Switching and Diffusion Models for Gene Regulation Networks
Switching and Diffusion Models for Gene Regulation Networks
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DOI：
10.1137/080735412
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
Somkid Intep;D. Higham;X. Mao
中科院分区：
文献类型：
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作者：
Somkid Intep;D. Higham;X. Mao
我们分析了一个层次的三个制度建模基因调控。最完整的模型是一个时间连续、状态空间离散、马尔可夫跳变的过程。一个中间的“开关加扩散”模型的形式是一个独立的连续时间马尔可夫开关驱动的随机微分方程。在第三个“开关加ODE”模型中，开关保留，但扩散被移除。后两种模型允许多尺度模拟，为了计算效率，系统组件根据其丰度不同对待。开关加ODE方案由Paszek [Bull. Math. Biol.，69（2007），pp. 1567-1601]，他分析了稳态行为，表明均值被保留，但方差仅近似于完整模型的方差。在这里，我们表明，随机微积分的工具可以用来分析所有时间的第一和第二时刻。一个需要解决的技术问题是离散值开关的状态空间是infin…
We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate “switch plus diffusion” model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third “switch plus ODE” model the switch remains, but the diffusion is removed. The latter two models allow for multiscale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The switch plus ODE regime was proposed by Paszek [Bull. Math. Biol., 69 (2007), pp. 1567–1601], who analyzed the steady state behavior, showing that the mean was preserved, but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infin...