MHC molecule. The binding process requires that portions of the two binding structures have complementary shapes that can closely approach each other. A bound receptor-ligand complex will settle into a minimum (free) energy configuration, dissipating binding energy in the process, while the probability and permanence of the binding depends on whether the released binding energy exceeds some threshold energy. A common property of receptors is that they seem to interact with regions of about contact residues, as has been found experimentally and can be also understood theoretically.
We propose a statistical model that describes the receptor-ligand binding
and takes into account that the local binding energy depends on the
environement.
This approach allows us to calculate analytically the probability
distribution, , for the formation of a single binding region over
contact residues as a function of both the threshold energy and
the distribution of binding energies.
Furthermore, we introduce a binding parameter to study the case where
the binding process results into several seperate binding regions along the
receptor-ligand overlap region.
This enables us to compare receptor-ligand bindings that differ by the
number of seperate binding regions and to draw conclusions from the
underlying distribution of binding energies.
J.K. Percus, O.E. Percus, and A.S. Perelson, Proc. Natl. Acad. Sci. USA 90, 1691 (1993).
of Dictyostelium discoideum
Department of Chemical Engineering
and
Center for Nonlinear Dynamics of Chemical and Biological Systems
Institute of Chemical Technology, Technická 5, 166 28 Prague 6,
Czech Republic
The aggregation of Dictyostelium discoideum (DD) cells in the cell suspension is mediated by chemoattractant cyclic adenosin monophosphate (cAMP) which propagates from randomly organized centers in the form of spiral or circular pulses of increased cAMP concentration. DD cells feel the arriving cAMP and respond to it by both an autocatalytic production of cAMP and by the motion against the gradient of cAMP. The periodic emission of cAMP pulses from the centers enable DD cells to gather in these centers and create fruiting bodies. The propagation of cAMP pulses, resulting from the mutual interaction of both an autocatalytic production of cAMP in cells and the diffusive transport of cAMP through the intercellular space, can be altered by an externally applied electric field that can enhance the transport of negatively charged cAMP.
The presented poster will show the results of numerical studies
of an applied electric field on the cAMP pulses propagating
in the model, spatially 2 dimensional, layer of DD cells. In the model
the Martiel-Goldbeter kinetic scheme is used to describe
the production of cAMP and Nernst-Planck
equation is used to describe the intercellular transport
of cAMP both by diffusion and by electromigration.
Depending on the strength
and the orientation the electric fields of low intensities
(up to 6V/cm) were found to i) change both the propagation
velocity and the amplitude of the pulses, ii) to annihilate
the propagating pulse, and iii) to induce the formation of new centers
of cAMP pulses. The poster aims to present also
the results of now undertaken experimental studies of electric
field effects on some features of DD cells aggregation.
Voltage-Clamp Studies on Gap Junctions
University of Delhi South Campus
New Delhi 110021, India
Gap junction provides low resistance pathways for cell-to-cell communication via passive diffusion of ions, metabolites, second messengers etc. upto 1200 daltons and thus, controls embryonic development and differentiation, and neuronal communication. It has been pointed out in our previous work that passive diffusion channels behave cooperatively which in turn depends on the structural parameters and also membrane potentials (Ghosh, 1993; Ghosh & Mukherjee, 1993;). In the present work, we demonstrate through bilayer electrophysiological experiments that the cooperative behavior of gap junction multi-channels depends on the clamping potentials across the bilayer lipid membrane. Further, we establish that the voltage dependence of the fraction of gap-junction channels open has a sigmoidal pattern and the relation follows tan hyperbolic expression. We predict that the cooperative behavior of membrane channels which has very significant consequences in cellular processes, especially in embryonic tissues and neuronal communication.
in contracting muscle: regulation of contractile
function and ATP free energy potential
J.A.L. Jeneson, H.V. Westerhoff and M.J. Kushmerick
Department of Pediatrics, University Medical Center Utrecht, NL, Department of Molecular Cell Physiology, Faculty of Biology, Vrije Universiteit, Amsterdam, NL, Departments of Bioengineering, Physiology and Biophysics, and Radiology, School of Medicine, University of Washington, Seattle WA, USA.
The free energy of ATP hydrolysis constitutes the chemical energy that drives muscle contraction. Skeletal muscle contractile activity is under external, neural control, and so is therefore its ATP metabolic activity. Yet, empirically, ATP free energy demand during contraction cannot outstrip supply on a sustained basis. The muscle fatigues instead of going into rigor. This homeostatic regulation of the ATP potential in muscle is the subject of investigation here. We tested whether a minimal network model of ATP metabolism in contracting muscle composed of myofibrillar actomyosin ATPase, sarcoplasmic reticular Ca2+-ATPase and mitochondrial ATP synthase, would be homeostatic with respect to the cellular ATP potential. We used the mathematical theorems of modular metabolic control analysis that provide tools for such a network analysis under steady-state conditions. The analysis was applied to a set of in vivo 31P NMR spectroscopy data on steady-state energetics from human muscle. We found that kinetic control of the network resides in the main ATPase demand module in the network, the actomyosin ATPase, over much of the range of sustainable work rates. But this kinetic control of metabolic flow in the ATPase network shifts towards the mitochondria (= supply of ATP potential) at high work rates. As a consequence, ATP free energy consumption cannot outstrip the intrinsic cellular capacity for ATP free energy supply on a sustained basis. These two control properties endow the ATPase network in muscle with both apt regulation of contractile function as well as homeostatic regulation of the cellular ATP free energy potential.
Supported in part by NIH grant AR36281 (to M.J. Kushmerick) and the Netherlands Organization for Scientific Research (NWO; to H.V. Westerhoff).
Institute for Plant Genetics and Crop Plant Research, Gatersleben, Germany
In the last 15 years, much research effort has been focussed on the consequences of constitutively altering
the expression of genes encoding crucial metabolic enzymes. Whilst much knowledge has been obtained using this
approach it has several clear limitations. Inducible promoter systems could overcome these problems as they
allow a modification of enzyme activities in a precise and defined manner only during a specific point in
plant development.
An ethanol inducible gene switch has been used by Caddick and coworkers to manipulate carbon metabolism in
transgenic tobacco plants1. They showed that upon rapid induction of a yeast cytosolic invertase, a marked
phenotype appears in developing leaves that is absent from leaves that developed before induction or after
return to basal state.
In our project, we are currently establishing systems for enhanced expression
(and relaxation of expression) of different heterologous enzymes introduced into
the carbon metabolism in transgenic potato tubers. The transgenes are all
regulated by the same ethanol inducible promoter system. We have chosen three
enzymes all of which are well characterized concerning constitutive expression
and the effect thereof on carbohydrate metabolism: a yeast cytosolic
invertase and a bacterial sucrose phosphorylase (both cleaving sucrose and
therefore contributing to the generation of momomers for starch production), as
well as a bacterial pyrophosphatase (drawing away pyrophosphate from the UDP-glucose pyrophosphorylase
reaction, therefore producing a decrease in monomers required for starch production).
The aim of the project is to follow the perturbation on the level of
transcription, protein, enzyme activity, metabolite levels, and fluxes.
Preliminary results will be presented.
Caddick MX, Greenland AJ, Jepson I, Krause KP, Qu N, Riddell KV, Salter MG,
Schuch W, Sonnewald U, Tomsett AB (1998) An ethanol inducible gene switch for
plants used to manipulate carbon metabolism.Nat. Biotech. 16: 177-180
Trethewey RN, Fernie AR, Bachmann A, Fleischer-Notter H, Geigenberger P,
Willmitzer L (2001) Expression of a bacterial sucrose phosphorylase in potato
tubers results in a glucose-independent induction of glycolysis.Plant Cell
Environ. 24: 357-365
Farré EM, Bachmann A, Willmitzer L, Trethewey RN (2001) Sprouting of potato
tubers is significantly accelerated by the expression of an alien
pyrophosphatase. Nat. Biotech. 19: 268-272.
by molecular nanomachines
Institute for Cellular and Molecular Biology
Center for Nano and Molecular Science
Texas Materials Institute
All eukaryotic cells (any cell more advanced in evolution than a bacterium) depend in their internal structure, organization, and function on the cytoskeleton, a polymer mesh within the cell interior. Cells reversibly assemble protein filaments (actin filaments, intermediate filaments, microtubles) and accessory proteins into extensive, three-dimensional networks. Among these proteins, actin forms semiflexible polymers, which create stress fibers spanning the entire cell interior and a homogeneous network underlying the cell membrane, with unique physical properties. These properties enable cells to migrate and to respond to deforming stresses (including active feedback). The polymer dynamics of conventional polymer systems and the consequential viscoelastic properties are a result of the Brownian motions of the polymer chains. In the case of the actin cytoskeleton, actin-binding proteins behave as energy consuming nanomachines (e.g.. the molecular motor myosin), which control its polymer dynamics. These proteins impact on the resulting viscoelasticity cannot be described by existing polymer theories. To unravel the physics underlying the complex and highly dynamic features of actin networks, we synergetically apply soft condensed matter physics, nonlinear dynamics, nano-particles, laser physics, single molecule microscopy, and genetic techniques to study, in vivo, the actin cytoskeleton of cells as well as, in vitro, reconstituted elements of this cytoskeleton. Due to the central role of the actin cytoskeleton for cell function our newly gained knowledge in polymer physics directly results in novel strategies for the early detection of cancer cells and for quick nerve regeneration.
In the paper we prove the existence of travelling wave solutions
for systems of reaction-diffusion equations of the form:
where , , , .
We assume that the functions satisfy so called local monotonicity
conditions. To be more precise, we assume that for all
we have:
(1)
for all satisfying ,
(2)
for all satisfying .
The species corresponding to the variables
may be called mutually symbiotic, whereas the species
corresponding to may be called competitive.
Such systems may thus be called -symbiotic -competitive.
They may describe various kinds of biological phenomena,
e.g. the dynamics of mutualist macrophages in tumours.
A dynamical model for helper T cell differentiation following antigen presentation
The proliferation of helper T cells following antigen presentation by dendritic cells is mediated by cytokines produced by both cell types, costimulatory interactions between the two, and physical parameters like cell crowding. We present a mathematical model which integrates these elements to reproduce certain fundamental dynamics of helper T cell population development. Our model, calibrated to both in vitro and in vivo data from the literature, accounts for the competition of naive and memory T cells for presented antigen, the expansion and interaction of naive, effector, and memory populations, and the activation-induced cell death, growth factor withdrawal apoptosis, and anergization of T cells under various conditions.
Variations in antigen concentration, costimulation, and intercellular adhesion have, in particular, been shown in the literature to influence the Th1/2 polarization of a naive immune response. Our model demonstrates that these factors can regulate Th1/2 polarization through population dynamics alone, without recourse to explicit cellular signalling. Emergent regulation of this sort may reinforce other mechanisms governing the Th1/2 differentiation of naive cells.
Institut für Neuro- und Bioinformatik
Seelandstraße 1a, 23569 Lübeck, Germany
Regulatory networks are systems that mediate a large array of central biological processes, such as cell differentiation and morphogenesis. Computer models simulating regulatory networks within the contexts of these processes are important tools for making progress in understanding the fundamental biological principles underlying the wide range of functions exerted by such networks. It is desirable to use a common framework for representing regulatory networks within such models. Providing such a framework is the motivation of transsys.
The transsys core is a computer language like formalism for describing regulatory networks. transsys network descriptions can readily be integrated into a variety of models of morphogenesis, development, pattern formation, differentiation etc. Currently, transsys has been built into Lindenmayer systems and lattice models. In the contribution, an outline of the theoretical basis of transsys and results obtained with the two modelling frameworks mentioned above will be presented.
Institut für Neuro- und Bioinformatik
Seelandstraße 1a, 23569 Lübeck, Germany
Transcription factors and their binding sites have become a focal point of bioinformatics research since it became clear that regulatory networks are a centerpiece of genetic information processing. Transcription factor binding sites are short sequence words. Knowledge about the location of these binding sites on the genome gives important information not only about the structure of the regulatory networks the transcription factor is involved in but also e.g. about the location of genes and other coding regimes on the genome. A number of recognition schemes have been developed in bioinformatics, however, finding these binding sites has turned out to be a difficult task which can only be solved with prior knowledge about the principle binding behavior of transcription factors.
A model for the basic probability distributions underlying the coevolution of the transcription factor and its binding sites within the genome is presented. Maximum entropy arguments give insight into the connection between the information content of these binding sites and the binding behavior of the transcription factor. This might be used as prior kowledge for improved recognition schemes. Further, it gives insight into an intriguing finding that still awaits a complete bioinformatic explanation, namely the observation that transcription factor binding sites seem to occur on the genome approximately with a frequency which corresponds to their information content. It is shown that this is not necessarily the case.
A simple deterministic model of Brownian motors
Nöthnitzer Str. 38, 01187 Dresden, Germany
We analyse the diffusion of Brownian particles in a simple system of deterministically coupled maps. For certain values of its two control parameters this model is reminiscent of a simple random walk on the line, however, there is always an infinite memory in the particle dynamics. This enables to study whether microscopic dynamical correlations can play a role in Brownian motion. We first show that our model is a time-discrete version of the dynamics of Brownian particles in asymmetric periodic potentials under the influence of a periodic force. We then exactly calculate the drift and diffusion coefficients for our model. We find that there exist current reversals under parameter variation, as is well-known for Brownian motors. We argue that these current reversals are due to microscopic correlations in the particle dynamics. Such simple models might as well be used to study the correlated motion of cells on substrates.
