多位点磷酸化反应随机Hill函数参数域的确定
Finding Acceptable Parameter Regions of Stochastic Hill functions for Multisite Phosphorylation Mechanism
摘要：
多位点磷酸化在调节开关样蛋白活性中起着重要作用，并在数学模型中得到广泛应用。随着新的实验技术的发展和更多的分子数据，分子磷酸化过程出现在许多系统中，越来越复杂和规模。这些发展需要简单而有效的随机模型来描述各种多位点磷酸化过程，特别是在大型和复杂的生化网络。为了降低模型的复杂性，这项工作的目的是简化的多位点磷酸化机制的随机希尔函数模型。此外，这项工作优化了参数空间的区域，以匹配随机希尔函数的模拟结果与分布式多位点磷酸化过程。虽然传统的参数优化方法一直专注于寻找最佳的参数向量，在大多数情况下，建模者希望找到一组参数向量，产生类似的系统动力学和结果。基于拟牛顿随机优化（QNSTOP）算法，提出了一种通用的$α$-$β$ - $γ$规则，用于返回随机Hill函数的可接受参数区域.不同的目标函数的模拟为基础的经验数据的不同特征进行了研究，其中近似最大对数似然方法是推荐的一般应用。数值结果表明，在适当的参数向量值，随机希尔函数模型描述的多位点磷酸化过程，除了初始（瞬态）阶段。
英文摘要：
Multisite phosphorylation plays an important role in regulating switchlike protein activity and has been used widely in mathematical models. With the development of new experimental techniques and more molecular data, molecular phosphorylation processes emerge in many systems with increasing complexity and sizes. These developments call for simple yet valid stochastic models to describe various multisite phosphorylation processes, especially in large and complex biochemical networks. To reduce model complexity, this work aims to simplify the multisite phosphorylation mechanism by a stochastic Hill function model. Further, this work optimizes regions of parameter space to match simulation results from the stochastic Hill function with the distributive multisite phosphorylation process. While traditional parameter optimization methods have been focusing on finding the best parameter vector, in most circumstances modelers would like to find a set of parameter vectors that generate similar system dynamics and results. This paper proposes a general $α$-$β$-$γ$ rule to return an acceptable parameter region of the stochastic Hill function based on a quasi-Newton stochastic optimization (QNSTOP) algorithm. Different objective functions are investigated characterizing different features of the simulation-based empirical data, among which the approximate maximum log-likelihood method is recommended for general applications. Numerical results demonstrate that with an appropriate parameter vector value, the stochastic Hill function model depicts the multisite phosphorylation process well except the initial (transient) period.
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