Information Processing, Noise, and Adaptation in Living Systems

Pluripotent stem cells (PSCs) are pivotal in regenerative medicine due to their unique characteristics: pluripotency, the ability to differentiate into any cell type without developmental restrictions, and self-renewal, the capacity to be expanded indefinitely in vitro while maintaining an undifferentiated state. Studying the differentiation of these cells holds significant promise for enhancing reprogramming protocols. It is worthwhile since reprogramming, by generating PSCs from somatic cells, can address ethical concerns surrounding the use of embryonic stem cells. In our study, we focused on a set of transcription factors that guide the differentiation of PSCs by regulating each other. We described PSCs as computation cores where these genes are organised in a Gene Regulatory Network (GRN) able to compute external biochemical signals, the inputs, and take biological decisions, the outputs. To do so, we developed an unsupervised flexible computational model based on the Kinetic Ising model. Starting from gene expression data, it infers the GRN as a solution to an inverse problem. With this model, we uncovered the gene interactions consistent with the observed qualitative dynamics of PSCs in decision-making. Moreover, the model can predict the GRN behaviour in response to a perturbation. We simulated single or triple gene knockout, and IGNITE properly resembled the experimental data. To test the model performance, we compared it to three other modelling strategies: (i) Pearson correlation coefficient, (ii) Maximum entropy approach, (iii) CellOracle, and (iv) SCODE, the actual gold-standard method. These models were evaluated against experimental data. The results showed that IGNITE outperformed the other models in inferring known interactions, generating new data and simulating the gene knockout perturbation. Overall, our findings suggest that IGNITE is a promising tool for studying the behaviour of PSCs and could lead to new insights in describing the differentiation process.

MicroRNAs have evolved to play a variety of important regulatory roles in eukaryotic organisms, including controlling the noise levels of protein expression. However this noise control comes at a significant metabolic cost: in order to compensate for the effects of microRNA-mediated interference in translation, the transcription rates of regulated genes have to be increased. In effect, organisms have to sacrifice a fraction of messenger RNAs (via enhanced degradation and translation suppression due to microRNAs) to achieve the same expression levels with lower variability in protein numbers. How would such a costly regulation evolve in the first place, and has microRNA regulation been fine-tuned to minimize the energetic prices? In this work, we study how the metabolic costs of microRNA noise regulation depend on interaction affinities. We show for the first time that microRNA-mRNA affinities lie in an evolutionary sweet spot: sequences that are much longer or short would not have the right binding properties to optimally reduce noise. Moreover, we argue that the energetic costs of microRNA regulation can become sufficiently high that natural selection could drive them to this precise sweet spot. These results illustrate how selective pressure toward metabolic efficiency has potentially shaped a crucial regulatory pathway in eukaryotes.

Precise estimation of extracellular cues is crucial for eliciting sharp cellular responses. In sensing morphogen concentrations and their gradients, cells often utilise signalling networks involving multiple receptor types and compartmentalisation of cellular biochemistry, along with local cell-autonomous feedback/feedforward control mechanisms. In a previous study, we arrived at optimal distributed cellular architectures for morphogenetic decoding of positional information during development. In this study, we look at the design principles underlying the functioning of such optimised cellular architectures. We evaluate the thermodynamic cost of implementing such design principles with feedback control and study the energy-time-accuracy trade-offs involved. We further show that accurate estimation of concentration gradients requires robust intercellular communication. Our study paves the way towards an understanding of the role of local cell-autonomous control mechanisms in enabling global tissue-level tasks.

Biomolecular condensates play an important role facilitating various cellular processes and can be modelled by the physics of phase separation. The sub-cellular environment is typically out of equilibrium; for example, condensates can dynamically nucleate, grow, shrink, fuse and dissolve. It is important to assess how far from equilibrium they are. We consider single-molecule trajectories crossing the phase boundary between the condensates and their surroundings, which are experimentally accessible. We obtain analytical insight by considering solvable non-equilibrium steady states. Based on the statistics of interface crossings, we calculate divergence metrics that characterise the degree of irreversibility and show that such metrics provide a lower bound for entropy production. This will allow us to discuss under what conditions these experimentally accessible measures capture most of the dissipation of the system. Our results, motivated by the physics of biomolecular condensates, promise wide applicability to other stochastic systems modelled by overdamped Langevin equations.

