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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

Eigenstates of the System.The figure shows the normalized eigenstates, P(m), vs. the number of matches, m, as a function of temperature and maximum immune response, A. Each distribution, P(m), represents the quasispecies distribution (i.e. probability of a given number of matches) at fixed A and temperature. The temperatures shown here are 0.01,0.03,0.05,0.1,0.3,0.5,1,2,3,4,5,10,…,100*,110,120,130,140,150,200,250,300 (*step by 5) for each immunity indicated. Low temperature is represented by the narrow distribution at high match (at far right).
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pone.0137482.g005: Eigenstates of the System.The figure shows the normalized eigenstates, P(m), vs. the number of matches, m, as a function of temperature and maximum immune response, A. Each distribution, P(m), represents the quasispecies distribution (i.e. probability of a given number of matches) at fixed A and temperature. The temperatures shown here are 0.01,0.03,0.05,0.1,0.3,0.5,1,2,3,4,5,10,…,100*,110,120,130,140,150,200,250,300 (*step by 5) for each immunity indicated. Low temperature is represented by the narrow distribution at high match (at far right).

Mentions: The probability of a virus having a given number of matches, m, at a specific temperature and maximum immune response (Eq 4), A, is the normalized eigenstate, Pm (Fig 5). Each Pm can be thought of as the steady state quasispecies distribution, the peak of which represents the most “robust” virus type in the quasistates [14–16,20–22,30]. The width of each distribution reflects the accessible states and can be viewed as an indicator of evolvability or adaptive genetic diversity [4].


Statistical Mechanics and Thermodynamics of Viral Evolution.

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

Eigenstates of the System.The figure shows the normalized eigenstates, P(m), vs. the number of matches, m, as a function of temperature and maximum immune response, A. Each distribution, P(m), represents the quasispecies distribution (i.e. probability of a given number of matches) at fixed A and temperature. The temperatures shown here are 0.01,0.03,0.05,0.1,0.3,0.5,1,2,3,4,5,10,…,100*,110,120,130,140,150,200,250,300 (*step by 5) for each immunity indicated. Low temperature is represented by the narrow distribution at high match (at far right).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4589373&req=5

pone.0137482.g005: Eigenstates of the System.The figure shows the normalized eigenstates, P(m), vs. the number of matches, m, as a function of temperature and maximum immune response, A. Each distribution, P(m), represents the quasispecies distribution (i.e. probability of a given number of matches) at fixed A and temperature. The temperatures shown here are 0.01,0.03,0.05,0.1,0.3,0.5,1,2,3,4,5,10,…,100*,110,120,130,140,150,200,250,300 (*step by 5) for each immunity indicated. Low temperature is represented by the narrow distribution at high match (at far right).
Mentions: The probability of a virus having a given number of matches, m, at a specific temperature and maximum immune response (Eq 4), A, is the normalized eigenstate, Pm (Fig 5). Each Pm can be thought of as the steady state quasispecies distribution, the peak of which represents the most “robust” virus type in the quasistates [14–16,20–22,30]. The width of each distribution reflects the accessible states and can be viewed as an indicator of evolvability or adaptive genetic diversity [4].

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