Potential for evolution of complex defense strategies in a multi-scale model of virus-host coevolution

Abstract

Background: Host resistance and viral pathogenicity are determined by molecular interactions that are part of the evolutionary arms race between viruses and their hosts. Viruses are obligate intracellular parasites and entry to the host cell is the first step of any virus infection. Commonly, viruses enter host cells by binding cell surface receptors. We adopt a computational modeling approach to study the evolution of the first infection step, where we consider two possible levels of resistance mechanism: at the level of the binding interaction between the host receptor and a virus binding protein, and at the level of receptor protein expression where we use a standard gene regulatory network model. At the population level we adopted the Susceptible-Infected-Susceptible (SIS) model. We used our multi-scale model to understand what conditions might determine the balance between use of resistance mechanisms at the two different levels.

Results: We explored a range of different conditions (model parameters) that affect host evolutionary dynamics and, in particular, the balance between the use of different resistance mechanisms. These conditions include the complexity of the receptor binding protein-protein interaction, selection pressure on the host population (pathogenicity), and the number of expressed cell-surface receptors. In particular, we found that as the receptor binding complexity (understood as the number of amino acids involved in the interaction between the virus entry protein and the host receptor) increases, viruses tend to become specialists and target one specific receptor. At the same time, on the host side, the potential for resistance shifts from the changes at the level of receptor binding (protein-protein) interaction towards changes at the level of gene regulation, suggesting a mechanism for increased biological complexity.

Conclusions: Host resistance and viral pathogenicity depend on quite different evolutionary conditions. Viruses may evolve cell entry strategies that use small receptor binding regions, represented by low complexity binding in our model. Our modeling results suggest that if the virus adopts a strategy based on binding to low complexity sites on the host receptor, the host will select a defense strategy at the protein (receptor) level, rather than at the level of the regulatory network - a virus-host strategy that appears to have been selected most often in nature.

Keywords: Gene regulatory network; Host cell surface receptor; Virus entry.

Fig. 1

Diagram of gene regulatory network (GRN) and host-virus interaction scheme. a the GRN is composed of a transcription factor regulation sub-network and a receptor protein coding regulation sub-network. Mutations at the network level can be used to shut down the targetable receptor. Mutations at the protein level can result in a protein mismatch to block virus protein binding. b If more than ϵ _seqM % of amino acids are one-to-one matched, we assume the virus protein can bind to the matched receptor (top). If less than the threshold (ϵ _seqM) are matched, we assume the virus protein fails to bind the receptor

Fig. 2

Transmissibility changes for different receptor binding complexity and host protein mutation rate. The mean transmissibility (ξ) for the last 250 time points (Error bar: one std. dev. over 100 simulations). ξ increases as the receptor binding complexity decreases (shorter L) in which case viruses can target multiple receptors and as the host protein mutation rate (μ _hp) decreases which is due to the more limited speed of protein mutations to counteract the rapidly evolving viruses

Fig. 3

Two different virus infection strategies: Targeting a specific receptor or non-specific multiple receptors. a The fraction of time points that multiple receptors are targeted simultaneously and b the Gini coefficient of the frequency of targeted receptors for different receptor binding complexities (Ls) (Error bar: std. dev. over 100 simulations). A lower Gini coefficient (close to zero) indicates evenness and one that is close to one indicates inequality. As the receptor binding complexity increases (longer L) viruses target a specific receptor and do not change the target receptor over time

Fig. 4

Preference for resistance using gene regulatory network (GRN) rewiring rather than protein mutations. The fraction of simulations where GRN rewiring strategy is used more often than protein binding site change for successful resistance under different protein binding complexities (Ls) and host receptor sequence mutation rates (μ _hp). In a more complex receptor binding system, hosts tend to select the GRN rewiring strategy more often than the protein mutation strategy due to the single receptor targeting infection strategy. Since low μ _hp means a lower rate of protein mutations to counteract the rapidly evolving viruses, hosts tend to favor a protein mutation strategy less

Fig. 5

Trade-offs in the resistance potential between the gene regulatory network and receptor proteins. For the susceptible host population, the ability to resist using a GRN rewiring and b protein binding site changes is measured for different receptor binding complexities (Error bar: std. dev. over 100 simulations). As the receptor binding complexity increases, hosts increase evolutionary potential more on the GRN while decreasing it on receptor proteins (μ _hp = 0.01, N _ER/N _R = 3/5, ϵ _seqM = 90 %, k _I = 0.8)

Fig. 6

Host range measured by infected host population’s genetic diversity under different conditions. The first column is the gene regulatory network diversity, the second column is the phenotype diversity and the last column is the receptor protein sequence diversity. Viruses become specialists when receptor binding complexity (L) increases (a, b, c), survival rate for offspring from infected parents (k _I) decreases (d, e, f) and amino acid matching threshold for protein binding (ϵ _seqM) decreases (g, h, i). For low ϵ _seqM and k _I, population dynamics generally follows that shown in Additional file 2: Figure S1 b. Hence, in d ~ i) we considered all 100 simulations for measuring the genetic diversity