Proteins, crucial building blocks of life, play pivotal roles in regulating biological processes with high specificity and precision, attributes directly influenced by their structure. Despite transformations in sequences due to the forces of natural selection, proteins often maintain remarkable structural similarities. This study delves into the correspondence between different levels of protein structure, ranging from primary sequences to tertiary structure, aiming to comprehend how secondary structure constraints on protein folding. We developed a pipeline to study the relationship between protein secondary structure and tertiary structure and we further compressed secondary structure to much shorter secondary structure elements which allows efficient protein structure searching. Our objective is to refine our understanding of this interrelationship and to pioneer a methodology for predicting protein folding patterns solely based on secondary structures. This endeavour not only seeks to expand our comprehension of protein architecture but also to explore the potential of secondary structures as a predictive tool for folding mechanisms, thereby contributing to the broader field of structural biology and its applications in understanding biological processes and evolution.

In developing embryos, cells acquire distinct identities depending on their position in a tissue. Secreted signaling molecules, known as morphogens, act as long-range cues to provide the spatial information that controls these cell fate decisions. In several tissues, both the level and the duration of morphogen signalling appear to be important for determining cell fates. In the forming vertebrate nervous system, antiparallel morphogen gradients pattern the dorsal-ventral axis by partitioning the tissue into sharply delineated domains of molecularly distinct neural progenitors. How the information in the gradients is decoded to generate precisely positioned boundaries of gene expression remains an open question. Here, we adopt tools from information theory to quantify the positional information that neural cells receive and investigate how temporal changes in signaling influence patterning precision. The results reveal that the use of signaling dynamics, as well as signaling level, substantially increases the precision possible for the estimation of position from morphogen gradients. This analysis links the dynamics of opposing morphogen gradients with precise pattern formation and provides an explanation for why cells rely on time-varying signals to impart positional information.

In the hearing, signal velocities are 1,481 m/s of sound in water, 343 m/s in air, 55 m/s is a mean of active traveling wave in the cochlea, and 10 m/s takes propagation of spikes in the auditory nerve. The distances traveled by the signal in the auditory pathway enable both hearing and sound localization. In sound localization, microsecond timing differences are employed. We ask, what are essential parameters influencing sound localization and perception in microsecond signal propagation ranges in humans? Previous literature did not generalize the biophysical description of these phenomena. Measuring the in vivo traveling wave in the cochlea is not possible with current technology. We model data from indirect measurements. We study the roles of separate parameters and apply them to both cochlear and vestibular signaling. Cochlear implant stimulation protocols do not reproduce microsecond timing in electrically evoked spike trains in hearing with cochlear implants. Nevertheless, binaural implantees possess sound localization ability. Our research is applicable to better reverse-engineering designs of aids for the hearing impaired.

Common pool resources (CPRs) are goods that are both non-excludable, meaaning that it's very hard to regulate access to them, and subtractable, meaning that their usage by one consumer diminishes rheir quantity or degrades their quality for the others. Classic examples of common pool resources are fisheries, forests, irrigation systems, the atmosphere and so on. By definition, CPRs are prone to overexploitation, namely the outcome known as "Tragedy of the commons", a phrase coined by Garrett Hardin in a seminal paper published in 1968. At the same time, however, there are examples of societies that devised methods, for example via regulations and istitutions, to achieve a sustainable use of such resources; this is central to the work of Elinor Ostrom, Nobel prize in economics in 2009. Thus, the aim of the work is to understand the conditions under which these scenarios realize. In order to that, we devised a model bringing together elements of theoretical ecology, statistical mechanics, network theory, theory of dynamical systems and evolutionary game theory regarding the strategies of resource harvesting, social network structure and its interaction with the environment.

Heteroclinic dynamics are a suitable framework for describing transient and reproducible dynamics such as cognitive processes in the brain. We demonstrate how heteroclinic units can act as pacemakers to entrain larger sets of units from a resting state to hierarchical heteroclinic motion such as fast oscillations modulated by slow oscillations. The entrainment range depends on the type of coupling, the spatial location of the pacemaker and the individual bifurcation parameters of the pacemaker and the driven units. Noise as well as a small back-coupling to the pacemaker considerably facilitate synchronization. Units can be synchronously entrained to different temporal patterns, depending on the selected path in the hierarchical heteroclinic network. Such patterns are believed to code information in brain dynamics. Depending on the number and the location of pacemakers on a two-dimensional grid, synchronization can be maintained in the presence of a large number of resting state units and mediated via target waves when the pacemakers are concentrated to a small area of such a grid. Our results indicate a possibly ample repertoire for coding information in temporal patterns, produced by sets of synchronized units entrained by pacemakers, without finetuning of the parameters, and distributed in space. We also summarize results on relaxation times in heteroclinic dynamics, which decide about a fast adaptation to new external input. When oscillations are arrested by a quench of a bifurcation parameter from a parameter regime of oscillations to a regime of equilibrium states, the relaxation is underdamped. It depends on the nesting of the attractor space, the size of the attractor’s basin of attraction, the depth of the quench, and the level of noise. In the case of coupled heteroclinic units, it depends on the coupling strength, the coupling type, and synchronization between different units. Depending on how these factors are combined, finite relaxation times may support or impede a fast switching to new external input.