Transmission experiments to investigate the effect of vaccines on the transmission of infectious diseases
Wageningen University and Research Centre (Wageningen UR), Institute for Animal Science and Health, P.O. Box 65, 8200 AB Lelystad, The Netherlands
Vaccines are often designed to reduce morbidity and mortality due to infectious diseases. However, to ban an infectious agent out of a population of hosts, its transmission between individual hosts should be reduced as well. In fact, it should be reduced to such an extent, that the average number of individuals infected by one infectious individual, i.e. the basic reproduction ratio , is smaller than 1.
In veterinary epidemiology, reduction of transmission is often an even more important goal than reduction of clinical signs, because of trade reasons (to maintain the status freedom of infection, for example foot-and-mouth disease) or because the infection is a zoonosis (bovine TB, Salmonella etc.). To test vaccine effectiveness for the reduction of transmission, transmission experiments are helpful tools. Transmission experiments are experiments in which some animals in a group of animals are infected with an infectious agent and transmission of the agent to the initially uninfected, susceptible animals is followed in time. By comparing experiments with and without vaccination of all animals and by estimating from experiments, vaccine effectiveness can be investigated.
This poster will present some statistical methods to deal with transmission experiments. These methods are based on a mathematical model for the spread of infectious diseases, the so-called S-I-R model (Susceptible - Infectious - Removed). Using an example experiment with classical swine fever virus it will be shown how to test vaccine effectiveness against a control group and how to estimate basic reproduction ratio . Advantages and pitfalls of this experimental approach will be discussed.
Invalidenstr. 42, 10115 Berlin, Germany
With the techniques of genome-wide transcriptional analysis the gene expression of yeast under several conditions can be measured (eg. [1,2]). These measurements confirm that cells are able to adjust the expression of genes to the environmental conditions and to the necessities of the cellular state. From the view point of metabolic modelling the regulated gene expression leads to two interesting questions: 1) Given be a state of a cell (or a limited metabolic network) characterized by metabolite concentrations, fluxes, presence of enzymes and activity of genes. If the cell is now faced with an environmental change (stress, supply of a new substrate), which would be the best way for the cell to react on this change? Which fluxes must be increased or decrease to balance the cellular metabolism, which enzymes must be generated to make use of the new substrate, which genes should be activated to produce the necessary enzymes, which genes must be repressed to take care of resources? A mathematical model is used to explain for a simple linear chain of metabolic reactions the optimal temporal pattern of enzyme concentration if an initial substrate has to be transformed into a vital product as soon as possible and under the condition of limited cellular resources. Extensions of this model include the optimal pattern of gene activity and mRNA formation to approach the favourable pattern of enzyme concentations [3,4]. 2) In many cases it is known in principle how the flow of information from an external signal like stress or supply of substrate via a signalling cascade to an altered gene expression and finally to an adjustment of the cellular metabolism proceeds. One can try to understand the dynamics of this process by describing the reactions with a set of differential equations,which in turn can be analysed with mathematical tools. For the answer of yeast cells to osmotic stress a model is developed which shall help to understand the dynamics in the signaling pathway and which may point out why the cells increase or decrease the expression of several genes the products of which play an important role in the energy metabolism of the cell and in the glycerol production. Metabolic control analysis is applied to detect pattern and strength of influence between the different subsystems which take part in the cellular response to the stress [5].
[1] DeRisi, J.L., Iyer, V.R. & Brown, P.O. 1997. Exploring the metabolic and genetic control of gene expression on a genomic scale. Science, 278, 680-686.
[2] Rep, M., Krantz, M., Thevelein, J.M. & Hohmann, S. 2000. The transcriptional response of Saccharomyces cerevisiae to osmotic shock. J. Biol. Chem., 275, 8290-8300.
[3] Klipp, E. and Heinrich, R., 1999, Competition for enzymes in metabolic pathways, BioSystems, 54, 1-14.
[4] Klipp, E., H.-G. Holzhütter and Heinrich, R., 2000, Reprogramming of metabolic systems by altering gene expression. In: Animating the Cellular Map (ed. Hofmeyr, J.H.S. et al., Proceedings of the 9th International Meeting on Biothermokinetics), Stellenbosch University Press, Stellenbosch.
[5] Hofmeyr, J.-H.S. & Westerhoff, H.V. 2001. Building the cellular puzzle. Control in multi-level reaction networks. J. Theor. Biol., 208, 261-285.
Tracer studies of thermally and non-thermally activated
dynamics of semi-flexible actin filaments
11 rue Pierre et Marie Curie, 75005 Paris, France
In this work, we present studies of actin filament dynamics, from
single filaments to highly entangled solutions, including active
systems in the presence of ATP and myosin S1 motor protein domains.
Since the rheology of actin has classically been carried out in bulk
and at thermal equilibrium, the interaction between actin and myosin
represents a source of non-thermal excitation coupled to ATP
hydrolysis. We investigate these non-thermal fluctuations by two
approaches: tracer particle micro-rheology of semi-dilute F-actin
solutions in the presence of the motor domain of skeletal muscle
myosin is investigated by diffusing wave spectroscopy (DWS), and
single filament dynamics are probed by video microscopy and image
contour analysis. We find that microfilaments show enhanced dynamics
and an anomalous tangent correlation function. These observations
raise questions about the interplay between myosin activity and
microfilament mechanics and dynamics.
In addition, we present a new method to probe the conformations of
single actin filaments by fluorescence microscopy. By end-to-end
annealing labelled and unlabelled filament fragments, we create long
filaments whose ends are specifically tagged by fluorescent tracers.
These end-tracers are tracked by image analysis to measure the radial
distribution function and projected length fluctuations, showing good
agreement with recent theoretical predictions [1-3]. This new
tagging procedure offers the advantage that the majority of the
filament does not need to be labelled and stabilized (i.e. with
phalloidin derivatives) and greatly eases the image analysis to study
filament conformation and position. An application to an automatic
analysis of motility assays will be discussed.
1. Whilem J., Frey E. Phys. Rev. Lett., 77, 2581 (1996)
2. Granek R. J. Phys. II 7, 1761 (1997)
3. Gittes F, MacKintosh F.C., Phys. Rev. E, 58, R1241, (1997)
Benno Hess
Faradayweg 4-6, D-14195 Berlin, Germany
Max-Planck-Institut für Molekulare Physiologie,
Otto-Hahn-Str. 11, D-44227 Dortmund, Germany
present address: Max-Planck-Institut für Medizinische Forschung,
Jahnstr. 29, D-69120 Heidelberg, Germany
Enzymes are single-molecule catalysts representing chemical protein machines. We show that enzymic reactions in small spatial volumes, characteristic for a living biological cell, may proceed in a special kinetic regime of a molecular network. In this regime the enzymic population behaves like a network of communicating machines. When interactions between the machines are sufficiently intensive, strong correlations between intramolecular dynamics of individual machines in the network can emerge. Thus, mutual synchronization of enzymic turnover cycles develops. The theoretical analysis, which has been performed for allosteric product-activated and product-inhibited reactions, as well for the non-allosteric reactions with substrate loops, show that coherent intramolecular dynamics is a robust phenomenon, which persists even when significant intramolecular fluctuations are present. For allosteric enzymes composed of several subunits, both the synchronization of reaction cycles of the whole set of enzymes is possible in addition to synchronization of reaction cycles of subunits within enzymes.
Humboldt-Universität zu Berlin
Invalidenstraße 42, 10115 Berlin, Germany
Cells react to external stimuli and to their internal needs by the induction or repression of genes. The expression of each gene relies on the specific processing of a number of regulatory inputs, which are still unknown in most cases. Constructing large genetic networks in an unsupervised fashion, thus from expression data alone, suffers from two drawbacks: firstly, the observed expression values carry large errors, and secondly, a realistic network model would involve many quantities besides the concentrations of mRNA species. However, the coregulation of genes may be described assuming a small number of ``effective'' regulators, each acting on a large group of genes and varying between distinct biological situations. In contrast to clusterings, linear models rely on the idea of a combinatorial control, describing the expression levels of genes as linear functions of common hidden variables. Ideally, these variables might be related to distinct biological causes of variation in the data, like regulators of gene expression, cellular tasks, or responses to experimental treatments. We applied independent component analysis (ICA) to gene expression data, deriving a linear model whose hidden variables we term ``expression modes''. According to the ICA model, the linear influences of different modes show a minimal statistical dependence. Each mode defines a cluster of specifically up- and downregulated genes. The expression modes and their influences can be used to visualize the samples and genes in low-dimensional spaces. Studying cell cycle-related gene expression in yeast, we found that the dominant expression modes could be related to distinct regulatory processes, like phases of the cell cycle or the mating response. Cell-cycle behaviour was mainly manifested by three modes showing a periodic behaviour. The influences of the dominant modes showed distributions with large tails, indicating that they exert strong effects on specific groups of genes. A projection to these modes helps to define problem-relevant metrics highlighting particular biological functions, to denoise the data, and to compress them in a biologically sensible way. Reducing the number of data dimensions may be useful to lower the effort in further analysis, while the most relevant biological information is maintained. Identifying a small number of effective key variables may also be a first step towards simple dynamic models of gene regulation.
Stochastic processes in immunosenescence: stress as noise and
T lymphocyte population dynamics
Via Irnerio 46, 40126 Bologna, Italy
We propose a stochastic dynamical system for the Virgin (CD8+CD95-) and Memory (CD8+CD95+) T lymphocytes evolution on the whole human life span. The changes occuring in the Immune System (IS) during life (Immunosenescence), can be envisaged as a consequence of a continuous remodeling of IS. The IS aging is not a simple involution of defensive functions in the elderly people but a profound reshaping of all mechanisms involved in the recognition and neutralization of damaging agents, called antigens. Describing the evolution of Virgin and Memory T cells in the peripheral system from new borns to centenarians we investigate the effect of an aspecific chronic stress impinging upon both populations over long time scale. The crucial phenomena in Immunosenescence such as the Shrinking of Immunological space (due to the competition between T memory clones), the conversion within the T cells compartments and the fluctuations of the environmental stress have been taken into account in the model, obtaining a nice agreement with the experimental data. The stochastic approach, with the hypothesis that the depletion of virgin CD8+ T cells can be considered a reliable biomarker of mortality, produces a survival curve capable of fitting demographic data whose rate of mortality is definitely different from the Gomperz exponential law.
Uppal Road, Hyderabad 500 007, India
Designing simple biochemical networks that can regulate temporal expression of multiple genes and their products can provide, among other applications, a theoretical framework for understanding regulation of gene expression in cells. We have modelled a simple three-step biochemical network which is negatively regulated in three distinct biologically realistic manner as observed in cellular systems. We have studied the dynamic behaviour of the three models for changes in parameters and the state variable. The robustness of the three networks varies considerably under perturbations.
Im Neuenheimer Feld 294, 69 120 Heidelberg, Germany
The aim is to build a model for pattern formation in Hydra. Hydra, a fresh-water polyp, is one of the oldest and simplest multi-cellular organisms and plays an imporatant role as a prototype for morphogenetic patterning. This polyp is endowed with an amazing capacity to regenerate any lost body part. Old and damaged cells are unceasingly replaced by newly-generated ones. The location of cells determines their function, which can be shown by a very simple cutting experiment.
The concept of pattern generation is that cells are endowed with positional memory tightly linked to a gradient in the potential for head formation in the intact animal (positional value). The objective here is to build a receptor-based model without imposing any initial gradient. The model is based on the idea that epithelial cells secrete a regulatory biochemical, which diffuses locally within the interstitial space and binds to free receptors on the cell surface. Positional value is determined by the density of bound receptors.
The model is given in the form of three diffusion-type equations. It takes into consideration the density of free receptors, bound receptors and the ligands. It is shown when in such model patterns can evolve due to a diffusion-driven instability (Turing-type instability). Different nonlinear kinetics are considered and simulations are made to illustrate the analysis.
the role of waves in pattern formation
Spemannstraße 35, D-72076 Tübingen
The usual way to generate patterns proceeds by forming first local signals that subsequently trigger the corresponding cell differentiation. However, several systems can be best described by assuming travelling waves. The use of travelling waves is a reasonable strategy if large fields have to become organized with molecules that have only a limited range. Early blood vessel formation, somite formation and the selection of a single cell to form a sensory bristle will be discussed under this point of view. In these examples the waves have very different functions. In somite formation, periodic waves cause the addition of pattern elements in a sequential fashion. This conversion of a periodic pattern in time into a periodic pattern space allows the generation of very regular patterns even in extended fields. In the formation of sensory bristles, first a larger patch of cells becomes competent. A subsequent wave-like OFF-reaction starting at the periphery of the patch causes a reliable selection of a single cell. The formation of complex net-like structures that contain preferentially closed loops such as the early blood vessel system can described by the assumption that first a plate is formed. A standard patterning system generates holes in this plate. These holes grow in a wave-like manner until only narrow bridges remain. This implies that the pattern forming mechanism does not specify where a particular structure is formed but where it is not formed and the spreading waves restrict the pattern further. It will be shown that this is very economic way to generate these complex patterns. As an example for a pattern forming process within a single cell, the mechanism that allows an E.coli-bacterium to find its center will be discussed. This is essential for the correct initiation of cell division. Travelling waves of a protein (MinE) remove another protein (MinC/D) from the membrane that blocks the assembly of the division apparatus. Waves of MinE function like a windshield wiper of a car to clear the membrane. This occurs more efficiently at the center. Thus, on time average, the concentration of the division inhibitor MinCD is lowest at the center, allowing a correct division of the cell.
