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Statistical mechanics and thermodynamics of viral evolution

This paper analyzes a simplified model of viral infection and evolution using the 'grand canonical ensemble' and formalisms from statistical mechanics and thermodynamics to enumerate all possible viruses and to derive thermodynamic variables for the system. We model the infection process as a series of energy barriers determined by the genetic states of the virus and host as a function of immune response and system temperature. We find a phase transition between a positive temperature regime of normal replication and a negative temperature 'disordered' phase of the virus. These phases define different regimes in which different genetic strategies are favored. Perhaps most importantly, it demonstrates that the system has a real thermodynamic temperature. For normal replication, this temperature is linearly related to effective temperature. The strength of immune response rescales temperature but does not change the observed linear relationship. For all temperatures and immunities studied, we find a universal curve relating the order parameter to viral evolvability. Real viruses have finite length RNA segments that encode for proteins which determine their fitness; hence the methods put forth here could be refined to apply to real biological systems, perhaps providing insight into immune escape, the emergence of novel pathogens and other results of viral evolution.

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