Abstract
The Fluctuation-Dissipation theorem (FDT) connects the "memory" in the fluctuation in equilibrium to the response of a system after a perturbation, which has been a fundamental ground in many branches of physics. When viewing a cell as a stochastic biochemical system, the cell's response under a perturbation is related to its intrinsic steady-state correlation functions via the FDT, a theorem we derived and present in this work. FDT allows us to use the noise to derive dynamic response and infer dynamic properties in the system. We tested FDT's validity with gene regulation models and found that it is limited to the linear response. For an indirect regulation pathway where unknown components may exist, FDT still works within the linear response region. Thus, FDT may be used for systems with partial knowledge, and it is potentially possible to identify the existence of unobserved components. With FDT, the dynamic response can be composed of steady-state measurements without the complete detailed knowledge for the regulation or kinetics. The response function derived can give important insights into the dynamics and time scales of the system.
Highlights
The probabilistic nature of chemical reactions, and the low-copy numbers of mRNA and some proteins in a cell lead to significant fluctuations in their abundances
The fluctuations in equilibrium and the response to a perturbation are connected in the Fluctuation-Dissipation theorem (FDT)
With FDT, the dynamic response of a system can be derived from the noise in the steady-state
Summary
The probabilistic nature of chemical reactions, and the low-copy numbers of mRNA and some proteins in a cell lead to significant fluctuations in their abundances. Description, characterization, and the biological consequences of such uncertainty have been important areas of study.. With advances in single-cell techniques, it is possible to obtain time-correlation functions of molecule number fluctuation in a living cell.. The response of cells under periodic perturbations was measured.. The fluctuations in equilibrium and the response to a perturbation are connected in the Fluctuation-Dissipation theorem (FDT).. Since both the steady-state correlation functions and the response under time-dependent perturbations can be measured nowadays, one may wonder whether similar FDT exists in their reaction kinetics. Description, characterization, and the biological consequences of such uncertainty have been important areas of study. With advances in single-cell techniques, it is possible to obtain time-correlation functions of molecule number fluctuation in a living cell. In addition, the response of cells under periodic perturbations was measured. In statistical thermodynamics, the fluctuations in equilibrium and the response to a perturbation are connected in the Fluctuation-Dissipation theorem (FDT). In a living cell, since both the steady-state correlation functions and the response under time-dependent perturbations can be measured nowadays, one may wonder whether similar FDT exists in their reaction kinetics.
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