Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We generalize these models of quasispecies evolution to include horizontal gene transfer. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.Comment: 5 pages, 1 figure, to appear in Physics Review Letter

A Novel Sequence-Based Antigenic Distance Measure for H1N1, with Application to Vaccine Effectiveness and the Selection of Vaccine Strains

H1N1 influenza causes substantial seasonal illness and was the subtype of the 2009 influenza pandemic. Precise measures of antigenic distance between the vaccine and circulating virus strains help researchers design influenza vaccines with high vaccine effectiveness. We here introduce a sequence-based method to predict vaccine effectiveness in humans. Historical epidemiological data show that this sequence-based method is as predictive of vaccine effectiveness as hemagglutination inhibition (HI) assay data from ferret animal model studies. Interestingly, the expected vaccine effectiveness is greater against H1N1 than H3N2, suggesting a stronger immune response against H1N1 than H3N2. The evolution rate of hemagglutinin in H1N1 is also shown to be greater than that in H3N2, presumably due to greater immune selection pressure.Comment: 26 pages, 7 figures, 2 tables, supplemen

Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.Comment: RevTex forma

Reaction, Levy Flights, and Quenched Disorder

We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With a model of the disorder that obeys detailed balance, however, the rate of reaction initially increases and then decreases as a function of the disorder strength. The physical behavior obtained with this second model is in accord with that for reactive turbulent flow, indicating that Levy flight statistics can model aspects of turbulent fluid transport.Comment: 6 pages, 5 pages. Phys. Rev. E. 65 (2002) 011109--1-

Reactive Turbulent Flow in Low-Dimensional, Disordered Media

We analyze the reactions $A+A \to \emptyset$ and $A + B \to \emptyset$ occurring in a model of turbulent flow in two dimensions. We find the reactant concentrations at long times, using a field-theoretic renormalization group analysis. We find a variety of interesting behavior, including, in the presence of potential disorder, decay rates faster than that for well-mixed reactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.

The epitope regions of H1-subtype influenza A, with application to vaccine efficacy

The recent emergence of H1N1 (swine flu) illustrates the ability of the influenza virus to create antigens new to the human immune system, even within a given hemagglutinin and neuraminidase subtype. This new H1N1 strain is sufficiently distinct, for example, from the A/Brisbane/59/2007 (H1N1)-like virus strain of influenza in the 2008/09 Northern hemisphere vaccine that protection is not expected to be substantial. The human immune system responds primarily to the five epitope regions of the hemagglutinin protein. By determining the fraction of amino acids that differ between a vaccine strain and a viral challenge strain in the dominant epitope regions, a measure of antigenic distance that correlates with epidemiological studies of H3 influenza A vaccine efficacy in humans with R2 = 0.81 is derived. This measure of antigenic distance is called pepitope. The relation between vaccine efficacy and pepitope is given by E = 0.47 – 2.47 × pepitope. We here identify the epitope regions of H1 hemagglutinin, so that vaccine efficacy may be reliably estimated for H1N1 influenza A

A Multi-Scale Model for Correlation in B Cell VDJ Usage of Zebrafish

The zebrafish (\emph{Danio rerio}) is one of the model animals for study of immunology because the dynamics in the adaptive immune system of zebrafish are similar to that in higher animals. In this work, we built a multi-scale model to simulate the dynamics of B cells in the primary and secondary immune responses of zebrafish. We use this model to explain the reported correlation between VDJ usage of B cell repertoires in individual zebrafish. We use a delay ordinary differential equation (ODE) system to model the immune responses in the 6-month lifespan of a zebrafish. This mean field theory gives the number of high affinity B cells as a function of time during an infection. The sequences of those B cells are then taken from a distribution calculated by a "microscopic" random energy model. This generalized $NK$ model shows that mature B cells specific to one antigen largely possess a single VDJ recombination. The model allows first-principles calculation of the probability, $p$, that two zebrafish responding to the same antigen will select the same VDJ recombination. This probability $p$ increases with the B cell population size and the B cell selection intensity. The probability $p$ decreases with the B cell hypermutation rate. The multi-scale model predicts correlations in the immune system of the zebrafish that are highly similar to that from experiment.Comment: 29 pages, 10 figures, 1 tabl

Self diffusion in a system of interacting Langevin particles

The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature $\beta$ and the particle density $\rho$. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small $\beta$ and $\rho\beta$ constant. The one-loop result can also be re-summed using a semi-phenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signalled by the vanishing of the diffusion constant -- possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two-dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.Comment: 12 pages, 8 figures .ep