Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry

TL;DR

This paper reviews the limitations of mean field equations in modeling living cell biochemistry, emphasizing the importance of diffusion-controlled reactions and fluctuation effects in complex biochemical environments.

Contribution

It highlights when mean field equations fail and discusses their derivation from diffusion-controlled reaction theory, challenging their widespread use in cell biochemistry modeling.

Findings

Mean field equations often fail in low-mixing conditions.

Diffusion-controlled reactions are crucial for accurate biochemical modeling.

Fluctuation effects dominate in certain cellular environments.

Abstract

In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.