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Biomedical subjects

R M May

Publications and source records attributed to R M May.

At least 37 records · Page 2Linked to original sources
PubMed1996

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

Acquired Immunodeficiency Syndrome↗
PubMed1996

Spatial heterogeneity in epidemic models.

Spatial heterogeneity is believed to play an important role in the persistence and dynamics of epidemics of childhood diseases because asynchrony between populations within different regions allows global persistence, even if the disease dies out locally. A simple multi-patch (metapopulation) model for spatial heterogeneity in epidemics is analysed and we examine conditions under which patches become synchronized. We show that the patches in non-seasonal deterministic models often oscillate in phase for all but the weakest between patch coupling. Synchronization is also seen for stochastic models, although slightly stronger coupling is needed to overcome the random effects. We demonstrate that the inclusion of seasonal forcing in deterministic models can lead to the maintenance of phase differences between patches. Complex dynamic behaviour is observed in the seasonally forced spatial model, along with the coexistence of many different behaviours. Compared to the non-spatial model, chaotic solutions are observed for weaker seasonal forcing; these solutions have a more realistic minimum number of infectives.

Child↗
PubMed1996

The maintenance of strain structure in populations of recombining infectious agents.

Using mathematical models that combine population genetic and epidemiological processes, we resolve the paradox that many important pathogens appear to persist as discrete strains despite the constant exchange of genetic material. We show that dominant polymorphic determinants (that is, those that elicit the most effective immune responses) will be organized into nonoverlapping combinations as a result of selection by the host immune system, thereby defining a set of discrete independently transmitted strains. By analysing 222 isolates of Neisseria meningitidis, we show that two highly polymorphic epitopes of the outer membrane protein PorA exist in nonoverlapping combinations as predicted by this general framework. The model indicates that dominant polymorphic determinants will be in linkage disequilibrium, despite frequent genetic exchange, even though they may be encoded by several unlinked genes. This suggests that the detection of nonrandom associations between epitope regions can be employed as a novel strategem for identifying dominant polymorphic antigens.

Genes, Dominant↗
PubMed1996

The population biology of the interaction between HIV-1 and HIV-2: coexistence or competitive exclusion?

BACKGROUND: The emergence and rapid world-wide spread of HIV provides an unusual opportunity for the study of the evolution and maintenance of virulence in a major human pathogen. OBJECTIVE: To analyse the available biological and epidemiological data on the pathogenicity, transmissibility and antigenic similarity of HIV-1 and HIV-2, and use simple mathematical models of competition between the two viral types within a defined host community. RESULTS AND CONCLUSIONS: Analysis revealed a positive association between pathogenicity and reproductive success. A mathematical model of the concomitant transmission of the two viruses suggests that HIV-1 will competitively displace HIV-2 in the longer term in areas where both viruses are being transmitted within the same sexually active population.

Female↗
PubMed1995

Coinfection and the evolution of parasite virulence.

Analyses of the selection pressures acting on parasite virulence are made more complicated when individual hosts can simultaneously harbour many different strains or genotypes of a parasite. Here we explore the evolutionary dynamics of host-parasite associations in which individual hosts can be coinfected with many different parasite strains. (We take coinfection to mean that each strain transmits at a rate unaffected by the presence of others in the same host.) This study thus represents the opposite extreme to our earlier work on superinfection in which there is a dominance hierarchy such that only the most virulent strain present in a host is transmitted. For highly diverse populations of parasite strains, we find that such coinfection leads to selection for strains whose virulence-levels lie in a relatively narrow band close to the maximum consistent with the parasite's basic preproductive ratio, R0, exceeding unity.

Animals↗
PubMed1995

Immune responses against multiple epitopes.

