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Fits of mathematic models to the decline in HIV-1 RNA after antiretroviral therapies have yielded estimates for the life span of productively infected cells of 1 to 2 days. In a previous report, we described the mathematic properties of an extended model that accounts for imperfect viral suppression and the eclipse phase of the viral life cycle (the intracellular delay between initial infection and release of progeny virions). In this article, we fit this extended model to detailed data on the decline of plasma HIV-1 RNA after treatment with the protease inhibitor ritonavir. Because the therapy in this study was most likely not completely suppressive, we allowed the drug efficacy parameter to vary from 70% to 100%. Estimates for the clearance rate of free virus, c, increased with the addition of the intracellular delay (as reported previously) but were not appreciably affected by changes in the drug efficacy parameter. By contrast, the estimated death rate of virus-producing cells, delta, increased from an average of 0.49 day-1 to 0.90 day-1 (an increase of 84%) because the drug efficacy parameter was reduced from 100% to 70%. Neglecting the intracellular delay, the comparable increase in delta was only about 55%. The inferred increases in delta doubled when the model was extended to account for possible increases in target cell densities after treatment initiation. This work suggests that estimates for delta may be greater than previously reported and that the half-life of a cell in vivo that is producing virus, on average, may be 1 day.

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A latent pool of HIV-1 is established early in memory CD4+ T lymphocytes and persists during antiretroviral therapy. Also, viral replication may continue in subjects despite undetectable viremia. However, it remains unclear whether this residual replication results in any significant sequence evolution. We were therefore interested in studying the viral evolution and HIV-1 DNA dynamics in subjects with primary infection receiving or not receiving early potent antiretroviral therapy. In 16 subjects, HIV-1 DNA load was monitored from 1 to 23 days, up to 1253 days, after onset of symptoms. Extensive sequential cloning and sequence analysis of the V3 region was performed in four subjects. In the treated subjects a continuous decline in the proviral load was found, corresponding to a half-life of about 6 months. As expected in newly infected individuals the founder virus populations showed high intrasubject sequence similarity. Also, a limited increase in the viral divergence was detected during the first 6 months in three treated subjects. Thereafter, no significant sequence changes were found despite analysis of a large number of clones. Our data thus suggest that early and successful therapy in compliant subjects with primary HIV-1 infection results in a highly restricted viral evolution and a decline in the proviral load close to the decay rate of human memory T lymphocytes.

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Replication-competent HIV-1 can be isolated from infected patients despite prolonged plasma virus suppression by anti-retroviral treatment. Recent studies have identified resting, memory CD4+ T lymphocytes as a long-lived latent reservoir of HIV-1 (refs. 4,5). Cross-sectional analyses indicate that the reservoir is rather small, between 103 and 107 cells per patient. In individuals whose plasma viremia levels are well suppressed by anti-retroviral therapy, peripheral blood mononuclear cells containing replication-competent HIV-1 were found to decay with a mean half-life of approximately 6 months, close to the decay characteristics of memory lymphocytes in humans and monkeys. In contrast, little decay was found in a less-selective patient population. We undertook this study to address this apparent discrepancy. Using a quantitative micro-culture assay, we demonstrate here that the latent reservoir decays with a mean half-life of 6.3 months in patients who consistently maintain plasma HIV-1 RNA levels of fewer than 50 copies/ml. Slower decay rates occur in individuals who experience intermittent episodes of plasma viremia. Our findings indicate that the persistence of the latent reservoir of HIV-1 despite prolonged treatment is due not only to its slow intrinsic decay characteristics but also to the inability of current drug regimens to completely block HIV-1 replication.

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BACKGROUND: In chronic HIV-1 infection, dynamic equilibrium exists between viral production and clearance. The half-life of free virions can be estimated by inhibiting virion production with antiretroviral agents and modelling the resulting decline in plasma HIV-1 RNA. To define HIV-1 and hepatitis C virus (HCV) dynamics, we used plasma apheresis to increase virion clearance temporarily while leaving virion production unaffected. METHODS: Plasma virus loads were measured frequently before, during, and after apheresis in four HIV-1-infected patients, two of whom were also co-infected with HCV. Rates of virion clearance were derived by non-linear least-square fitting of plasma virus load to a model of viral dynamics. FINDINGS: Virion clearance rate constants were 0.0063/min (9.1/day) to 0.025/min (36.0/day; half-life 28-110 min) for HIV-1 and 0.0038/min (5.5/day) to 0.0069/min (9.9/day; half-life 100-182 min) for HCV. These values provided estimates of daily particle production of 9.3 log10-10.2 log10 particles for HIV-1 and 11.6 log10-13.0 log10 particles for HCV. INTERPRETATION: Our findings confirm that HIV-1 and HCV are produced and cleared extremely rapidly. New estimates for HIV-1 clearance are up to ten times higher than previous ones, whereas HCV clearance is similar to previous estimates.

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We present and analyze a model for the interaction of human immunodeficiency virus type 1 (HIV-1) with target cells that includes a time delay between initial infection and the formation of productively infected cells. Assuming that the variation among cells with respect to this 'intracellular' delay can be approximated by a gamma distribution, a high flexible distribution that can mimic a variety of biologically plausible delays, we provide analytical solutions for the expected decline in plasma virus concentration after the initiation of antiretroviral therapy with one or more protease inhibitors. We then use the model to investigate whether the parameters that characterize viral dynamics can be identified from biological data. Using non-linear least-squares regression to fit the model to simulated data in which the delays conform to a gamma distribution, we show that good estimates for free viral clearance rates, infected cell death rates, and parameters characterizing the gamma distribution can be obtained. For simulated data sets in which the delays were generated using other biologically plausible distributions, reasonably good estimates for viral clearance rates, infected cell death rates, and mean delay times can be obtained using the gamma-delay model. For simulated data sets that include added simulated noise, viral clearance rate estimates are not as reliable. If the mean intracellular delay is known, however, we show that reasonable estimates for the viral clearance rate can be obtained by taking the harmonic mean of viral clearance rate estimates from a group of patients. These results demonstrate that it is possible to incorporate distributed intracellular delays into existing models for HIV dynamics and to use these refined models to estimate the half-life of free virus from data on the decline in HIV-1 RNA following treatment.

