Thermodynamic uncertainty relation to assess biological processes

Abstract

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states, and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product $\mathcal{Q}$ of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration $[S]$ is at the Michaelis constant ($K_\text{M}$), and some of the key biological processes are found to work around this condition. We illustrate the utility of $\mathcal{Q}$ in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes) we discuss how their optimality quantified in terms of $\mathcal{Q}$ is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of $\mathcal{Q}$ recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.