The current understanding of antigenic escape dynamics is based on models with single epitopes. The usual idea is that a mutation which enables a pathogen (virus, bacteria, etc) to escape from a given immune response confers a selective advantage. The "escape mutant" may then increase in abundance until it induces a new specific response against itself. In this paper a new picture is developed, based on mathematical models of immune responses against several epitopes; the simplest such models can have very complicated dynamics, with some surprising features. The emergence of an escape mutant can shift the immunodominant response to another epitope. Even in the absence of mutations, antigenic oscillation is found, with distinct peaks of different virus variants and fluctuations in the size and specificity of the immune responses. The model also provides a general theory for immunodominance in the presence of antigenic variation. Immunodominance is determined by the immunogenicity and by the antigenic diversity of the competing epitopes. Antigenic oscillations and fluctuations in the cytotoxic T-lymphocyte response have been observed in infections with the human immunodeficiency virus (HIV). Shifting the immune responses to weaker epitopes can represent a mechanism for disease progression based on evolutionary dynamics and antigenic diversity of the virus.

Antigenic Variation↗
PubMed1995

The population dynamics of vertically and horizontally transmitted parasites.

We analyse a model of the transmission dynamics of a parasite transmitted both vertically and horizontally. The basic reproductive ratio (R0) of the parasite is shown to be a sum of horizontal and vertical components. We derive expressions for the equilibrium prevalence of infection for a mixture of horizontal and vertical transmission; prevalence can reach 100% if transmission is sufficiently high. At the endemic equilibrium, if prevalence is high, most transmission will in general be vertical, but horizontal transmission rates must be high to reach and stably maintain such an equilibrium. Surprisingly, for such parasites the highest equilibrium rates of vertical transmission are observed when horizontal transmission is very effective. We discuss the implications for assessing the importance of horizontal v. vertical transmission from field data, and we suggest some implications for the evolution of virulence.

Animals↗
PubMed1995

Antigenic oscillations and shifting immunodominance in HIV-1 infections.

A typical protein antigen contains several epitopes that can be recognized by cytotoxic T lymphocytes (CTL), but in a characteristic antiviral immune response in vivo, CTL recognize only a small number of these potential epitopes, sometimes only one, this phenomenon is known as immunodominance. Antigenic variation within CTL epitopes has been demonstrated for the human immunodeficiency virus HIV-1 (ref. 11) and other viruses and such 'antigenic escape' may be responsible for viral persistence. Here we develop a new mathematical model that deals with the interaction between CTL and multiple epitopes of a genetically variable pathogen, and show that the nonlinear competition among CTL responses against different epitopes can explain immunodominance. This model suggests that an antigenically homogeneous pathogen population tends to induce a dominant response against a single epitope, whereas a heterogeneous pathogen population can stimulate complicated fluctuating responses against multiple epitopes. Antigenic variation in the immunodominant epitope can shift responses to weaker epitopes and thereby reduce immunological control of the pathogen population. These ideas are consistent with detailed longitudinal studies of CTL responses in HIV-1 infected patients. For vaccine design, the model suggests that the major response should be directed against conserved epitopes even if they are subdominant.

Amino Acid Sequence↗
PubMed1995

The arithmetics of mutual help.

Computer experiments show how cooperation rather than exploitation can dominate in the Darwinian struggle for survival.

Animals↗
PubMed1994

Superinfection, metapopulation dynamics, and the evolution of diversity.

Using both analytic and numerical methods, we elucidate the dynamical properties of a class of metapopulation models in which many different species/strains contend for persistence, with local extinction of subpopulations being balanced by colonization of other patches. The species/strains have a strict competitive hierarchy with a given species/strain "taking over" any patch occupied by a lower-ranking species/strain; competitively inferior species/strains compensate by having higher colonization rates and/or lower patch death rates. New species/strains keep appearing, so that we can follow the evolution of the system. Such models may be metaphors for multispecies metapopulations, or for the evolution of virulence (where the patches are hosts, who are infected with various strains of a pathogen, and then die or recover at strain-dependent rates). Our emphasis is on a set of questions relating to the evolution of diversity. How many species/strains are present after a long time, t? Asymptotically, this number continues to increase very slowly, as ln t. What are the relative abundances of the species/strains? Under a broad range of assumptions about the mutations which produce new species/strains, the rank-abundance distribution is roughly geometric (as is commonly observed in early succession and other "ecologically one-dimensional" situations); some of our analysis here is based in part on an interesting but unproved mathematical conjecture about a new kind of probabilistic/combinatorial problem. If the number of patches/hosts is permanently reduced--by habitat destruction or vaccination--what happens? Characteristically, there is an initial sharp loss of species/strains (with selective removal of the competitive dominants), with subsequent slow recovery as new mutants continue to partition the now-diminished "niche space" (but the pristine levels of virulence are not regained).

