Dynamics of virus and immune response in multi-epitope network

Abstract

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

Predator-Prey Dynamics of Intra-Host Simian Immunodeficiency Virus Evolution Within the Untreated Host

“…The model description so far yields our base model (see Figure 6), a special case of the general system consisting of m virus strains and n immune responses analyzed in (60). This model with simulated random mutation is sufficient for producing cross-correlated cycles in Ne and an adaptive (e.g., CD8) population (see Supplementary Information).…”

“…The model depicts a heterogeneous viral population interacting with several immune responses that differ in strength determined by their immunodominance hierarchy, a key factor in driving viral evolution so that different combinations of multiple epitope escapes in the viral population rise and fall (60,61). The model can, thus, be considered a hybrid of the Red Queen model ( 62), describing co-evolution of competing species, and the classical predatorprey model (35,36), wherein these species are not competing but rather locked in a cycle of growth response based on species interaction.…”

“…We consider the following extension of a general virus-immune dynamics model analyzed in Browne et al (2018) (60), which includes a population of target cells (X), m competing virus strains (Y i denotes strain i infected cells), and n variants of adaptive immune response (Z j ), along with an innate immune response (W):…”

“…We assume each epitope mutation imparts equal independent multiplicative fitness costs, i.e. if (i 1 … i n ) represents the epitope sequence of strain i, then b i = b 0 (1 − k ) i 1 +⋯ +i n , which corresponds to a positive epistasis that promotes a sequential nested immune escape trajectory (60). Furthermore in this example simulation, we prescribe a fixed immunodominance hierarchy with equal immune strength for epitopes 3 and 4, and epitopes 5,6,7, which allows us to illustrate the impact of clonal interference on phase lags between viral Ne and the immune population.…”

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

“…We show that connecting population genetics and dynamics offers a way to extract biological meaningful relationships from the equilibria stability conditions of a complex network differential equation for interacting species' variants. We build off of our previous analysis of a multi-variant virus-immune model [9], which established different regimes of attractors, each with a distinct set of viral strains persisting by extending Lyapunov function methods first applied to generalized L-V equations [20,24]. In particular, the stability of certain equilibria structures and associated bifurcations are sharply determined by relevant circuits, which recast strain invasion rates as algebraic combinations of binary sequences shaping viral fitness landscape epistasis.…”