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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

Testing for a Thermodynamic Temperature.The figure shows thermodynamic temperature Tthermo vs Tmodel. For Tmodel below the phase transition, the relationship is linear with slope kB. From Eq (15) the effective kBTthermo is the inverse slope derived from a plot of lnΩ(E) vs. E. Above the phase transition a negative temperature is observed as expected. In the inset we plot the slope of Tthermo vs Tmodel for the values of maximum immune response, A, shown in the color legend, and observe that they all fall on a single line. This suggests that the effective kB decreases linearly with increasing immune amplitude, A, and shows that immune strength rescales temperature.
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pone.0137482.g011: Testing for a Thermodynamic Temperature.The figure shows thermodynamic temperature Tthermo vs Tmodel. For Tmodel below the phase transition, the relationship is linear with slope kB. From Eq (15) the effective kBTthermo is the inverse slope derived from a plot of lnΩ(E) vs. E. Above the phase transition a negative temperature is observed as expected. In the inset we plot the slope of Tthermo vs Tmodel for the values of maximum immune response, A, shown in the color legend, and observe that they all fall on a single line. This suggests that the effective kB decreases linearly with increasing immune amplitude, A, and shows that immune strength rescales temperature.

Mentions: For Tmodel less than the critical temperature (Figs 5 and 6), the system is in a regime of normal replication. In this phase, Fig 11 demonstrates that the thermodynamic temperature is defined, positive, and approximately linearly related to Tmodel. The constant of proportionality is the effective Boltzmann constant. Observe that the temperature scale set by the entropy and the number of states is tied to the genetic properties of the virus+host target pair. A different type of virus with a protein receptor of different length or different degeneracy, or a different target (host) receptor would change the entropy and the energy and therefore the corresponding temperature scale. Lowering temperature can cause some virions to fail to infect any cell (in a particular host) which might otherwise been able to infect a cell. This is analogous to changing immunity, which can cause some virions to die, which may not have otherwise died. Changing temperature changes a virion’s fitness and shifts the steady state quasispecies distribution.


Statistical Mechanics and Thermodynamics of Viral Evolution.

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

Testing for a Thermodynamic Temperature.The figure shows thermodynamic temperature Tthermo vs Tmodel. For Tmodel below the phase transition, the relationship is linear with slope kB. From Eq (15) the effective kBTthermo is the inverse slope derived from a plot of lnΩ(E) vs. E. Above the phase transition a negative temperature is observed as expected. In the inset we plot the slope of Tthermo vs Tmodel for the values of maximum immune response, A, shown in the color legend, and observe that they all fall on a single line. This suggests that the effective kB decreases linearly with increasing immune amplitude, A, and shows that immune strength rescales temperature.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0137482.g011: Testing for a Thermodynamic Temperature.The figure shows thermodynamic temperature Tthermo vs Tmodel. For Tmodel below the phase transition, the relationship is linear with slope kB. From Eq (15) the effective kBTthermo is the inverse slope derived from a plot of lnΩ(E) vs. E. Above the phase transition a negative temperature is observed as expected. In the inset we plot the slope of Tthermo vs Tmodel for the values of maximum immune response, A, shown in the color legend, and observe that they all fall on a single line. This suggests that the effective kB decreases linearly with increasing immune amplitude, A, and shows that immune strength rescales temperature.
Mentions: For Tmodel less than the critical temperature (Figs 5 and 6), the system is in a regime of normal replication. In this phase, Fig 11 demonstrates that the thermodynamic temperature is defined, positive, and approximately linearly related to Tmodel. The constant of proportionality is the effective Boltzmann constant. Observe that the temperature scale set by the entropy and the number of states is tied to the genetic properties of the virus+host target pair. A different type of virus with a protein receptor of different length or different degeneracy, or a different target (host) receptor would change the entropy and the energy and therefore the corresponding temperature scale. Lowering temperature can cause some virions to fail to infect any cell (in a particular host) which might otherwise been able to infect a cell. This is analogous to changing immunity, which can cause some virions to die, which may not have otherwise died. Changing temperature changes a virion’s fitness and shifts the steady state quasispecies distribution.

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