论文标题
化学反应系统中可行的自催化集的预期数量
The expected number of viable autocatalytic sets in chemical reaction systems
论文作者
论文摘要
已经研究了化学反应系统中自我维持的自催化网络的出现，作为对生命系统首次产生的建模的可能机制。几十年来，在简单的随机催化过程中，此类网络将在聚合物系统（在裂解和结扎反应下）中形成，此后进行了数学分析。在本文中，我们为将在一般化学反应系统中形成的自我维持的自催化网络的预期数量提供了确切的表达，并且这些网络的预期数量也将无法抑制（通过系统产生的某些分子）。使用这些方程式，我们能够描述催化和抑制的模式，以最大化或最大程度地减少此类网络的预期数量。我们应用结果来得出有关催化和抑制之间权衡取舍的一般定理，并提供了一些深入了解预期的自我维持的自催化网络数量的程度，与至少存在这样一个系统的可能性相吻合。
The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modelling how living systems first arose. It has been known for several decades that such networks will form within systems of polymers (under cleavage and ligation reactions) under a simple process of random catalysis, and this process has since been mathematically analysed. In this paper, we provide an exact expression for the expected number of self-sustaining autocatalytic networks that will form in a general chemical reaction system, and the expected number of these networks that will also be uninhibited (by some molecule produced by the system). Using these equations, we are able to describe the patterns of catalysis and inhibition that maximise or minimise the expected number of such networks. We apply our results to derive a general theorem concerning the trade-off between catalysis and inhibition, and to provide some insight into the extent to which the expected number of self-sustaining autocatalytic networks coincides with the probability that at least one such system is present.
