A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.
Author summary The evolution of human immunodeficiency virus within patients is an important part of the disease process. In particular, the presence of mutants that are resistant against anti-viral drugs can result in challenges to the long-term control of the infection. To study disease progression, computer simulations have been useful. However, in some cases these simulations can be difficult because of the complexity of the model. Here, we use a computational complexity reducing algorithm to simulate mutant dynamics in large populations, which can approximate the full model at a fraction of the time. The use of this algorithm allows us to study different transmission methods, viral processes that occur between virus strains within individual cells, and important quantities such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We find that the direct synaptic cell-to-cell transmission of the virus through virological synapses can have strong biological consequences because it can promote potentially defective viruses that carry genetic diversity which can be incorporated into functional virus genomes during infection. Through this process, synaptic transmission in human immunodeficiency virus might promote virus evolvability.