Departament de Ciències Mèdiques Bàsiques, Institut de Recerca Biomèdica de Lleida, Universitat de Lleida, Montserrat Roig 2, 25008-Lleida, Spain.
BMC Bioinformatics. 2009 Nov 24;10:386. doi: 10.1186/1471-2105-10-386.
Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements.
We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer-approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock
Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.
优化方法允许对系统进行设计更改，以实现特定目标。这些技术是代谢工程的基础。然而，它们不能直接应用于研究代谢适应环境变化的进化。虽然生物系统是通过自然选择进化而来的，并且结果是适应良好的系统，但我们很难期望实际的代谢过程处于可以通过优化分析得到的理论最优状态。更可能的是，自然系统处于与全球生理需求兼容的可行区域内。
我们首先提出了一种新的方法，用于全局优化基于广义质量作用（GMA）表示的代谢途径的非线性模型。优化任务被表述为一个非凸非线性规划（NLP）问题，通过外逼近算法求解。该方法依赖于迭代求解简化的 NLP 从问题和混合整数线性规划（MILP）主问题，分别提供全局解的有效上限和下限原始 NLP。该方法的能力通过将其应用于酿酒酵母的厌氧发酵途径来说明。我们接下来介绍了一种识别允许系统满足一组生理约束的可行参数区域的方法，这些约束可以通过代数方程以数学方式表示。该技术基于在缩小的搜索空间上迭代应用外逼近算法，以识别包含问题可行解的区域并丢弃不存在可行解的区域。作为一个例子，我们描述了与酵母酿酒酵母对热冲击的适当适应响应兼容的可行酶活性变化的特征。
我们的结果表明，所提出的方法可用于研究适应环境变化的进化。该方法可用于其他重要应用，例如评估与健康和疾病状态兼容的参数变化。
