Wierzbicki W, Berteloot A, Roy G
Département de Physique, Université de Montréal, Québec, Canada.
J Membr Biol. 1990 Jul;117(1):11-27. doi: 10.1007/BF01871562.
Kinetic studies of cotransport mechanisms have so far been limited to the conventional steady-state approach which does not allow in general to resolve either isomerization or rate-limiting steps and to determine the values of the individual rate constants for the elementary reactions involved along a given transport pathway. Such questions can only be answered using presteady-state or relaxation experiments which, for technical reasons, have not yet been introduced into the field of cotransport kinetics. However, since two recent reports seem compatible with the observation of such transient kinetics, it would appear that theoretical studies are needed to evaluate the validity of such claims and to critically evaluate the expectations from a presteady-state approach. We thus report such a study which was performed on a simple four-state mechanism of carrier-mediated transport. The time-dependent equation for zero-trans substrate uptake was thus derived and then extended to models with p intermediary steps. It is concluded that (p-1) exponential terms will describe the approach to the steady state but that such equations have low analytical value since the parameters of the flux equation cannot be expressed in terms of the individual rate constants of the elementary reactions for models with p greater than 5. We thus propose realistic simplifications based on the time-scale separation hypothesis which allows replacement of the rate constants of the rapid steps by their equilibrium constants, thereby reducing the complexity of the kinetic system. Assuming that only one relaxation can be observed, this treatment generates approximate models for which analytical expressions can easily be derived and simulated through computer modeling. When performed on the four-state mechanism of carrier-mediated transport, the simulations demonstrate the validity of the approximate solutions derived according to this hypothesis. Moreover, our approach clearly shows that presteady-state kinetics, should they become applicable to (co)transport kinetics, could be invaluable in determining more precise transport mechanisms.
迄今为止，共转运机制的动力学研究仅限于传统的稳态方法，这种方法通常无法解析异构化或限速步骤，也无法确定给定转运途径中涉及的基本反应的各个速率常数的值。只有使用预稳态或弛豫实验才能回答这些问题，但由于技术原因，这些实验尚未引入共转运动力学领域。然而，由于最近的两篇报道似乎与这种瞬态动力学的观察结果相符，因此似乎需要进行理论研究来评估这些说法的有效性，并严格评估预稳态方法的预期效果。因此，我们报告了这样一项研究，该研究是在载体介导转运的简单四态机制上进行的。由此推导了零转运底物摄取的时间依赖性方程，然后将其扩展到具有p个中间步骤的模型。得出的结论是，（p - 1）个指数项将描述达到稳态的过程，但这些方程的分析价值较低，因为对于p大于5的模型，通量方程的参数无法用基本反应的各个速率常数来表示。因此，我们基于时间尺度分离假设提出了切实可行的简化方法，该假设允许用其平衡常数替代快速步骤的速率常数，从而降低动力学系统的复杂性。假设只能观察到一种弛豫，这种处理方法会生成近似模型，其解析表达式可以很容易地推导出来，并通过计算机建模进行模拟。当对载体介导转运的四态机制进行模拟时，结果证明了根据该假设推导的近似解的有效性。此外，我们的方法清楚地表明，预稳态动力学如果适用于（共）转运动力学，在确定更精确的转运机制方面可能具有极高的价值。
