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Journal of Molecular Evolution

, Volume 86, Issue 8, pp 501–510 | Cite as

Computational Models of Polymer Synthesis Driven by Dehydration/Rehydration Cycles: Repurination in Simulated Hydrothermal Fields

  • Mason Hargrave
  • Spencer K. Thompson
  • David Deamer
Original Article

Abstract

Cycles of biologically relevant reactions are an alternative to an origin of life emerging from a steady state away from equilibrium. The cycles involve a rate at which polymers are synthesized and accumulate in microscopic compartments called protocells, and two rates in which monomers and polymers are chemically degraded by hydrolytic reactions. Recent experiments have demonstrated that polymers are synthesized from mononucleotides and accumulate during cycles of hydration and dehydration, which means that the rate of polymer synthesis during the dehydrated phase of the cycle is balanced (but not dominated) by the rate of polymer hydrolysis during the hydrated phase of the cycle. Furthermore, depurination must be balanced by the reverse process of repurination. Here we describe a computational model that was inspired by experimental results, can be generalized to accommodate other reaction parameters, and has qualitative predictive power.

Keywords

Cyclic reactions Condensation and hydrolysis Kinetic traps Prebiotic polymerization 

List of Symbols

\(s_n\)

A vector describing the state of the system after an n number of cycles

\(P_n\)

The mass of intact RNA polymer in the system after an n number of cycles

\(\pi _n\)

The mass of depurinated RNA polymer in the system after an n number of cycles

\(M_n\)

The mass of intact RNA monomer in the system after an n number of cycles

\(\mu _n\)

The mass of depurinated RNA monomer in the system after an n-number of cycles

C

The matrix that describes the transformation applied to the system over the course of one cycle

h

The proportion of polymer mass converted to monomer mass per cycle by the cleavage of phosphodiester bonds during the wet phase

m

The proportion of monomer mass converted to polymer mass per cycle by the formation of phosphodiester bonds during the dry phase

\(d_{\text{m}}\)

The proportion of monomer mass depurinated per cycle during the wet phase

\(d_{\text{p}}\)

The proportion of polymer mass depurinated per cycle during the wet phase

\(r_{\text{m}}\)

The proportion of degraded monomer mass repurinated per cycle during the dry phase

\(r_{\text{p}}\)

The proportion of degraded polymer mass repurinated per cycle during the dry phase

D

The matrix that describes the transformation applied to the system over the course of the dry phase of one cycle

W

The matrix that describes the transformation applied to the system over the course of the wet phase of one cycle

n

The n number of cycles after which the mass of depurinated (non-reactive) RNA monomer has accumulated

Notes

Acknowledgements

We would like to thank Paul Higgs and David Ross for valuable discussion of the manuscript. Further, we would like to thank Gilbert Strang for inspiring us to take a linear algebraic approach to the analysis of these processes. Finally, we would like to thank the referees for taking the time to review and provide their council regarding this research.

Funding

The funding was provided by Hierarchical Systems Foundation.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of California Santa Cruz Santa CruzUSA

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