This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.

中文翻译：

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使用linlog动力学的分支路径的动态模拟和代谢重新设计。

本文提出了一种用于体内动力学建模和代谢重新设计的新数学框架：线性逻辑方法。此方法是代谢控制分析（MCA）的扩展，适用于酶和代谢物水平的大变化。此外，提出的框架将MCA与动力学建模相结合，从而也结合了两种方法的优点。linlog框架包括根据酶水平和细胞外浓度给出稳态通量和代谢物浓度的一般表达式，以及当控制和响应系数可用时，可以直接计算所需稳态所需酶水平的代谢设计方程式。还推导了给出控制系数随酶水平变化的表达式。通过将线性对数动力学应用于具有部分保守性，可逆反应和变构相互作用的分支途径，可以证明线性对数近似在代谢建模中的有效性。结果表明，线性对数逼近法能够很好地描述浓度高达20的浓度变化时该途径的非线性动力学。另外，代谢设计方程也得到了成功测试。