Models for pattern formation in Hydra and the invention of the bilateral body plan
The freshwater polyp Hydra with its almost unrestricted capability for pattern regulation was a challenging system to test models of biological pattern formation. For a theory developed together with Alfred Gierer long time ago Hydra was, therefore, a primary testing ground. These theories have found fresh support by recent observations at the molecular-genetic level. Hydra patterning can be described under the following assumptions: (i) Pattern formation requires local autocatalysis and long-range inhibition. The region of a high activator concentration becomes the ``head'' of the Hydra, the opening of the gastric column. (ii) This pattern feeds back on the ability of the cells to generate this pattern. Thus, cells at a distance from the head become less competent to generate the head-forming signal. In this way, only a single head-forming signal can be maintained even in large animals. The body column obtains a polarity such that regeneration occurs with a predictable orientation without requiring a time-consuming symmetry break. (iii) The signal for foot formation is generated preferentially in cells that are less competent to form the head signal. Thus, as the rule, foot formation occurs opposite to the side of head formation. (iv) The head generates on long range the precondition for tentacle formation but inhibit tentacle formation locally. Thus, tentacle formation can only occur in a narrow zone next to the oral end of the animal.
Currently, patterning in Hydra became interesting from an evolutionary point of view since this radial-symmetric gastrula-like organism can be regarded as being close to the point where the bilateral body plan of higher organisms were invented. Possible scenarios for the transition from a radial to bilateral symmetry will be discussed and compared with recent molecular-genetic observations.
Michael Meyer-Hermann
Different aspects of the dynamical development of germinal centers in humoral immune response are presented. B-cells are activated by interaction with antigen fragments. These cells migrate to follicular dendritc cells and initiate (polyclonally) the germinal center reaction. These few B-cells encode antibodies with a specific phenotype and a given (but not optimal) affinity to the activating antigen. The very high proliferation and somatic hypermutation rates for centroblasts in germinal centers lead to a large number of cells in the germinal center and to a broadening of specifity in a phenotype space. On the other hand the highly specific selection process in the light zone of the germinal center allows an optimization of the affinity with respect to the antigen. The nonselected cells die through apoptosis, while apoptosis is inhibited in the case of a positive selection. The rescued cells further differentiate to plasma and memory cells which encode antibodies of high affinity to the antigen.
These dynamical properties are described with an appropriate set of differential equations with parameters which are exculsively fixed by experimental data. The influence of single quantities on the behavior of the germinal center as well as some characteristics of the whole reaction are examined. Criterions of how the germinal center reaction works optimally (number and quality of resulting plasma and memory cells) are discussed. Special attention is devoted to the recycling hypothesis that the optimization process may be an iterative one. A test is proposed in order to verify this hypothesis.
of a Single GFP-Actin Fibroblast
Universität Heidelberg, Biophysikalische Chemie
Institut für Physikalische Chemie, INF 253, D-69120 Heidelberg
Institut Curie, Paris
Differentiation and genetic expression of cells as well as development of first embryonic states are constantly regulated processes where biochemical and mechanical interactions between a cell and its environment play a major role. We want to stimulate a cell by defined biochemical receptors and controlled external mechanical stress. The chemical-physical properties of synthetic macromolecules and peptides have been used to modify surfaces on the molecular level. These surfaces were used to manipulate the adhesion and motility properties of GFP-actin fibroblast cells. The interaction of cells with such surfaces were studied by applying a uniaxial force to an individual cell. Conditions of constant stress or constant strain allowed the determination of the dynamic reaction of a cell to an external, mechanical stimulation. By using GFP-actin fibroblast cells, the dynamic development of actin filaments were monitored in-situ during defined external stimulation.
A model for the role of Frizzled in epithelial planar polarity
Sheffield, S10 2JF, U.K
During imaginal and pupal development in Drosophila, many epithelial cells become polarized within the plane of the epithelium. Genetic analyses have revealed the involvement of an intercellular signalling mechanism involving the transmembrane receptor Frizzled in this process. However, the role of Frizzled-dependent signalling in the generation and coordination of epithelial planar polarity remains unclear. Here, a model is investigated in which Frizzled operates in a local cell-cell (juxtacrine) interaction. The key assumption of the model is that each cell has the capacity to polarize its signalling activity in response to non-uniform receptor activation. This cellular polarization allows cells to both interpret and propagate polarity information. The model accounts well for the results of experiments in which Frizzled signalling is altered in small clones of cells, and provides a novel framework in which to study the phenotypes of planar polarity mutants.
Signaling Cascades
D-39120 Magdeburg
Institute of Cell Biology and Immunology, University of Stuttgart
D-70569 Stuttgart, Germany
A new concept for computational modeling and simulation of signal transduction is described comprising an integrated quantitative, dynamic and topological resolution of intracellular signal networks based on known components of epidermal growth factor (EGF) receptor signal pathways. The EGF receptor belongs to the family of tyrosine kinase receptors and is expressed in virtually all organs of mammals. EGF receptors play a complex role during embryonic and postnatal development and in the progression of tumors. The model provides new insights into signal response relationships and show a remarkable stability of regulation. Initial velocities of receptor activation are the critical parameter in determining signal efficacy. Experimental verification of the simulations at the ERK and target gene level indicate the high predictive potential of computational modeling. This optimized computerized model was used to test several hypotheses based on experimental data and to elucidate from this quantitative and kinetically resolved model to date unrecognized principles of EGF receptor signaling. Experiences gained with this computational modeling technique will facilitate the extraction of new interaction principles of more complicated signaling networks of tyrosine kinase receptors, comprising more hidden layers, and involving signal crosstalk emanating from related and unrelated membrane receptor families.
Otto-von-Guericke-Universität Magdeburg
Nearly all functions of the body exhibit nonlinear behaviour, a prominent example being the physiological
rhythms that are autonomous in nature. Entrainment, as for example by light or temperature, leads to
adaptation of the body rhythms to changes in the environment (e. g. time lag). Perturbations of such nonlinear
functions represent serious diseases, which manifest themselves as typical dynamical changes, e. g. in the
frequency domain. Well known examples are arrhythmic activity of the heart or brain, but also the
endocrinological system. During the last twenty years, clinical practise has more and more recognized the
fundamental meaning of rhythmicity for the therapy of diseases. For example, chemotherapeutic treatment of
cancer is improved when there is a periodic instead of a linear dosage. Our own work is closely related to
such dynamical diseases. We investigate three different systems for their nonlinear dynamics with respect to
particular control mechanisms:
A) Spreading depression in the brain is a phenomenon of spatio-temporal disorders of neuronal activity. It
has great similarity to the well known reaction-diffusion waves and is thought to contribute to the generation
of the aura of classical migraine.
B) The re-entry phenomenon of electrical heart excitation is a serious cause of heart fibrillation and
infarction. Controlled annihilation of spiral wave activity is a necessary prerequisite to prevent the death
of patients. As a basis to find suitable methods for controlled movement of spiral wave activity, we
investigate such processes in a chemical model system.
C) Diabetes is a disorder of the glucose household in the body, caused by perturbed secretion of the
hormone insulin. In this context the glucose metabolism of insulin secreting cells plays a crucial role for
the proper control of insulin secretion. Our work about oscillations and waves in glycolysis is directly
related to this control.
MPI of Immunology, Stübeweg 51,79108 Freiburg, Germany
Considerable progress has been made identifying the
molecular composition and interconnections of multiple
signalling pathways. Although the qualitative understanding
has increased strongly, quantitative descriptions of the
dynamical behaviour of signalling pathways are still
difficult to establish, in most cases due to the complexity
of the networks.
In the pursuit of finding a biochemically meaningful, yet
simple mathematical model to describe the data, linking
biochemical knowledge and measurements with data-driven
mathematical approaches becomes more and more important.
Starting from a specific biochemical system where some
dynamical components can be measured, we will describe the
process of modeling the data. We will focus on the most
important steps necessary to find and rank mathematical
models.
This approach is exemplified by data gained from an
experiment with a specific STAT5 signaling pathway and it is shown that
this pathway can be described with a system of delay differential equations.
References:
U. Klingmüller:
The role of tyrosine phosphorylation in profileration and maturation
of erythroids progenitor
cells. Eur. J. Biochem. 249, 1997, 637-647
J. Timmer, T. Müller, W. Melzer: Numerical methods to determine calcium release flux from calcium transients in muscle cells. Biophys. J. 74 1998, 1694-1707
Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
2) Plant Cell Biology, Wageningen University
Arboretumlaan 4, 6703 BD Wageningen, The Netherlands
Plant cell walls are surprisingly regular fibre-laminate structures. The role of the fibres is played by cellulose microfibrils (CMFs). These fibres are deposited in an oriented fashion in layered textures. The origin of these textures has been the subject of much debate in the plant cell community. We present a dynamical mathematical model that aims to explain plant cell wall architecture. Based on a geometrical theory proposed earlier [1] the present model [2-3] describes the space-time evolution of the density of the so-called rosettes, the CMF synthesizing complexes. The motion of these rosettes in the plasma membrane is assumed to be governed by an optimal packing constraint on the CMFs plus adherent matrix material, that couples the direction of motion, and hence the orientation of the CMF being deposited, to the local density of rosettes. The rosettes are created inside the cell in the endoplasmatic reticulum and reach the cell-membrane via vesicles derived from Golgi-bodies. After being inserted into the plasma membrane they are assumed to be operative for a fixed, finite lifetime. The plasma membrane domains within which rosettes are activated are themselves also supposed to be mobile. We propose a feedback mechanism that precludes the density of rosettes to rise beyond a maximimum dictated by the geometry of the cell. The above ingredients lead to a quasi-linear first order PDE for the rosette-density. Using the method of characteristics this equation can be cast into a set of first order retarded ODEs. We discuss the analytic solutions of the model that give rise to helicoidal, crossed polylamellate, helical and axial textures, as all cell walls are composed of (or combinations of) these textures.
- [1]
- A. M. C. Emons: Plant, Cell and Environment 17 3-14
(1994)
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- A. M. C. Emons and B. M. Mulder: Proc. Natl. Acad. Sci. USA
95 7215-7219 (1998)
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- B. M. Mulder and A. M. C. Emons: J. Math. Biol. 42 261-289 (2001)
Steps towards a model for tip growth in plant cells
Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
2) Plant Cell Biology, Wageningen University
Arboretumlaan 4, 6703 BD Wageningen, The Netherlands
Tip growth occurs in organisms as diverse as fungal hyphae and root hairs of higher plants. The morphology of a tip growing cell, roughly speaking a cylinder of constant thickness capped by a more or less pointed apical tip at which the actual growth processes occur, is beguilingly simple. As such, tip growth is a beautiful example of morphogenesis and one for which the explicit mechanisms could possibly be elucidated. In the past a few groups [1,2] have proposed explicit mathematical models for tip-growth, mainly of a purely geometrical nature. We believe that a more unified theoretical picture of tip growth should include the physical aspects of the growth process i.e. the forces involved and the material properties of the nascent cell wall. On the basis of a discussion of the factors that influence tip growth in root hairs, we sketch a model of tip growth based on two assumptions: (1) the existence of a gradient in growth activity across the apical region linked to the regulation of exocytotic activity and (2) the existence of a plasticity gradient in the cell wall as one moves away from the tip due to progressive ''hardening'' of the wall material. The model thus aims to implement the ''soft spot'' hypothesis of Harold [3]. The result will be a model for tip growth, in which the tip morphology is self-regulated by the wall hardening process.
- [1]
- F. H. D. van Batenburg, R. Jonker, and J. W. Kijne: Physiol.
Plant. 66 476 (1986)
- [2]
- S.Bartnicki-Garcia, F. Hergert, and G. Gierz: Protoplasma
153 46 (1989)
- [3]
- F. M. Harold: Protoplasma 197 137 (1997)
embryonic head induction
Bingyu Mao, Wei Wu, Andrei Glinka, Dana Hoppe, Peter Stannek, Yan Li and Christof Niehrs
Deutsches Krebsforschungszentrum
Im Neuenheimer Feld 280
D-69120 Heidelberg, Germany
Work in amphibians suggested that inhibition of WNT and BMP signals is essential for head development and that head induction by Spemann's organizer may be mediated by secreted WNT antagonists. Dickkopf1 (Dkk1) is member of a novel gene family encoding secreted, cystein-rich proteins which is expressed in the vertebrate organizer. Dkk1 acts as a Wnt inhibitor and is able, together with BMP inhibitors, to induce the formation of ectopic embryonic heads in Xenopus. However, the mechanism by which Dkk1 blocks Wnt signalling is unknown. We will present evidence from binding experiments in transfected cells that Dkk1 may not interact directly with either Wnt or Fz proteins but that Dkk1 function requires another extracellular protein involved in Wnt signalling.
