第5回講演会 発表要旨

“Thermodynamic Structure of Population Dynamics in Changing Environment”

Tetsuya Kobayashi (The University of Tokyo)

　 In this work, we consider dynamics of population of growing cells that are influenced by changing environment. In evolutionary biology, this setup is related to the unsolved and old problem how fluctuation of environment can impact the evolutionary process of cells. In systems biology, the problem attracts renewed attention because the setup is relevant for persistence and drug resistance of cells if we identify the changing environment with dynamic perturbation to the population by, e.g., drug administration. We firstly show that a thermodynamic structure underlies the population dynamics in changing environment by employing path integral formulation of the dynamics. Then, by using the theory of steady state thermodynamics, we clarify that the population growth can be decomposed into three parts. The first part is explained only by the largest eigenvalues of dynamics under constant environments. The second one accounts for the contribution from the associated right and left eigenvectors. The last one is an entropy production term that should be related to the other eigen spectrum of the dynamics. We finally discuss on controllability of the population from the thermodynamic viewpoint.