Viral proteome size and CD8+ T cell epitope density are correlated: the effect of complexity on selection.

The relation between the complexity of organisms and proteins and their evolution rates has been discussed in the context of multiple generic models. The main robust claim from most such models is the negative relation between complexity and the accumulation rate of mutations. Viruses accumulate escape mutations in their epitopes to avoid detection and destruction of their host cell by CD8+ T cells. The extreme regime of immune escape, namely, strong selection and high mutation rate, provide an opportunity to extend and validate the existing models of relation between complexity and evolution rate as proposed by Fisher and Kimura. Using epitope prediction algorithms to compute the epitopes presented on the most frequent human HLA alleles in over 100 fully sequenced human viruses, and over 900 non-human viruses, we here study the correlation between viruses/proteins complexity (as measured by the number of proteins in the virus and the length of each protein, respectively) and the rate of accumulation of escape mutation. The latter is evaluated by measuring the normalized epitope density of viral proteins. If the virus/protein complexity prevents the accumulation of escape mutations, the epitope density is expected to be positively correlated with both the number of proteins in the virus and the length of proteins. We show that such correlations are indeed observed for most human viruses. For non-human viruses the correlations were much less significant, indicating that the correlation is indeed induced by human HLA molecules.

Diffusion rate determines balance between extinction and proliferation in birth-death processes.

We here study spatially extended catalyst induced growth processes. This type of process exists in multiple domains of biology, ranging from ecology (nutrients and growth), through immunology (antigens and lymphocytes) to molecular biology (signaling molecules initiating signaling cascades). Such systems often exhibit an extinction-proliferation transition, where varying some parameters can lead to either extinction or survival of the reactants. When the stochasticity of the reactions, the presence of discrete reactants and their spatial distribution is incorporated into the analysis, a non-uniform reactant distribution emerges, even when all parameters are uniform in space. Using a combination of Monte Carlo simulation and percolation theory based estimations; the asymptotic behavior of such systems is studied. In all studied cases, it turns out that the overall survival of the reactant population in the long run is based on the size and shape of the reactant aggregates, their distribution in space and the reactant diffusion rate. We here show that for a large class of models, the reactant density is maximal at intermediate diffusion rates and low or zero at either very high or very low diffusion rates. We give multiple examples of such system and provide a generic explanation for this behavior. The set of models presented here provides a new insight on the population dynamics in chemical, biological and ecological systems.

Predator-prey dynamics in a uniform medium lead to directed percolation and wave-train propagation.

The dynamics of birth-death processes with extinction points that are unstable in the deterministic average description has been extensively studied, mainly in the context of the stochastic transition from the mean-field attracting fixed point to the absorbing state. Here we study the opposite case of a small perturbation from the zero-population absorbing state. We show that such perturbations can grow beyond the mean-field attracting fixed point and then can collapse back into the absorbing state. Such dynamics can represent, for example, the fast growth of a pathogen and then its destruction by the immune system. We show that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: (a) a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and (b) wave trains representing the transition of the entire space to the mean-field stable positive fixed point.

Optimal viral immune surveillance evasion strategies.

Following cell entry, viruses can be detected by cytotoxic T lymphocytes. These cytotoxic T lymphocytes can induce host cell apoptosis and prevent the propagation of the virus. Viruses with fewer epitopes have a higher survival probability, and are selected through evolution. However, mutations have a fitness cost and on evolutionary periods viruses maintain some epitopes. The number of epitopes in each viral protein is a balance between the selective advantage of having fewer epitopes and the reduced fitness following the epitope removing mutations. We discuss a bioinformatic analysis of the number of epitopes in various viral proteins and propose an optimization framework to explain these numbers. We show, using a genomic analysis and a theoretical optimization framework, that a critical factor affecting the number of presented epitopes is the expression stage in the viral life cycle of the gene coding for the protein. The early expression of epitopes can lead to the destruction of the host cell before budding can take place. We show that a lower number of epitopes is expected in early proteins even if late proteins have a much higher copy number.

Catalyst-induced growth with limited catalyst lifespan and competition.

Spatially extended catalyst-induced growth processes are studied. This type of processes exists in all domains of biology, ranging from ecology (nutrients and growth), through immunology (antigens and lymphocytes) to molecular biology (signaling molecules initiating signaling cascades). The extinction-proliferation transition is considered for a system containing discrete catalysts (A) that induces the proliferation of a discrete reactant (B). The realization of this model on an infinite capacity d-dimensional discrete lattice for immortal catalysts has been previously considered (the AB model). It was shown that the adaptation of the reactants to the diffusive noise induced by stochastic fluctuations of catalyst density yields proliferation even if the average environmental conditions lead to extinction. This model is extended here to include more realistic situations, like finite lifespan of the catalysts and finite carrying capacity of the reactants. By using a combination of Monte Carlo simulation, percolation-theory-based estimations and an analytic perturbative analysis, the asymptotic behavior of these systems is studied. In both cases studied, it turns out that the overall survival of the reactant population at the long run is based on the size and shape of a typical single colony, related to the localized proliferation around spatio-temporal catalyst density fluctuations. If the density of these colonies (based on the lifetime of the spatial fluctuation and the carrying capacity of the medium) is large enough, i.e. above the percolation threshold, the reactant population survives even in (on average) hostile environment. This model provides a new insight on the population dynamics in chemical, biological and ecological systems.