JENS NIELSEN
In the central dogma of biology the focus on overall regulation is at the genetic and protein level. However, metabolites also play a very important role in overall regulation. Even though the metabolome is a function of the proteome, which again is a function of the transcriptome, there is a substantial feed-back in the system and the metabolome therefore also influences the transcriptome and the proteome. Thus, metabolites interact with proteins and hereby activate or inactive signal transduction pathways leading to altering gene expression or protein function. Furthermore, pathway intermediates interact with the individual enzymes of specific pathways, and hereby play an important role in controlling flux through the different branches of the metabolic network operating within the cell. Measurement of the metabolome is therefore extremely valuable, both in the context of evaluating flux control, but also as a tool for pathway identification. Since the metabolome is the result of many individual reactions interacting, it is essential to apply mathematical model to upgrade the information level of metabolome analysis. Thus, metabolome analysis consists of two elements: 1) mathematical models describing the metabolic network and 2) advanced measurement techniques that enable analysis of intracellular metabolites. In this presentation different experimental techniques will be presented for analysis of intracellular metabolites - both for identification of the pathway topology, for quantification of fluxes, and for evaluation of the role metabolite levels play in signal transduction. Furthermore, the construction and use of whole genome based metabolic models will be discussed. Application of the different techniques will be demonstrated for identification of the metabolic network operating in S. cerevisiae grown at different conditions, and for analysis of the mechanism of glucose repression in S. cerevisiae. In the presentation it will also be discussed how metabolome analysis may play a role in functional analysis, especially through combination with DNA chip analysis.
and Ravi Iyengar
(2) Department of Pharmacology, Mount Sinai School of Medicine, New York, NY, USA
CEACAM1 is a signaling cell adhesion molecule abundantly expressed in epithelial cells, endothelial cells, and leukocytes. It regulates cell proliferation, apoptosis, T cell cytotoxicity, angiogenesis, and tumor growth. A puzzling finding is that CEACAM1 can have both stimulatory and inhibitory effects on cell proliferation. This may be related to the finding that the signaling isoform, CEACAM1-L, can bind both src-family kinases and protein tyrosine phosphatases to the same tyrosine-phosphorylated motif in its cytoplasmic domain. The other major isoform, CEACAM1-S, that is co-expressed with CEACAM1-L in various ratios in different cell types and cellular states, does not bind kinases or phosphatases, but there is evidence that the S-isoform can regulate the activity of the L-isoform. In order to expand our understanding of the dual effects of CEACAM1 on signal transduction, we asked the simple question what the factors are, that decide if the L-domain will bind a src-kinase or a tyrosine phosphatase (SHP-1 or SHP-2). Based on available molecular, biochemical and functional data we constructed a reaction scheme for the intermolecular binding interactions between CEACAM1-L, CEACAM1-S, c-src, and SHP-1. This reaction scheme was analyzed in a kinetic model, in which all the reactions were described by ordinary, first order differential equations. Because binding of both c-src and SHP-1 to the tyrosine-phosphorylated CEACAM1 L-domain has been shown to activate these enzymes, we used the binding to CEACAM1-L as a measure of activity. We then determined the steady state ratios of bound c-src to bound SHP-1 at various concentrations of CEACAM1-L and CEACAM1-S, corresponding to different cellular states of epithelial cells in culture and in transfected tumor cells. We also varied the extent of cell-cell adhesion in the simulations. The results showed that the system can switch between predominant c-src activation and predominant SHP-1 activation. The most dramatic effects were obtained by varying the L:S expression ratios. Thus, in this model CEACAM1-S can clearly regulate the activity of CEACAM1-L. If we assume that the differential activation of c-src and SHP-1 reflects the influence of CEACAM1 on cell proliferation, this model can explain how CEACAM1 can act as both a co-stimulatory and a co-inhibitory system.
Friedrich-Schiller-Universität, Erbertstr. 1, 07743 Jena, Germany
The skull and the cranial musculature have played prominent roles in many major adaptive transitions during vertebrate evolution. We study the migration, pattern formation and fate of the cells (neural crest and cranial mesoderm) which give rise to the skeleton and muscle of the head in organisms spanning the transition from water to land. Methods used include conventional histology, scanning electron microscopy and confocal light microscopy, as well as fate mapping using fluorescent markers such as DiI and GFP. Results sofar indicate that the early migration and pattern formation of neural crest cells in the head region is surprisingly conserved. Both the amphibians investigated and the Australian lungfish have the same number of migrating neural crest streams, and the identity of the streams is preserved. The major difference lies in the timing of migration, where there has been a heterochronic shift such that cell migration starts much later in the Australian lungfish than in the amphibians. This late onset of cranial neural crest cell migration explains the earlier reports in the literature which claim that there are no migrating cranial neural crest cells in the Australian lungfish. There are indeed such cells, but their migration starts very late.
a model system for understanding macroscopic patterns from microscopic rules
University of Minnesota
Minneapolis, MN
Chemotaxis in the bacterium E. coli is widely-studied because of its accessibility and because it incorporates processes that are important in the response of numerous sensory systems to stimuli: signal detection and transduction, excitation, adaptation, and a change in behavior. Quantitative data on the change in behavior is available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. In this talk we will discuss a mathematical model of single cells that can reproduce many of the major features of signal transduction, adaptation and aggregation, and which incorporates the interaction of the chemotactic protein with the flagellar motor. We also address the problem of how to obtain macroscopic equations for population-level behavior that incorporate certain features of the microscopic model.
Mechanical Aspects of Cell Behavior and Motion
on leave from Universität Heidelberg Institut für Physikalische Chemie, D-69120 Heidelberg, Germany
on leave from Princeton University, Dept. of Physics, Jadwin Hall, Princeton, NJ 085440, USA
We present recent experiments concerning cell motion and mechanical behavior. The bacterium Listeria monocytogene can be seen as a model system for force generation through actin polymerization. Such a mechanism is used very often in biological systems, for instance during cell motion. Our measurements by means of optical tweezers show that the response of the Listeria polymerized actin tail is elastic with respect to small deformations. The measured value of the elasticity is in good agreement with a crosslinked gel structure. This leads us to the suggestion that motion is dominated by friction caused by the deformation of the latter. We further present the recently developed microplate-technique, which we use to probe force generation of single eucaryotic cells. Cells are suspended between two ''microwalls''; forces and displacement of both surfaces can be cleanly measured. Values of the associated viscoelastic constants describe well the passive mechanical properties of these cells. Interestingly, results indicate short time behavior similar to what is observed for the Listeria tail. We show that the active response of the cell, its contractility, is a well-regulated answer to stimulation by exterior pulling forces.
Organic Chemistry III, Universität Ulm, Albert-Einstein-Allee 11,89081 Ulm
Controlling adhesion is an important aspect in investigating cellular functions. Adhesion properties are studied in order to understand cell proliferation, shape, motility, signalling or rejection of biological implants. We want to examine the phenomena of cell adhesion on a molecular level - at the interface of materials science and life sciences. Grafting star shaped polyethyleneglycol derivates functionalized with isocyanate endgroups on silica or glass allows us to inhibit specific cell adhesion. Micellular deposition of Au nanoclusters from block copolymers and binding of an Arg-Gly-Asp peptide sequence (RGD) modified with an thiol endgroup to the gold leads to a surface which facilitates the specific binding of integrin. Combining both methods with lithography techniques enables us to pattern a surface with ligands promoting focal adhesion contacts, and to forestall specific adhesion on the remaining part of the sample. Since the cell is presented with a pattern whose characteristic size is comparable in order of magnitude to the receptors themselves these substrates allow focal adhesion to be investigated on the molecular level. Recognition of these chemically heterogeneous nanopatterns by green fluorescent protein (GFP) modified fibroblasts and osteoplasts and the replication of the patterning into the extracellular matrix is investigated by scanning fluorescence microscopy. Such interfaces are powerful tools to study and to actively manipulate cell adhesion, cell motility, and gene expression.
Many treatments for cancer, including radiotherapy and many chemotherapies, specifically target proliferating cells. The downside of this is that quiescent cells, normally resident in regions with depleted of vital nutrients, may begin dividing as the loss of the proliferating layer is accompanied by restored nutrient levels. Macrophages infiltrate hypoxic and necrotic regions of tissue, and can be 'armed' with therapeutic genes which are only transduced under hypoxia, enabling the efficient targeting of this therapy-resistant population of tumour cells. We have developed models for macrophage infiltration and hypoxia dependent tumour cell targeting, in order to determine where macrophages aggregate, their effect on tumour size, the role of chemotaxis, and how sub-populations of normal and 'armed' macrophages interact.
Institut Curie, Physico-Chimie Curie, UMR 168 CNRS/IC
26 rue d'Ulm, F-75248 Paris Cedex 05, France
Dipartimento di Scienze Fisiche and Unità INFM, Università "Federico II Complesso Monte S. Angelo, I-80126 Napoli, Italy
We introduce a general framework to study the processivity of molecular motors moving along a polar filament and discuss the average time spent attached to the filament as a function of a tangentially applied load. Our study of specific models suggests that the attachment time of a motor decreases with increasing ATP concentration and that double-headed motors such as kinesins lose their processivity under forcing conditions while processive single-headed motors are less sensitive to tangential forcing.
For a reaction-diffusion system we consider the problem of existence of travelling waves in a half space assuming the Dirichlet or other boundary conditions on .
We assume also that far from the boundary the wave approaches
the plane wave solution with some prescribed propagation vector .
Then we prove that
waves of permanent shape, i.e such that
exist if and only if the following inequality is satisfied.
Here N is the exterior normal to the boundary . In the presence of convective terms the appropriate condition is more complicated. We discuss also some biological applications, e.g. the growth of tumour or propagation of travelling waves in myocardium in the presence of a boundary.
Travelling waves and pattern generation and propagation in discrete cellular lattices
Agricultural University of Norway, Aas
Travelling waves seem to be a generic feature in lattices of discrete cells with closest neighbour interaction. However, proving the existence of travelling wave solutions and investigating their properties is hard, and only results of a very general nature have so far been obtained for very special systems. In particular the discrete Nagumo equation has been subject to intense investigations.
For the discrete Fisher equation the existence of travelling wave solutions was proved by Zinner et al. (1993). Using linear analysis I derive their existence condition and the dispersion relation between wave front steepness and wave speed, and show analytically that the actual wave speed seen in numerical simulations is the minimum possible wave speed.
Multicellular systems with more than one cell state variable may have stable states exhibiting periodic spatial patterns. Rather that bringing the system from one homogeneous state to another as in e.g. the Fisher equation, a travelling wavefront in such systems may generate a spatial periodic pattern in its wake. An example is the model for Delta-Notch lateral inhibition by Collier et al. (1996). Taking the existence of travelling wave solutions for granted and using linear approximations in the same way as for the Fisher equation, I show that the dominant alternating pattern of the system is the only pattern that can arise from a travelling, pattern generating wave. The calculated minimum wave speed agrees extremely well with numerical simulations.
Based on these results I argue that pattern propagation by a travelling wave is a possible mechanism for generating periodic patterns in discrete cell lattices. If the right pattern arises (perhaps by random perturbations) somewhere in the lattice, a travelling wave is initiated, propagating the pattern all over the lattice. Ahead of the wave front the cells occupy their initial state, behind it the periodic patterns is generated as the wave propagates. The mechanism is compared to the well-known Turing mechanism for pattern formation. The analysis indicates that in certain systems, travelling waves may be the pattern formation mechanism.
Invalidenstr. 42, D-10115 Berlin, Germany
A large number of cells respond to external stimuli with changes in cytosolic calcium concentration. The spatio-temporal patterns of the concentration changes can take the form of intracellular waves as well as repetitive spiking (calcium oscillations). Experiments on multicellular systems suggest that calcium signaling is not limited to intracellular transduction pathways but that it could serve as an intercellular communication route. Intercellular waves originating from local stimulation sites can spread over many cell layers. In globally stimulated cells coordinated changes of the through all the system are observed (e.g hepatocytes multiplets [Tordjmann97], blowfly salivary gland [Zimmermann99]). We analyze a possible route, mediated by calcium diffusion, for the intercellular communication of globally stimulated cells as hepatocytes multiplets. Former work ([Hoefer99]) has shown that cells with different intrinsic calcium oscillation frequency can oscillate synchronously if coupled through gap junctional calcium diffusion. The present mathematical model considers a chain of coupled cells. The calcium dynamics in each cell is described by partial and ordinary differential equations for the cytosolic and ER compartment, resulting in a reaction diffusion system. The reactions terms include terms for the InsP mediated calcium induced calcium release (CICR) and uptake into the ER and for the fluxes over the plasma membrane. Calcium diffuses in the cytosolic compartment. The effects of calcium buffers are included in the model via a rapid-equilibrium approximation. This yields effective reaction terms, cytosolic diffusion coefficients and gap junctional permeabilities. For cells exhibiting calcium oscillations we show that there exists a critical gap junctional calcium permeability over which the oscillations are synchronous, the value of strongly depends on the buffer composition and on the difference between the cells (see also [Hoefer01]). The model allows to make predictions about the effects of buffer injection, a putative experimental setup, on the intercellular communication.
