Frank Till D, Daffertshofer Andreas, Beek Peter J
J Biol Phys. 2002 Mar;28(1):39-54. doi: 10.1023/A:1016256613673.
Biological systems possess the ability to adapt quickly andadequately to both environmental and internal changes. This vital ability cannot be explained in terms ofconventional stochastic processes because such processes arecharacterized by atrade-off between flexibility and accuracy, that is, they either show shorttransition times (large Kramers escape rates) to broad steady-statedistributions or long transition times to sharply peaked distributions. To develop a stochastic theory for systemsexhibiting both flexibility and accuracy, we study systems under the impact of white noise multiplied with anaccordant statistical measure, here the probability density. Thisresults in negative feedback and circular causality: the more probable a stable state the lessit will be affected by noise and, conversely, the less a stable state is affected by noisethe more probable it is. Using nonlinear Fokker-Planckequations, steady states are computed via transformations ofsolutions of the corresponding linear Fokker-Planck equations. Transients reveal rapidly evolving and sharply peaked probability densities and thus mimic systems characterized by both flexibility and accuracy.
生物系统具备快速且充分地适应环境变化和内部变化的能力。这种至关重要的能力无法用传统的随机过程来解释，因为此类过程的特点是在灵活性和准确性之间存在权衡，也就是说，它们要么具有较短的过渡时间（较大的克莱默斯逃逸率）以达到宽泛的稳态分布，要么具有较长的过渡时间以达到尖锐峰值的分布。为了发展一种适用于兼具灵活性和准确性的系统的随机理论，我们研究在白噪声与相应统计量（在此为概率密度）相乘影响下的系统。这会导致负反馈和循环因果关系：一个稳定状态的概率越高，它受噪声影响就越小，反之，一个稳定状态受噪声影响越小，其概率就越高。利用非线性福克 - 普朗克方程，通过对相应线性福克 - 普朗克方程的解进行变换来计算稳态。瞬态过程显示出快速演化且尖锐峰值的概率密度，从而模拟出兼具灵活性和准确性的系统。
