Modelling the evolution and spread of HIV immune escape mutants

During infection with human immunodeficiency virus (HIV), immune pressure from cytotoxic T-lymphocytes (CTLs) selects for viral mutants that confer escape from CTL recognition. These escape variants can be transmitted between individuals where, depending upon their cost to viral fitness and the CTL responses made by the recipient, they may revert. The rates of within-host evolution and their concordant impact upon the rate of spread of escape mutants at the population level are uncertain. Here we present a mathematical model of within-host evolution of escape mutants, transmission of these variants between hosts and subsequent reversion in new hosts. The model is an extension of the well-known SI model of disease transmission and includes three further parameters that describe host immunogenetic heterogeneity and rates of within host viral evolution. We use the model to explain why some escape mutants appear to have stable prevalence whilst others are spreading through the population. Further, we use it to compare diverse datasets on CTL escape, highlighting where different sources agree or disagree on within-host evolutionary rates. The several dozen CTL epitopes we survey from HIV-1 gag, RT and nef reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. For many epitopes in HIV, occasional rapid within-host evolution is not reflected in fast evolution at the population level.     

Recent mumps outbreaks in vaccinated populations: no evidence of immune escape

Recently, numerous large-scale mumps outbreaks have occurred in vaccinated populations. Clinical isolates sequenced from these outbreaks have invariably been of genotypes distinct from those of vaccine viruses, raising concern that certain mumps virus strains may escape vaccine-induced immunity. To investigate this concern, sera obtained from children 6 weeks after receipt of measles, mumps, and rubella (MMR) vaccine were tested for the ability to neutralize a carefully selected group of genetically diverse mumps virus strains. Although the geometric mean neutralizing antibody titer of the sera was lower against some virus strains than others, all viruses were readily neutralized, arguing against immune escape.     

Stochastic models for the spread of HIV in a mobile heterosexual population

An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these models, using a convenient rescaling technique, and analyze their stability conditions and equilibrium behavior. We illustrate the dynamic behavior of the models and their approximations via a range of numerical experiments.     

Dynamics of immune escape during HIV/SIV infection

Several studies have shown that cytotoxic T lymphocytes (CTLs) play an important role in controlling HIV/SIV infection. Notably, the observation of escape mutants suggests a selective pressure induced by the CTL response. However, it remains difficult to assess the definite role of the cellular immune response. We devise a computational model of HIV/SIV infection having a broad cellular immune response targeting different viral epitopes. The CTL clones are stimulated by viral antigen and interact with the virus population through cytotoxic killing of infected cells. Consequently, the virus population reacts through the acquisition of CTL escape mutations. Our model provides realistic virus dynamics and describes several experimental observations. We postulate that inter-clonal competition and immunodominance may be critical factors determining the sequential emergence of escapes. We show that even though the total killing induced by the CTL response can be high, escape rates against a single CTL clone are often slow and difficult to estimate from infrequent sequence measurements. Finally, our simulations show that a higher degree of immunodominance leads to more frequent escape with a reduced control of viral replication but a substantially impaired replicative capacity of the virus. This result suggests two strategies for vaccine design: Vaccines inducing a broad CTL response should decrease the viral load, whereas vaccines stimulating a narrow but dominant CTL response are likely to induce escape but may dramatically reduce the replicative capacity of the virus.     

Apoptosis as an HIV strategy to escape immune attack

Viruses have evolved numerous mechanisms to evade the host immune system and one of the strategies developed by HIV is to activate apoptotic programmes that destroy immune effectors. Not only does the HIV genome encode pro-apoptotic proteins, which kill both infected and uninfected lymphocytes through either members of the tumour-necrosis factor family or the mitochondrial pathway, but it also creates a state of chronic immune activation that is responsible for the exacerbation of physiological mechanisms of clonal deletion. This review discusses the molecular mechanisms by which HIV manipulates the apoptotic machinery to its advantage, assesses the functional consequences of this process and evaluates how new therapeutics might counteract this strategy.     

Vaccine-induced T cells control reversion of AIDS virus immune escape mutants

Many current-generation human immunodeficiency virus (HIV) vaccines induce specific T cells to control acute viremia, but their utility following infection with escape mutant virus is unclear. We studied reversion to wild type of an escape mutant simian-HIV in major histocompatibility complex-matched vaccinated pigtail macaques. High levels of vaccine-induced CD8+ T cells strongly correlated with maintenance of escape mutant virus during acute infection. Interestingly, in animals with lower CD8+ T-cell levels, transient reversion to wild-type virus resulted in better postacute control of viremia. Killing of wild-type virus facilitated by transient reversion outweighs the benefit of a larger CD8+ T-cell response that only maintains the less fit escape mutant virus. These findings have important implications for the further development of T-cell-based HIV vaccines where exposure to escape mutant viruses is common.     

Dynamics of escape mutants

We use multi-type Galton-Watson branching processes to model the evolution of populations that, due to a small reproductive ratio of the individuals, are doomed to extinction. Yet, mutations occurring during the reproduction process, may lead to the appearance of new types of individuals that are able to escape extinction. We provide examples of such populations in medical, biological and environmental contexts and give results on (i) the probability of escape/extinction, (ii) the distribution of the waiting time to produce the first individual whose lineage does not get extinct and (iii) the distribution of the time it takes for the number of mutants to reach a high level. Special attention is dedicated to the case where the probability of mutation is very small and approximations for (i)-(iii) are derived.     