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The phenomenon of antibiotic resistance is of practical importance and theoretical interest. As a foundation for further studies by simulation, experiment, and observation, we here develop a mathematical model for the dynamics of resistance among the bacteria resident in a population of hosts. The model incorporates the effects of natural selection within untreated hosts, colonization by bacteria from the environment, and the rapid increase of resistance in hosts who receive antibiotics. We derive explicit formulas for the distribution of resistance among hosts and for the rise or fall of resistance when the frequency of treatment is changed.

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The observation that the density of CD8+ T-lymphocytes increases as the density of CD4+ T-cells declines in adult HIV-1/AIDS patients, together with evidence that the total density of T-cells is regulated (homeostasis) has led to the suggestion that competition between lineages, and classes of T-cells contributes to the pathology of HIV. We use a mathematical model of the interactions between populations of T-cells, HIV, and other parasites to explore the effects of T-cell homeostasis and competition on the progression to AIDS. We demonstrate that as a consequence of parasite-mediated T-cell replication, of competition within and between different T-cell clones, and random processes (T-cell drift), some CD4+ lineages will be represented by relatively few cells, dearths, and some lineages may be lost, leaving holes in the immune repertoire. By killing CD4+ T-lymphocytes, HIV accelerates the rate at which these dearths and holes accumulate and leads to an early breakdown of the immune control of HIV and other parasites, AIDS. When this model allows for intense, but not complete, competition between the CD4+ and CD8+ T-cell populations, it can account for most of the features of an HIV-1 infection in adults, including the gradual decline in CD4+ T-cell densities and concomitant increase in HIV density, as well as the variability in time from infection to AIDS and the decline in the time from infection to AIDS in older patients.

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While the molecular mechanisms underlying lysogeny and induction in bacteriophage have been intensely studied, relatively little has been done to relate these findings to their presumed selective functions. To explore the ecological basis for these traits, I have used a resource-based model for competition between bacteriophage with different probabilities of lysogeny and different spontaneous induction rates. In any given habitat the fitness of a phage will depend on the inputs of sensitive cells and nutrient resources. In equable environments (modeled here using chemostats with constant inputs of nutrients and sensitive cells), bacteriophage with low probabilities of lysogeny and low induction rates can always invade when rare and will generally be good competitors. In variable environments (chemostats with seasonal inputs), bacteriophage with higher probabilities of lysogeny and higher induction rates are favored. In both equable and variable environments, the ability of a phage to invade when rare will depend on the properties of the resident phage, and it is possible for phages with divergent parameter values to coexist. The modeling suggests that bacteriophage that have evolved moderately low induction and lysogeny rates will be able to "hedge their bets" against environmental change without sacrificing the ability to compete well in a constant environment. Implications of this theory for understanding the molecular basis of gene regulation in temperate bacteriophage and other viruses are discussed.

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According to neo-Darwinian theory, random mutation produces genetic differences among organisms whereas natural selection tends to increase the frequency of advantageous alleles. However, several recent papers claim that certain mutations in bacteria and yeast occur at much higher rates specifically when the mutant phenotypes are advantageous. Various molecular models have been proposed that might explain these directed mutations, but the models have not been confirmed. Critics contend that studies purporting to demonstrate directed mutation lack certain controls and fail to account adequately for population dynamics. Further experiments that address these criticisms do not support the existence of directed mutations.

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The directed mutation hypothesis suggests that some mutations occur more often when selectively advantageous than when neutral or disadvantageous, challenging the principle that the selective value of a mutation does not affect the rate of its occurrence. Mutations in the bgl operon of Escherichia coli have been reported to be a case of directed mutation. E. coli K12 strains chi342LD cannot grow on salicin but derivatives with two mutations in the bgl operon, an excision of IS150 (formally called IS103) from bglF and a point mutation or insertion in bflR, grow rapidly on this sugar. When chi342LD is grown on a medium containing salicin, bglF excision mutants accumulate to a frequency of greater than 1%, even though these mutants are reportedly unable to grown on salicin, and Sal+ double mutants subsequently attain a high frequency. Comparable accumulations of excision mutants and Sal+ double mutants are not observed in the absence of salicin. As salicin is not mutagenic, it has been suggested that excision mutations in bglF might serve only to create the potential for a secondary selectively advantageous mutation. We show here, however, that these double mutants can be accounted for by spontaneous mutation to intermediate genotypes in non-growing populations, coupled with slow growth of some of these intermediates on salicin, which enables their populations to reach a size where secondary mutations allowing rapid growth on salicin become common.

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According to the directed mutation hypothesis, certain mutations in bacteria occur more frequently in environments in which the resulting phenotype is selectively favoured than in non-selective environments. This hypothesis therefore challenges the fundamental tenet that mutations occur spontaneously, irrespective of effects on the organism's fitness. One purported case of directed mutation is the excision of a Mu sequence from Escherichia coli strain MCS2 in minimal lactose-arabinose medium. Here, we show that this case can be more simply explained by an accelerated rate of excision mutation in response to non-specific physiological stresses of starvation and by slight growth of MCS2 on minimal lactose-arabinose medium.

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