Clustering of activated CD8 T cells around Malaria-infected hepatocytes is rapid and is driven by antigen-specific cells

Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages which in mice 48 h later escape into blood and cause clinical malaria. Vaccine-induced activated or memory CD8 T cells are capable of locating and eliminating all liver stages in 48 h, thus preventing the blood-stage disease. However, the rules of how CD8 T cells are able to locate all liver stages within a relatively short time period remains poorly understood. We recently reported formation of clusters consisting of variable numbers of activated CD8 T cells around Plasmodium yoelii (Py)-infected hepatocytes. Using a combination of experimental data and mathematical models we now provide additional insights into mechanisms of formation of these clusters. First, we show that a model in which cluster formation is driven exclusively by T-cell-extrinsic factors, such as variability in “attractiveness” of different liver stages, cannot explain distribution of cluster sizes in different experimental conditions. In contrast, the model in which cluster formation is driven by the positive feedback loop (i.e., larger clusters attract more CD8 T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific CD8 T cells) are attracted to the clusters, we found no evidence that non-specific CD8 T cells play a role in cluster formation. Third and finally, mathematical modeling suggested that formation of clusters occurs rapidly, within few hours after adoptive transfer of CD8 T cells, thus illustrating high efficiency of CD8 T cells in locating their targets in complex peripheral organs, such as the liver. Taken together, our analysis provides novel insights into and attempts to discriminate between alternative mechanisms driving the formation of clusters of antigen-specific CD8 T cells in the liver

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

Stochastic Models of Lymphocyte Proliferation and Death

Quantitative understanding of the kinetics of lymphocyte proliferation and death upon activation with an antigen is crucial for elucidating factors determining the magnitude, duration and efficiency of the immune response. Recent advances in quantitative experimental techniques, in particular intracellular labeling and multi-channel flow cytometry, allow one to measure the population structure of proliferating and dying lymphocytes for several generations with high precision. These new experimental techniques require novel quantitative methods of analysis. We review several recent mathematical approaches used to describe and analyze cell proliferation data. Using a rigorous mathematical framework, we show that two commonly used models that are based on the theories of age-structured cell populations and of branching processes, are mathematically identical. We provide several simple analytical solutions for a model in which the distribution of inter-division times follows a gamma distribution and show that this model can fit both simulated and experimental data. We also show that the estimates of some critical kinetic parameters, such as the average inter-division time, obtained by fitting models to data may depend on the assumed distribution of inter-division times, highlighting the challenges in quantitative understanding of cell kinetics

Killing of Targets by CD8+ T Cells in the Mouse Spleen Follows the Law of Mass Action

It has been difficult to correlate the quality of CD8 T cell responses with protection against viral infections. To investigate the relationship between efficacy and magnitude of T cell responses, we quantify the rate at which individual CD8 effector and memory T cells kill target cells in the mouse spleen. Using mathematical modeling, we analyze recent data on the loss of target cells pulsed with three different peptides from the mouse lymphocytic choriomeningitis virus (LCMV) in mouse spleens with varying numbers of epitope-specific CD8 T cells. We find that the killing of targets follows the law of mass-action, i.e., the death rate of individual target cells remains proportional to the frequency (or the total number) of specific CD8 T cells in the spleen despite the fact that effector cell densities and effector to target ratios vary about a 1000-fold. The killing rate of LCMV-specific CD8 T cells is largely independent of T cell specificity and differentiation stage. Our results thus allow one to calculate the critical T cell concentration at which growth of a virus with a given replication rate can be prevented from the start of infection by memory CD8 T cell response

Emergence of Variability in Isogenic Escherichia coli Populations Infected by a Filamentous Virus

