Mathematical Analysis of a Prototypical Autocatalytic Reaction Network

Abstract

Network autocatalysis, which is autocatalysis whereby a catalyst is not directly produced in a catalytic cycle, is likely to be more common in chemistry than direct autocatalysis is. Nevertheless, the kinetics of autocatalytic networks often does not exactly follow simple quadratic or cubic rate laws and largely depends on the structure of the network. In this article, we analyzed one of the simplest and most chemically plausible autocatalytic networks where a catalytic cycle is coupled to an ancillary reaction that produces the catalyst. We analytically analyzed deviations in the kinetics of this network from its exponential growth and numerically studied the competition between two networks for common substrates. Our results showed that when quasi-steady-state approximation is applicable for at least one of the components, the deviation from the exponential growth is small. Numerical simulations showed that competition between networks results in the mutual exclusion of autocatalysts; however, the presence of a substantial noncatalytic conversion of substrates will create broad regions where autocatalysts can coexist. Thus, we should avoid the accumulation of intermediates and the noncatalytic conversion of the substrate when designing experimental systems that need autocatalysis as a source of positive feedback or as a source of evolutionary pressure.

Autocatalysis: Kinetics, Mechanisms and Design

“…Often, the autocatalytic network does not involve a series of catalysts – only one catalyst and a series of non‐catalytic intermediates (Figure 3c). Semenov and Skorb showed that thioester autocatalysis, [22] some variants of azide‐alkyne autocatalysis [23] and the formaldehyde sulfide reaction [24] all belong to this type of network structure [25] . This network always results in exponential growth after some lag phase where growth is slower than an exponential rate.…”

“…The contribution of the direct reaction to the overall production of products is an important characteristic of a particular autocatalytic reaction. If the contribution of the direct reaction is too strong, the dynamic effects of autocatalysis will be masked; the system properties emerging from autocatalysis such as Darwinian selection, [25] bistability, propagation of the reaction front, and oscillations will not appear [11a] . Let's consider the simplest example of an autocatalytic reaction: …”

“…The design of the thioester autocatalytic network is a good example of applying the branching structure. Although this network can be represented by the motif in Figure 3c, [25] finding a catalytic cycle in this system is nontrivial. By contrast, the branching in this reaction is straightforward – the reaction of the thioester with cysteamine generates two thiol molecules from one (Figure 14).…”

Immersive Molecular Dynamics in Virtual Reality: Increasing Efficiency of Educational Process with Companion Converter for NarupaXR

“…Due to the rapid development of computer technologies, more attention is paid to the areas of their intersection with chemistry, including infochemistry [ 1 , 2 , 3 , 4 ]. In order to prepare the 21st century students to be successful researchers and engineers in emerging fields of chemistry, informatics and programming, it is necessary to provide more educational tools to ensure deeper understanding of the fundamental principles in the aforementioned areas.…”

A Companion Converter for Immersive Molecular Dynamics in Virtual Reality to Save Time on Creating Simulation Files

“…Due to the rapid development of computer technologies, more attention is paid to the areas of their intersection with chemistry, including infochemistry [1][2][3][4]. In order to prepare the 21st century students to be successful researchers and engineers in emerging fields of chemistry, informatics and programming, it is necessary to provide more educational tools to ensure deeper understanding of the fundamental principles in the aforementioned areas.…”