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Statistical Mechanics and Thermodynamics of Viral Evolution.

Jones BA, Lessler J, Bianco S, Kaufman JH - PLoS ONE (2015)

Bottom Line: The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics.This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work.Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used 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.

View Article: PubMed Central - PubMed

Affiliation: Almaden Research Center, IBM, San Jose, California, United States of America.

ABSTRACT
This paper uses methods drawn from physics to study the life cycle of viruses. The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics. Using this approach we enumerate all possible genetic states of a model virus and host as a function of two independent pressures-immune response and system temperature. We prove the system has a real thermodynamic temperature, and discover a new phase transition between a positive temperature regime of normal replication and a negative temperature "disordered" phase of the virus. We distinguish this from previous observations of a phase transition that arises as a function of mutation rate. From an evolutionary biology point of view, at steady state the viruses naturally evolve to distinct quasispecies. This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work. Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used 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.

No MeSH data available.


Related in: MedlinePlus

The Grand Canonical Ensemble for a System of Viruses.The three thermodynamic elements of the system are shown. The “Reservoir” of all possible virus is usually referred to as the “thermal bath”.[23] In this case the bath of possible viral sequences is very large (effectively infinite). Free virus in the environment, at steady state, is populated from the reservoir with a distribution based on temperature and immunity. In the infection phase, virus that successfully infect cells are drawn from the environment. Virus that fails to infect are returned to the reservoir. Immunity may remove virus (from the cells back to the reservoir), and reproduction draws new offspring from the reservoir and repopulates the environment (emptying the cells). The double arrows indicate population from and return to the reservoir. The curved arrows show the virus life cycle.
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pone.0137482.g008: The Grand Canonical Ensemble for a System of Viruses.The three thermodynamic elements of the system are shown. The “Reservoir” of all possible virus is usually referred to as the “thermal bath”.[23] In this case the bath of possible viral sequences is very large (effectively infinite). Free virus in the environment, at steady state, is populated from the reservoir with a distribution based on temperature and immunity. In the infection phase, virus that successfully infect cells are drawn from the environment. Virus that fails to infect are returned to the reservoir. Immunity may remove virus (from the cells back to the reservoir), and reproduction draws new offspring from the reservoir and repopulates the environment (emptying the cells). The double arrows indicate population from and return to the reservoir. The curved arrows show the virus life cycle.

Mentions: So far we have discussed our model in terms of viruses in the cells and in the environment. It is clear that as temperature and immunity are changed, both the energy and the number of virions change. Energy and number are both conserved only if we imagine that our cells and environment are both in contact with a third reservoir or bath that includes all possible viruses in thermal and “chemical” equilibrium with the rest of the system. Chemical equilibrium in our model requires conservative flow of virus between the reservoir and the system. Classically, for particle number to have an associated chemical potential, chemical potential of the system must be conserved during the internal dynamics of the system, and only able to change when the system exchanges particles with an external reservoir. This is the classic definition of a macro-canonical or grand canonical ensemble (Fig 8). This ensemble is the natural statistical ensemble for modeling any system of viruses. It ensures conservation of both number and energy. Any viruses not in cells or the environment (e.g., those eliminated by immune response) are in the reservoir, and any new viruses entering the system (e.g., mutated offspring) are drawn from the reservoir.


Statistical Mechanics and Thermodynamics of Viral Evolution.

Jones BA, Lessler J, Bianco S, Kaufman JH - PLoS ONE (2015)

The Grand Canonical Ensemble for a System of Viruses.The three thermodynamic elements of the system are shown. The “Reservoir” of all possible virus is usually referred to as the “thermal bath”.[23] In this case the bath of possible viral sequences is very large (effectively infinite). Free virus in the environment, at steady state, is populated from the reservoir with a distribution based on temperature and immunity. In the infection phase, virus that successfully infect cells are drawn from the environment. Virus that fails to infect are returned to the reservoir. Immunity may remove virus (from the cells back to the reservoir), and reproduction draws new offspring from the reservoir and repopulates the environment (emptying the cells). The double arrows indicate population from and return to the reservoir. The curved arrows show the virus life cycle.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4589373&req=5

pone.0137482.g008: The Grand Canonical Ensemble for a System of Viruses.The three thermodynamic elements of the system are shown. The “Reservoir” of all possible virus is usually referred to as the “thermal bath”.[23] In this case the bath of possible viral sequences is very large (effectively infinite). Free virus in the environment, at steady state, is populated from the reservoir with a distribution based on temperature and immunity. In the infection phase, virus that successfully infect cells are drawn from the environment. Virus that fails to infect are returned to the reservoir. Immunity may remove virus (from the cells back to the reservoir), and reproduction draws new offspring from the reservoir and repopulates the environment (emptying the cells). The double arrows indicate population from and return to the reservoir. The curved arrows show the virus life cycle.
Mentions: So far we have discussed our model in terms of viruses in the cells and in the environment. It is clear that as temperature and immunity are changed, both the energy and the number of virions change. Energy and number are both conserved only if we imagine that our cells and environment are both in contact with a third reservoir or bath that includes all possible viruses in thermal and “chemical” equilibrium with the rest of the system. Chemical equilibrium in our model requires conservative flow of virus between the reservoir and the system. Classically, for particle number to have an associated chemical potential, chemical potential of the system must be conserved during the internal dynamics of the system, and only able to change when the system exchanges particles with an external reservoir. This is the classic definition of a macro-canonical or grand canonical ensemble (Fig 8). This ensemble is the natural statistical ensemble for modeling any system of viruses. It ensures conservation of both number and energy. Any viruses not in cells or the environment (e.g., those eliminated by immune response) are in the reservoir, and any new viruses entering the system (e.g., mutated offspring) are drawn from the reservoir.

Bottom Line: The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics.This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work.Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used 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.

View Article: PubMed Central - PubMed

Affiliation: Almaden Research Center, IBM, San Jose, California, United States of America.

ABSTRACT
This paper uses methods drawn from physics to study the life cycle of viruses. The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics. Using this approach we enumerate all possible genetic states of a model virus and host as a function of two independent pressures-immune response and system temperature. We prove the system has a real thermodynamic temperature, and discover a new phase transition between a positive temperature regime of normal replication and a negative temperature "disordered" phase of the virus. We distinguish this from previous observations of a phase transition that arises as a function of mutation rate. From an evolutionary biology point of view, at steady state the viruses naturally evolve to distinct quasispecies. This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work. Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used 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.

No MeSH data available.


Related in: MedlinePlus