Advances in imaging have allowed us to computationally analyse biological systems that lend themselves to be naturally modelled by complex networks. We use connectivity to assigned node labels to define vectors associated to each node that undergo clustering to retrieve meaningful groupings of nodes in a network. We demonstrate this on the connectome data sets of Drosophila melanogaster and Caenorhabditis elegans, but the developed analyses are generally applicable to network data sets with extensive node labelling. For the Drosophila ventral nerve cord, we considered hemilineage labels in our connectivity and performed hierarchical clustering to extract groupings of six neurons constituting a serial homologue. For complex downstream clustering patterns, we used Shannon entropy to quantify the specialism of a node’s connectivity to the set of existing node label types. In C. elegans, neurons that scored highly in the entropic metric had high neuropeptide network degrees.

In the present study we have considered the impact of environmental noise on prey-predator interactions with seasonal fluctuations of water level. Both intensity of noise and water level variations together play significant role on the dynamics of an aquatic prey-predator system. Analytically, we have shown existence of positive solution and its uniqueness; ultimate bound of systems solutions; global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go to extinction are derived and their biological significance also discussed. The sufficient condition of stochastic permanence is also analysed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic system and observed some significant dynamics on the considered system.

We provide a simple framework for the study of state-dependent (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations multiplicative noise surprisingly causes the mass of the stationary probability distribution to become increasingly concentrated around fix points, whilst also exhibiting a kind of intermittent burst like jumps between these fix points. In the case that there is only one fixed point this causes on-off intermittency. Our framework relies on first term expansions, which become more accurate for larger noise intensities. In this work we show that the full width half maximum in addition to the maximum is appropriate for quantifying the stationary probability distribution (instead of the mean and variance, which are often undefined). We define a corresponding new kind of stationarity. Such results have to extreme events and tipping points. We apply the general ideas to the a problem of synchronisation chaos, showing that noise improves synchronisation between chaotic systems/ noisy oscillators.

The availability of time- and disease-dependent single-cell gene expression data has opened new opportunities for integrating these datasets into mathematical models representing the evolution and switching between cellular states. In this talk, I will focus on Hopfield recurrent networks, a mathematical framework from statistical physics that captures the multi-stable dynamics inherent in complex cell signaling networks, interpreting gene expression patterns as associative memories. Hopfield recurrent networks can mathematically implement Waddington’s interpretation of normal and abnormal cell phenotypes as dynamical attractors within epigenetic landscapes. I will discuss applications of this framework in modeling the onset of angiogenesis, the dynamics of disease progression in Multiple Myeloma (MM), and the cell cycle. In our angiogenesis model, we use data to visualize the cellular transition from stalk-like to tip-like endothelial cells, corresponding to the formation of capillary sprouts in blood vessels. The MM model employs scRNA-seq data from bone marrow aspirates of MM patients and those diagnosed with two medical conditions that often progress to full MM. Finally, I will introduce our Digital Cell Sorter (DCS) platform to analyze single-cell RNA-seq data. Beyond its capabilities based on the Hopfield networks framework, the DCS includes additional features such as automated cell type annotation and the quantification of cell anomaly. Supported by NIH/R35GM149261

n multi-cellular organisms, cells differentiate to multiple types as they divide. Here these cell types as well as the developmental course is known to be robust to external perturbations, as conceptualized by Waddington’s epigenetic landscape where cells embed themselves in valleys corresponding with final cell types. How is such robustness in developmental path, termed as homeorhesis, achieved by developmental dynamics and evolution? To address the question, we consider a model of splitting cells with gene expression dynamics and epigenetic feedback, governed by the gene regulation network. By evolving the network to achieve more cell types, we identified three basic mechanisms and expression dynamics to promote cell differentiation, that emerge depending on the noise level in the dynamics. Under noise, the gene expression dynamics first reach oscillatory dynamics described by low-dimensional orbit space, whereas sub-cycles are generated to make hierarchical differentiation. Higher noise levels however seem to avoid oscillatory dynamics but creates hierarchy through branched splitting to attractors. The final scenario seem to take a more intermediate approach while having orbits moving through parallel lines and planes. The three mechanisms differ in the nature of initial oscillatory dynamics and sub-cycle generation, which also lead to difference in their robustness to initial perturbations, mutations and in their final cell type distribution. Relevance of initial attraction to the oscillatory state to robust development is noted, whereas evolution of multicellular development to achieve multiple cell types is discussed.

