Fluctuating Diffusivity of RNA-Protein Particles: Analogy with Thermodynamics.

Yuichi Itto

doi:10.3390/e23030333

Abstract

A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs of the quantity of heat and work are identified. The Clausius-like inequality is shown to hold for the entropy associated with diffusivity fluctuations, which plays a role analogous to the thermodynamic entropy, and the analog of the quantity of heat. The change of the statistical fluctuation distribution is also examined from a geometric perspective. The present discussions may contribute to a deeper understanding of the fluctuating diffusivity in view of the laws of thermodynamics.

Highlights

We study a formal analogy of the fluctuating diffusivity to thermodynamics for the RNA-protein particles in the cytoplasm of the Escherichia coli cell as well as Saccharomyces cerevisiae cell
We show that the analog of the Clausius inequality holds for the entropy associated with diffusivity fluctuations, which is analogous to the thermodynamic entropy, and the analog of the quantity of heat
We have developed a formal analogy between fluctuating diffusivity and thermodynamics for RNA-protein particles in both Escherichia coli cell and Saccharomyces cerevisiae cell

Summary

Introduction

Diffusivity of RNA-Protein Particles: Analogy with Thermodynamics. There are growing experimental observations showing exotic physical properties of messenger RNA molecules in living cells. The cytoplasm is regarded as a medium consisting of many local blocks (or regions), a typical size of which has been estimated based on the experimental data In each of these local blocks, the diffusivity in Equation (1) slowly varies on a time scale much larger than that of dynamics of the RNA-protein particles. Let us consider the thermodynamic-like situation in such a way that D0 slowly changes, the time scale of which should be much larger than that of variation of diffusivity fluctuations mentioned above It is shown, for the entropy in Equation (3) with the distribution in Equation (2), that. The present discussions may give a step toward understanding the fluctuating diffusivity from the viewpoint of the laws of thermodynamics

Analogs of the Quantity of Heat and Work

Dependences on Temperature and the Analog of External Parameter

Analog of the Clausius Inequality

Geometric Perspective of the Change of Statistical Fluctuation

Conclusions