Efficient, sparse biological network determination
Efficient, sparse biological network determination
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DOI：
10.1186/1752-0509-3-25
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发表时间：
2009-02-23
影响因子：
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通讯作者：
Papachristodoulou, Antonis
中科院分区：
文献类型：
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作者：
August, Elias;Papachristodoulou, Antonis
背景：确定生物系统的相互作用拓扑结构是当前吸引重大研究兴趣的主题。这种系统的典型模型采用涉及多项式和有理函数的微分方程的形式。这样的非线性模型使得从时间序列实验数据中确定生化网络的连通性变得更加困难。使用线性动力学和线性化技术，在过去已经提出可以规避这一点，但一般的问题，开发有效的算法模型，提供更准确的系统的描述仍然open.Results：我们提出了一个网络确定算法，可以处理模型描述与多项式和有理函数，它不利用线性化。为了这个目的，我们利用的观察，生化网络一般是“稀疏的”，并尽量减少决策变量的1-范数（加权网络连接的总和），而约束保持数据和网络动态之间的误差小。我们的方法的重点是确定的互连拓扑结构，而不是具体的反应常数，它考虑到必要的属性，化学反应网络应该有-的东西，基于线性化的技术不能。该问题可以用公式表示为线性规划（Linear Program），这是一个凸优化问题，对于该凸优化问题，有有效的算法可以有效地处理大数据集以及数据或模型参数中的不确定性。所提出的方法能够准确和有效地预测化学反应网络与质量作用动力学和基因调控网络从模拟数据的连接结构，即使动态这些系统的非多项式（理性）和数据的不确定性考虑在内。并给出了一个能解释L. lactis，与文献中发现的相似。因此，基于线性规划的数值方法可以帮助从大数据集中有效地确定生物系统的网络结构。这项工作的总体目标是提供方法来增加我们对复杂生化系统的理解，特别是通过它们的相互连接和非平衡行为。
Background: Determining the interaction topology of biological systems is a topic that currently attracts significant research interest. Typical models for such systems take the form of differential equations that involve polynomial and rational functions. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data much harder. The use of linear dynamics and linearization techniques that have been proposed in the past can circumvent this, but the general problem of developing efficient algorithms for models that provide more accurate system descriptions remains open.Results: We present a network determination algorithm that can treat model descriptions with polynomial and rational functions and which does not make use of linearization. For this purpose, we make use of the observation that biochemical networks are in general 'sparse' and minimize the 1-norm of the decision variables (sum of weighted network connections) while constraints keep the error between data and the network dynamics small. The emphasis of our methodology is on determining the interconnection topology rather than the specific reaction constants and it takes into account the necessary properties that a chemical reaction network should have - something that techniques based on linearization can not. The problem can be formulated as a Linear Program, a convex optimization problem, for which efficient algorithms are available that can treat large data sets efficiently and uncertainties in data or model parameters.Conclusion: The presented methodology is able to predict with accuracy and efficiency the connectivity structure of a chemical reaction network with mass action kinetics and of a gene regulatory network from simulation data even if the dynamics of these systems are non-polynomial (rational) and uncertainties in the data are taken into account. It also produces a network structure that can explain the real experimental data of L. lactis and is similar to the one found in the literature. Numerical methods based on Linear Programming can therefore help determine efficiently the network structure of biological systems from large data sets. The overall objective of this work is to provide methods to increase our understanding of complex biochemical systems, particularly through their interconnection and their non-equilibrium behavior.