Revisiting Estimates of CTL Killing Rates In Vivo

Recent experimental advances have allowed the estimation of the in vivo rates of killing of infected target cells by cytotoxic T lymphocytes (CTL). We present several refinements to a method applied previously to quantify killing of targets in the spleen using a dynamical model. We reanalyse data previously used to estimate killing rates of CTL specific for two epitopes of lymphocytic choriomeningitis virus (LCMV) in mice and show that, contrary to previous estimates the “killing rate” of effector CTL is approximately twice that of memory CTL. Further, our method allows the fits to be visualized, and reveals one potentially interesting discrepancy between fits and data. We discuss extensions to the basic CTL killing model to explain this discrepancy and propose experimental tests to distinguish between them

Spatial heterogeneity and peptide availability determine CTL killing efficiency in vivo

The rate at which a cytotoxic T lymphocyte (CTL) can survey for infected cells is a key ingredient of models of vertebrate immune responses to intracellular pathogens. Estimates have been obtained using in vivo cytotoxicity assays in which peptide-pulsed splenocytes are killed by CTL in the spleens of immunised mice. However the spleen is a heterogeneous environment and splenocytes comprise multiple cell types. Are some cell types intrinsically more susceptible to lysis than others? Quantitatively, what impacts are made by the spatial distribution of targets and effectors, and the level of peptide-MHC on the target cell surface? To address these questions we revisited the splenocyte killing assay, using CTL specific for an epitope of influenza virus. We found that at the cell population level T cell targets were killed more rapidly than B cells. Using modeling, quantitative imaging and in vitro killing assays we conclude that this difference in vivo likely reflects different migratory patterns of targets within the spleen and a heterogeneous distribution of CTL, with no detectable difference in the intrinsic susceptibilities of the two populations to lysis. Modeling of the stages involved in the detection and killing of peptide-pulsed targets in vitro revealed that peptide dose influenced the ability of CTL to form conjugates with targets but had no detectable effect on the probability that conjugation resulted in lysis, and that T cell targets took longer to lyse than B cells. We also infer that incomplete killing in vivo of cells pulsed with low doses of peptide may be due to a combination of heterogeneity in peptide uptake and the dissociation, but not internalisation, of peptide-MHC complexes. Our analyses demonstrate how population-averaged parameters in models of immune responses can be dissected to account for both spatial and cellular heterogeneity

Virus Replication Strategies and the Critical CTL Numbers Required for the Control of Infection

Vaccines that elicit protective cytotoxic T lymphocytes (CTL) may improve on or augment those designed primarily to elicit antibody responses. However, we have little basis for estimating the numbers of CTL required for sterilising immunity at an infection site. To address this we begin with a theoretical estimate obtained from measurements of CTL surveillance rates and the growth rate of a virus. We show how this estimate needs to be modified to account for (i) the dynamics of CTL-infected cell conjugates, and (ii) features of the virus lifecycle in infected cells. We show that provided the inoculum size of the virus is low, the dynamics of CTL-infected cell conjugates can be ignored, but knowledge of virus life-histories is required for estimating critical thresholds of CTL densities. We show that accounting for virus replication strategies increases estimates of the minimum density of CTL required for immunity over those obtained with the canonical model of virus dynamics, and demonstrate that this modeling framework allows us to predict and compare the ability of CTL to control viruses with different life history strategies. As an example we predict that lytic viruses are more difficult to control than budding viruses when net reproduction rates and infected cell lifetimes are controlled for. Further, we use data from acute SIV infection in rhesus macaques to calculate a lower bound on the density of CTL that a vaccine must generate to control infection at the entry site. We propose that critical CTL densities can be better estimated either using quantitative models incorporating virus life histories or with in vivo assays using virus-infected cells rather than peptide-pulsed targets

Estimation of heterogeneity in malaria transmission by stochastic modelling of apparent deviations from mass action kinetics

