具有振荡动力学的随机反应网络的矩封闭稳定性分析
Moment Closure Stability Analysis of Stochastic Reaction Networks with Oscillatory Dynamics
摘要：
具有振荡行为的生化反应在微观尺度的合成生物学中起着重要的作用。虽然宏观极限下确定性化学振子的鲁棒稳定性理论已经存在，但随机振子的动力学稳定性仍是一个正在进行的研究对象。化学主方程与动力学蒙特卡罗模拟一起构成了建模微观系统的最准确方法。然而，由于求解完全概率模型的挑战，大多数稳定性分析的研究都集中在描述外部扰动振荡器。本文应用最大熵原理作为振荡网络矩方程的闭合准则，对内扰振荡器网络进行了稳定性分析。特别地，我们讨论了动力学参数和尺寸参数对这一具有内禀噪声的随机振动系统动力学行为的影响。我们的数值实验表明，动力学参数的变化导致现象学和动力学的Hopf分岔，而减少系统的规模在振荡区域可以扭转随机的Hopf动力学分岔在系综水平。这是振荡系统随机动力学的一个独特特征，在宏观极限中具有未知的平行性。
英文摘要：
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical stability of stochastic oscillators is an object of ongoing research. The Chemical Master Equation along with kinetic Monte Carlo simulations constitute the most accurate approach to modeling microscopic systems. However, because of the challenges of solving the fully probabilistic model, most studies in stability analysis have focused on the description of externally disturbed oscillators. Here we apply the Maximum Entropy Principle as closure criterion for moment equations of oscillatory networks and perform the stability analysis of the internally disturbed Brusselator network. Particularly, we discuss the effects of kinetic and size parameters on the dynamics of this stochastic oscillatory system with intrinsic noise. Our numerical experiments reveal that changes in kinetic parameters lead to phenomenological and dynamical Hopf bifurcations, while reduced system sizes in the oscillatory region can reverse the stochastic Hopf dynamical bifurcations at the ensemble level. This is a unique feature of the stochastic dynamics of oscillatory systems, with an unknown parallel in the macroscopic limit.
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