Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics

JOURNAL OF THEORETICAL BIOLOGY

卷:481

Article

Eilertsen, Justin¹  Stroberg, Wylie¹  Schnell, Santiago^1,2 

[1] Univ Michigan, Dept Mol & Integrat Physiol, Med Sch, Ann Arbor, MI 48109 USA

[2] Univ Michigan, Dept Computat Med & Bioinformat, Med Sch, Ann Arbor, MI 48109 USA

关键词: Timescales;    Chemical kinetics;    Enzyme kinetics;    Slow and fast dynamics;    Perturbation methods;    Nonlinear dynamical systems;   

DOI  :  10.1016/j.jtbi.2019.01.005

来源: Elsevier

【 摘 要 】

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems. (C) 2019 Elsevier Ltd. All rights reserved.

【 授权许可】

Free