Solution of the quasispecies model for an arbitrary gene network

Area of Science:

• Evolutionary Biology
• Theoretical Biology
• Genetics

Background:

• Eigen's quasispecies model describes error catastrophe in molecular evolution.
• Gene networks involve multiple interacting genes, each with a master sequence.
• Understanding genome stability under mutation is crucial for evolutionary dynamics.

Purpose of the Study:

• To investigate the equilibrium behavior of quasispecies equations for arbitrary gene networks.
• To analyze the impact of mutation rates on gene functionality and genome stability.
• To identify transitions in gene network behavior beyond a single error catastrophe.

Main Methods:

• Applied Eigen's quasispecies equations to a multi-gene genome model.
• Assumed a single fitness peak model for each individual gene.
• Analyzed model behavior in the limit of infinite sequence length.

Main Results:

• Observed a series of localization-delocalization transitions, termed an 'error cascade', instead of a single error catastrophe.
• Increased mutation rates lead to loss of selective advantage and delocalization of gene populations.
• The network progressively inactivates genes through sequential transitions until genome-wide delocalization.

Conclusions:

• The 'error cascade' model predicts sequential gene inactivation and provides criteria for loss of functionality.
• Offers insights into gene network responses to mutagens and relative gene importance.
• Implications for mutational robustness and 'survival of the flattest' concepts in evolution.