The thermodynamic uncertainty relation in biochemical oscillations

Abstract

<jats:p>Living systems regulate many aspects of their behaviour through periodic oscillations of molecular concentrations, which function as ‘biochemical clocks.’ The chemical reactions that drive these clocks are intrinsically stochastic at the molecular level, so that the duration of a full oscillation cycle is subject to random fluctuations. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered ‘thermodynamic uncertainty relation’ yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule and confirm that it approaches the optimal precision as this number increases.</jats:p>

Thermodynamic Cost, Speed, Fluctuations, and Error Reduction of Biological Copy Machines

“…This form of TUR holds for most of biological processes that can be represented either by stochastic jump processes on a kinetic network or by overdamped Langevin dynamics [23][24][25][26], though extensions to more general conditions, which adjust the lower bound of the original relation, have also been discussed in recent years [14,[27][28][29][30][31][32][33][34]. Briefly,…”

Oscillations in feedback-driven systems: Thermodynamics and noise

“…At the end of the time-interval the transition rates are updated by a change in the magnetic field given by Eq. (15). The initial condition for our simulations was h = 0 for the external field and M = N for the magnetization.…”

The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

“…The relation was originally derived for classical systems, particularly for continuous time Markov jump processes on networks and for overdamped Langevin dynamics in nonequilibrium steady states (NESS) [1,2,4], and it has been extended to the one at finite-time [5][6][7] and discrete-time Markov processes [8]. The significance of TURs has been illuminated in specific contexts of biological processes [9][10][11][12][13][14][15], heat engines [16][17][18][19], and other dynamical processes [20][21][22][23]. More recently, the universal bound of TUR has been used to infer the dissipation rate from the fluctuating currents of dynamical processes [24].…”