The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled single-domain proteins, it was shown that misfolded entangled subpopulations might escape the cell quality control. Therefore, investigating the role of entanglement in shaping folding kinetics for such a class of proteins is crucial. In this contribution, I will present our recent work on the thermodynamics and refolding characterization of a small, natively entangled, antifreeze RD1 protein. We introduce a novel entanglement indicator, based on the linking number, and analyse simulations of a coarse-grained, structure-based model. Despite its small size, RD1 displays a rich refolding behaviour, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a longer-lived, non-entangled, near-native state. The former directs refolding along a fast pathway, whereas the latter is a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop forms without being threaded by the N-terminal residues. Trapping does not occur because contacts at the closure of the lasso-like loop form after those involved in the N-terminal thread, confirming previous predictions regarding the “late-entanglement” formation.

My contribution will describe strategies for optimal resource allocation in microbial organisms, in particular cyanobacteria. Cyanobacteria, as "evolutionary inventors" of oxygenic photosynthesis, are microbes of global importance and are an integral part of global biogeochemical cycles. We are interested in understanding how cyanobacterial cells adapt to different natural environments. In particular, the dependence on light as a primary source of energy, as well as the fact that light at high intensities can be detrimental (photodamage), gives rise to additional challenges with respect to sensing and processing environmental information. I will describe optimal strategies of metabolic resource allocation, from a computational and theoretic ppoint of view, and how the cell might implement such strategies given known interaction networks. I am in particular interested in combining our work on resource allocation with frameworks that describe robust information processing. These frameworks show how cells can sense and process environmental information despite imperfect "knowledge" and in the face of stochastic fluctuations of internal components.

Kyrell Vann B. Verano, Emanuele Panizon, Antonio Celani Tracking an odor source in a turbulent environment is an extremely difficult navigation task for small searchers such as insects. Despite the fact that odor signals are diminished and intermittently received, insects are able to decode the sequence of sparse odor encounters and use this information about the source location to build a successful search strategy. A key role in this process is played by the memory that the insect has to keep about the history of previous odor detections. Current algorithms require a continuous and/or high dimensional memory space, which are usually difficult to interpret. Here, we show in a computational model of olfactory search that finite-state controllers, very simple algorithmic devices endowed with a minimal memory, are rich enough to explain the occurrence of several behavioral patterns that are indeed observed in nature. Reference: Kyrell Vann B. Verano, Emanuele Panizon, and Antonio Celani. “Olfactory search with finite-state controllers”. In: Proceedings of the National Academy of Sciences 120.34 (2023), e2304230120.

Boyi Wang1, Patrick Pietzonka1,2, Frank Jülicher1,3,4 1 Max Planck Institute for the Physics of Complex Systems, Dresden, Germany 2School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom 3 Center for Systems Biology Dresden (CSBD), Dresden, Germany 4 Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany Chiral activity in soft matter[1], exemplified by phenomena like odd viscosity[2] and odd elasticity[3], drives unique topologically protected transportation[4] and phase separation behaviours[5]. To understand it in a minimal way, we introduce chiral activity into a lattice model with Ising interac- tions, achieved by stochastic locally rotating. Monte Carlo simulations at low temperature reveal a path to condensate formation, marked by the evolution of the droplet’s edge into a particular tilted orientation relative to the square lattice, thus reflecting the chirality of the model on a macroscopic scale. Furthermore, we investigate the stability of the chiral tilted angle in the droplet’s lattice field, and identify a persistent slope-dependent edge current flowing along the droplet’s interface. Our findings provide a novel perspective on chiral non-equilibrium systems, expanding our under- standing of how chiral driving forces influence the formation, adaptation and interface transportation behavior of active droplets. References [1] S. Fürthauer, M. Strempel, S. W. Grill, and F. Jülicher. Active chiral fluids. The European Physical Journal E, 35(9):89, September 2012. [2] Debarghya Banerjee, Anton Souslov, Alexander G. Abanov, and Vincenzo Vitelli. Odd viscosity in chiral active fluids. Nature Communications, 8(1):1573, December 2017. [3] Colin Scheibner, Anton Souslov, Debarghya Banerjee, Piotr Surowka, William T. M. Irvine, and Vincenzo Vitelli. Odd elasticity. Nature Physics, 16(4):475–480, April 2020. Number: 4 Publisher: Nature Publishing Group. [4] Qing Yang, Hongwei Zhu, Peng Liu, Rui Liu, Qingfan Shi, Ke Chen, Ning Zheng, Fangfu Ye, and Mingcheng Yang. Topologically Protected Transport of Cargo in a Chiral Active Fluid Aided by Odd-Viscosity-Enhanced Depletion Interactions. Physical Review Letters, 126(19):198001, May 2021. [5] Zhiyuan Zhao, Boyi Wang, Shigeyuki Komura, Mingcheng Yang, Fangfu Ye, and Ryohei Seto. Emergent stripes of active rotors in shear flows. Physical Review Research, 3(4):043229, December 2021.