Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability.
Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability.
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DOI：
10.1186/1752-0509-2-30
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发表时间：
2008-03-29
影响因子：
--
通讯作者：
Liang, Jie
中科院分区：
文献类型：
--
作者：
Cao, Youfang;Liang, Jie
当分子浓度在0.1μM到10 nm(一个细胞中大约100到10个拷贝)的范围内时，随机性在许多分子网络中起着重要的作用。化学主方程为研究这些网络提供了一个基本的框架，而整个微态上随时间变化的景观概率分布，即分子物种拷贝数的组合，提供了网络动力学的完整表征。微态空间的完整表征是获得网络全景概率分布的先决条件。然而，对于给定的分子网络，既没有闭合形式的解，也没有完全描述所有微观状态的算法。我们开发了一种算法，在新合成的分子的净增益小于预定极限的情况下，可以穷尽地列举小拷贝数分子网络的微态。我们还描述了一种计算微态上精确的平均或稳态景观概率分布的简单方法。我们展示了如何完全刻画稳态中自我调节基因和触发开关的基因网络的全景概率。我们还给出了一个使用MAPK级联网络的例子。数据和服务器将在URL：上提供。我们的算法适用于用有限拷贝数可合成的网络分子缓冲的小拷贝数网络，而不考虑反应化学计量比，并且在存储和时间复杂性方面都是最优的。该算法还可以用来计算给定反应的微态之间的所有跃迁速率和反应速率。缓冲区大小受可用内存或磁盘存储的限制。我们的算法适用于一类生物网络，当分子的拷贝数较小时，网络是封闭的，或者网络是开放的，但新合成分子的净增益不超过预定的缓冲容量。对于这些网络，我们的方法允许完全随机地描述平均横向概率分布以及存在的稳态。
Stochasticity plays important roles in many molecular networks when molecular concentrations are in the range of 0.1 μM to 10nM (about 100 to 10 copies in a cell). The chemical master equation provides a fundamental framework for studying these networks, and the time-varying landscape probability distribution over the full microstates, i.e., the combination of copy numbers of molecular species, provide a full characterization of the network dynamics. A complete characterization of the space of the microstates is a prerequisite for obtaining the full landscape probability distribution of a network. However, there are neither closed-form solutions nor algorithms fully describing all microstates for a given molecular network. We have developed an algorithm that can exhaustively enumerate the microstates of a molecular network of small copy numbers under the condition that the net gain in newly synthesized molecules is smaller than a predefined limit. We also describe a simple method for computing the exact mean or steady state landscape probability distribution over microstates. We show how the full landscape probability for the gene networks of the self-regulating gene and the toggle-switch in the steady state can be fully characterized. We also give an example using the MAPK cascade network. Data and server will be available at URL: . Our algorithm works for networks of small copy numbers buffered with a finite copy number of net molecules that can be synthesized, regardless of the reaction stoichiometry, and is optimal in both storage and time complexity. The algorithm can also be used to calculate the rates of all transitions between microstates from given reactions and reaction rates. The buffer size is limited by the available memory or disk storage. Our algorithm is applicable to a class of biological networks when the copy numbers of molecules are small and the network is closed, or the network is open but the net gain in newly synthesized molecules does not exceed a predefined buffer capacity. For these networks, our method allows full stochastic characterization of the mean landscape probability distribution, and the steady state when it exists.
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影响因子：
5.6
作者：
HAWLEY, DK;MCCLURE, WR
通讯作者：
MCCLURE, WR
影响因子：
2.3
作者：
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通讯作者：
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DOI：
10.1073/pnas.040411297
发表时间：
2000-02-29
影响因子：
11.1
作者：
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通讯作者：
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DOI：
10.1073/pnas.0509874103
发表时间：
2006-05-09
影响因子：
11.1
作者：
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通讯作者：
van Oudenaarden, Alexander
影响因子：
3.5
作者：
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通讯作者：
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