Animals↗
PubMed1994

The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses.

According to conventional wisdom, parasites and pathogens should evolve reduced virulence to their hosts, because more virulent parasites and pathogens are more likely to drive their hosts, and themselves, to extinction. But this view has been criticized for its reliance on group selection. According to an alternative perspective, selection will favor whatever level of virulence maximizes the rate of increase of the parasite or pathogen. This optimum virulence depends on the functional relationship between a parasite or pathogen's transmissibility and its effect on host mortality, with selection often favoring an intermediate degree of virulence. The thesis of this paper is that models in which intermediate levels of virulence are favored lead quite naturally to the further conclusion that parasites and pathogens should-up to a point-become less virulent over time, once the feedbacks between ecological and evolutionary processes are incorporated into the analysis. As a consequence of successive adaptations by the parasite or pathogen, the density of susceptible hosts is reduced, thereby altering the balance between selective forces so as to favor reduced virulence. However, the evolutionarily stable strategy that is achieved is bounded away from complete avirulence. We conclude that models in which intermediate virulence is favored do not necessarily contradict the conventional wisdom in the long run; in fact, these models provide a simple mechanistic explanation for the evolution of reduced virulence.

Animals↗
PubMed1994

Conceptual aspects of the quantification of the extent of biological diversity.

This paper begins by asking to what extent numbers of species are an adequate measure of biological diversity, either locally or globally; both for evolutionary understanding and for practical applications, biodiversity may often be better quantified at lower or higher levels, from genes to ecosystems. The subsequent discussion, however, focuses on species, and discusses questions that arise in estimating how many species there have ever been, how many there currently are in various taxonomic groups, and how we may quantify the differing degrees of 'independent evolutionary history' or 'taxonomic distinctiveness' in different species or groups. I conclude with opinions about how the practical task of identifying and recording species diversity might be better managed.

Animals↗
PubMed1994

The reconstructed evolutionary process.

Phylogenies reconstructed from contemporary taxa do not contain information about lineages that have gone extinct. We derive probability models for such phylogenies, allowing real data to be compared with specified null models of evolution, and lineage birth and death rates to be estimated.

Animals↗
PubMed1994

Spatial games and the maintenance of cooperation.

The Prisoner's Dilemma (PD) is a widely employed metaphor for problems associated with the evolution of cooperative behavior. We have recently proposed an alternative approach to the PD, by exploring "spatial games" in which players--who are either pure cooperators, C, or pure defectors, D--interact with neighbors in some spatial array; in each generation, players add up the scores from all encounters, and in the next generation a given cell is retained by its previous owner or taken over by a neighbor, depending on who has the largest score. Over a wide range of the relevant parameters, we find that C and D persist together indefinitely (without any of the complex strategies that remember past encounters, and anticipate future ones, which characterize essentially all previous work on the iterated PD). Our earlier work, however, dealt with symmetric spatial lattices in two dimensions, deterministic winning and discrete time. We show here that the essential results remain valid in more realistic situations where the spatial distributions of cells are random in two or three dimensions, and where winning is partly probabilistic (rather than being determined by the largest local total). The essential results also remain valid (pace Huberman and Glance [Huberman, B. A. & Glance, N. S. (1993) Proc. Natl. Acad. Sci. USA 90, 7716-7718]) when interactions occur in continuous rather than discrete time.

Cooperative Behavior↗