A Toy Model for the Evolution of Directed Motility Open Access

Abstract

Nonequilibrium systems dissipate energy and hence break time reversal symmetry. As a result, a polarization vector in such systems is allowed to couple to the system's velocity vector. Thus, one expects that, generically, a polarized nonequilibrium system would exhibit directed motion along the polarization direction. However, the coupling between the polarization and the motion may be very weak. Here we conduct a computational experiment with a model of a 1-d gas of active agents (motors) in an enclosure (cell) with polarized mechanical properties to demonstrate that (1) generic values of the parameters of the system, indeed, result in a weak directed motion, and (2) a biological evolution-inspired genetic algorithm can strongly amplify the polarization-velocity coupling in relatively few generations. This toy model suggests that directed motility (e.g., chemotaxis) may be present generically in the context of living cells, and evolution may only need to amplify the taxis speed instead of performing a much harder task of evolving the taxis from scratch.

Table of Contents

1 Introduction.......................................................1

1.1 The evolution of cell motility............................1

1.2 A physical perspective: generic motility.............3

1.3 Evolution and generic motility..........................4

2 Methods............................................................6

2.1 A minimal system capable of motility................6

2.1.1 System overview...........................................6

2.1.2 Motor details................................................7

2.2 A genetic algorithm.........................................8

2.2.1 Initialization................................................9

2.2.2 Scoring........................................................10

2.2.3 Selection.....................................................11

2.2.4 Mutation.....................................................11

2.2.5 An edge case................................................12

2.3 Limitations.....................................................12

3 Results and Discussion.......................................14

3.1 Sanity Check...................................................14

3.2 Convergence to motility...................................14

3.3 Coupling between v and p................................17

3.4 Conclusions....................................................18

3.5 Future directions.............................................19

Bibliography

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, General Biophysics, General
Keyword	nonequilibrium dynamics computational physics directed motility
Committee Chair / Thesis Advisor	Jennifer Rieser, Emory University Daniel Weissman, Emory University Ilya Nemenman, Emory University

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