Developing Ito stochastic differential equation models for neuronal signal transduction pathways
Developing Ito stochastic differential equation models for neuronal signal transduction pathways
复制标题
DOI：
10.1016/j.compbiolchem.2006.04.002
复制
发表时间：
2006-08-01
影响因子：
3.1
通讯作者：
Ruohonen, Keijo
中科院分区：
文献类型：
--
作者：
Manninen, Tiina;Linne, Marja-Leena;Ruohonen, Keijo
由于细胞内复杂功能的实验知识越来越多，动态生化系统的数学建模和模拟受到了相当大的关注。除了确定性的方法，几个随机的方法已被开发用于模拟生化系统的时间序列行为。然而，与确定性方法相比，随机方法的问题是更大的计算时间。因此，有必要研究其他方法来纳入随机性，并寻求减少模拟所需的计算时间，但保留所讨论的系统的特征行为的方法。在这项工作中，我们开发了一个计算框架的基础上伊藤随机微分方程的神经元信号转导网络。有几种不同的方法将随机性纳入确定性微分方程模型，并获得伊藤随机微分方程。两个发达国家的模型被发现最适合神经元信号转导的随机建模。最佳模型给出稳定的响应，这意味着响应随时间的方差不会增加，并且避免了负浓度。对Ito随机微分方程、Langevin化学方程和吉莱斯皮随机模拟算法进行了比较分析。不同种类的随机方法可用于产生神经元蛋白激酶C信号转导通路的类似反应。响应的精细细节略有不同，这取决于方法和参数值。然而，当模拟大量的化学物种时，吉莱斯皮算法在计算上比Ito随机微分方程和化学Langevin方程慢几个数量级。此外，化学朗之万方程产生负浓度。伊藤随机微分方程在这项工作中开发的，以克服获得负值的问题。(c)2006爱思唯尔有限公司保留所有权利。
Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Ito stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Ito stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Ito stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Ito stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The Ito stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values. (c) 2006 Elsevier Ltd. All rights reserved.