Department of Biostatistics, Epidemiology, and Systems Science, Medical University of South Carolina, Charleston, South Carolina 29425-2503, USA.
Biotechnol Bioeng. 1992 Aug;40(5):572-82. doi: 10.1002/bit.260400504.
As of yet, steady-state optimization in biochemical systems has been limited to a few studies in which networks of fluxes were optimized. These networks of fluxes are represented by linear (stoichiometric) equations that are used as constraints in a linear program, and a flux or a sum of weighted fluxes is used as the objective function. In contrast to networks of fluxes, systems of metabolic processes have not been optimized in a comparable manner. The primary reason is that these types of integrated biochemical systems are full of synergisms, antagonisms, and regulatory mechanisms that can only be captured appropriately with nonlinear models. These models are mathematically complex and difficult to analyze. In most cases it is not even possible to compute, let alone optimize, steady-state solutions analytically. Rare exceptions are S-system representations. These are nonlinear and able to represent virtually all types of dynamic behaviors, but their steady states are characterized by linear equations that can be evaluated both analytically and numerically. The steady-state equations are expressed in terms of the logarithms of the original variables, and because a function and its logarithms of the original variables, and because a function and its logarithm assume their maxima for the same argument, yields or fluxes can be optimized with linear programs expressed in terms of the logarithms of the original variables.
到目前为止，生化系统中的稳态优化仅限于少数几个研究，其中网络通量被优化。这些通量网络由线性（计量）方程表示，这些方程被用作线性规划的约束条件，而通量或加权通量的总和被用作目标函数。与通量网络相比，代谢过程系统没有以类似的方式进行优化。主要原因是这些类型的综合生化系统充满了协同作用、拮抗作用和调节机制，只有使用非线性模型才能恰当地捕捉到这些机制。这些模型在数学上很复杂，难以分析。在大多数情况下，甚至不可能计算，更不用说分析优化稳态解了。罕见的例外是 S 系统表示。这些是非线性的，能够表示几乎所有类型的动态行为，但它们的稳态由线性方程表示，可以通过分析和数值方法进行评估。稳态方程是用原始变量的对数表示的，因为一个函数及其对数在原始变量中，并且因为一个函数和它的对数对于相同的参数取最大值，所以产量或通量可以用原始变量的对数表示的线性规划来优化。