Additionally to the main inorganic and organic components hydroxyapatite, and collagen I the extracellular matrix of bone contains a vast number of noncollagenous proteins. Those synthesized by bone cells, are believed to be closely connected with the crystallization process. Two mechanisms are assumed to be relevant: proteins could influence the nucleation processes, and they could have an inhibiting activity during crystal growth. The important group of acidic proteins of extracellular bone matrix contains osteocalcin, osteonectin, osteopontin, and bone sialoprotein. Among these proteins synthesized by osteoblasts, only osteocalcin and bone sialoprotein are believed to be specific to mineralized tissues
In the present study we have examined the influence of the bone specific protein osteocalcin on hydroxyapatite ( ) formation. Different functions in biomineralization are attributed to osteocalcin connected with its binding property, including binding but also inhibition of precipitation. To study nucleation process and crystal growth a model system with osteocalcin-controlled dissolution-reprecipitation of brushite ( ) to was investigated. Scanning Force Microscopy (SFM) showed that reprecipitation had taken place only in osteocalcin-containing solution. Thin apatitelike crystals with hexagonal symmetry grew on the (010) brushite planes. Apatite (0001) planes were fully covered with osteocalcin molecules as revealed with SFM and fluorescence microscopy. Consequently osteocalcin has been found to regulate formation in two different ways: (i) it accelerates nucleation, and (ii) osteocalcin effects as a specific inhibitor of the apatite (0001) plane suppressing crystal growth perpendicular to this plane.
The impact of osteocalcin onto the interaction of bone cells with -collagen I-cements was studied in a cell culture system using the human osteosarcoma cell line SAOS-2. Results suggest, that osteocalcin influences the initial adherence of osteoblasts, whereas proliferation of the cells is not effected.
With the increasing use of high-throughput analytical instruments, massive parallel sample analysis and data interpretation tools, the number of new drug targets and options for therapeutic interventions have clearly increased. Besides an improvement in prevention and control of infectious diseases which still account for some of annual deaths worldwide, new therapies for cancer or hereditary diseases seem possible. Many of the existing as well as potential new drugs are produced in eukaryotic cells which conduct RNA splicing as well as posttranslational protein modifications but show poor productivity compared to classical fermentation processes. To achieve the full potential with respect to yield or reproducibility not only highly developed cell culture technology and sophisticated downstream processing are required but also our understanding of the complex mechanisms underlying cell growth and product formation has to be improved considerably.
In terms of product numbers and social impact, vaccine production is one of the most challenging areas of cell culture. After a general overview of production methods used today, production limits with respect to cell growth and virus replication and the role of mathematical modeling for supervision and control of the respective processes are discussed. Finally, an outlook on recent progress in developing recombinant subunit and DNA vaccines is presented.
We present a new comprehensive model concept of hematopoietic stem cell development which consistently explains a large variety of experimentally and clinically observed phenomena including clonal regeneration and competition, kinetic heterogeneity or microenvironmental dependence. It permits to understand different kinds of in vitro and in vivo assays, genetic marker studies and is able to describe single cell as well as cell population behavior.
The model concept is based on the paradigm of micro-plasticity, a fundamentally new principle of stem cell organization. Within this paradigm individual cells may reversibly change their properties qualitatively and quantitatively depending on influences of the actual growth environment. In contrast to previous concepts, stemness is not treated as an explicit cell property but as a result of a dynamic self-organizing process.
Qualitatively different experimental settings have been simulated using a single cell based Monte-Carlo approach. Herein not only the cell system but also sampling and measuring techniques have been incorporated. Moreover a differential equation representation of the model is applied to investigate general system properties.
Potential applications of the simulation model are conceivable in designing clone tracking strategies in gene therapeutic settings and to optimize clinical trials in the treatment of clonal disorders.
Lately, statistical properties of genetic regulatory networks
have become accessible to experimental research, as for example
the average connectivity in the genome of E. Coli [1].
It is an open question, how mutation and selection can lead
to self-organization of genetic networks with the observed
properties in the course of biological evolution. Discrete
logical (Boolean) networks have been discussed in Theoretical Biology
as models of principal dynamical properties of genetic regulatory
networks since about 30 years. In the framework of such models
we discuss possible mechanisms of structural self-organization of genetic
regulatory networks as a consequence of functional change at the
single-gene level and selection [2]. Indeed one observes self-organization
processes stabilizing the dynamics of model regulatory networks in
a regime of non-chaotic dynamics. Its consequences, in principle,
could be observable by modern experimental techniques as microarrays.
[1] Thieffry, D., Huerta, A.M., Perez-Rueda, E., Collado-Vides, J. (1998)
Bioessays 20, p. 433 - 440
[2] Bornholdt,S. and Rohlf, T.: Topological Evolution of Dynamical
Networks: Global Criticality from Local Dynamics. Phys. Rev. Lett.
84 (2000), p. 6114 - 6117
Fibroblast cells are animal and human extracellular matrix cells which are rather motile and participate in for instance the healing of small wounds. By displacing themselves the cells exert forces onto their focal adhesion contacts or cells adapt externally applied stresses. This poster discusses a method (i) to guide the location of focal adhesion contacts, (ii) to determine focal adhesion forces with 100 pN resolution and (iii) to apply external stresses. The method is based on Si(100) technology and colloidal probe technique. The fabrication envolves a combination of photolithographic techniques, gas plasma and wet etching processes. The array consists of regularly placed silicon pillars onto which the cells do attach selectively. While cells are moving forward the pillars bend. Analysis of the pillar displacement evaluates the exerted point forces.
This work deals with investigation of general principles which regulate
infection immunity depending on environmental factors. In contrast to the
approach existed which utilized optimal control theory to study extremal
properties of the immune response, a new approach is used to estimate
effectiveness of the immune system function on the base of comparison of
infection immunity long-term energy expenditures, including the periods of
infections as well as of the healthy state.
An approach considered is based on the assumption that a correlation exists
between the organism's fitness and energy expenditures on various functions. By
the example of the mathematical model of pneumonia a quantitative energy cost
estimates of the main processes of disease and of the health maintenance are
compared. The problem of parameter's identification is formulated using
the principle of minimal energy dissipation. Particular case of the problem is
considered for which the dependence of optimal defense regimens from
infection rate and microorganism's virulence is studied.
One of the actual problems of modern medicine is the elaboration and
substantiation of the treatment methods of chronic bacterial infections. As is
known, the conventional methods of acute bacterial infections therapy, such as
application of antibiotics, are much less effective in case of chronic
infections because of high risk of side effects, including immunosupression and
drug resistance. As a result of numerical experiments, the point of view is
formulated on the increasing rate of chronic infections not only as a
consequence of immune status deviations, but also as a result of the immune
system adaptation process which leads (in appropriate conditions) to
energetically profitable state of more prolonged contacts with the pathogen.
Also, the results obtained helped to explain theoretically one of the methods
of chronic bacterial infections treatment, namely, immunostimulation, which
consists of preventive measures against acute or exacerbation of chronic viral
infections followed with application of bacterial antigens.
An introduction of general principles of the immune system structure and
function makes it possible to get from studying essentially transitional
processes of the immune response to particular antigen(s) to more common view
of the immune system function as a complex dynamical process of its adaptation
to environmental conditions. The approach used has a wide spectrum of possible
applications, including analysis of host-pathogen relations on organismic and
population levels, immunoepidemiology and immunotherapy.
M a r c h u k G. I. Mathematical models in immunology. Numerical methods and
experiments. - Moscow: Nauka, 1991 (in Russian).
P e r e l s o n A. S. Optimal strategies for an immune response // Lectures
on Mathematics in the Life Sciences. - Providence: The American Mathematical
Society, 1979. - V. 11. - P. 109-163.
R o m a n y u k h a A. A., R u d n e v S. G. Mathematical modelling of
immune-inflammatory processes in lungs. Searching for optimality (in Russian)
// Proc. of the Jubilee Conference ``Numerical Mathematics and Mathematical
Modelling'' dedicated to the 75-th birthday of Academician
G.I.Marchuk and to the 20-th anniversary of the INM RAS.
Vol. 2. - Moscow, 2000. - P. 212-233.
R o m a n y u k h a A. A., R u d n e v S. G. On application of a
variational principle for the problems of modelling infection immunity by the
example of the mathematical model of pneumonia (in Russian) // Math.
Modelling. - 2001 (accepted for publication).
R u d n e v S. G. Mathematical modelling of defensive immunophysiological
reaction in pneumonia. - Abstract of PhD thesis (in Russian). Moscow, 2000. -
27 p.
R u d n e v S. G., R o m a n y u k h a A. A. Mathematical modelling of
immune-inflammatory reaction in acute pneumonia // J. Biol.
Systems. - 1995. - V. 3, No. 2. - P. 429-439.
In order to function as physiological clocks, circadian
(and certain ultradian) rhythms contain homeostatic mechanisms which
compensate for external temperature variations and other environmental
influences. In this talk a theory for temperature-compensation and
general homeostasis for physiological clocks is presented.
Implications of the theory are compared with experimental results from
the model organisms Neurospora and Drosophila. We
start with the assumption that all component processes of a
physiological oscillator are (in principle) known together with the
corresponding rate constants and the activation energies .
It can then be shown that temperature-compensation is expected to
occur whenever the -weighted sum of the period-
sensitivities is zero, i.e.,
where
is the function which
describes how the period depends on the rate constants .
Although there is an infinite number of activation energy combinations
which will satisfy eq.
Exo/endocytotic activity is reflected as the change in the cell membrane
surface area, which is readily measured with patch-clamp
membrane-capacitance measurements. This is a method of choice to assign
the
regulated exo/endocytotic activity of variety of neuronal and
neuroendocrine
cell preparations. dependent exo/endocytosis can be studied at
high
temporal resolution by dialysation experiments or caged calcium flash
photolysis experiments. However, the exo/endocytosis based capacitance
measurements during more physiological stimuli like membrane
depolarization
are hindered by the fact that the capacitance change can also have a
voltage
dependence as a result of the mobilization of charges in polarizable
membrane proteins, e.g. gating charges of voltage-dependent channels.
In the
preparations with large ion channels densities this problem is
particularly augmented. Cells in the acute tissue slices were reported
to
express ion channels at significantly lower densities. We used
rat
pituitary tissue slices as a model to test whether we can reliable
measure
exo/endocytosis based membrane capacitance changes also during
depolarization pulses without contamination with the gating charge
movements. As predicted from the smaller peak Na+ currents the gating
current contribution to the voltage dependent capacitance change were
below
the sensitivity of our detection system and that we can assign the total
measured capacitance changes to exo/endocytotic activity. Our results
suggest that it is possible to continuously measure fast exo/endocytotic
activity due to depolarizations and that we can modulate the
dependent
exo/endocytic activity with physiological agonist and antagonists.
The central aim is to show that magnetic bead microrheology provides a valuable
tool to measure local viscoelastic moduli of heterogeneous actin networks, cell
envelope(s) and cytoskeletons and to measure local forces mediating intracellular
trafficking.
In the first part, correlations between phenomenological viscoelastic properties
and single chain dynamics are summarized which are determined by the subtle
interplay of enthropic and enthalpic contributions to the elastic free energy
of single filaments. One major purpose is to demonstrate that rheometry provides
a valuable tool to explore the effects of actin regulation proteins on the single
chain elasticity or dynamics and the structure of the networks. We then show
that gradual cross-linking of entangled actin networks leads to a universal
percolation transition into a microgel state (consisting of dense cross-linked
clusters interconnected by few actin cables) which exhibit unique elastic and
transport properties.
The last part deals with the application of magnetic bead microrheometry
Physiological engagement of the T cell antigen receptor initiates a complex
series of intracellular signaling events that ultimately activate the expression
of a panel of genes involved in both initiating and coordinating the immune
response. The nuclear factor of activated T cells (NFAT) constitute a family of
transcription factors which play a pivotal role in the regulation of these
events [Rao97]. NFAT proteins are present in an inactive, highly phosphorylated
state in the cytoplasm of resting T-cells and other immune cells. As result of
T-cell stimulation, they become activated and subsequent nuclear localized when
dephosphorylated by the calcium/calmodulin-dependent phosphatase calcineurin
[Kiani00].
Recent experimental reports suggest a conformational switch mechanism to explain
the NFAT activation and nuclear translocation [Okamura00]. According to this mechanism, the phosphorylation state of NFAT controls the switching between two alternative confomational states: an äctiveconformation (Nuclear Localization Sequence (NLS) exposed / Nuclear Export Sequence (NES) masked) and the reciprocal ïnactiveconformation (NLS masked / NES exposed) that are either nuclear import (active state) or export (inactive state) conducive. Both phosphorylated and dephosphorylated NFAT can assume both conformational states but with significantly different probabilities. The probability of the active state is low in the fully phosphorylated protein but progressively increased by dephosphorylation.
A mathematical model based on this conformational switch paradigm is presented here. In this model we consider that the multiple dephosphorylations of NFAT occur as ordered trantitions between dephosphorylated and phosphorylated forms. Both forms are present in the cytoplasm and in the nuclear compartment but with asymmetry in the values of the transition rate constants. Besides, it is assumed that the equilibrium constants of the conformational transitions depend on the phosphorylation state. Taking also phosphorylation and dephosphorylation and the conformational transitions to be much faster than nuclear translocation of NFAT, we could reduce the differential equation system governing the NFAT states to a first order scalar differential equation. From its solution, the dynamical behavior of all possible NFAT conformations in both compartments is obtained. The steady states, characteristic time and time course of different NFAT forms are analyzed for different stimuli (calcineurin concentrations). Moreover our proposed model is compared with other variants where the dephosphorylation of NFAT takes place only in the cytosol or where there is symmetry in the kinetic constants at both sides of the nuclear membrane. Our theoretical results suggest that a complex mechanism of NFAT regulation involving cooperative and multiple dephosphorylations can create a threshold for transcriptional activation.
