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Replication and mutation on neutral networks.

C Reidys1, C V Forst, P Schuster

  • 1Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Bulletin of Mathematical Biology
|January 9, 2001
PubMed
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RNA sequences fold into specific structures, but many sequences share the same structure. This study models evolution on these "neutral networks" to understand how populations maintain dominant RNA shapes.

Area of Science:

  • * Molecular Biology
  • * Evolutionary Biology
  • * Bioinformatics

Background:

  • * RNA secondary structures are determined by base pairing, creating a map from sequence to structure.
  • * This mapping is non-invertible, meaning multiple RNA sequences can fold into the same minimum free energy structure (shape).
  • * Neutral networks represent sets of sequences that fold into the same shape, acting as pre-images to the structure map.

Purpose of the Study:

  • * To extend the molecular quasispecies theory to understand evolution on degenerate multi-peak fitness landscapes derived from neutral networks.
  • * To model replication and mutation dynamics on these neutral networks using phenomenological rate equations and a stochastic birth-and-death model.
  • * To investigate the concept of a phenotypic error threshold and its role in separating distinct evolutionary scenarios.

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Main Methods:

  • * Application of random graph theory to model neutral networks in sequence space.
  • * Development of phenomenological rate equations and a stochastic birth-and-death model for RNA replication and mutation.
  • * Analysis of single-shape landscapes where one master shape is assigned superior fitness.
  • * Computer simulations to complement analytical results and validate models.

Main Results:

  • * Defined a phenotypic error threshold analogous to the error threshold in sequence space.
  • * Identified two distinct evolutionary scenarios: a stationary master shape or population drift through shape space.
  • * Derived analytical expressions for the mean fraction of master shapes and phenotypic error thresholds on single-shape landscapes.
  • * Demonstrated that phenomenological predictions align well with tRNA(phe) replication/mutation kinetics and stochastic simulations.

Conclusions:

  • * Neutral networks provide a framework for understanding RNA sequence-structure relationships and evolution.
  • * The phenotypic error threshold governs the stability and diversity of RNA populations in relation to their structures.
  • * Models developed accurately predict evolutionary dynamics on degenerate fitness landscapes, validated by experimental data and simulations.