<p>Abstract</p> <p>Background</p> <p>Quantifying heterogeneity in malaria transmission is a prerequisite for accurate predictive mathematical models, but the variance in field measurements of exposure overestimates true micro-heterogeneity because it is inflated to an uncertain extent by sampling variation. Descriptions of field data also suggest that the rate of <it>Plasmodium falciparum </it>infection is not proportional to the intensity of challenge by infectious vectors. This appears to violate the principle of mass action that is implied by malaria biology. Micro-heterogeneity may be the reason for this anomaly. It is proposed that the level of micro-heterogeneity can be estimated from statistical models that estimate the amount of variation in transmission most compatible with a mass-action model for the relationship of infection to exposure.</p> <p>Methods</p> <p>The relationship between the entomological inoculation rate (EIR) for falciparum malaria and infection risk was reanalysed using published data for cohorts of children in Saradidi (western Kenya). Infection risk was treated as binomially distributed, and measurement-error (Poisson and negative binomial) models were considered for the EIR. Models were fitted using Bayesian Markov chain Monte Carlo algorithms and model fit compared for models that assume either mass-action kinetics, facilitation, competition or saturation of the infection process with increasing EIR.</p> <p>Results</p> <p>The proportion of inocula that resulted in infection in Saradidi was inversely related to the measured intensity of challenge. Models of facilitation showed, therefore, a poor fit to the data. When sampling error in the EIR was neglected, either competition or saturation needed to be incorporated in the model in order to give a good fit. Negative binomial models for the error in exposure could achieve a comparable fit while incorporating the more parsimonious and biologically plausible mass action assumption. Models that assume negative binomial micro-heterogeneity predict lower incidence of infection at a given average exposure than do those assuming exposure to be uniform. The negative binomial model moreover provides an estimate of the variance of the within-cohort distribution of the EIR and hence of within cohort heterogeneity in exposure.</p> <p>Conclusion</p> <p>Apparent deviations from mass action kinetics in parasite transmission can arise from spatial and temporal heterogeneity in the inoculation rate, and from imprecision in its measurement. For parasites like <it>P. falciparum</it>, where there is no plausible biological rationale for deviations from mass action, this provides a strategy for estimating true levels of heterogeneity, since if mass-action is assumed, the within-population variance in exposure becomes identifiable in cohort studies relating infection to transmission intensity. Statistical analyses relating infection to exposure thus provide a valid general approach for estimating heterogeneity in transmission but only when they incorporate mass action kinetics and shrinkage estimates of exposure. Such analyses make it possible to include realistic levels of heterogeneity in dynamic models that predict the impact of control measures on transmission intensity.</p

Similar Impact of CD8+ T Cell Responses on Early Virus Dynamics during SIV Infections of Rhesus Macaques and Sooty Mangabeys

Despite comparable levels of virus replication, simian immunodeficiency viruses (SIV) infection is non-pathogenic in natural hosts, such as sooty mangabeys (SM), whereas it is pathogenic in non-natural hosts, such as rhesus macaques (RM). Comparative studies of pathogenic and non-pathogenic SIV infection can thus shed light on the role of specific factors in SIV pathogenesis. Here, we determine the impact of target-cell limitation, CD8+ T cells, and Natural Killer (NK) cells on virus replication in the early SIV infection. To this end, we fit previously published data of experimental SIV infections in SMs and RMs with mathematical models incorporating these factors and assess to what extent the inclusion of individual factors determines the quality of the fits. We find that for both rhesus macaques and sooty mangabeys, target-cell limitation alone cannot explain the control of early virus replication, whereas including CD8+ T cells into the models significantly improves the fits. By contrast, including NK cells does only significantly improve the fits in SMs. These findings have important implications for our understanding of SIV pathogenesis as they suggest that the level of early CD8+ T cell responses is not the key difference between pathogenic and non-pathogenic SIV infection

