The Expected Number of Viable Autocatalytic Sets in Chemical Reaction Systems

The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modeling 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 analyzed. 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 maximize or minimize 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.

Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary $$\Gamma $$ Γ -convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

Accelerated Simulation of Large Reaction Systems Using a Constraint-Based Algorithm

Simulation of reaction systems has been employed along decades for a better understanding of such systems. However, the ever-growing gathering of biological data implied in larger and more complex models that are computationally challenging for current discrete-stochastic simulation methods. In this work, we propose a constraint-based algorithm to simulate such reaction systems, called the Constraint-Based Simulation Algorithm (CBSA). The main advantage of the proposed method is that it is intrinsically parallelizable, thus being able to be implemented in GPGPU architectures. We show through examples that our method can provide valid solutions when compared to the well-known Stochastic Simulation Algorithm (SSA). An analysis of computational efficiency showed that the CBSA tend to outperform other considered methods when dealing with a high number of molecules and reaction channels. Therefore, we believe that the proposed method constitutes an interesting alternative when simulating large chemical reaction systems.

Side Reactions Do Not Completely Disrupt Linear Self-Replicating Chemical Reaction Systems

A crucial question within the fields of origins of life and metabolic networks is whether or not a self-replicating chemical reaction system is able to persist in the presence of side reactions. Due to the strong nonlinear effects involved in such systems, they are often difficult to study analytically. There are however certain conditions that allow for a wide range of these reaction systems to be well described by a set of linear ordinary differential equations. In this article, we elucidate these conditions and present a method to construct and solve such equations. For those linear self-replicating systems, we quantitatively find that the growth rate of the system is simply proportional to the sum of all the rate constants of the reactions that constitute the system (but is nontrivially determined by the relative values). We also give quantitative descriptions of how strongly side reactions need to be coupled with the system in order to completely disrupt the system.