Large deviation theory and the dynamics of a bacterium

Jafarpour Hamadani, Farhad; Namvar, Mehrangiz

doi:10.47176/ijpr.24.4.81964

Large deviation theory and the dynamics of a bacterium

Document Type : Original Article

Authors

Farhad Jafarpour Hamadani

Mehrangiz Namvar

Department of physics, Bu-Ali Sina University, Hamedan, Iran

https://doi.org/10.47176/ijpr.24.4.81964

Abstract

Bacteria can move for various reasons, including in response to chemical stimuli in the environment. In this article, we model the movement patterns of a typical bacteria in the form of a discrete-time Markov chain in one dimension (one-dimensional running and tumble model). Then with the help of the large deviation theory, the behavior of the probability density function of current (displacement per unit time), as a dynamical variable that is defined on the moving path, is studied. We will show that it is possible to observe a dynamical phase transition in the system.

Keywords

large deviation theory

dynamical phase transition

chemotaxis

run and tumble model

stochastic process

Subjects

Complex Systems

J Adler, Rev. Biochem. 44 (1975) 341.
C Zimmer, “Microcosm: E. coli and the New Science of Life”, Pantheon Books, New York (2008).
H C Berg, “ coli in Motion Biological and Medical Physics, Biomedical Engineering”, Springer, New York (2004).
‎ H C Berg,“Random Walks in Biology: New and Expanded Edition”, Princeton University Press (2018).
O Farago and N R Smith, Rev. E. 109 (2024) 044121.
H Touchette, Rep. 478 (2009) 1.
D Poland and H A Scheraga, Chem. Phys. 45 (1966) 1456.
D Poland and H A Scheraga, Chem. Phys. 45 (1966) 1464.
R J Harris and H Touchette, Phys. A: Math. Theor. 50 (2017) 10LT01.
A Dhar, et al., Rev. E. 99 (2019) 032132.
L Angelani, R Di Leonardo, and M Paoluzzi, Phys. J. E 37 (2014) 59.
D Breoni, et al., Phys. J. E 45 (2022) 83.
D Saintillan, Rev. E. 108 (2023) 064608.
G Gradenigo and S N Majumdar, Stat Mech. (2019) 053206.