Delgado J, Liao J C
Department of Chemical Engineering, Texas A & M University, College Station 77843-3122, USA.
Biosystems. 1995;36(1):55-70. doi: 10.1016/0303-2647(95)01528-s.
The bases underlying the distribution of metabolic control have been elusive, even though many intuitive arguments exist. To analyze this problem, we have applied the structural properties of the control coefficients to systems in which the eigenvalues of the Jacobian of the system are widely separated, that is, systems with time-scale separation. We show that time-scale separation is an effective way to localize metabolic control to only a few enzymes. To achieve time-scale separation, the cell can overproduce most of the enzymes relative to the required activity for the steady state, and control the expression level of only a few enzymes, provided that the overexpressed enzymes do not cause adverse effects. The overexpressed enzymes are responsible for the small response times of the system, and the reactions catalyzed by them are termed 'fast' reactions. The metabolite concentration control coefficients of the 'fast' reactions are always small compared with the 'slow' reactions. Furthermore, the 'fast' reactions do not have effective control on the overall flux. However, the 'fast' reactions may compete with each other at a branch point, leading to significant control coefficients for fluxes to the branches. These results are useful in justifying lumping of 'fast' reactions in mathematical modelling or in the experimental determination of control coefficients. The theoretical results are derived under the assumption that the system possesses a unique, asymptotically stable steady-state and that the reaction steps of the system under analysis are well represented by linear kinetics around the steady state. The application of the results presented in this article are demonstrated with three illustrative examples.
尽管存在许多直观的观点，但代谢控制分布的基础一直难以捉摸。为了分析这个问题，我们将控制系数的结构特性应用于系统雅可比矩阵的特征值广泛分离的系统，即具有时间尺度分离的系统。我们表明，时间尺度分离是将代谢控制仅定位到少数几种酶的有效方法。为了实现时间尺度分离，细胞可以相对于稳态所需的活性过量产生大多数酶，并仅控制少数几种酶的表达水平，前提是过量表达的酶不会产生不利影响。过量表达的酶决定了系统的短响应时间，由它们催化的反应被称为“快速”反应。与“慢速”反应相比，“快速”反应的代谢物浓度控制系数总是很小。此外，“快速”反应对整体通量没有有效的控制。然而，“快速”反应可能在分支点相互竞争，导致通向各分支通量的显著控制系数。这些结果有助于在数学建模中或在控制系数的实验测定中对“快速”反应进行归并。理论结果是在系统具有唯一的、渐近稳定的稳态以及所分析系统的反应步骤在稳态附近由线性动力学很好地表示的假设下得出的。本文给出的结果通过三个示例进行了说明。
