Evolution of Antigen Drift/Switching: Continuously Evading Pathogens

Abstract

Following infection to a host, some pathogens repeatedly alter their antigen expression, and thereby escape the immune defense (antigen drift/switching). This paper examines the evolutionarily stable mutation rate of pathogens which maximizes the stationary pathogen density in a host. Assumptions are: (i) most mutations are deleterious but a minor fraction, p, of mutations can contribute to the alternation of antigenic property of the pathogen; and (ii) potential antigen types can be indexed in a one-dimensional lattice (the stepping-stone model). The model reveals that: (a) if the mutation rate is higher than a threshold μc = R0/(l - p ), where R0 is the per capita growth rate of pathogen before the immune system is activated, pathogens cannot maintain themselves because too many progeny are lost by lethal mutations; (b) if the mutation rate lies between zero and μc, the system converges to a traveling wave of antigen variants with a constant wave speed; (c) the evolutionarily stable mutation rate μESS is unexpectedly high: more than 0·25 per genome per replication even if most mutations are lethal. Hence more than a fourth of progeny are born defective in the evolutionarily stable state; (d) the μESS is even higher if multiple infections by pathogens are common.The paper also studies the evolutionarily stable mutation rate if every mutant antigen belongs to a different type (the infinite allele model), and the evolution of antigen switching between a finite number of antigen variants stored in the pathogen genome.