Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Statistical Physics of Biological Systems I (joint session DY/BP)

DY 20.2: Talk

Tuesday, March 19, 2024, 10:00–10:15, BH-N 334

Theory for Adaptive Systems: Collective Robustness of Genotype-Phenotype Evolution — •Tuan Pham and Kunihiko Kaneko — Niels Bohr Institute, University of Copenhagen

Biological and neural networks are adaptive - their connections slowly change in response to the state of the coupled elements making up the systems. The dynamics of such adaptive networks are intriguingly complex, rendering it extremely difficult to answer the fundamental question of how the resulting collective states of biological and neural systems are functionally robust against environmental stochasticity. We tackle this problem by developing a new framework based on the path-integral formalism of non-equilibrium statistical physics. We demonstrate the wide applicability of our framework to various very high-dimensional dynamical systems on multiple timescales, often encountered in biological evolution and neural network learning. As a specific example of our theory, we apply it to biological evolution, where phenotypes are shaped by gene-expression fast dynamics that are subjected to an external noise while genotypes are encoded by the configurations of a network of gene regulations. This network slowly evolves under natural selection with a mutation rate, depending on how adapted the shaped phenotypes are. Here we find phenotypes with a robust high-valued mean gene-expression level within an intermediate level of noise. The emergence of such robustness can be characterised analytically within our framework as the onset of instability of the attractor state with zero gene-expression levels.

Keywords: Genotype-phenotype maps; Adaptation; Gene regulatory networks; Neural networks; Dynamical Mean-Field Theory