Nonlinear thermodynamics of biological signal transduction for predicting conservation of entropy production rate

Cell signal transduction is an example of a nonequilibrium phenomenon. In this study, a nonequilibrium nonlinear thermodynamic model was formulated. First, we obtained a condition in which the Onsager's reciprocity theorem holds in the signal transduction. Second, it was found that the entropy production rate per signal molecule is conserved through signal transduction. Finally, it was determined that when Onsager's reciprocity theorem does not hold, fluctuation circulation is given by the phosphorylation rate of signal molecules. The simple relation implies that the fluctuation circulation can be an essential quantity of the signal transduction amount. These results expand the limit of nonequilibrium thermodynamics and can be used to provide ideas for signal transduction quantification.