Scaling law characterizing the dynamics of the transition of HIV-1 to error catastrophe

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations-within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

Physical 'strength' of the multi-protein chain connecting immune cells: Does the weakest link limit antibody affinity maturation?: The weakest link in the multi-protein chain facilitating antigen acquisition by B cells in germinal centres limits antibody affinity maturation

The affinities of antibodies (Abs) for their target antigens (Ags) gradually increase in vivo following an infection or vaccination, but reach saturation at values well below those realisable in vitro. This 'affinity ceiling' could in many cases restrict our ability to fight infections and compromise vaccines. What determines the affinity ceiling has been an unresolved question for decades. Here, we argue that it arises from the strength of the chain of protein complexes that is pulled by B cells during the process of Ag acquisition. The affinity ceiling is determined by the strength of the weakest link in the chain. We identify the weakest link and show that the resulting affinity ceiling can explain the Ab affinities realized in vivo, providing a conceptual understanding of Ab affinity maturation. We explore plausible evolutionary underpinnings of the affinity ceiling, examine supporting evidence and alternative hypotheses and discuss implications for vaccination strategies.

Stochastic Modeling and Simulation of Viral Evolution

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different fitness distributions representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called lethal mutagenesis and mutational meltdown. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.