Dibrov B F, Zhabotinsky A M, Kholodenko B N
J Math Biol. 1982;15(1):51-63. doi: 10.1007/BF00275788.
The paper is concerned with the conditions of dynamic (asymptotic) stability of steady states in unbranched metabolic pathways. The stationary flux in such pathways is generally determined by the concentration of the end product due to the effector action of this product on the reactions proceeding in its synthetic pathway. The delay in feedback circuits causes violation of dynamic stability at large static stabilization factors. A methods permitting analytic estimation of the critical stabilization factor is suggested. Sufficient and necessary conditions for asymptotic stability of the steady state in the general case of the pathway with a single feedback loop have been established. Mechanisms for maintenance of the steady state asymptotic stability at large static stabilization factors are studied. It has been shown that the range of dynamic stability can be widened greatly, if the pathway contains one or two reactions (but not more) of relatively small effective rate constants. Short strong negative feedback is also found to extend considerably the range of dynamic stability of the pathway. The feedback is more effective if it acts on the reaction with small effective rate constant.
本文关注无分支代谢途径中稳态的动态（渐近）稳定性条件。由于该途径中终产物对其合成途径中进行的反应具有效应作用，此类途径中的固定通量通常由终产物的浓度决定。反馈回路中的延迟会导致在较大静态稳定因子时动态稳定性遭到破坏。本文提出了一种允许对临界稳定因子进行解析估计的方法。在具有单个反馈回路的途径的一般情况下，已确立了稳态渐近稳定性的充分必要条件。研究了在较大静态稳定因子时维持稳态渐近稳定性的机制。结果表明，如果途径包含一两个有效速率常数相对较小的反应（但不超过此数），则动态稳定范围可大幅拓宽。还发现短而强的负反馈会显著扩展途径的动态稳定范围。如果反馈作用于有效速率常数较小的反应，则反馈效果更佳。