Population-Wide Emergence of Antiviral Resistance during Pandemic Influenza

Background: The emergence of neuraminidase inhibitor resistance has raised concerns about the prudent use of antiviral drugs in response to the next influenza pandemic. While resistant strains may initially emerge with compromised viral fitness, mutations that largely compensate for this impaired fitness can arise. Understanding the extent to which these mutations affect the spread of disease in the population can have important implications for developing pandemic plans. Methodology/Principal Findings: By employing a deterministic mathematical model, we investigate possible scenarios for the emergence of population-wide resistance in the presence of antiviral drugs. The results show that if the treatment level (the fraction of clinical infections which receives treatment) is maintained constant during the course of the outbreak, there is an optimal level that minimizes the final size of the pandemic. However, aggressive treatment above the optimal level can substantially promote the spread of highly transmissible resistant mutants and increase the total number of infections. We demonstrate that resistant outbreaks can occur more readily when the spread of disease is further delayed by applying other curtailing measures, even if treatment levels are kept modest. However, by changing treatment levels over the course of the pandemic, it is possible to reduce the final size of the pandemic below the minimum achieved at the optimal constant level. This reduction can occur with low treatment levels during the early stages of the pandemic, followed by a sharp increase in drug-use before the virus becomes widely spread. Conclusions/Significance: Our findings suggest that an adaptive antiviral strategy with conservative initial treatment levels, followed by a timely increase in the scale of drug-use, can minimize the final size of a pandemic while preventing large outbreaks of resistant infections

The Efficiency of the Human CD8+ T Cell Response: How Should We Quantify It, What Determines It, and Does It Matter?

Multidisciplinary techniques, in particular the combination of theoretical and experimental immunology, can address questions about human immunity that cannot be answered by other means. From the turnover of virus-infected cells in vivo, to rates of thymic production and HLA class I epitope prediction, theoretical techniques provide a unique insight to supplement experimental approaches. Here we present our opinion, with examples, of some of the ways in which mathematics has contributed in our field of interest: the efficiency of the human CD8+ T cell response to persistent viruses

Simian-Human Immunodeficiency Infection – Is the Course Set in the Acute Phase?

Identifying early predictors of infection outcome is important for the clinical management of HIV infection, and both viral load and CD4+ T cell level have been found to be useful predictors of subsequent disease progression. Very high viral load or extensively depleted CD4+ T cells in the acute phase often result in failure of immune control, and a fast progression to AIDS. It is usually assumed that extensive loss of CD4+ T cells in the acute phase of HIV infection prevents the establishment of robust T cell help required for virus control in the chronic phase. We tested this hypothesis using viral load and CD4+ T cell number of SHIV-infected rhesus macaques. In acute infection, the lowest level of CD4+ T cells was a good predictor of later survival; animals having less than 3.3% of baseline CD4+ T cells progressed to severe disease, while animals with more than 3.3% of baseline CD4+ T cells experienced CD4+ T cell recovery. However, it is unclear if the disease progression was caused by early depletion, or was simply a result of a higher susceptibility of an animal to infection. We derived a simple relationship between the expected number of CD4+ T cells in the acute and chronic phases for a constant level of host susceptibility or resistance. We found that in most cases, the depletion of CD4+ T cells in chronic infection was consistent with the prediction from the acute CD4+ T cell loss. However, the animals with less than 3.3% of baseline CD4 T cells in the acute phase were approximately 20% more depleted late in the infection than expected based on constant level of virus control. This suggests that severe acute CD4 depletion indeed impairs the immune response

Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model

<p>Abstract</p> <p>Background</p> <p>Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection <it>in vitro</it>.</p> <p>Results</p> <p>We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef<it>-</it>negative (target) and Nef<it>-</it>positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID₅₀, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced.</p> <p>Conclusions</p> <p>Our method, combining <it>in vitro </it>experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the <it>in vitro </it>determination of the effect and efficacy of antiviral compounds.</p