Savageau M A
Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor 48109-0620, USA.
Biosystems. 1998 Jun-Jul;47(1-2):9-36. doi: 10.1016/s0303-2647(98)00020-3.
Recent evidence has shown that elementary bimolecular reactions under dimensionally-restricted conditions, such as those that might occur within cells when reactions are confined to two-dimensional membranes and one-dimensional channels, do not follow traditional mass-action kinetics, but fractal kinetics. The power-law formalism, which provides the context for examining the kinetics under these conditions, is used here to examine the implications of fractal kinetics in a simple pathway of reversible reactions. Starting with elementary chemical kinetics, we proceed to characterise the equilibrium behaviour of a simple bimolecular reaction, derive a generalised set of conditions for microscopic reversibility, and develop the fractal kinetic rate law for a reversible Michaelis-Menten mechanism. Having established this fractal kinetic framework, we go on to analyse the steady-state behaviour and temporal response of a pathway characterised by both the fundamental and quasi-steady-state equations. These results are contrasted with those for the fundamental and quasi-steady-state equations based on traditional mass-action kinetics. Finally, we compare the accuracy of three local representations based on both fractal and mass-action kinetics. The results with fractal kinetics show that the equilibrium ratio is a function of the amount of material in a closed system, and that the principle of microscopic reversibility has a more general manifestation that imposes new constraints on the set of fractal kinetic orders. Fractal kinetics in a biochemical pathway allow an increase in flux to occur with less accumulation of pathway intermediates and a faster temporal response than is the case with traditional kinetics. These conclusions are obtained regardless of the level of representation considered. Thus, fractal kinetics provide a novel means to achieve important features of pathway design.
最近的证据表明，在维度受限条件下的基本双分子反应，比如当反应局限于二维膜和一维通道内时细胞中可能发生的反应，并不遵循传统的质量作用动力学，而是分形动力学。幂律形式体系为研究这些条件下的动力学提供了背景，在此用于研究分形动力学在一个简单可逆反应途径中的意义。从基本化学动力学出发，我们进而描述一个简单双分子反应的平衡行为，推导微观可逆性的一组广义条件，并为可逆米氏机制建立分形动力学速率定律。建立了这个分形动力学框架后，我们接着分析由基本方程和准稳态方程表征的一个途径的稳态行为和时间响应。这些结果与基于传统质量作用动力学的基本方程和准稳态方程的结果形成对比。最后，我们比较基于分形动力学和质量作用动力学的三种局部表示的准确性。分形动力学的结果表明，平衡比是封闭系统中物质总量的函数，并且微观可逆性原理有更一般的表现形式，这对分形动力学阶数集施加了新的约束。生化途径中的分形动力学允许通量增加，同时途径中间体的积累比传统动力学情况下更少，时间响应更快。无论考虑何种表示水平，都能得出这些结论。因此，分形动力学为实现途径设计的重要特征提供了一种新方法。
