Optimal size for emergence of self-replicating polymer system

Abstract

A biological system consists of a variety of polymers that are synthesized from monomers, by catalysis that exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization. We analyze here the stochastic polymerization reaction dynamics, to investigate the transition time from a state with almost no catalysts to a state with sufficient catalysts. We found an optimal volume that minimizes this transition time, which agrees with the inverse of the catalyst concentration at the unstable fixed point that separates the two states, as is theoretically explained. Relevance to the origin of life is also discussed.All life systems known so far consist of a wide variety of polymers that catalyze each other and are replicated through catalytic reactions. In cells, for instance, ribosomes whose main component are RNAs that synthesize a variety of protein species, such as polymerases, that catalyze RNA replication [1]. When considering the origins of life, it is therefore necessary to understand the emergence of a primordial polymer system that allows for self-replicating catalytic reactions, in which resource monomers such as amino acids or nucleotides, which are the building blocks of polymers, are supplied [2,3]. It is also important to understand the timescale of the synthesis of catalytic polymers by polymerizing reactions of the monomers.In this scenario, a polymer has to be long enough to function as a catalyst. In general, without catalysts, a chemical reaction to synthesize such a long polymer is extremely slow, while polymers, even if they are synthesized, are constantly degraded or diffused out. The synthesis can overcome possible degradation or diffusion only under catalysts (enzyme for protein; ribozyme for RNA) that accelerate the reaction by 10 7 ∼ 10 19 [4]. To sustain such a catalytically active state, a certain amount of catalysts is needed, which in turn is only synthesized from catalysts. Hence, the reaction system with autocatalytic polymers is expected to exhibit bi-stability between the inactive state with almost no catalysts and the active state with abundant catalysts that reproduce themselves. In fact, the importance of the transition from the inactive to active state for the emergence of a primitive replicating system has already been pointed out in the seminal work by Dyson [5], while catalytic reaction networks have also been extensively studied [6][7][8][9][10][11]. Here, we study this problem by considering a simple autocatalytic polymerization process, with an aim to obtain the time required for the transition from the inactive to active states.The existence of bistable states and the transition to a catalytically active state has been discussed recently [12,13]. In these studies, the rate equation of the concentrations of the monomers and polymers were often adopted. However, when considering the emergence of catalytic polymers, the number of molecules with negligible fluctuations may not be so large. These fluctuations enable...

Motif analysis for small-number effects in chemical reaction dynamics

“…Specifically, several recent theoretical studies have reported that, in certain chemical reaction systems, the chemical compositions and underlying dynamics can be drastically altered under a small-number condition [3][4][5][6][7][8][9][10][11][12][13][14][15][16]23,24 compared to those expected in the rate equation assuming with a large volume and a large number of molecules. These phenomena are induced by molecular discreteness and its associated stochasticity, designated as "small-number effects" or "discreteness-induced transitions," which are exemplified by the emergence of multi-modality, [3][4][5][6][7][10][11][12] reversal of reaction current, 16 and slow relaxation.…”

Recent Advances in Origins of Life Research by Biophysicists in Japan

“…Theory and computation are thus two very important aspects of origins of life research, and two of the main pioneers in theoretical evolution studies are Kunihiko Kaneko and Takashi Ikegami of the University of Tokyo [3,132,133]. Recent theoretical work by the Kaneko Laboratory has featured optimizing parameters for self-replicating polymer systems [134], designing replicatory protocells [135], and identifying the effect on selection pressure magnitude on evolutionary systems [136], just to name a few. In fact, many of their initial studies on origins and evolution of life are relevant to artificial life systems, both in silico and in real systems, resulting in a large amount of their research specifically on the topic of what characteristics define life and studying the emergence of these complex life-defining phenomena, such as signaling [137] or motility [138].…”

Kinetic Selection of Template Polymer with Complex Sequences

“…In the prebiotic world, complex monomer sequences therefore have been synthesized by reactions with templates as catalysts, which are also synthesized via such template reaction. Thus, the polymerization processes are autocatalytic in nature, as has been extensively investigated [9][10][11][12][13][14][15] 24], including theoretical models that explicitly consider template-like selfreplicating polymerization [8,[16][17][18][19][20][21][22][23] and some synthesis experiments [6, 25, 26].If there exist multiple catalytic polymers with sufficient lengths, then the autocatalytic process for their synthesis can select one of such polymers. Here we study the dependence of the selected sequence on the flow rate of monomers.…”

“…In the prebiotic world, complex monomer sequences therefore have been synthesized by reactions with templates as catalysts, which are also synthesized via such template reaction. Thus, the polymerization processes are autocatalytic in nature, as has been extensively investigated [9][10][11][12][13][14][15]24], including theoretical models that explicitly consider template-like selfreplicating polymerization [8,[16][17][18][19][20][21][22][23] and some synthesis experiments [6,25,26].…”

“…3), and are selected dominantly under the presence of noise. If the noise strength is too small, no transitions occur among the attractors, whereas if it is too large, no specific sequence dominates [39] (see also [40,41] for attractor selection of a higher cellular growth, and [14,42,43] for relevance of noise to chemical evolution).…”