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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

Three Limiting Cases of the Effect of Viral Mutation in a Single Codon.The transition probabilitiy (Pmut) as a function of the number of matches, m (pre-mutation). Curves labeled ‘+1’ represent the probability of a mutation increasing the number of matches between the virus and target genomes, ‘-1’ the probability of decreasing the number of matches, and ‘0’ the probability of no change. Given alphabet length ‘a,’ the figure shows the limiting behavior for: (a) Small a, highly degenerate target; (b) a ≈ target+1, i.e., medium degeneracy; (c) Large a, i.e., low target degeneracy.
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pone.0137482.g003: Three Limiting Cases of the Effect of Viral Mutation in a Single Codon.The transition probabilitiy (Pmut) as a function of the number of matches, m (pre-mutation). Curves labeled ‘+1’ represent the probability of a mutation increasing the number of matches between the virus and target genomes, ‘-1’ the probability of decreasing the number of matches, and ‘0’ the probability of no change. Given alphabet length ‘a,’ the figure shows the limiting behavior for: (a) Small a, highly degenerate target; (b) a ≈ target+1, i.e., medium degeneracy; (c) Large a, i.e., low target degeneracy.

Mentions: These general cases are shown in Fig 3. It should be noted that these results hold for matches determined by complete overlay of the target binding sites by the virus. We do not consider alignments where the target extends past the end of the virus giving only partial overlay of the target binding sites. This alternative method would yield different limiting cases, as well as different expressions below for the mutation. For clarity, in our model there exist only v-t+1 allowed alignments, where v and t are the length of virus and target, respectively. (This is in contrast to the ‘extended alignment’ method, not implemented here, which has v+t-1 alignments.) The limiting cases shown in Fig 3 are derived for the specific choice of a virus genome segment exactly twice as long as the target segment (our model system).


Statistical Mechanics and Thermodynamics of Viral Evolution.

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

Three Limiting Cases of the Effect of Viral Mutation in a Single Codon.The transition probabilitiy (Pmut) as a function of the number of matches, m (pre-mutation). Curves labeled ‘+1’ represent the probability of a mutation increasing the number of matches between the virus and target genomes, ‘-1’ the probability of decreasing the number of matches, and ‘0’ the probability of no change. Given alphabet length ‘a,’ the figure shows the limiting behavior for: (a) Small a, highly degenerate target; (b) a ≈ target+1, i.e., medium degeneracy; (c) Large a, i.e., low target degeneracy.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4589373&req=5

pone.0137482.g003: Three Limiting Cases of the Effect of Viral Mutation in a Single Codon.The transition probabilitiy (Pmut) as a function of the number of matches, m (pre-mutation). Curves labeled ‘+1’ represent the probability of a mutation increasing the number of matches between the virus and target genomes, ‘-1’ the probability of decreasing the number of matches, and ‘0’ the probability of no change. Given alphabet length ‘a,’ the figure shows the limiting behavior for: (a) Small a, highly degenerate target; (b) a ≈ target+1, i.e., medium degeneracy; (c) Large a, i.e., low target degeneracy.
Mentions: These general cases are shown in Fig 3. It should be noted that these results hold for matches determined by complete overlay of the target binding sites by the virus. We do not consider alignments where the target extends past the end of the virus giving only partial overlay of the target binding sites. This alternative method would yield different limiting cases, as well as different expressions below for the mutation. For clarity, in our model there exist only v-t+1 allowed alignments, where v and t are the length of virus and target, respectively. (This is in contrast to the ‘extended alignment’ method, not implemented here, which has v+t-1 alignments.) The limiting cases shown in Fig 3 are derived for the specific choice of a virus genome segment exactly twice as long as the target segment (our model system).

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