Rates of HIV immune escape and reversion: implications for vaccination

HIV-1 mutates extensively in vivo to escape immune control by CD8+ T cells (CTLs). The CTL escape mutant virus might also revert back to wild-type upon transmission to new hosts if significant fitness costs are incurred by the mutation. Immune escape and reversion can be extremely fast if they occur very early after infection, whereas they are much slower when they begin later during infection. Immune escape presents a significant barrier to vaccination, because escape of vaccine-mediated immune responses could neutralise any benefits of vaccination. Here, we consider the dynamics of immune escape and reversion in vivo in natural infection, and suggest how understanding of this can be used to predict optimal vaccine targets and design vaccination strategies that maximise immune control. We predict that inducing synchronous, broad CTL by vaccination should limit the likelihood of viral escape from immune control.     

The effects of population structure on the spread of the HIV infection

A model for the spread of human immunodeficiency virus (HIV) in a population of male homosexuals is presented. The population is divided into five groups on the basis of degree of sexual activity. Within each group, the individuals are classified as 1) susceptible; 2) infective; or 3) removed because of a lack of sexual activity associated with advanced acquired immunodeficiency disease (AIDS). The infective individuals are further subdivided into four stages of infection. Analyses of the model address two questions with regard to the spread of HIV: (1) What is the effect of level of sexual activity on an individual's risk for infection, and (2) What is the effect that assumptions about mixing between groups have on both individual risk and transmission throughout a population? Results from analyses using a number of different parameter estimates show that increased levels of sexual activity increase the likelihood that an individual will become infected. In addition, the initial spread of the disease is markedly affected by variation in the amount of contact among individuals from different subpopulations. The steady-state incidence of the disease is not markedly affected by variation in the contact patterns, but the size of the steady-state population and therefore the proportion of infected individuals in the population does vary significantly with changes in the degree of mixing among subpopulations. These results show clearly the sensitivity of model outcomes to variation in the patterns of contact among individuals and the need for better data on such interactions to aid in understanding and predicting the spread of HIV.     

The effect of structural behavior change on the spread of HIV in a one-sex population.

Within a preferred mixing type of model for the spread of HIV in a one-sex population, the effects of structural behavior change, that is movements of individuals from one activity class to another, with accompanying changes of contact pattern are investigated. It is concluded that such behavior change makes it more difficult for an epidemic to arise if the contact pattern is of the restricted type, whereas the effect is indeterminate in the proportional mixing case. Some of the problems in analyzing sexual activity data from a population within which this behavior change mechanism is at work are also commented upon.     

Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS

A theoretical model is proposed for a community which has the structure of two classes (direct and indirect) of commercial sex workers (CSW), and two classes of sexually active male customers with different levels of sexual activity. The direct CSW’s work in brothels while the indirect CSW’s are based in commercial establishments such as bars, cafes, and massage parlours where sex can be bought on request and conducted elsewhere. Behaviour change and the resulting change of activity class occurs between the two classes of CSW’s and two classes of males under the setting of the proliferation of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome epidemic and the subsequent intervention programmes. In recently years, this phenomenon has been observed in several countries in Asia. Given the lower levels of condom use and higher HIV prevalence of the indirect CSW’s, ascertaining the impact of this change in the structure of the sex industry on the spread of HIV is the main focus of this paper. The complete analysis of the disease-free model is given. For the full model, local analysis will be performed for the case of preferred mixing without activity class change, as well as the case with activity class change and restricted mixing. The basic reproduction number for the spread of epidemic will be derived for each case. Results of biological significance include: (i) the change of behaviour by the CSW’s has a more direct effect on the spread of HIV than that of the male customers; (ii) the basic reproduction number is obtained by considering all possible infection cycles of the heterosexual transmission of HIV which indicates the importance of understanding the sexual networking in heterosexual transmission of HIV; (iii) the social dynamics of the sex industry is not just a simple ’supply and demand’ mechanism driven by the demand of the customers, hence highlighting the need for further understanding of the changing structure of the sex industry. The main points of this work will be illustrated with numerical examples using the HIV data of Thailand.     

Modelling HIV immune response and validation with clinical data

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.     

SARS-CoV-2 prolonged infection during advanced HIV disease evolves extensive immune escape

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Modelling the dynamics of senescence spread

Cellular senescence is a cell surveillance mechanism that arrests the cell cycle in damaged cells. The senescent phenotype can spread from cell to cell through paracrine and juxtacrine signalling, but the dynamics of this process are not well understood. Although senescent cells are important in ageing, wound healing and cancer, it is unclear how the spread of senescence is contained in senescent lesions. In the absence of the immune system, senescence could theoretically spread infinitely from one cell to another, but this contradicts experimental evidence. To investigate this issue, we developed both a minimal mathematical model and a stochastic simulation of senescence spread. Our results suggest that differences in the number of signalling molecules secreted between subtypes of senescent cells can limit the spread of senescence. We found that dynamic, time-dependent paracrine signalling prevents the uncontrolled spread of senescence, and we demonstrate how model parameters can be determined using Bayesian inference in a proposed experiment.     

The penetration of HIV into the population of Moscow homosexuals and its spread

The article deals with the epidemiological investigation of cases of HIV infection among the population of homosexuals. 119 representatives of this population were checked in their sexual contacts; of these, 13 persons proved to be infected with HIV. HIV infection was found to penetrate into the homosexual population of the USSR from the countries of Western Europe and the USA by sexual route. In 1988 the intensive spread of this infection began.     

HIV: a new role for Nef in the spread of HIV.

The HIV Nef protein downregulates the cell-surface expression of the HIV receptor glycoprotein CD4, but the significance of this event has remained obscure. Recent data suggest that Nef reduces cell-surface CD4 to promote the efficient spread of the virus.