The propagation of intercellular waves occurs in a wide variety cells.
waves can propagate between cells of the same type as well as between
cells of different types. The functional significance of waves is
thought to be a mechanism for coordinating cooperative activity. However,
the mechanism underlying wave propagation has been controversial. The
original idea was that local waves, induced by mechanical stimulation,
propagated by the diffusion of IP3 through gap junctions. However, waves in
other cells appear to utilize the movement of through gap junctions.
Other mobilizing messengers may also move between cells. More recently,
evidence has been found for an extracellular messenger, probably ATP, in the
propagation of waves. The source of the ATP is unclear but may this may be
related to the presence of gap junction hemichannels. Although these
multiple mechanism of wave propagation appear to be in conflict, each relies
on the signaling mechanisms of the individual cell. As a result, a
unifying hypothesis can be presented that encompasses each mechanism. The
conclusion of this hypothesis is that waves in different cells can be
propagated by different but related mechanisms and that it is likely that
individual cells uses these multiple mechanisms of propagation
simultaneously.
The response of Rhodobacter spheroides cells to change in nutrient
concentration is analysed when the cells where tethered by their flagella
and subjected to temporal uniform and stepwise changes in concentration
signals. Using motion analysis, changes in flagellar motor rotation speed of
individual cells were measured. They were used to model mathematically
bacterial spatio-temporal response.
Based on the individual cell behaviour a stochastic approach at cellular
level leads to the macroscopic Fokker-Plank partial-differential equation,
which describes the population behaviour. This accounts for both the random
motility of the cells and the drift behaviour related to chemotaxis in such
chemical cues. It contains both diffusion and convection terms. The
Fokker-Plank equation has two macroscopic parameters, which have a nonlinear
dependence on the nutrient concentration and were obtained by fitting the
experimental results. The drift coefficient measures the chemotaxis
sensitivity. It is the first time that this coefficient is derived based on
experimental observations. Our result shows that it has a sigmoidal, single
peaked form. Our model predictions indicate the optimum range of taxis
response as well as showing that taxis is eventually destroyed at very large
concentrations. The same behaviour is uncovered in the motility (diffusion)
coeffient as the strength of the cue increases. However, we show that taxis
is stronger than diffusion (motility). We analyse the PDE Fokker-Plank
analytically and numerically and obtain prediction of the spatio-temporal
behaviour (distance and speed of the spreadings). Our results map the
response to the full nutrient range and therefore are applicable to any full
detail models.
This is the first time modelling of the chemotaxis response in
temporal gradients is based on experimental data akin to a physiological
context as opposed to previous studies that were based on heuristic
assumptions. Our theoretical approach is not restricted to only analysing
responses to flat gradients and can be used to understand the response to
non-linear gradients as well. This will be presented elsewhere.
The dynamic responses of E. coli LJ210 (scr+) to a sucrose-puls
and stop feeding in a continous fermentation have been measured. There are measurements
available for different glycolysis-metabolites and a component of the phosphotransferase
system (PTS). A detailed model of the PTS and the glycolysis describes well
the experimental data. Further implications for the signal transduction via
the PTS within the functional unit 'quest of food' are discussed based on simulation
studies.
We use single-molecule techniques, optical tweezers and laser interferometry, to study the dynamics of biological motor
proteins. Motor proteins are nanometer-sized mechanical engines converting chemical energy into mechanical work to drive
a large variety of dynamic processes in cells. They do this in a watery environment at room temperature. That means that
apart from the stochastic nature of the chemical reaction driving the process, the motors have to deal with or can maybe
harness the thermal energy of their environment. A multitude of simplified physical models have been proposed describing
these motors as ''thermal ratchets''.
High-resolution optical techniques have allowed us to detect intramolecular motions on the nanometer scale. I will report
on recent experimental results on a motors of the kinesin protein family, namely the ncd motor. This motor is
non-processive and we could detect power strokes. This behavior is similar to that of myosin, but differs in an important
aspect. The power strokes occur at the end of attachment periods, which excludes certain classes of thermal ratchet
models.
Cell migration within confluent cultures is a complex phenomenon
requiring a subtle dynamical regulation of intercellular and basal
junctions. In addition, shear stress induces a broad variety of
molecular processes modifying migratory activity. We apply experimental
and theoretical techniques to detect and quantify these effects.
Confluent endothelial cells are observed by phase contrast microscopy.
Defining characteristic parameters to capture the
dynamics of individual cells and the cell ensemble, we find a typical
phase-like response to the onset of shear stress with the following
time-course: Resting conditions (phase I), change of motility (phase
II), onset of alignment (phase III), and finally cell elongation. In
addition, impedance spectroscopy delivers information about the
transendothelial electrical resistance (TER) calculated on the basis of
a mathematical model.
Bayesian data analysis is employed in the determination of the model parameters
in order to incorporate all information provided by the experiment.
Continous application of shear stress caused an
initial, transient, reversible and shear stress-dependent increase in
TER between 2 to 15% within 10 to 20 minutes followed by a decrease up
to 20% under control levels. After that time period TER increases over
control levels within hours. Alterations in TER correlate with changes in
cell motility and orientation. Finally, these results are related to
biological activities as time-dependent tyrosin phosphorylation and
actin (de-)polymerisation of the cytoskeleton.
Cell division of human cells is regulated by cytokines in particular by growth factors. Numerous cases of tumor development are based on malfunction of growth signaling cascades triggered by cytokines. In our work we compare the two cytokines TNF and EGF with respect to their ability to activate ERK via the MAP Kinase cascade. The mitogen activated protein (MAP) kinases transduce proliferative or differentiation signals to the nucleus. Tumor necrosis factor (TNF) is a pleitropic cytokine capable of inducing, depending on the cell type, very different cellular reactions like proliferation or apoptosis. Epidermal Growth Factor plays a complex role during embryonic and postnatal development. Increased expression of EGF receptor was found in human carcinomas suggesting a role for EGF receptor in tumor progression.
While the interacting molecules of the MAP kinase cascade are structurally and biochemically well characterized, the kinetics of the network of parallel and consecutive processes comprising positive and negative regulatory control are difficult to anticipate. This complexity of biological signaling, however may be approached by computational methods, particularly in quantitative terms.
In this work we compare the mechanisms and features of the TNF-R1 and EGF-R
induced ERK activation. We will discuss e. g. the influence of the receptor
number, cytokine concentration or the overexpression of certain signalling
molecules on ERK activation. The mathematical models are based on kinetic data
and observations retained from literature and own experimental data. The
experimental verfication of hypotheses and of predictions indicate that
mathematical modelling can serve as a tool to gain a hoilistic understanding
of complex biological systems.
Mitosis, the process by which identical copies of the replicated genome are distributed to the daughter products of each nuclear division, depend upon the action of the mitotic spindle, a bipolar machine made of microtubules and microtubule-based motor proteins (1). We are studying the mechanics of spindle action using early Drosophila embryos as a model system. We are studying mitotic motors in order to learn how multiple microtubule-dependent motors contribute to spindle morphogenesis and chromatid segregation in Drosophila syncitial blastoderm-stage embryos. These embryos are amenable to biochemical, genetic and cytological analysis of mitotic mechanisms, and previous work showed how three mitotic motors, a bipolar kinesin, KLP61F (2,3), a C-terminal kinesin, Ncd and cortical dynein, function in a coordinated pathway that serves to precisely position spindle poles during spindle assembly, maintenance and elongation (4-6). Unpublished work shows that a fourth mitotic motor, KLP3A, also contributes to the balance of forces that positions spindle poles during mitosis (Kwon et al, 2001; in preparation). In collaboration with Dr Alex Mogilner (UCD department of Mathematics) we have recently initiated mathematical modeling studies that are aimed at producing quantitative descriptions of how multiple motor proteins might contribute to the positioning of spindle poles. Finally, we have been studying the relative roles of microtubule flux and kinetochore motors on anaphase chromosome-to-pole motion in Drosophila embryos. Our data suggest that flux is too slow to account for the rates of chromatid-to-pole motion that we observe, and we favour the hypothesis that dynein localized on the kinetochore plays an important role in transporting chromatids to opposite spindle poles during anaphase A (7).
References:
Binding and unbinding of lipid membranes or of specific receptor/
ligand pairs are ubiquitous phenomena in biophysics. Model systems
for studying these problems include vesicles interacting with substrates
and, on a more local scale, dynamical force spectroscopy of such
receptor/ligand pairs using AFMs or membrane force probes.
In both cases, not only equilibrium quantities like adhesion or binding
energy contribute but also dynamical, i.e., non-equilibrium aspects.
Specifically, a recent experiment has shown that bound vesicles can
undergo a dynamically induced unbinding transition in shear flow. A
theoretical analysis of this phenomenon based on low Reynolds number
hydrodynamics yields the critical shear rate as a function of the equilibrium
adhesion energy and the geometry of the vesicle [1,2].
For the unbinding of adhesion patches involving several specific molecule
pairs, a simple model is introduced. Based on known properties of the unbinding
of a single pair, predictions are made how the critical force required to
rupture several parallel bonds depends on both the number of bonds initially
present and the dynamical loading rate [3]. In particular, we show how the
continuum limit is reached for quasi-static pulling when rebinding events
are included [4].
[1] U. Seifert, Phys. Rev. Lett. 83, 876 (1999)
[2] S. Sukumaran and U. Seifert, Phys. Rev. E, in press
[3] U. Seifert, Phys. Rev. Lett. 84, 2750 (2000)
[4] U. Seifert, in preparation
The aggregation of Dictyostelium discoideum (DD) cells in the cell
suspension is mediated by chemoattractant
cyclic adenosin monophosphate (cAMP) which propagates from randomly
organized centers in the form of spiral or circular pulses
of increased cAMP concentration. DD cells feel the arriving cAMP
and respond to it by both an autocatalytic production of cAMP and
by the motion against the gradient of cAMP. The periodic
emission of cAMP pulses from the centers enable DD cells to gather
in these centers and create fruiting bodies.
The propagation of cAMP pulses, resulting from the mutual interaction
of both an autocatalytic production of cAMP in cells
and the diffusive transport of cAMP through
the intercellular space, can be altered by an externally
applied electric field that can enhance the transport of
negatively charged cAMP.
In a network of chaotic elements when the strength of the interaction among elements is small enough, motion
of elements seems to be independent each other. Accordingly, the system is in a high-dimensional chaotic
state. However, a certain macroscopic quantity shows some dynamical property, rather than fluctuations,
ranging from low dimensional
torus to high-dimensional chaos. This has been called collective motion in a network of chaotic elements. In
this presentation, we will study the effect of external fluctuations or the effect of external forcing on such
collective motions.
[1] Tatsuo Shibata and Kunihiko Kaneko,
``Tongue-Like Bifurcation Structures of the Mean-Field Dynamics in a Network of Chaotic Elements'',
Physica 124D, (1998) 177-200.
[2]
Tatsuo Shibata and Kunihiko Kaneko, ``Collective Chaos'',
Physical Review Letters 81, (1998) 4116-4119.
[3]
Tatsuo Shibata, Tsuyoshi Chawanya and Kunihiko Kaneko,
``Noiseless Collective Motion out of Noisy Chaos'',
Physical Review Letters 82, (1999)4424.
Designing simple biochemical networks that can
regulate temporal expression of multiple genes and
their products can provide, among other applications,
a
theoretical framework for understanding regulation of
gene expression in cells.
We have modelled a simple three-step biochemical
network which is negatively regulated in three
distinct biologically realistic manner as observed in
cellular systems. We have studied the dynamic
behaviour of the three models for changes in
parameters and the state variable. The robustness of
the three networks varies considerably under
perturbations.
We present a powerful, general method of fitting a model of
a biochemical pathway to experimental metabolite
concentrations and dynamical properties measured at a
stationary state, when the mechanism is largely known but
kinetic parameters are lacking. Rate constants and maximum
velocities are calculated from the experimental data by
simple algebra without numerical integration of the kinetic
equations. Using this direct approach, we fit a
comprehensive model of glycolysis and glycolytic
oscillations in intact yeast cells to data measured on a
suspension of living cells of Saccharomyces cerevisiae
near a Hopf bifurcation and to a large set of stationary
concentrations and other data estimated from comparable
batch experiments. The resulting model agrees with almost
all experimentally known stationary concentrations, with the
frequence of oscillation, and with the majority of other
experimentally known kinetic and dynamic variables. From the
fittet parameters we have calculated the parameters of the
corresponding set of coupled Stuart-Landau equations
describing the behavior of the yeast cell population. This
system of equations have been used to get new information on
the mechanism of synchonization of glycolytic oscillations
in yeast cells.
Mathematical models based on experimental data obtained on the intact system are fundamental for characterizing the system behavior in situ. Modeling strategy are usually based on classical enzyme kinetics rate-laws derived from in vitro experiments. Besides leading to complicated models that are difficult to analyze, the convenience of using in vitro derived rate-laws must be careful evaluated. In general, there is no guaranty that these in vitro rate-laws represent the enzyme kinetics in situ. Characterization in isolation does not assure a realistic identification of interactions and regulatory influences. Furthermore, in vitro experiments operate far from the actual conditions within the cell.
