Killing of targets by effector CD8 T cells in the mouse spleen follows the law of mass action

In contrast with antibody-based vaccines, it has been difficult to measure the efficacy of T cell-based vaccines and to correlate the efficacy of CD8 T cell responses with protection again viral infections. In part, this difficulty is due to poor understanding of the in vivo efficacy of CD8 T cells produced by vaccination. Using a: recently developed experimental method of in vivo cytotoxicity we have investigated quantitative aspects of killing of peptide-pulsed targets by effector and memory CD8 T cells, specific to three epitopes of lymphocytic choriomeningitis virus (LCMV), in the mouse spleen. By analyzing data on killing of targets with varying number of epitope-specific effector and memory CD8 T cells, we find that killing of targets by effectors follows the law of mass-action, that is the death rate of peptide-pulsed targets is proportional to the frequency of CTLs in the spleen. In contrast, killing of targets by memory CD8 T cells does not follow the mass action law because the death rate of targets saturates at high frequencies of memory CD8 T cells. For both effector and memory cells, we also find little support for the killing term that includes the decrease of the death rate of targets with target cell density. Interestingly, our analysis suggests that at low CD8 T cell frequencies, memory CD8 T cells on the per capita basis are more efficient at killing peptide-pulsed targets than effectors, but at high frequencies, effectors are more efficient killers than memory T cells. Comparison of the estimated killing efficacy of effector T cells with the value that is predicted from theoretical physics and based on motility of T cells in lymphoid tissues, suggests that limiting step in the killing of peptide-pulsed targets is delivering the lethal hit and not finding the target. Our results thus form a basis for quantitative understanding of the process of killing of virus-infected cells by T cell responses in tissues and can be used to correlate the phenotype of vaccine-induced memory CD8 T cells with their killing efficacy in vivo

Estimating Residence Times of Lymphocytes in Ovine Lymph Nodes

The ability of lymphocytes to recirculate between blood and secondary lymphoid tissues such as lymph nodes (LNs) and spleen is well established. Sheep have been used as an experimental system to study lymphocyte recirculation for decades and multiple studies document accumulation and loss of intravenously (i.v.) transferred lymphocytes in efferent lymph of various ovine LNs. Yet, surprisingly little work has been done to accurately quantify the dynamics of lymphocyte exit from the LNs and to estimate the average residence times of lymphocytes in ovine LNs. In this work we developed a series of mathematical models based on fundamental principles of lymphocyte recirculation in the body under non-inflammatory (resting) conditions. Our analysis suggested that in sheep, recirculating lymphocytes spend on average 3 h in the spleen and 20 h in skin or gut-draining LNs with a distribution of residence times in LNs following a skewed gamma (lognormal-like) distribution. Our mathematical models also suggested an explanation for a puzzling observation of the long-term persistence of i.v. transferred lymphocytes in the efferent lymph of the prescapular LN (pLN); the model predicted that this is a natural consequence of long-term persistence of the transferred lymphocytes in circulation. We also found that lymphocytes isolated from the skin-draining pLN have a 2-fold increased entry rate into the pLN as opposed to the mesenteric (gut-draining) LN (mLN). Likewise, lymphocytes from mLN had a 3-fold increased entry rate into the mLN as opposed to entry rate into pLN. In contrast, these cannulation data could not be explained by preferential retention of cells in LNs of their origin. Taken together, our work illustrates the power of mathematical modeling in describing the kinetics of lymphocyte migration in sheep and provides quantitative estimates of lymphocyte residence times in ovine LNs

