Assessing Onsager’s reciprocity difference in signal transduction cascade model: a new metric for evaluating cellular response dynamics

Abstract

AbstractThe cell signaling system translates extracellular changes into biochemical reactions within the cell, ultimately affecting gene expression. This system is crucial for responding to environmental stressors through a series of chemical interactions among intracellular molecules. Although Onsager’s reciprocity theorem is foundational in analyzing non-equilibrium systems, its limitations are evident in the nonlinear responses characteristic of the chemical reactions essential for signal transduction. In this study, we demonstrate that the reciprocity coefficients between signal molecule Xj, Lj:j+1 in the transmission from the jth step to the j + 1th step and molecule Xj+1, Lj+1:j from the j + 1th step to the jth step are not necessarily equal due to nonlinear interactions. This disparity, quantified as Jj:j+1 = −Lj:j+1 + Lj+1:j, reflects the amount of signal transduced between these steps, coupled with the phosphorylation rate of signaling molecules. Through kinetic model simulations, we analyzed the cellular response to external radiation exposure, monitoring how signal transduction progresses via phosphorylation reactions over time. The simulation showed a transition from an unstable to a stable, unimodal signaling pattern at varying radiation doses, correlating well with actual cellular responses. In conclusion, our findings suggest that the discrepancy in Onsager’s reciprocity coefficients correlates with signal transduction velocity, providing novel insights into the thermodynamic underpinnings of cellular signaling mechanisms.