Error thresholds in the presence of epistatic interactions

Area of Science:

• Virology
• Statistical Mechanics
• Genetics

Background:

• Models of RNA viruses utilize the quasispecies concept, where exceeding an error threshold causes genetic information loss and population collapse (error catastrophe).
• Understanding the error catastrophe as a phase transition can provide new insights into viral population dynamics.

Purpose of the Study:

• To analyze the viral error catastrophe as a second-order phase transition.
• To investigate this transition in both simple (single-peak) and complex (rugged) fitness landscapes.
• To explore the role of mutation rates and back-mutation rates in this phenomenon.

Main Methods:

• Theoretical modeling of viral populations under high mutation rates.
• Analogy to phase transitions in statistical mechanics, specifically ferroparamagnetic transitions.
• Numerical simulations on rugged fitness landscapes incorporating epistatic interactions.
• Utilizing replica symmetry breaking mechanisms and genotype similarity distribution as an order parameter.

Main Results:

• Crossing the error threshold is demonstrated as a second-order phase transition, even with lethal mutations.
• In single-peak fitness landscapes, the collapse is analogous to a ferroparamagnetic transition, with back-mutation rate acting as a magnetic field.
• Rugged fitness landscapes exhibit a transition from high to low average fitness, signaled by a sharp change in susceptibility to mutation rate variations.

Conclusions:

• The viral error catastrophe can be effectively modeled as a phase transition, offering a unified framework for understanding viral population dynamics.
• This framework extends to complex, biologically relevant rugged fitness landscapes, highlighting universal principles in evolutionary dynamics.
• The study provides a novel perspective on viral evolution, linking molecular mechanisms to macroscopic phenomena in statistical physics.