The energy cost and optimal design of networks for biological discrimination

Yu, Qiwei; Kolomeisky, Anatoly B.; Igoshin, Oleg A.

Many biological processes discriminate correct and incorrect substrates through the kinetic proofreading mechanism which enables lower error at the cost of higher energy dissipation. Although it is apparently beneficial for the organisms to reduce both error and energy cost of the discrimination process, it remains unclear to what extent these two quantities can be minimized simultaneously. Here, with a chemical kinetic formalism, we identify a fundamental error-cost bound which tightly constrains the system's performance under any parameter variations preserving the rate discrimination between substrates. The analytic form of bound is obtained in a large class of proofreading networks and supported by numeric sampling. Furthermore, this bound is kinetically controlled, i.e. completely determined by the difference between the transition state energies of corresponding enzymatic reactions on the free energy landscape. The importance of the bound is analyzed for three biological processes. DNA replication by T7 DNA polymerase is shown to be nearly optimized, i.e. its kinetic parameters place it in the immediate proximity of the error-cost bound. The isoleucyl-tRNA synthetase (IleRS) of E. coli also operates close to the bound, but further optimization is prevented by the need for reaction speed. On the contrary, speed requirement forces E. coli ribosome to operate in a high-dissipation regime. Together, these findings establish a fundamental relation between error and energy cost in biological proofreading networks and provide a theoretical framework for studying error-dissipation trade-off in other systems with biological discrimination.