Statistical Physics of Evolving Self-Replicators and Ring Neural Networks

Abstract

Biology is a treasure box of emergent phenomena. A diverse array of biopolymers self-organize into hierarchical structures to form cells and various tissues. Birds flock and bacteria swarm, presenting striking spatiotemporal patterns. Living organisms self-replicate, interact with environments, and evolve. Networks of neurons in the brain perceive the world and compute to achieve sophisticated cognitive tasks. Even though physicists have elucidated fundamental laws in the quantum world, the complexity of biology at a much higher level of organisms appears to obey its own operational principles. Recent experimental advances provide ways to precisely measure and manipulate biological building blocks such as DNA and a neuron. Now, it's the time to build theoretical bridges between microscopic "mechanic", "genetic", and "synaptic" interactions and the macroscopic phases that lead to "living matter", "evolution", and "cognition". In this thesis, I describe attempts to build the bridges across length and time scales by applying the tools and ideas of statistical physics. The first half of this thesis studies non-equilibrium phases of particles that convert chemical fuels into time-dependent-interactions and spatial translations. In Chapter 1, we seek specific and dynamic interaction rules that enable colloidal clusters to self-replicate and evolve, motivated by developments in DNA nanotechnology. In molecular dynamics simulation of colloidal particles, we observe Fisher population waves and genetic drift at the expanding front. Chapter 2 studies depletion-like attractive forces between two highly diffusive particles immersed in a sea of less diffusive particles. In the second half, starting with Chapter 3, we present population dynamics of engineered spatial gene drives constructs that evade the laws of conventional Mendelian population genetics. We find that gene drives over a certain range of selective disadvantages can nevertheless spread via a bistable wave that is both more controllable and socially responsible. Finally, Chapter 4 studies the eigenvalues and eigenvectors of a class of non-Hermitian ring random matrices. We then extend and apply the model to study the effect of disorder in ring attractor neural networks, motivated by recent experiments on the head direction cells in the Drosophila central brain.