To overcome these problems, we should focus on methods that can provide a valid description for the whole system investigated in situ. Different methods based on sensitivity analysis have been suggested to fit this goal. Among others, Biochemical Systems Theory (BST) and Metabolic Control Analysis (MCA) provide practical approximations for complex pathways. If we are interested in numerical simulations and steady-state analysis, models based on the power-law formalism provide a useful approach. These models are the fundaments of BST and they are especially suited for investigating design principles in metabolic pathways and for critically evaluating large models. Although these models have produced an important amount of useful results, the problem of model building from data on the intact system is still not fully solved. As a contribution towards a systematic way of building an useful model from steady-state experimental data, we present the use of power-law models based on least-square estimation of the required parameters.
The power-law formalism was initially derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The resulting models, either as Generalized Mass Action (GMA) or as S-systems models, allow to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. While this definition is appropriate from a theoretical point of view, its application to measured data may lead to some practical problems. Particularly, experimental data covering a given operational range may conflict with the single operating point used in the Taylor approach. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [1, 2]. Besides providing an alternative to the classical Taylor power-law, that can be considered a particular case when the operating interval is reduced to a single point, the LS power-law so defined is more consistent with the results that can be obtained by fitting experimental data points. The resulting power-law is unique within the considered operating range in contrast with the different Taylor power-laws that could be derived considering different operating points in this range. In that sense, the kinetic orders are constant for a given operating range. According to its averaging nature, LS power-law models are indicated for simulating the system's behavior within the studied range. This is particularly advantageous when the system variables fluctuates as a response to some forcing function. We shall present some examples and discuss the implications of the LS strategy for modeling a metabolic pathway. Simulation experiments will show the utility of this approach on building-up a mathematical model of a pathway from steady-state experimental data [3].
References
[1] Hernández-Bermejo, B.; Fairén, V.; Sorribas, A. Power-law modeling based on least-squares minimization criteria. Math. Biosc. (1999) 161:83-94
[2] Hernández-Bermejo, B.; Fairén, V.; Sorribas, A. Power-law modeling based on least-squares criteria: Consequences for system analysis and simulation. Math. Biosc. (2000) 167:87-107
[3] Sorribas, A.; Hernández-Bermejo, B. Modeling a metabolic pathway from
steady-state measurements on the intact system: on the usefulness of
least-squares derived power-law models. (2001) Biochem.J. (submitted)
The response of cells to topography of substratum was one of the first phenomena observed in tissue culture and several studies have shown that surface topography is an important factor in controlling the shape and function of cells.
The chemical-physical properties of synthetic macromolecules and peptides have been used to modify surfaces on the molecular level. These surfaces were used to manipulate the adhesion and motility properties of GFP-actin fibroblast cells based on single receptors allowing the cells to be probed with a pattern made of single receptors.
We investigated the regulation of cell shape of cultured human melanocytes grown on surfaces with different topography and biochemical pattern. The cellular morphology of melanocytes is a measurable indicator for cell reaction to the cellular environment. The characteristic cellular shape of different cell cultures was quantified by different shape parameters like the number and length of dendrites. A mathematical model describes the adjustment of the cell shape parameters by a set-point and additive intrinsic noise. A decreased signal-to-noise ratio was found for melanocyte cells concerning the number of dendrites and orientation of dendrites if cultured on biochemically and topographically structured substrates.
Motor proteins and microtubules are of crucial importance for self-organization of the intracellular architecture. Here, we study the morphogenetic properties of mixtures of two oligomeric motor proteins with opposite directionality. In in vitro systems consisting of purified proteins, we observe how motor/microtubule networks organize themselves into specific patterns. We also use numerical computer simulations to reproduce these observations and to study the influence of individual kinetic parameters on pattern formation. We find that mixtures of oligomeric motors with opposite directionality are capable of organizing microtubules into a variety of structures like asters, vortices or mixtures of these patterns. Under certain conditions, interconnected microtubule networks consisting of spindle-like structures arise. Which type of pattern forms, depends on the two motors' kinetic properties and their concentrations. While some parameters influence only the 'intensity' of self-organization of a given type of pattern, others are identified to be crucial for determining the 'type' of the generated pattern itself. These results demonstrate the combinatorial power of mixtures of motors with different kinetic properties and emphasize the structural role of kinetic parameters in self-organizing motor/microtubule networks.
Considerable progress has been made identifying the molecular composition of
complex signalling networks controlling cell proliferation, differentiation
and survival. However, to discover general building principles and quantitatively
predict the behavior of signalling networks it is essential to develop data
driven dynamic mathematical models describing experimental observations.
Here we report a dynamical model of the core module of the JAK-STAT signalling
pathway based on experimental data. The parameters of the four coupled
differential equations were estimated from time resolved measurements of the
receptor activation and tyrosine phosphorylated STAT (signal transducer and
activator of transcription)-5. In contrast to the widely accepted assumption of
a linear entity terminated by nuclear export, we demonstrate that effective
signal transmission requires multiple successive STAT-5 activation-inactivation
cycles. Based on the fitted model we can determine the quantitative behavior
of STAT-5 populations not accessible to experimental measurements and reveal
that under conditions used STAT-5 resides in the nucleus for approximately
6 minutes. Unexpectedly our studies identify nuclear shuttling as the step
most sensitive for perturbations of the system. Thus, quantitative dynamic
modeling of signalling pathways can promote functional understanding and
identification of targets for medical intervention.
Polymerizing networks of actin filaments are capable of exerting significant mechanical forces, used by many
eukaryotic cells to change shape or to move. Certain intracellular bacterial pathogens, including Listeria
monocytogenes, have developed the ability to induce the polymerization of host cell actin filaments on their surface
and to harness the resulting force for efficient intra- and intercellular spread. For L. monocytogenes, nucleation of
host cell actin filaments is indirectly catalyzed by the bacterial surface protein ActA. ActA is expressed
asymmetrically on the bacterial surface, enabling unidirectional movement. Polystyrene microspheres uniformly
coated with ActA are, under certain conditions, able to spontaneously break symmetry and initiate unidirectional
actin-based movement. The ability to break symmetry is influenced by particle size, ActA protein density, and actin
concentration. We have developed a simple stochastic model where each actin filament is modeled as an elastic
Brownian ratchet that quantitatively accounts for the observed symmetry-breaking behavior. The presence of the
bead effectively couples the polymerization of different filament tips, such that small stochastic fluctuations to be
amplified and symmetry-breaking can readily occur for the system as a whole. Once particles start moving, speeds
vary considerably among apparently identical individuals, and fluctuate significantly over time. We are currently
attempting to expand our stochastic model to account for these speed variations.
We study mathematically the fire-diffuse-fire model of Ca
release in the both the continuum limit and the limit in which
calcium stores are arranged on a regular lattice. The speed and
waveform of solitary pulses is explicitly calculated in terms of
physiologically significant system parameters.
A linear stability analysis shows that it is the faster of the two
possible solutions that is stable.
The original FDF model is shown to be inadequate for the description
of periodic travelling waves.
With the inclusion of a simple refractory process the FDF model is
shown to sustain periodic waves of the type consistent with more
detailed biophysical models. Moreover, a kinematic analysis of the
continuum model predicts the existence of doubly periodic waves that
bifurcate from those with a single period. Interestingly waves in
the lattice FDF model are shown to travel with a non-constant
(lurching) profile.
We develop a discrete model of malignant invasion using a thermodynamic argument. An extension of the Potts model is used to simulate a population of malignant cells experiencing interactions due to both cell-cell and cell-extracellular matrix (ECM) adhesion while also secreting proteolytic enzymes and experiencing a haptotactic gradient. In this way we investigate the influence of changes in cell-cell adhesion on the invasion process. We demonstrate that the morphology of the invading front is influenced by changes in the adhesiveness parameters, and detail how the invasiveness of the tumour is related to adhesion. We show that cell-cell adhesion has less of an influence on invasion compared with cell-medium adhesion, and that increases in both proteolytic enzyme secretion rate and the coefficient of haptotaxis act in synergy to promote invasion. We extend the simulation by including proliferation, and, following experimental evidence, develop an algorithm for cell division in which the mitotic rate is explicitly related to changes in the relative magnitudes of cell-cell and cell-ECM adhesiveness. We show that although an increased proliferation rate usually results in an increased depth of invasion into the extracellular matrix, it does not invariably do so, and may, indeed, cause invasiveness to be reduced.
We study a three-state model for myosin-like molecular motors and show
that a hysteresis in the force-displacement (as well as in the
force-velocity) relation can occur. If the stiffness of the elastic
element coupled to the motor is considered as an external parameter,
the system passes through a bifurcation and can generate oscillations
above the bifurcation. We determine the frequency, amplitude and shape
of these oscillations.
We apply the results to the model for auditory hair-cells found in
non-mammalian vertebrates. There a system of mechanically activated
transduction-channels and myosin motors provides a self-tuned
Hopf-bifurcation which can amplify weak input signals and detect a
broad range of amplitudes.
Modern methods of genomics are producing an unprecedented amount of raw data.
The interpretation and explanation of these data constitute a major,
well-recognized challenge. The standard approach of analysis is clustering
either by the degree of expression in a given cell line, by experimental
conditions across cell lines, or by both simultaneously. This approach provides
an excellent tool for searching genes with yet unknown function. However,
clustering does not tell the whole story. For instance, we analyzed expression
profiles in yeast following heat shock and found that even within the same
pathway (glycolysis), genes coding for subsequent catalytic steps show very
different levels of expression.
The presentation briefly reviews a static model of the heat shock
scenario [1], which we formulated as an S-system within the framework of
Biochemical Systems Theory (BST) [2, 3] and analyzed with the freeware
PLAS(c) [4]. Insights from this model offer some explanations of the
differences in expression. They also indicate that dynamical features
must be considered for a fuller understanding. The presentation
discusses some preliminary findings concerning these critical dynamical
features.
[1] Voit, E.O., and T. Radivoyevitch: Biochemical systems analysis of genome-wide expression data,
Bioinformatics 16(11), 1023-1037, 2000
The deterministic and the noise-dependent dynamics of a ring of
three ohmically coupled electronic relaxation oscillators are
considered by means of numerical simulations. Each isolated
oscillator is described by a set of two ordinary differential
equations with very different characteristic times. The emergence
of the limit cycle via the Hopf bifurcation results from the
N-shaped current-versus-voltage characteristic of the nonlinear
resistor. The phase diagram for a ring of three such oscillators
was calculated in the presence of a small detuning. Special
attention is focused on two parameter areas, one near a transition
to the homogeneous and the other to the inhomogeneous stable
steady state. Along with other nontrivial limit cycles,
essentially asymmetrical limit cycles, termed dynamic traps, may
arise in these two areas. The dynamic trap is the regime in which
one or two oscillators do not perform full-amplitude oscillations
and, correspondingly, do not generate spikes. The interspike
interval distributions in the presence of noise were calculated as
a function the coupling strength in both areas of the parameter
plane. The distributions proved extremely polymodal near the
homogeneous steady state even if the in-phase limit cycle was
dominating. The origins of this abnormal enhancement of ISI
variability are discussed in detail. Similar analysis showed that
nontrivial periodic attractors were observable in the vicinity of
the inhomogeneous stable steady states only if the level of noise
was relatively low. In this case, the dominance of the in-phase
limit cycle basin resulted in an almost unimodal distribution of
interspike intervals.
Our group pursues several studies in which we think dynamical models,
reconstituted from known facts in the way biochemists reconstitute metabolic
processes from purified components, will help us understand how simple rules
governing myriad interactors lead to complex behavior. I'll mention two
such projects briefly, and one, modeling gene networks, in more detail.
Some years ago we became interested in the idea that developmental
mechanisms consist of modules, where modulemeans a group of tightly
interconnected genes and gene products that together exhibit some intrinsic
behavior. We've explored this idea using dynamical models in which we
represent a gene network as a system of coupled ordinary differential
equations. We've concocted models of two modules: the segment polarity and
neurogenic networks, characterized first in Drosophila. Both are ancient,
and both play diverse roles in development in flies and diverse animals. We
wanted to know, is there something about these networks that causes them to
be conserved through deep evolutionary time, and that causes them to be
re-deployed in so many developmental contexts? Or is it just evolutionary
conservatism? We found that even minimal models of both networks are
astonishingly robust to changes in parameters (i.e., the rate constants and
coefficients that govern biochemical interactions) and initial conditions,
and even architecture. I'll describe where we think this kind of robustness
comes from, mechanistically and teleologically: the former, in these two
cases at least, has partly to do with cooperativity,äs anticipated by the
biochemists who first described the phenomenon of allostery, and the latter,
we suspect, may have partly to do with evolutionary pressure to tolerate the
presence of multiple alleles in sexually reproducing populations.
In recent years modeling and simulation of metabolic processes in
vivo has become an important tool, particularly with regard to the quantity
of data being generated and stored in huge databases. Aims are the
evaluation of metabolic experiments, an understanding of metabolic
regulation and the prediction of effects induced by genetic manipulations.
The metabolism of microbial, plant and animal cells is build of thousands of
elementary reaction steps. The structure of the stationary chemical reaction
network is in general described by:
In contrast to classical reaction networks the reaction kinetics
in metabolic models originate
in biochemistry. The cells complex regulatory structure leads to specific
problems in modeling and simulation, since enzymatically catalyzed reactions
in general depend on a multitude of factors. In particular, the study of
enzymes in vivo is possible quite recently. Due to the system being to be
examined as a whole, enzyme functionality is measurable only indirectly.
