The energy cost and optimal design for synchronization of coupled molecular oscillators

Abstract

A model of coupled molecular biochemical oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs addition energy to drive the exchange reaction (chemical interaction) between individual oscillators. By solving the steady state of the many-body system analytically, we show that the system goes through a nonequilibrium phase transition driven by energy dissipation, and the critical energy dissipation depends on both the frequency and strength of the exchange reaction. Moreover, our study reveals the optimal design for achieving maximum synchronization with a fixed energy budget. We apply our general theory to the Kai system in Cyanobacteria circadian clock and predict a relationship between the KaiC ATPase activity and synchronization of the KaiC hexamers. The theoretical framework can be extended to study thermodynamics of collective behaviors in other extended nonequilibrium active systems.

Mechanism of autonomous synchronization of the circadian KaiABC rhythm

“…Various hypotheses have been proposed to explain the observed synchronization of KaiC hexamers [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] . One of the earliest theories was based on the assumption that synchronization is realized through the direct association of multiple KaiC hexamers 15 .…”

“…However, no experimental evidence has been shown for such assembly of KaiC hexamers in an oscillating solution. Another hypothesis focuses on the assumption of communication among KaiC hexamers through the exchange of KaiC monomers [16][17][18][19][20] . It was argued that this monomer-exchange hypothesis is consistent with the experimental observation on the entrainment of oscillations 13,32 .…”

Trade-Offs between Speed, Accuracy, and Dissipation in tRNAIleAminoacylation

“…The recent years have seen tremendous progress in stochastic energetics, which revealed the minimum free energy cost of key biological processes, such as maintaining the coherence and synchrony of biochemical oscillations. 42,43 Applying the framework and methodology there to KPR systems may provide new insights to the underlying principle of biological proofreading.…”

The cost of synchronization

“…One such essential task is to display robust and precise biological rhythmssuch as circadian oscillations. This process relies on the synchronization of biochemical network oscillations and has been shown to require energy dissipation in a theoretical model developed by Dongliang Zhang and co-workers, as reported in Nature Physics 1 .…”