Towards a coherent theory for stochastic kinetics in biology

许多基因、RNA和蛋白质在每个细胞中的数量如此之少，以至于单个分子的随机出生和死亡在浓度上引起显著的“噪音”。这样的波动会导致各种各样的人类疾病，而许多细胞控制回路在如何容忍、利用或消除随机化的威胁方面得到了最好的理解。然而，由于缺乏全面的概念框架，对噪声的研究一直难以解释。我们将通过以下几种方式扩展现有的框架：1）确定波动耗散定理（FDT）对具有非线性速率函数的遗传网络的适用性。2)将FDT扩展到更高的矩和更好的近似，系统地重写生物学可观测量方面的数学定理。3)分析分子的逐渐老化如何影响细胞之间的随机波动。4)评估和扩展一个共同的近似，其中生长细胞中的组分稀释是由降解建模。在所有情况下，我们将结果与单细胞的实验结果进行比较。由于“分子混乱”，细胞中的浓度波动会自发出现，其中单个分子在反应前随机碰撞。这种随机性在许多关键细胞成分的极低水平上尤其明显，其中单个化学事件具有较大的相对影响。许多实验研究测量了由此产生的变化，但结果很难解释，因为传统的数学框架不适合细胞。使用统计物理学的概念，我们将扩展以前的方法，以创建一个更有效的框架来分析和解释波动。这将有助于探索细胞中的物理条件，并更好地理解由于无法纠正扰动而导致的生理障碍的基础。

Many genes, RNAs and proteins are present in such low numbers per cell that random births and deaths of individual molecules cause significant 'noise' in concentrations. Such fluctuations cause a wide range of human disorders, and many cellular control circuits are best understood in terms of how they tolerate, exploit, or eliminate the threat of randomization. However, studies of noise have been difficult to interpret due to a lack of comprehensive conceptual frameworks. We will extend the existing frameworks in several ways, by: 1) Determining the applicability of the fluctuation-dissipation theorem (FDT) to genetic networks with nonlinear rate functions. 2) Extending the FDT to higher moments and better approximations, systematically rewriting mathematical theorems in terms of biological observables. 3) Analyzing how the gradual aging of molecules affect random fluctuations between cells. 4) Evaluating and extending a common approximation where dilution of components in growing cells is modeled by degradation. In all cases, we compare the results with experimental findings for single cells. Fluctuations in concentrations arise spontaneously in cells due to 'molecular chaos' where individual molecules randomly collide before reacting. This randomness is particularly pronounced at the extremely low levels of many crucial cellular components, where individual chemical events have large relative effects. Many experimental studies have measured the resulting variation, but the results are difficult to interpret because the conventional mathematical frameworks are poorly suited to cells. Using concepts from statistical physics, we will extend previous methods to create a more effective framework to analyze and interpret fluctuations. This will help explore the physical conditions in the cell, and better understand the basis of physiological disorders that result from an incapacity to correct perturbations.