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Biomedical subjects

M A Nowak

Publications and source records attributed to M A Nowak.

At least 127 records · Page 7Linked to original sources
PubMed1994

Defective escape mutants of HIV.

The virological literature presents two broad types of defective virus mutants that can alter the outcome of viral infection. In some infections, defective interfering particles reduce the replication of wild-type virus and lead to an attenuated or persistent infection. In other cases, very specific and highly pathogenic defective mutants lead to virulent disease in the presence of a much less pathogenic but replication-competent helper virus. Here, we outline the theoretical possibility that defective mutants of HIV, which escape from some of the immune responses directed at the wild-type virus, can have a positive effect on total virus growth in HIV infections. The high error rate of HIV may generate many mutants that have some altered epitope (escape mutants), but at the cost of greatly reduced or completely impaired reproductive abilities. If these mutants retain some ability to impair immune cell function, then the production of such "defective escape" mutants may enhance overall virus reproduction. This will be illustrated by a mathematical model.

Defective Viruses↗
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

Intra-host versus inter-host selection: viral strategies of immune function impairment.

We investigate the evolution of viral strategies to counteract immunological attack. These strategies can be divided into two classes: those that impair the immune response inside or at the surface of a virus-infected cell and those that impair the immune response outside an infected cell. The former strategies confer a "selfish" individual selective advantage for intra-host competition among viruses. The latter strategies confer an "unselfish" selective advantage to the virus population as a group. A mutant, defective in the gene coding for the extracellular immune function-impairment strategy, may be protected from immune attack because the wild-type virus in the same host successfully impairs the host's immune function. Such "unselfish" defense strategies are neutral with respect to intra-host competition. We present simple models of viral intra-host and combined inter- and intra-host evolution. We show that selfish strategies can evolve by intra-host evolution. Unselfish strategies may evolve if inter-host selection pressures outweigh intra-host selection, suggesting that such strategies can only evolve in viruses with low mutation rates.

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↗
PubMed1994

Superinfection and the evolution of parasite virulence.

Earlier ideas that parasites evolve toward becoming harmless to their hosts have, in recent years, given way to more analytic studies, focused on the 'basic reproductive rate', R0, of individual parasites. In general, the biology of the parasite life cycle will lead to constraining relations between virulence (parasite-associated host death or reduction in fertility) and transmissibility: the maximum R0 may then be attained by virulence being high, or low, or at some intermediate level, depending on the details of the constraining relations. Such studies have not generally included superinfection (where an already-infected host is infected by another parasite). Here we propose a general, but simple, model of superinfection, which is amenable to analytical treatment. In such models selection does not simply act to maximize R0; superinfection leads to selection for higher levels of virulence, highly polymorphic parasite populations and very complicated dynamics. We calculate the equilibrium distribution of parasite strains and the maximum level of virulence that can be maintained by superinfection. We also note the equivalence between our 'superinfection model' and recent approaches to the study of the meta-population dynamics of multi-species interactions.

Animals↗
PubMed1994

Adaptive evolution of highly mutable loci in pathogenic bacteria.

Bacteria have specific loci that are highly mutable. We argue that the coexistence within bacterial genomes of such 'contingency' genes with high mutation rates, and 'housekeeping' genes with low mutation rates, is the result of adaptive evolution, and facilitates the efficient exploration of phenotypic solutions to unpredictable aspects of the host environment while minimizing deleterious effects on fitness.

Animals↗
PubMed1994

A cellular model to explain the pathogenesis of infection by the hepatitis B virus.

The natural history of infection by the hepatitis B virus (HBV) depends on many factors, including the age and immunological status of the patient, and can range from acute transient infection to subclinical chronic hepatitis. Persistent infection often leads to the development of primary hepatocellular carcinoma. We consider a cellular model of HBV infection based on the hypothesis that the liver contains two populations of cells with contrasting responses to the virus. Our findings show that the model can be used to account for the wide variety of clinical manifestations of infection and can explain the observed age dependence of the main different outcomes of the disease.

Carcinoma, Hepatocellular↗
PubMed1992

Coexistence and competition in HIV infections.

In this paper we extend our explanation of a model for the dynamics of the interaction between HIV and the cells of the immune system (Nowak et al., 1990). We show that the Simpson index of viral diversity is a Lyapunov function for a simplified version of this model. We also present a more general mathematical characterization of the nature of the diversity threshold exhibited by the model, including for the first time heterogeneity in parameters like virus replication rate, cytopathicity and antigenicity. The more general diversity threshold condition includes the different contributions of strains with higher replication rates and cytopathicities or strains that are only weakly recognized by the immune system. This leads to some new insights and a more detailed understanding of why the viral diversity falls once the diversity threshold is exceeded.

