The emergence of dynamic, functional organization from collections of interacting macromolecules is a fundamental problem in theoretical biophysics. A unified understanding of how physical interactions, sequence-encoded features, and regulatory mechanisms shape self-assembly, phase transitions, and spatial organization in living systems remains an open challenge. This seminar will present a theoretical and computational framework that elucidates the physical principles governing biomolecular organization across scales, from molecular self-assembly to cellular functional architectures. In my doctoral research, using analytically tractable models of conformationally switching polymers, we demonstrate how coupling between internal structural transitions and polymerization kinetics produces distinct growth regimes, structural polymorphism, and concentration-independent assembly dynamics. These results provide a mechanistic basis for understanding ordered protein aggregates, including amyloid fibrils, as emergent outcomes of coupled order–disorder transitions. Building on these foundations, coarse-grained and atomistic simulations of multivalent and intrinsically disordered proteins reveal how sequence valency, interaction patterning, and post-translational modifications collectively determine phase behavior, material properties, and intra-cluster dynamics of biomolecular condensates. A salient finding is the identification of phosphorylation as an evolutionary regulatory mechanism that suppresses pathological liquid–solid transitions by locally attenuating amyloidogenic interactions, while maintaining phase separation capacity. Comparative sequence analyses indicate that phosphosites are systematically enriched near aggregation-prone motifs, suggesting an evolutionary strategy to preserve functional liquidity while preventing aberrant solidification. Complementary modeling demonstrates that RNA molecules act as superscaffolds, extending interaction networks, promoting condensate formation at physiological concentrations, and modulating their morphology and dynamical exchange. At the mesoscale, reaction–diffusion and network simulations reveal that transient, weak enzyme–enzyme interactions can drive the emergence of metabolons, leading to substantial enhancements in pathway flux for reaction-limited enzymatic networks. These findings delineate a general physical mechanism by which spatial organization compensates for suboptimal catalytic efficiency. Collectively, my research so far delineates a continuum of organizing principles linking microscopic assembly to macroscopic phenotypical features (and function). It underscores how evolutionary constraints and regulatory modifications finely tune interaction landscapes to position cells near critical organizational regimes. These self-organizing principles ensure functional adaptability while mitigating pathological aggregation. These findings not only offer a predictive insight into the design rules of living matter but also provide a foundation for rational engineering of synthetic biomolecular assemblies with prescribed physical and functional characteristics. https://zoom.us/j/2884416023 Meeting ID: 288 441 6023 Passcode: physbio

Classical models of statistical mechanics such as the dimer, spanning-tree and Ising models hide rich algebraic and geometric structures. In this talk I will describe versions of the spectral transform, originally introduced by Kenyon and Okounkov for the dimer model, which parameterize these models in terms of algebro-geometric data. I will then explain how this parameterization reveals the discrete integrability of their local dynamics.