An enzymes specific activity is proportional to its actual amount
in the living cell. It depends on the systems metabolic state, which is
regulated on the genetic scale. This regulation has to be modeled in order
to predict the effect of genetic manipulations. To identify the many
parameters of complex models various data sources have to be exploited
simultaneously: enzyme and metabolite concentrations, intracellular fluxes
and kinetic parameters estimated by in vitro experiments.
Validating and discriminating complex model approaches is the current
problem in modeling metabolic networks. Here the aim is a selection of
meaningful models that additionally allows an experimental validation. With
respect to simulation technologies most of the questions arising in this
context have not yet been examined for systems of a whole cells complexity.
Moreover, simulation tools for the study of model validation and
discrimination are widely missing. This contribution gives an overview to
the questions which is currently worked on.
When microorganisms invade a new environment under stringent, i.e. nutrient limiting, conditions, the formation of branched colony patterns can be observed. This mode of growth allows for the capture of a maximum of the surrounding area in the search for new nutrient resources at a minimum expense of biomass and energy.
Even single cell organisms, such as bacteria and yeasts are able to form complex fractal structures. This process requires a coordinated growth of the cells that form the colony.
Therefore, although the growth pattern is built up of separated cells, on a higher scale the colony can be rather regarded as a single organism that adopts its structure to the environmental conditions in order to ensure the survival of the population.
Whereas pattern formation of bacterial colonies was extensively studied throughout the recent years, the growth of yeast colonies has not been in the focus of research yet. However, yeasts represent an ideal model to study the invasion of low nutrient environments by higher fungi that bears ecological and technical relevance. Therefore, we here present the first results of a study of the growth of yeast colonies under nutrient limiting conditions. The model organism used was Saccharomyces cerevisiae. This simple fungus is a well characterized food yeast that cannot form true hyphae and is easily susceptible to genetic manipulations. Transport of nutrients and information within the mycelium can be neglected which simplifies the system that we intend to describe mathematically. The labeling of key genes in the metabolism of the yeast with the green fluorescent protein (GFP) enables us to monitor metabolic activity and cell status on a single cell level by simple fluorescence microscopy.
In our studies, S. cerevisiae was cultivated on agar plates and exposed to either nitrogen or carbon limitation. Nitrogen limitation induced the differentiation of the cells to the elongated pseudohyphal growth form. In contrast, cells exposed to carbon limitation remained round-shaped. The differentiation on the single cell scale lead to the formation of essentially different patterns on the colony scale. Whereas nitrogen limited populations of S. cerevisiae formed branched structures similar to colonies of higher fungi, carbon limited populations formed patterns similar to structures formed by immobile bacteria under nutrient limitation.
The major challenge in the mathematical simulation of the colony growth is the verification of simulated data and model assumptions by experimental results. In this context, the identification of stationary cells within the pattern represents a crucial problem to compare data acquired from simulations and experiments. As a part of the general stress response, the gene HSP26 is expressed in S. cerevisiae during entry into stationary phase. The labeling of the promotor of HSP26 with GFP leads to an intensive fluorescence of stationary cells and makes it easy to identify them within the pattern.
In our contribution we describe the pattern evolution of S. cerevisiae
colonies depending on nutrient supply and the use of molecular biological
techniques in the monitoring of the growth process during pattern formation.
Starvation results in the chemotactic aggregation of single cells of the social amoebae Dictyostelium discoideum to form a fruiting body. Morphogenesis results from the coordinated movement of differentiating cells. We study the dynamics and geometry signals controlling cell movement during all stages of development. Cell movement is controlled by propagating waves of the chemo-attractant cyclic MP (cAMP). During aggregation these waves have the form of target patterns or simple spirals. In the mound and slug stage of development the waves have more complex geometry's, such as multi-armed scroll waves. We can visualise the dynamics of cAMP signaltransduction in individual cells in the multicellular stages and are analysing the dynamics of cAMP signalling in all celltypes during development in a variety of signalling and motility and chemotaxis mutants. We correlate the signalling and movement response of individual cells and begin to understand how the geometry of the waves in conjunction with a celltype specific differential chemotactic movement results in the organism's characteristic morphogenesis. We have formalised these findings into both continuous and discrete mathematical models that can describe the aggregation, mound and slug stages of Dictyostelium development.
The Golgi apparatus of eukaryotic cells is of crucial
importance for the modification of newly synthesized proteins ('cargo').
This organelle is located in a juxtanuclear position and consists of a
polarized stack of distinct flattened compartments ('cisternae'). Cargo
enters the stack at the cis face and leaves it via the trans
cisterna. Golgi-resident enzymes exhibit peaked steady-state distributions
across the stack, i.e. some locate to the cis face while others are
most abundant in medial or trans cisternae. This steady state
is interesting since all cisternae are subject to a default cis to
trans movement ('maturation'), i.e. the trans-most cisterna
disassembles while a new cisterna is assembled at the cis face de
novo. Thus, cargo never needs to leave the cisternae while being
processed. To accomplish the observed steady state distributions of
Golgi-resident proteins, however, this default anterograde flux needs to
be compensated by retrograde transport via coated vesicles, which contain
only little amounts of cargo molecules. In this contribution it is shown
that a simple triggered sorting mechanism can account for the
experimentally observed robust steady state distributions. Furthermore, a
more detailed model is proposed how Golgi-resident enzymes are
distinguished from cargo while forming the retrograde vesicles. This model
is in well agreement with experimental observations.
With the sequencing of entire genomes, the inventory of autonomously living
cells has become complete. However, the parts list of a Boeing 747 gives
little insight in how the plane flies and neither does the inventory of
yeast explain why it lives. Dominant aspects of living cells extend
beyond the information that is contained in the linear sequence of its DNA.
The former include (i) hysteresis, i.e. that living systems only arise as
extensions of preexisting living systems, (ii) biocomplexity, i.e. that
many functional properties arise in the nonlinear interactions between
molecular processes, (iii) limited self organization controlled by
prespecification, and (iv) the requirement to be removed from equilibrium
yet robust. Simple organisms have eight times more genes than essential.
More evolutionary time has been spent in optimizing already successful life
(phase II) than in generating it (phase I).
Of course we shall need to identify the structure and molecular activity of
most gene products to understand phase I, and I shall illustrate a new and
FANCY method that may help to do so. However, it will be even more
important to come to grips with phase II. Here sophisticated analysis of
the Function and Regulation of Cellular Systems will require Experiments
and Models to go hand in hand. I will briefly describe the corresponding
Silicon Cell initiative of the BioCentrum Amsterdam. I will illutrate it
by discussing experiments and models that support the thesis that the
essence of as 'simple' a cell as E. coli resides more in its macromolecular
neural network than in its individual molecules.
vaccines, viral vectors and recombinant proteins
Leipzigerstr. 44, D-39120 Magdeburg, Germany
University of Leipzig, Leipzig, Germany
der Christian-Albrechts-Universität Kiel
Leibnitzstraße 15, 24098 Kiel
INF 253, D- 69120 Heidelberg
and Adaptation of the Immune Defence
S.G.Rudnev, A. A.Romanyukha
Gubkinstr. 8, 119991 Moscow, Russia
P. O. Box 2557 Ullandhaug, 4091 Stavanger,
Norway
![[*]](file:/usr/local/lib/latex2html/icons/crossref.gif){kind=icon}
, it seems that evolution
has ``converged'' to definite {}-sets within organisms.
Results obtained from different organisms indicate that circadian
pacemakers are based on one or several negative feedback loops where
protein products of certain clock genes are inhibitors of their own
transcription. We have simulated the occurence of
temperature-compensation by using a simple reaction-kinetic model (the
so-called Goodwin oscillator) which mimicks the negative feedback loop
of a circadian pacemaker. The comparison between simulation
calculations and experiments from Neurospora and
Drosophila clock mutants shows that both period length and
temperature-compensation appear to be closely connected through the
stability/degradation rate of clock proteins.
Waldweg 33, 37073
Goettingen, Germany
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
M. Dichtl and E. Sackmann
James-Franck-Strasse, D-85747 Garching, Germany
Institute of Biology, Group of Theoretical Biophysics
Invalidenstr. 42, 10115 Berlin
University of Massachusetts
Worcester, MA 01655, USA
Co-authors: Helen Packer, Judy Armitage, Philip Maini
University of Oxford, Oxford OX1 3LB, UK.
T. Sauter and E.D. Gilles
Pfaffenwaldring
9, D-70550 Stuttgart, Germany
Dept. Biophysics and Physics of Complex Systems
in endothelial cultures
Centre for Interdisciplinary Plasma Science, Max-Planck-Institut
für Plasmaphysik Garching, Germany
Max-Planck-Institute for Dynamics of Complex Technical Systems
Leipziger Str. 44, 39120 Magdeburg, Germany
Allmandring 31,
70569 Stuttgart, Germany
Mitotic Motors, Microtubule Flux and the Mechanism of Mitosis
1. Sharp et al (2000) Nature, 407; 41-47.
2. Cole et al (1994) J. Biol. Chem, 269; 22913-22916.
3. Kashina et al (1996) Nature, 379; 270-272.
4. Sharp et al (1999) J. Cell Biol., 144; 125-138.
5. Sharp et al (1999) Nature Cell Biol. 1; 51-54.
6. Sharp et al (2000) Mol Biol. Cell., 11; 241-253.
7. Sharp et al (2000) Nature Cell Biol., 2; 922-930.
14424 Potsdam, Germany
of Dictyostelium discoideum
Center for Nonlinear Dynamics of Chemical and Biological Systems
Institute of Chemical Technology, Technická 5, 166 28 Prague 6,
Czech Republic
The presented poster will show the results of numerical studies
of an applied electric field on the cAMP pulses propagating
in the model, spatially 2 dimensional, layer of DD cells. In the model
the Martiel-Goldbeter kinetic scheme is used to describe
the production of cAMP and Nernst-Planck
equation is used to describe the intercellular transport
of cAMP both by diffusion and by electromigration.
Depending on the strength
and the orientation the electric fields of low intensities
(up to 6V/cm) were found to i) change both the propagation
velocity and the amplitude of the pulses, ii) to annihilate
the propagating pulse, and iii) to induce the formation of new centers
of cAMP pulses. The poster aims to present also
the results of now undertaken experimental studies of electric
field effects on some features of DD cells aggregation.
Fritz-Haber-Institut der Max-Planck-Gesellschaft
Faradayweg 4-6, 14195 Berlin, Germany
Uppal Road, Hyderabad 500 007, India
F. Hynne, S. Danø and P. G. Sørensen
&
Center for Chaos and Turbulence Studies (CATS)
H. C. Ørsted Institute
University of Copenhagen
Albert Sorribas, Benito Hernández-Bermejo
Av. Rovira Roure 44, 25198-Lleida, Spain.
Stimulating, Manipulating, and Probing the Mechanical Behaviour of Fibroblast and Melanocyte Cells on Nanostructured Surfaces
Wouter Roos
D-69120 Heidelberg, Germany
ORGANIZATION OF MICROTUBULES BY TWO MOTORS WITH OPPOSITE
DIRECTIONALITY
European Molecular Biology Laboratory, Cell Biology and Biophysics
Meyerhofstr. 1, 69117 Heidelberg, Germany
MPI of Immunbiology, Stübeweg 51, 79108 Freiburg, Germany
Center for Data Analysis and Modeling, Eckerstr.1, 79104 Freiburg, Germany
Stanford University School of Medicine
Stanford, CA 94305-5307, USA
Loughborough University, Department of Mathematical Sciences
72 Abberton Way, LE11 4WG, Loughborough, Leicestershire, UK
Department of Mathematics
Heriot-Watt University
EH14 4AS Edinburgh, Scotland
Collective oscillations of molecular motors
Madingley Road, CB3 0HE, Cambridge, UK
Eberhard O. Voit
Medical University of South
Carolina
Charleston, SC 29425, U.S.A.
[2] Savageau, M.A.: Biochemical Systems Analysis. J. Theor. Biol. 25, 365-369 & 370-379, 1969
[3] Voit, E.O.: Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and
Molecular Biologists, xii + 530 pp., Cambridge University Press, Cambridge, U.K., 2000
[4] PLAS(c): http://correio.cc.fc.ul.pt/ aenf/plas.html (António
E. N. Ferreira)
Leninskii 53, Moscow, Russia
Friday Harbor Labs, Friday Harbor, WA,
98250, USA
Here,
denotes the vector of reaction-kinetic
parameters,
the vector of extracellular substrate
concentrations,
the vector of enzyme concentrations and
the vector of metabolite concentrations. denotes
the stoichiometric matrix, describing the networks topology induced by mass
conservation. In many aspects metabolic networks are similar to networks
used for instance in chemical, electrical and hydraulic engineering.
Institut für Lebensmittel- und Bioverfahrenstechnik
Bergstr. 120,
01069 Dresden
Wellcome Trust Biocentre, Dundee, DD1 5EH, UK
Dormann, D., Vasiev, B. & Weijer, C. J. (2000) Phil. Trans. Royal Soc. B 355, 983-991.
Patel, H., Guo, K. D., Parent, C., Gross, J., Devreotes, P. N. & Weijer, C. J.
(2000) Embo J.l 19, 2247-2256.
Meyerhofstr. 1, 69117 Heidelberg, Germany
The genome alive: intelligent functioning of the living cell
BioCentrum Amsterdam