HIV↗
PubMed1992

Analysis of a cellular model to account for the natural history of infection by the hepatitis B virus and its role in the development of primary hepatocellular carcinoma.

Infection with the hepatitis B virus (HBV) can have many different outcomes. Transient infection may result in acute hepatitis or may remain subclinical. Persistent infection may also be subclinical, or may involve chronic active hepatitis, and can finally lead to the development of primary hepatocellular carcinoma. A mathematical model is given to account for the many different outcomes of HBV pathogenesis. The model is based on the assumption that the liver contains two cell populations with differing abilities to support active HBV replication and/or viral integration into the genome. The model helps account for the relationship of the different clinical courses of HBV infection to the age when the disease is acquired, together with the state of the immune system of the patient.

Carcinoma, Hepatocellular↗
PubMed1992

The optimal number of major histocompatibility complex molecules in an individual.

A straightforward argument is presented to calculate the number of different major histocompatibility complex (MHC) molecules in an individual that maximizes the probability of mounting immune responses against a large number of foreign peptides. It is assumed that increasing the number of MHC molecules per individual, n, has three different effects: (i) it increases the number of foreign peptides that can be presented; (ii) it increases the number of different T-cell receptors (TCRs) positively selected in the thymus; but (iii) it reduces the number of TCRs by negative selection. The mathematical analysis shows that n = 1/f maximizes the number of different TCRs that pass through positive and negative selection and that n = 2/f maximizes the probability to mount immune responses against a large fraction of foreign peptides. Here f is the fraction of TCRs deleted by one MHC molecule. Both results depend on approximations that are discussed in the paper. The model presented has implications for our understanding of the evolutionary forces acting on the MHC.

Animals↗
PubMed1992

Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model.

We develop a mathematical model for the initial growth of a tumour after a mutation in which either an oncogene is expressed or an anti-oncogene (i.e. tumour suppressor gene) is lost. Our model incorporates mitotic control by several biochemicals, with quite different regulatory characteristics, and we consider mutations affecting the cellular response to these control mechanisms. Our mathematical representation of these mutations reflects the current understanding of the roles of oncogenes and anti-oncogenes in controlling cell proliferation. Numerical solutions of our model, for biologically relevant parameter values, show that the different types of mutations have quite different effects. Mutations affecting the cell response to chemical regulators, or resulting in autonomy from such regulators, cause an advancing wave of tumour cells and a receding wave of normal cells. By contrast, mutations affecting the production of a mitotic regulator cause a slow localized increase in the numbers of both normal and mutant cells. We extend our model to investigate the possible effects of an immune response to cancer by including a first order removal of mutant cells. When this removal rate exceeds a critical value, the immune system can suppress tumour growth; we derive an expression for this critical value as a function of the parameters characterizing the mutation. Our results suggest that the effectiveness of the immune response after an oncogenic mutation depends crucially on the way in which the mutation affects the biochemical control of cell division.

Animals↗
PubMed1992

Variability of HIV infections.

Genetic variation is the hallmark of infections with lentiviruses in general and the human immunodeficiency viruses (HIV-1, HIV-2) in particular. This article reviews both experimental evidence for the variability of the HIV genome during the course of an individual infection and mathematical models that outline the potential importance of antigenic variation as a major factor to drive disease progression. The essential idea is that the virus evades immune pressure by the continuous production of new mutants resistant to current immunological attack. This results in the accumulation of antigenic diversity during the asymptomatic period. The existence of an antigenic diversity threshold is derived from the asymmetric interaction between the virus quasispecies and the CD4 cell population: CD4 cells mount immune responses some of which are directed against specific HIV variants, but each virus strain can induce depletion of all CD4 cells and therefore impair immune responses regardless of their specificity. Therefore, increasing HIV diversity enables the virus population to escape from control by the immune system. In this context the observed genetic variability is responsible for the fact that the virus establishes a persistent infection without being cleared by the immune response and induces immunodeficiency disease after a long and variable incubation period. Mathematical biology has revealed a novel mechanism for viral pathogenesis.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Models of interactions between HIV and other pathogens.

We investigate possible interactions between HIV and other pathogens that would arise if HIV replication were enhanced by the activation of T helper cells specific to other pathogens. Using mathematical models of the population dynamics of T helper cells, HIV and other pathogens we address three facets of the interactions between HIV and other pathogens: enhanced HIV replication due to immune stimulation by other pathogens; modified immune control of other pathogens due to immunosuppression by HIV; and the vicious circle formed by positive feedback between these two effects. The models predict that there is a correlation between higher levels of activated TH cells and disease progression and that there is a threshold number of activated TH cells above which the HIV infected immune system is unable to control pre-established pathogens. This threshold marks the boundary between a suppressed but still functioning immune system and the vicious circle of CD4 cell depletion that marks the final stages of AIDS.

