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.
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(Reproduced with permission from Da Silva et al. (2015))
(a Reproduced with permission from DeGuzman et al. (2014))
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Notes
The choice of a 2-min wet phase and 30-min dry phase in a cycle is based on previous laboratory studies. These durations are reasonable because the water levels of hydrothermal pools undergo periodic fluctuations related to precipitation and evaporation as well as geyser activity. A longer dry phase is required for condensation reactions leading to polymerization, while the wet phase must not be so long that the hydrolysis of polymers dominates over the synthesis of polymers.
Abbreviations
- \(s_n\) :
-
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
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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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Hargrave, M., Thompson, S.K. & Deamer, D. Computational Models of Polymer Synthesis Driven by Dehydration/Rehydration Cycles: Repurination in Simulated Hydrothermal Fields. J Mol Evol 86, 501–510 (2018). https://doi.org/10.1007/s00239-018-9865-5
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DOI: https://doi.org/10.1007/s00239-018-9865-5