Phase Transitions in Polymeric and Protein Systems

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We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of the Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension Eventually, the variational free energy landscape develops a complex structure with multiple competing minima. The work performed together with J.Kelly and R.Bruinsma

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We introduce a simple model to describe the interplay between specific and non-specific interactions. We study the influence of various physical factors on the static and dynamic properties of the specific interactions of our model and show that contrary to intuitive expectations, non-specific interactions can assist in the formation of specific complexes and increase their stability. We then discuss the relevance of these results for biological systems.

This talk will focus on the molecular grammar underlying the sequence-to-binodal relationships of multivalent proteins that are chimeras of ordered domains and disordered regions. A chain of multipoles formalism has become useful for understanding the sequence-encoded driving forces for proteins with predominantly disordered regions. This affords specificity and cooperativity of interactions even in the absence of specific three-dimensional structures. The role of disorder in determining the material properties of condensates will also be discussed.

The dynamics of phase-separated dense liquids and globular polymers is studied by simulations and scaling arguments. Results for the shear-flow induced unfolding, cyclization dynamics and the viscoelastic behavior are presented.

Macromolecular solubility in solvent mixtures often strikes as a paradoxical phenomenon. In a system where all particle interactions are repulsive, chains can nevertheless collapse. And when attractive interactions settle in, they might collapse or swell the chain. We will review in this contribution how the puzzling behavior of polymers in aqueous alcohol solutions triggered a better understanding of the interplay between solvent composition and polymer conformation. And how the resulting view on polymer collapse and swelling takes us well beyond mean-field descriptions … and alcohol. [1] Mukherji, D., Marques, C. M., Kremer, K. (2014). Polymer collapse in miscible good solvents is a generic phenomenon driven by preferential adsorption. Nature communications, 5882, 5. [2] Mukherji, D., Marques, C. M., Stuehn, T., Kremer, K. (2015). Co-non-solvency: Mean-field polymer theory does not describe polymer collapse transition in a mixture of two competing good solvents. The Journal of chemical physics, 142(11), 114903. [3] Mukherji, D., Wagner, M., Watson, M. D., Winzen, S., de Oliveira, T. E., Marques, C. M., & Kremer, K. (2016). Relating side chain organization of PNIPAm with its conformation in aqueous methanol. Soft Matter, 12(38), 7995. [4] Mukherji, D., Marques, C. M., Stuehn, T., Kremer, K. (2017). Depleted depletion drives polymer swelling in poor solvent mixtures. Nature communications, 1374, 8. [5] Mukherji, D., Marques, C. M., Kremer, K. (2017). Collapse in two good solvents, swelling in two poor solvents: defying the laws of polymer solubility? Journal of condensed matter, 024002, 30.

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