Mathematical Modeling Suggests Cooperation of Plant-Infecting Viruses

Viruses are major pathogens of agricultural crops. Viral infections often start after the virus enters the outer layer of a tissue, and many successful viruses, after local replication in the infected tissue, are able to spread systemically. Quantitative details of virus dynamics in plants, however, are poorly understood, in part, because of the lack of experimental methods which allow the accurate measurement of the degree of infection in individual plant tissues. Recently, a group of researchers followed the kinetics of infection of individual cells in leaves of Nicotiana tabacum plants using Tobacco etch virus (TEV) expressing either Venus or blue fluorescent protein (BFP). Assuming that viral spread occurs from lower to upper leaves, the authors fitted a simple mathematical model to the frequency of cellular infection by the two viral variants found using flow cytometry. While the original model could accurately describe the kinetics of viral spread locally and systemically, we found that many alternative versions of the model, for example, if viral spread starts at upper leaves and progresses to lower leaves or when virus dissemination is stopped due to an immune response, fit the data with reasonable quality, and yet with different parameter estimates. These results strongly suggest that experimental measurements of the virus infection in individual leaves may not be sufficient to identify the pathways of viral dissemination between different leaves and reasons for viral control. We propose experiments that may allow discrimination between the alternatives. By analyzing the kinetics of coinfection of individual cells by Venus and BFP strains of TEV we found a strong deviation from the random infection model, suggesting cooperation between the two strains when infecting plant cells. Importantly, we showed that many mathematical models on the kinetics of coinfection of cells with two strains could not adequately describe the data, and the best fit model needed to assume (i) different susceptibility of uninfected cells to infection by two viruses locally in the leaf vs. systemically from other leaves, and (ii) decrease in the infection rate depending on the fraction of uninfected cells which could be due to a systemic immune response. Our results thus demonstrate the difficulty in reaching definite conclusions from extensive and yet limited experimental data and provide evidence of potential cooperation between different viral variants infecting individual cells in plants

Estimating Costs and Benefits of CTL Escape Mutations in SIV/HIV Infection

Mutations that allow SIV/HIV to avoid the cytotoxic T lymphocyte (CTL) response are well documented. Recently, there have been a few attempts at estimating the costs of CTL escape mutations in terms of the reduction in viral fitness and the killing rate at which the CTL response specific to one viral epitope clears virus-infected cells. Using a mathematical model we show that estimation of both parameters depends critically on the underlying changes in the replication rate of the virus and the changes in the killing rate over time (which in previous studies were assumed to be constant). We provide a theoretical basis for estimation of these parameters using in vivo data. In particular, we show that 1) by assuming unlimited virus growth one can obtain a minimal estimate of the fitness cost of the escape mutation, and 2) by assuming no virus growth during the escape, one can obtain a minimal estimate of the average killing rate. We also discuss the conditions under which better estimates of the average killing rate can be obtained

Evaluating contribution of the cellular and humoral immune responses to the control of shedding of \u3cem\u3eMycobacterium avium\u3c/em\u3e spp. \u3cem\u3eparatuberculosis\u3c/em\u3e in cattle

Mycobacterium avium spp. paratuberculosis (MAP) causes a persistent infection and chronic inflammation of the gut in ruminants leading to bacterial shedding in feces in many infected animals. Although there are often strong MAP-specific immune responses in infected animals, immunological correlates of protection against progression to disease remain poorly defined. Analysis of cross-sectional data has suggested that the cellular immune response observed early in infection is effective at containing bacterial growth and shedding, in contrast to humoral immune responses. In this study, 20 MAP-infected calves were followed for nearly 5 years during which MAP shedding, antigen-specific cellular (LPT) and humoral (ELISA) immune responses were measured. We found that MAP-specific cellular immune response developed slowly, with the peak of the immune response occurring one year post infection. MAP-specific humoral immunity expanded only in a subset of animals. Only in a subset of animals there was a statistically significant negative correlation between the amount of MAP shedding and magnitude of the MAP-specific cellular immune response. Direct fitting of simple mechanistic mathematical models to the shedding data suggested that MAP-specific immune responses contributed significantly to the kinetics of MAP shedding in most animals. However, whereas the MAP-specific cellular immune response was predicted to suppress shedding in some animals, in other animals it was predicted to increase shedding. In contrast, MAP-specific humoral response was always predicted to increase shedding. Our results illustrate the use of mathematical methods to understand relationships between mycobacteria and immunity in vivo but also highlight problems with establishing cause-effect links from observational data

How Does Cross-Reactive Stimulation Affect the Longevity of CD8+ T Cell Memory?

Immunological memory—the ability to “remember” previously encountered pathogens and respond faster upon re-exposure is a central feature of the immune response in vertebrates. The cross-reactive stimulation hypothesis for the maintenance of memory proposes that memory cells specific for a given pathogen are maintained by cross-reactive stimulation following infections with other (unrelated) pathogens. We use mathematical models to examine the cross-reactive stimulation hypothesis. We find that: (i) the direct boosting of cross-reactive lineages only provides a very small increase in the average longevity of immunological memory; (ii) the expansion of cross-reactive lineages can indirectly increase the longevity of memory by reducing the magnitude of expansion of new naive lineages which occupy space in the memory compartment and are responsible for the decline in memory; (iii) cross-reactive stimulation results in variation in the rates of decline of different lineages of memory cells and enrichment of memory cell population for cells that are cross-reactive for the pathogens to which the individual has been exposed