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Studying Viral Populations with Tools from Quantum Spin Chains

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Abstract

We study Eigen’s model of quasi-species (Eigen in Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58(10):465, 1971), characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically considering excessive mutations in certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

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Notes

  1. This simple mutation–selection model ignores several issues such as competition between different strains, and stochastic fluctuations. It thus assumes large populations unconstrained by resources.

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Acknowledgements

The authors would like to thank the Galileo Galilei Institute in Florence, Italy where a part of this work was performed. This research was performed while CLB held an NRC Research Associateship award at the National Institute of Standards and Technology. MK is supported by NSF through Grant No. DMR-1708280.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, 08544, USA

    Saumya Shivam & S. L. Sondhi

  2. National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA

    Christopher L. Baldwin

  3. Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA

    Christopher L. Baldwin

  4. Department of Physics and Astronomy, University of California, Riverside, CA, 92521, USA

    John Barton

  5. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Mehran Kardar

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  1. Saumya Shivam
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  2. Christopher L. Baldwin
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  5. S. L. Sondhi
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Correspondence to Saumya Shivam.

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Communicated by Michael Lässig.

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Shivam, S., Baldwin, C.L., Barton, J. et al. Studying Viral Populations with Tools from Quantum Spin Chains. J Stat Phys 182, 38 (2021). https://doi.org/10.1007/s10955-021-02716-2

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