Phase transition in thermodynamically consistent biochemical oscillators

Abstract

Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality. The control parameter is the thermodynamic force which must be above a certain threshold for the onset of biochemical oscillations. This critical behavior is characterized by the thermodynamic flux associated with the thermodynamic force, its diffusion coefficient, and the stationary distribution of the oscillating chemical species. We discuss metrics for the precision of biochemical oscillations by comparing two observables, the Fano factor associated with the thermodynamic flux and the number of coherent oscillations. Since the Fano factor can be small even when there are no biochemical oscillations, we argue that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillations. Our results are obtained with three thermodynamically consistent versions of known models: the Brusselator, the activator-inhibitor model, and a model for KaiC oscillations.

Irreversibility in dynamical phases and transitions

“…Previous work has investigated the behavior of _ S at thermodynamic phase transitions with the work of 22 finding general signatures of discontinuous phase transitions in _ S which agree with our results. While 26 found _ S to have a discontinuity of its first derivative with respect to Δμ in a slightly modified version of the well-mixed Brusselator, work on the same system presented here did not find any non-analytic behavior in _ S true 30 . We show that a discontinuous phase transition exists in our model, but the magnitude of the discontinuity is small and difficult to detect in _ S true and is more easily seen in the coarse-grained _ S blind (Fig.…”

“…Recent advances in stochastic thermodynamics have highlighted entropy production as a quantity to measure a system's distance from equilibrium [14][15][16][17][18][19] . While much work has been done investigating the critical behavior of entropy production at continuous and discontinuous phase transitions [20][21][22][23][24][25][26][27][28] , dynamical phase transitions in spatially extended systems have only recently been investigated, and to date no non-analytic behavior in the entropy production has been observed 29,30 .…”

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

“…However, this condition is not enough as synchronization also requires the exchange frequency (rate) to be larger than a critical value Ω > Ω c (E 0 ). Unlike previously studied cases where nonequilibrium phase transitions are driven by varying temperature [21] or thermal force [22], this requirement for kinetic rates studied here is unique to nonequilibrium systems and has no counter part in equilibrium phase transitions.…”

High chemical affinity increases the robustness of biochemical oscillations

“…While recent work has established that increasing energy consumption improves the coherence of oscillations, our findings suggest that it plays the additional role of making the coherence and the average period of oscillations robust to fluctuations in rates that can result from the noisy environment of the cell.In principle, R depends on all the details of the rates k ± i in the network. However, in line with a large body of work that generically connects energy dissipation to accuracy in biophysical processes [20][21][22][23][24][25], it has been suggested that irrespective of these details the affinity bounds the coherence of biochemical oscillations [8,17,18,26]. In particular, Barato and Seifert recently conjectured an upper bound on R as a function of the number of states N and the affinity A of the biochemical network [8].…”