Abstract
As biochemical systems may frequently suffer from limited energy resources so that internal molecular fluctuation has to be utilized to induce random rhythm, it is still a great theoretical challenge to understand the elementary principles for biochemical systems with limited energy resources to maintain phase accuracy and phase sensitivity. Here, we address the issue by deriving the energy accuracy and the sensitivity-accuracy trade-off relations for a general biochemical model, analytically and numerically. We find that, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations, elucidating clearly the survival mechanism when energy resources are limited. Moreover, an optimal system size is predicted where both the highest sensitivity and accuracy can be reached at the same time, providing a new strategy for the design of biological networks with limited energy sources.
Highlights
It is still a great theoretical challenge to understand the elementary principles for biochemical systems with limited energy resources to maintain phase accuracy and phase sensitivity
By applying the concepts of stochastic thermodynamics as well as the phase reduction method, the energy-accuracy and the sensitivity-accuracy trade-off relations are derived, which provide general design principles for biochemical oscillations. Application of these principles shows that biochemical systems can keep almost equal efficiency to maintain precise processes at much lower energy cost by using noise-induced oscillations for limited energy resources compared with the efficiency achieved by using normal oscillations for sufficient energy supplies
For a general biochemical system of size V including N well-stirred species and M reactions (R1, . . . , RM ), its dynamics can be described by the chemical Langevin equation (CLE), which is expected to be satisfied for biochemical reaction systems with mesoscopic system size which ensures the existence of a “macro-infinitesimal time scale” [18] as
Summary
The calculation of entropy production is based on the concepts of stochastic thermodynamics [25]. The change rate of the trajectorydependent total entropy production stot(τ ) can be decomposed into two contributions: stot(τ ) = s(τ ) + sm(τ ). The latter term of the total entropy production sm(τ ) = V i Hixi is related to the change rate of the heat dissipation in the environment with q(τ ) = T sm(τ ). The change rate of currents near the Hopf bifurcation can be calculated by both spatial and temporal average:. Eq (B6) can be used to calculate the change rate of entropy flux by choosing i = Hi
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