Is HIV short-sighted? Insights from a multistrain nested model

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus

Coordinate actions of BMPs, Wnts, Shh and noggin mediate patterning of the dorsal somite

Shortly after their formation, somites of vertebrate embryos differentiate along the dorsoventral axis into sclerotome, myotome and dermomyotome. The dermomyotome is then patterned along its mediolateral axis into medial, central and lateral compartments, which contain progenitors of epaxial muscle, dermis and hypaxial muscle, respectively. Here, we used Wnt-11 as a molecular marker for the medial compartment of dermomyotome (the ‘medial lip’) to demonstrate that BMP in the dorsal neural tube indirectly induces formation of the medial lip by up-regulating Wnt-1 and Wnt-3a (but not Wnt-4) expression in the neural tube. Noggin in the dorsal somite may inhibit the direct action of BMP on this tissue. Wnt-11 induction is antagonized by Sonic Hedgehog, secreted by the notochord and the floor plate. Together, our results show that the coordinated actions of the dorsal neural tube (via BMP and Wnts), the ventral neural tube/notochord (via Shh) and the somite itself (via noggin) mediates patterning of the dorsal compartment of the somite

Neural tube-ectoderm interactions are required for trigeminal placode formation

Cranial sensory ganglia in vertebrates develop from the ectodermal placodes, the neural crest, or both. Although much is known about the neural crest contribution to cranial ganglia, relatively little is known about how placode cells form, invaginate and migrate to their targets. Here, we identify Pax-3 as a molecular marker for placode cells that contribute to the ophthalmic branch of the trigeminal ganglion and use it, in conjunction with DiI labeling of the surface ectoderm, to analyze some of the mechanisms underlying placode development. Pax-3 expression in the ophthalmic placode is observed as early as the 4-somite stage in a narrow band of ectoderm contiguous to the midbrain neural folds. Its expression broadens to a patch of ectoderm adjacent to the midbrain and the rostral hindbrain at the 8- to 10-somite stage. Invagination of the first Pax-3-positive cells begins at the 13-somite stage. Placodal invagination continues through the 35-somite stage, by which time condensation of the trigeminal ganglion has begun. To challenge the normal tissue interactions leading to placode formation, we ablated the cranial neural crest cells or implanted barriers between the neural tube and the ectoderm. Our results demonstrate that, although the presence of neural crest cells is not mandatory for Pax-3 expression in the forming placode, a diffusible signal from the neuroectoderm is required for induction and/or maintenance of the ophthalmic placode

Competence, specification and induction of Pax-3 in the trigeminal placode

Placodes are discrete regions of thickened ectoderm that contribute extensively to the peripheral nervous system in the vertebrate head. The paired-domain transcription factor Pax-3 is an early molecular marker for the avian ophthalmic trigeminal (opV) placode, which forms sensory neurons in the ophthalmic lobe of the trigeminal ganglion. Here, we use collagen gel cultures and heterotopic quail-chick grafts to examine the competence, specification and induction of Pax-3 in the opV placode. At the 3-somite stage, the whole head ectoderm rostral to the first somite is competent to express Pax-3 when grafted to the opV placode region, though competence is rapidly lost thereafter in otic-level ectoderm. Pax-3 specification in presumptive opV placode ectoderm occurs by the 8-somite stage, concomitant with robust Pax-3 expression. From the 8-somite stage onwards, significant numbers of cells are committed to express Pax-3. The entire length of the neural tube has the ability to induce Pax-3 expression in competent head ectoderm and the inductive interaction is direct. We propose a detailed model for Pax-3 induction in the opV placode

The Effectiveness of Contact Tracing in Emerging Epidemics

BACKGROUND: Contact tracing plays an important role in the control of emerging infectious diseases, but little is known yet about its effectiveness. Here we deduce from a generic mathematical model how effectiveness of tracing relates to various aspects of time, such as the course of individual infectivity, the (variability in) time between infection and symptom-based detection, and delays in the tracing process. In addition, the possibility of iteratively tracing of yet asymptomatic infecteds is considered. With these insights we explain why contact tracing was and will be effective for control of smallpox and SARS, only partially effective for foot-and-mouth disease, and likely not effective for influenza. METHODS AND FINDINGS: We investigate contact tracing in a model of an emerging epidemic that is flexible enough to use for most infections. We consider isolation of symptomatic infecteds as the basic scenario, and express effectiveness as the proportion of contacts that need to be traced for a reproduction ratio smaller than 1. We obtain general results for special cases, which are interpreted with respect to the likely success of tracing for influenza, smallpox, SARS, and foot-and-mouth disease epidemics. CONCLUSIONS: We conclude that (1) there is no general predictive formula for the proportion to be traced as there is for the proportion to be vaccinated; (2) variability in time to detection is favourable for effective tracing; (3) tracing effectiveness need not be sensitive to the duration of the latent period and tracing delays; (4) iterative tracing primarily improves effectiveness when single-step tracing is on the brink of being effective

A Strong Case for Viral Genetic Factors in HIV Virulence

HIV infections show great variation in the rate of progression to disease, and the role of viral genetic factors in this variation had remained poorly characterized until recently. Now a series of four studies [1–4] published within a year has filled this important gap and has demonstrated a robust effect of the viral genotype on HIV virulence

Antigen-driven T-cell turnover.

A mathematical model is developed to characterize the distribution of cell turnover rates within a population of T lymphocytes. Previous models of T-cell dynamics have assumed a constant uniform turnover rate; here we consider turnover in a cell pool subject to clonal proliferation in response to diverse and repeated antigenic stimulation. A basic framework is defined for T-cell proliferation in response to antigen, which explicitly describes the cell cycle during antigenic stimulation and subsequent cell division. The distribution of T-cell turnover rates is then calculated based on the history of random exposures to antigens. This distribution is found to be bimodal, with peaks in cell frequencies in the slow turnover (quiescent) and rapid turnover (activated) states. This distribution can be used to calculate the overall turnover for the cell pool, as well as individual contributions to turnover from quiescent and activated cells. The impact of heterogeneous turnover on the dynamics of CD4(+) T-cell infection by HIV is explored. We show that our model can resolve the paradox of high levels of viral replication occurring while only a small fraction of cells are infected

Semi-classical Quantization in N=4 Supersymmetric Yang-Mills Theory and Duality

At a generic point in the moduli space of vacua of an N=4 supersymmetric gauge theory with arbitrary gauge group the Higgs force does not cancel the magneto-static force between magnetic monopoles of distinct charge. As a consequence the moduli space of magnetically charged solutions is related in a simple way to those of the SU(2) theory. This leads to a rather simple test of S-duality. On certain subspaces of the moduli space of vacua the forces between distinct monopoles cancel and the test of S-duality becomes more complicated.Comment: 11 pages, plain tex with macro included, one Postscript figure, uses psfig.te

On the weak coupling spectrum of N=2 supersymmetric SU(n) gauge theory

The weak coupling spectrum of BPS saturated states of pure $N=2$ supersymmetric SU$(n)$ gauge theory is investigated. The method uses known results on the dyon spectrum of the analogous theory with $N=4$ supersymmetry, along with the action on these states of the semi-classical monodromy transformations. For dyons whose magnetic charge is not a simple root of the Lie algebra, it is found that the weak coupling region is divided into a series of domains, for which the dyons have different electric charge, separated by walls on which the dyons decay. The proposed spectrum is shown to be consistent with the exact solution of the theory at strong coupling in the sense that the states at weak coupling can account for the singularities at strong coupling.Comment: 19 pages, plain tex with macro included, 6 figures included using psfig.te