Length and sequence relaxation of copolymers under recombination reactions

Abstract

We describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry. We use two approaches: the first one, based on chemical rate equations and the mass-action law describes the infinite size limit, while the second one, based on the chemical master equation, describes systems of finite size. We compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium. We find that for some choice of initial conditions, the entropy of the sequence distribution can be lowered at the expense of increasing the entropy of the length distribution. We consider mainly energetically neutral reactions, except for one simple case of non-neutral reactions.

Random-sequence genetic oligomer pools display an innate potential for ligation and recombination

“…The pervasive spontaneous ligation and recombination activity displayed by oligomer pools described herein may seem counterintuitive, but such behaviour is both predicted and supported by theoretical arguments from statistical mechanics and thermodynamics. These suggest that under the right boundary conditions, recombination - with an concomitant increase in the diversity of length distribution of (RNA) polymer chains - is favoured by entropic factors ( Blokhuis and Lacoste, 2017 ). Remarkably, not only is the diversity in oligomer length distribution altered but recombined pools also display a shift towards an increased tendency for secondary structure formation ( Figure 5E ).…”

Template-directed growth of copolymers

“…The lines with the exponent values γ = 0, 1, 2 are obtained with Eqs. (52) and (53) for the present example. Thermodynamic equilibrium happens along the line γ = 0 where the growth is stopped together with the entropy production per monomer, A = 0.…”

“…The study of template-directed copolymerization beyond the low conversion conditions is also of great importance, in particular, to understand the emergence of replicating molecular species in prebiotic chemistry. 53,54 Moreover, we may wonder if effects similar to those observed in the template-directed growth of copolymers would not also manifest themselves in other growth processes of spatial structures with more than one dimension.…”

Thresholds in Origin of Life Scenarios

“…Finally, the transition scenario toward existence of a sustainable replicase may be revised by considering different polymer generation processes anterior to the replicase regime. Polymer generation could have been enhanced by catalysis of polymerization ( Hazen and Sverjensky, 2010 ), ligation ( Mutschler et al., 2018 ), or recombination ( Blokhuis and Lacoste, 2017 ), as well as by size selection ( Mizuuchi et al., 2019 ). An alternative is that autocatalytic sets could have preceded template-based replication and biased polymer populations toward longer and more functional sequences ( Vasas et al., 2012 ).…”