Marin-Sanguino Alberto, Voit Eberhard O, Gonzalez-Alcon Carlos, Torres Nestor V
Grupo de Tecnologia Bioquímica, Departamento de Bioquimica y Biologia Molecular, Facultad de Biologia, Universidad de La Laguna, 38206 La Laguna, Tenerife, Islas Canarias, Spain.
Theor Biol Med Model. 2007 Sep 26;4:38. doi: 10.1186/1742-4682-4-38.
In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary.
A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency.
GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal.
过去，代谢工程中基于模型的产量优化任务要么采用化学计量模型，要么采用结构化非线性模型，如S-系统或线性对数表示法。这些模型在大多数其他模型中脱颖而出，因为它们允许将优化任务转化为线性规划，而线性规划有广泛可用的高效求解方法。对于不是这些格式之一的途径模型，开发了一种间接优化方法（IOM），其中原始模型依次表示为S-系统模型，用线性规划方法以这种格式进行优化，重新解释为初始模型形式，并根据需要进一步优化。
针对此任务提出了一种新方法。我们在此表明，广义质量作用（GMA）系统的模型格式可以用几何规划技术非常有效地进行优化。我们简要回顾了GMA系统和几何规划的基础知识，展示了后者如何应用于前者，并用一个教学问题和两个基于实际系统模型的例子说明了组合方法。第一个是酿酒酵母厌氧发酵途径的一个相对较小但具有代表性的模型，而第二个描述了大肠杆菌中色氨酸操纵子的动力学。这两个模型以前都用于基准测试目的，因此便于与提出的新方法进行比较。在这些比较中，发现几何规划方法在成功识别最优解和效率方面与早期方法相当或更好。
GMA系统很重要，因为它们包含化学计量、质量作用和S-系统作为特殊情况，以及许多其他模型。此外，先前已表明变量的代数等价变换足以将几乎任何类型的动力学模型转换为GMA形式。因此，优化GMA系统的高效方法具有多方面的吸引力。
