Abstract

Polymer models are a widely used tool to study the prebiotic formation of metabolism at the origins of life. Counts of the number of reactions in these models are often crucial in probabilistic arguments concerning the emergence of autocatalytic networks. In the first part of this paper, we provide the first exact description of the number of reactions under widely applied model assumptions. Conclusions from earlier studies rely on either approximations or asymptotic counting, and we show that the exact counts lead to similar, though not always identical, asymptotic results. In the second part of the paper, we investigate a novel model assumption whereby polymers are invariant under spatial rotation. We outline the biochemical relevance of this condition and again give exact enumerative and asymptotic formulae for the number of reactions.

Keywords

  1. binary polymer model
  2. polymer
  3. peptides
  4. enumeration
  5. Möbius inversion
  6. origin of metabolism
  7. autocatalytic network
  8. RAF set

MSC codes

  1. 05A05
  2. 05A16
  3. 92D15

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Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 2304 - 2316
ISSN (online): 1095-7146

History

Submitted: 16 March 2020
Accepted: 6 July 2021
Published online: 4 October 2021

Keywords

  1. binary polymer model
  2. polymer
  3. peptides
  4. enumeration
  5. Möbius inversion
  6. origin of metabolism
  7. autocatalytic network
  8. RAF set

MSC codes

  1. 05A05
  2. 05A16
  3. 92D15

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