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Studying viral populations with tools from quantum spin chains. (English) Zbl 1458.92058

This paper investigates the fatal mutation load and the corresponding \(\mu_c\) rate for various types of HIV proteins using traditional tools for quantum spin interactions such as perturbation theory and mean field approximation. The authors use the ideas of interacting quantum systems to study Eigen’s quasi species model. Using past evaluation of HIV suitability landscapes, which are in good agreement with experimental data, the fatal mutation rate, \(\mu_c\), was calculated, beyond which viral populations are expected to decline due to reduced fertility. The authors find that first-order perturbation theory works remarkably well in predicting \(\mu_c\). Despite the fact that the authors do not have an exact result with which they can compare, neither higher-order nor non-perturbative terms, nevertheless the mean-field approximation gives significantly different results. G. R. Hart and A. L. Ferguson [“Error catastrophe and phase transition in the empirical fitness landscape of HIV”, Phys. Rev. E 91, No. 3, Article ID 032705, 5 p. (2015; doi:10.1103/PhysRevE.91.032705)] investigated the potential for catastrophic error for HIV using evaluative fitness landscapes. They found evidence of a phase transition to the low availability of the HIV p6 protein that is part of the gag. The transition occurs at temperatures above unity, which is interpreted as a signal of a mutation rate that is higher than what is observed in nature. However, their approach does not assess the critical mutation frequency precisely in terms of the probability of mutation per replication cycle. In fact, the immune system has special defenses that can cause viruses to make a “catastrophic mistake”. APOBEC proteins cause viral hypermutation, which almost always leads to the production of defective viruses. However, APOBEC proteins can be counteracted by the HIV vif protein, allowing uncontrolled viral replication to continue. It is clear that a detailed understanding of the “phase diagrams” of HIV proteins will be a useful tool for fighting the virus.

MSC:

92D15 Problems related to evolution
92D10 Genetics and epigenetics
81T99 Quantum field theory; related classical field theories

Software:

Ace
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Full Text: DOI arXiv

References:

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