The spread of epidemics not only depends on the average number of parasites produced per host, but also on the existence of highly infectious individuals. It is widely accepted that infectiousness depends on genetic and environmental determinants. However, even in clonal populations of host and viruses growing in homogeneous conditions, high variability can exist. Here we show that Escherichia coli cells commonly display high differentials in viral burst size, and address the kinetics of emergence of such variability with the non-lytic filamentous virus M13. By single-cell imaging of a virally-encoded fluorescent reporter, we monitor the viral charge distribution in infected bacterial populations at different time following infection. A mathematical model assuming autocatalytic virus replication and inheritance of bacterial growth rates quantitatively reproduces the experimental distributions, demonstrating that deterministic amplification of small host inhomogeneities is a mechanism sufficient to explain large and highly skewed distributions. This mechanism of amplification is general and may occur whenever a parasite has an initial phase of exponential growth within its host. Moreover, it naturally reproduces the shift towards higher virulence when the host is experimenting poor conditions, as observed commonly in host-parasite systems

Antigenic Diversity, Transmission Mechanisms, and the Evolution of Pathogens

Pathogens have evolved diverse strategies to maximize their transmission fitness. Here we investigate these strategies for directly transmitted pathogens using mathematical models of disease pathogenesis and transmission, modeling fitness as a function of within- and between-host pathogen dynamics. The within-host model includes realistic constraints on pathogen replication via resource depletion and cross-immunity between pathogen strains. We find three distinct types of infection emerge as maxima in the fitness landscape, each characterized by particular within-host dynamics, host population contact network structure, and transmission mode. These three infection types are associated with distinct non-overlapping ranges of levels of antigenic diversity, and well-defined patterns of within-host dynamics and between-host transmissibility. Fitness, quantified by the basic reproduction number, also falls within distinct ranges for each infection type. Every type is optimal for certain contact structures over a range of contact rates. Sexually transmitted infections and childhood diseases are identified as exemplar types for low and high contact rates, respectively. This work generates a plausible mechanistic hypothesis for the observed tradeoff between pathogen transmissibility and antigenic diversity, and shows how different classes of pathogens arise evolutionarily as fitness optima for different contact network structures and host contact rates

Delayed Differentiation Makes Many Models Compatible with Data for CD8+ T Cell Differentiation

Upon antigen stimulation, naïve CD8+ T cells differentiate into short-lived effectors and longer-lived memory T cells. The kinetics of expansion of antigen-specific CD8+ T cells is highly reproducible at the population level, but the fate of individual naïve cells is stochastic, as individual naïve CD8+ T cells produce different numbers of effector and memory cells. Using mathematical models to analyse experimental data on tracing the fate of individual naïve T cells, it was previously shown that a linear model where naïve CD8+ T cells first differentiate into memory precursors that subsequently differentiate into effector cells describes the data best. However, this ‘memory first’ linear model assumed that the proliferation and differentiation events were distributed exponentially, whereas several studies indicate that differentiation of CD8+ T cell subsets need not follow an exponential distribution. Here we investigate the effect of delayed differentiation by adding intermediate compartments and use similar ordinary differential equations and Gillespie simulations to evaluate alternate models of CD8+ T cell differentiation. Models where a substantial fraction of the naïve CD8+ T cells directly differentiate into effector cells, without going through a memory phase, exhibit population dynamics that are very similar to the original ‘memory first’ linear model. Because alternate models with delayed differentiation perform better than those without a delay, we conclude that non-exponential forms of cellular differentiation need to be considered when comparing models. Hence the exact pathway for the differentiation of naïve CD8+ T cells into effector and memory T cells remains an open question

Why Don't CD8+ T Cells Reduce the Lifespan of SIV-Infected Cells In Vivo?

In January 2010 two groups independently published the observation that the depletion of CD8+ cells in SIV-infected macaques had no detectable impact on the lifespan of productively infected cells. This unexpected observation led the authors to suggest that CD8+ T cells control SIV viraemia via non-lytic mechanisms. However, a number of alternative plausible explanations, compatible with a lytic model of CD8+ T cell control, were proposed. This left the field with no consensus on how to interpret these experiments and no clear indication whether CD8+ T cells operated primarily via a lytic or a non-lytic mechanism. The aim of this work was to investigate why CD8+ T cells do not appear to reduce the lifespan of SIV-infected cells in vivo