Acquired Immunodeficiency Syndrome↗
PubMed1992

Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV.

OBJECTIVE: To investigate competitive interactions between zidovudine-sensitive and resistant strains of HIV within the context of host-parasite population dynamic interactions between CD4+ cells and HIV. DESIGN: A mathematical model of the population dynamics of CD4+ cells, sensitive HIV and resistant HIV is developed. METHODS: The model is analysed numerically and analytically and model predictions are compared with previously published data on population dynamics of HIV and CD4+ cells in patients receiving zidovudine. A threshold result describing the critical dose of zidovudine above which resistant HIV will out-compete sensitive HIV is derived, as are expressions describing the critical effective doses for the eradication of sensitive and resistant strains. Numerical simulations of the dynamics of the shift from the pre-treatment, equilibrium to the treatment equilibrium are presented and an analytic expression approximating the time taken until virus growth restarts is derived. RESULTS: It is shown that competition between strains of virus is the important factor determining which type of virus will eventually start to grow during the course of zidovudine treatment, but host-parasite interactions are the important determinant of when viral resurgence occurs. CONCLUSIONS: Although resistant strains are observed after prolonged treatment with zidovudine, this model suggests that it is the growing supply of uninfected CD4+ cells which causes the eventual upsurge in viral burden.

CD4 Antigens↗
PubMed1991

A mathematical model of vaccination against HIV to prevent the development of AIDS.

Vaccination and post-exposure immunization against the human immunodeficiency viruses (HIV-1 and HIV-2) faces the problem of the extensive genetic and antigenic variability of these viruses. This raises the question of what fraction of all possible antigen strains of the virus must be recognized by the immune response to a vaccine to prevent development of acquired immunodeficiency disease (AIDS). The success of a vaccine can depend on the variability of the target epitopes. The different HIV variants must be suppressed faster than new escape mutants can be produced. In this paper the antigenic variation of HIV during an individual infection is described by a stochastic process. The central assumption is that antigenic drift is important for the virus to survive immunological attack and to establish a persistent infection that leads to the development of AIDS after a long incubation period. The mathematical analysis reveals that the fraction of antigenic variants recognized by the immune response, that is induced by a successful immunogen, must exceed 1-1/R, where R is the diversification rate of the virus population. This means that if each HIV strain can produce, on average, five new escape mutants, then more than 80% of the possible variants must be covered by the immunogen. A generic result of the model is that, no matter how immunogenic a vaccine is, it will fail if it does not enhance immune attack against a sufficiently large fraction of strains. Furthermore, it is shown that the timing of the application of post-exposure immunization is important.

AIDS Vaccines↗
PubMed1991

Antigenic diversity thresholds and the development of AIDS.

Longitudinal studies of patients infected with HIV-1 reveal a long and variable incubation period between infection and the development of AIDS. Data from a small number of infected patients show temporal changes in the number of genetically distinct strains of the virus throughout the incubation period, with a slow but steady rise in diversity during the progression to disease. A mathematical model of the dynamic interaction between viral diversity and the human immune system suggests the existence of an antigen diversity threshold, below which the immune system is able to regulate viral population growth but above which the virus population induces the collapse of the CD4+ lymphocyte population. The model suggests that antigenic diversity is the cause, not a consequence, of immunodeficiency disease. The model is compared with available data, and is used to assess how the timing of the application of chemotherapy or immunotherapy influences the rate of progress to disease.

Acquired Immunodeficiency Syndrome↗
PubMed1991

Another battle of the sexes: the consequences of sexual asymmetry in mating costs and predation risk in the guppy, Poecilia reticulata.

The risk of predation and cost or benefit of a mating attempt are rarely the same for both sexes. An excellent example is provided by the guppy. Poecilia reticulata, a species that has a promiscuous mating system in which female choice plays an important role. Male engage almost continuously in courtship behaviour but, as females are sexually receptive for short periods only, most male displays are ignored and sneaky mating attempts avoided. Experiments on guppies from wild Trinidad populations reveal that females appear to perceive themselves to be at a greater risk of predation and devote more time to antipredator behaviour, for example, schooling when threatened. Inspections of the predator are also mainly initiated and led by female guppies. Males exploit this behavioural switch by increasing their sneaky mating attempts. A game theoretical analysis is used to explore the sexual asymmetry in mating cost and predation risk. Together these approaches show that there is no intersexual cooperation during predator inspection behaviour in this species, and may explain the paradoxical increase in mating activity by male guppies under threat.

Animals↗