Limits...
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

Occupancy of Cells.The occupancy of the cells, ΨΞ (m), derived from the steady-state solution (Eq 6), is shown as a function of temperature and maximum immune response, A. The same phase transition observed as in Fig 6 is evident here.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4589373&req=5

pone.0137482.g007: Occupancy of Cells.The occupancy of the cells, ΨΞ (m), derived from the steady-state solution (Eq 6), is shown as a function of temperature and maximum immune response, A. The same phase transition observed as in Fig 6 is evident here.

Mentions: Fig 7 shows the occupancy of the cells after infection and immune response (before virus reproduction). One can view the occupancy as a measure of viral fitness. The occupancy fraction of the cells is between zero and 1. With zero immunity, A = 0, the cell occupancy is 1.0 for all T. As immunity is raised the occupancy decreases (approximately linearly in A) until reaching the phase boundary separating the regime of normal replication from the disordered phase. At high temperature and immune response the virus is in the disordered phase and cell occupancy plateaus at ~ 50%. These are viruses that never completely clear, but have low occupancy, low match, and evoke low immune response. At low temperature the virus never enters the disordered phase and cell occupancy decreases linearly with increasing A, eventually falling to zero. The region of phase space with zero virus (viruses that clear in steady state) appears small but for an individual with full immunity, it actually extends to T = 16 degrees which is 32% of the maximum mismatch energy (50) scaled by the effective Boltzmann constant. Likewise the region of zero virus is bounded by maximum immune response A> = 0.94. In the regime of large A and low temperature, one would expect a dynamic process with basic reproductive ratio below unity.


Statistical Mechanics and Thermodynamics of Viral Evolution.

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

Occupancy of Cells.The occupancy of the cells, ΨΞ (m), derived from the steady-state solution (Eq 6), is shown as a function of temperature and maximum immune response, A. The same phase transition observed as in Fig 6 is evident here.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0137482.g007: Occupancy of Cells.The occupancy of the cells, ΨΞ (m), derived from the steady-state solution (Eq 6), is shown as a function of temperature and maximum immune response, A. The same phase transition observed as in Fig 6 is evident here.
Mentions: Fig 7 shows the occupancy of the cells after infection and immune response (before virus reproduction). One can view the occupancy as a measure of viral fitness. The occupancy fraction of the cells is between zero and 1. With zero immunity, A = 0, the cell occupancy is 1.0 for all T. As immunity is raised the occupancy decreases (approximately linearly in A) until reaching the phase boundary separating the regime of normal replication from the disordered phase. At high temperature and immune response the virus is in the disordered phase and cell occupancy plateaus at ~ 50%. These are viruses that never completely clear, but have low occupancy, low match, and evoke low immune response. At low temperature the virus never enters the disordered phase and cell occupancy decreases linearly with increasing A, eventually falling to zero. The region of phase space with zero virus (viruses that clear in steady state) appears small but for an individual with full immunity, it actually extends to T = 16 degrees which is 32% of the maximum mismatch energy (50) scaled by the effective Boltzmann constant. Likewise the region of zero virus is bounded by maximum immune response A> = 0.94. In the regime of large A and low temperature, one would expect a dynamic process with basic reproductive ratio below unity.

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