Mathematical modeling suggests heterogeneous replication of Mycobacterium tuberculosis in rabbits

Tuberculosis (TB), the disease caused by Mycobacterium tuberculosis (Mtb), remains a major health problem with 10.6 million cases of the disease and 1.6 million deaths in 2021. It is well understood that pulmonary TB is due to replication of Mtb in the lung but quantitative details of Mtb replication and death in lungs of patients and how these rates are related to the degree of lung pathology are unknown. We performed experiments with rabbits infected with a novel, virulent clinical Mtb isolate of the Beijing lineage, HN878, carrying an unstable plasmid pBP10. In our in vitro experiments we found that pBP10 is more stable in HN878 strain than in a more commonly used laboratory-adapted Mtb strain H37Rv (the segregation coefficient being s = 0 . 10 in HN878 vs. s = 0 . 18 in H37Rv). Interestingly, the kinetics of plasmid-bearing bacteria in lungs of Mtb-infected rabbits did not follow an expected monotonic decline; the percent of plasmid-bearing cells increased between 28 and 56 days post-infection and remained stable between 84 and 112 days post-infection despite a large increase in bacterial numbers in the lung at late time points. Mathematical modeling suggested that such a non-monotonic change in the percent of plasmid-bearing cells can be explained if the lung Mtb population consists of several (at least 2) sub-populations with different replication/death kinetics: one major population expanding early and being controlled/eliminated, while another, a smaller population expanding at later times causing a counterintuitive increase in the percent of plasmid-bearing cells. Given that HN878 forms well circumscribed granulomas in rabbits, our results suggest independent bacterial dynamics in subsets of such granulomas. Our model predictions can be tested in future experiments in which HN878-pBP10 dynamics in individual granulomas is followed over time.

Heterogeneity in killing efficacy of individual effector CD8+ T cells against Plasmodium liver stages

Vaccination strategies in mice inducing high numbers of memory CD8+ T cells specific to a single epitope are able to provide sterilizing protection against infection with Plasmodium sporozoites. We have recently found that Plasmodium-specific CD8+ T cells cluster around sporozoite-infected hepatocytes but whether such clusters are important in elimination of the parasite remains incompletely understood. Here, we used our previously generated data in which we employed intravital microscopy to longitudinally image 32 green fluorescent protein (GFP)-expressing Plasmodium yoelii parasites in livers of mice that had received activated Plasmodium-specific CD8+ T cells after sporozoite infection. We found significant heterogeneity in the dynamics of the normalized GFP signal from the parasites (termed 'vitality index' or VI) that was weakly correlated with the number of T cells near the parasite. We also found that a simple model assuming mass-action, additive killing by T cells well describes the VI dynamics for most parasites and predicts a highly variable killing efficacy by individual T cells. Given our estimated median per capita kill rate of k = 0.031/h we predict that a single T cell is typically incapable of killing a parasite within the 48 h lifespan of the liver stage in mice. Stochastic simulations of T cell clustering and killing of the liver stage also suggested that: (i) three or more T cells per infected hepatocyte are required to ensure sterilizing protection; (ii) both variability in killing efficacy of individual T cells and resistance to killing by individual parasites may contribute to the observed variability in VI decline, and (iii) the stable VI of some clustered parasites cannot be explained by measurement noise. Taken together, our analysis for the first time provides estimates of efficiency at which individual CD8+ T cells eliminate intracellular parasitic infection in vivo.

Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks

Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues. Whether or not such control is achieved by utilizing different movement strategies in different tissues remains poorly understood. Liver-localized CD8 T cells perform correlated random walks  --- a type of a Brownian walk -- in liver sinusoids but in some condition these T cells may also perform Levy flights -- rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-localized CD8 T cells, specific to Toxoplasma gondii, perform generalized Levy walks -- a walk type in which T cells alternate pausing and displacing long distances --- which may indicate that brain is a unique organ where T cells exhibit movement strategies different from other tissues. Methods.  We quantified movement patterns of brain-localized Plasmodium berghei-specific CD4 and CD8 T cells by using well-established statistical and computational methods. Results.  We found that T cells change their movement pattern with time since infection and that CD4 T cells move faster and turn less than CD8 T cells. Importantly, both CD4 and CD8 T cells move in the brain by correlated random walks without long displacements challenging previous observations. We have also re-analyzed the movement data of brain-localized CD8 T cells in T. gondii-infected mice and found no evidence of Levy walks. We hypothesize that the previous conclusion of Levy walks of T. gondii-specific CD8 T cells in the brain was reached due to missing time-frames in the data that create an impression of large movement lengths between assumed-to-be-sequential movements.  Conclusion. Our results suggests that movement strategies of CD8 T cells are largely similar between LNs, liver, and the brain and consistent with correlated random walks and not Levy walks.

Appropriate sampling and long follow-up are required to rigorously evaluate longevity of humoral memory after Vaccination

One of the goals of vaccination is to induce long-term immunity against the infection and/or disease. However, evaluating the duration of protection following vaccination often requires long-term follow-ups that can conflict with the desire to rapidly publish results. Arunachalam et al. JCI 2023 followed individuals receiving third or fourth dose of mRNA COVID19 vaccines for up to 6 months and in finding that the levels of SARS-CoV2-specific antibodies (Abs) declined with similar rates for the two groups came to the conclusion that additional boosting is unnecessary to prolong immunity to SARS-CoV-2. However, this may be premature conclusion to make. Accordingly, we demonstrate that measuring Ab levels at 3 time points and only for a short (up to 6 month) duration does not allow to accurately and rigorously evaluate the long-term half-life of vaccine-induced Abs. By using the data from a cohort of blood donors followed for several years, we show that after re-vaccination with vaccinia virus (VV), VV-specific Abs decay bi-phasically and even the late decay rate exceeds the true slow loss rate of humoral memory observed years prior to the boosting. We argue that mathematical modeling should be used to better optimize sampling schedules to provide more reliable advice about the duration of humoral immunity after repeated vaccinations.

Cytotoxic T Lymphocytes Control Growth of B16 Tumor Cells in Collagen-Fibrin Gels by Cytolytic and Non-Lytic Mechanisms

Cytotoxic T lymphocytes (CTLs) are important in controlling some viral infections, and therapies involving the transfer of large numbers of cancer-specific CTLs have been successfully used to treat several types of cancers in humans. While the molecular mechanisms of how CTLs kill their targets are relatively well understood, we still lack a solid quantitative understanding of the kinetics and efficiency by which CTLs kill their targets in vivo. Collagen-fibrin-gel-based assays provide a tissue-like environment for the migration of CTLs, making them an attractive system to study T cell cytotoxicity in in vivo-like conditions. Budhu.et al. systematically varied the number of peptide (SIINFEKL)-pulsed B16 melanoma cells and SIINFEKL-specific CTLs (OT-1) and measured the remaining targets at different times after target and CTL co-inoculation into collagen-fibrin gels. The authors proposed that their data were consistent with a simple model in which tumors grow exponentially and are killed by CTLs at a per capita rate proportional to the CTL density in the gel. By fitting several alternative mathematical models to these data, we found that this simple "exponential-growth-mass-action-killing" model did not precisely describe the data. However, determining the best-fit model proved difficult because the best-performing model was dependent on the specific dataset chosen for the analysis. When considering all data that include biologically realistic CTL concentrations (E≤107cell/mL), the model in which tumors grow exponentially and CTLs suppress tumor's growth non-lytically and kill tumors according to the mass-action law (SiGMA model) fit the data with the best quality. A novel power analysis suggested that longer experiments (∼3-4 days) with four measurements of B16 tumor cell concentrations for a range of CTL concentrations would best allow discriminating between alternative models. Taken together, our results suggested that the interactions between tumors and CTLs in collagen-fibrin gels are more complex than a simple exponential-growth-mass-action killing model and provide support for the hypothesis that CTLs' impact on tumors may go beyond direct cytotoxicity.

Prioritization of the concepts and skills in quantitative education for graduate students in biomedical science

Substantial guidance is available on undergraduate quantitative training for biologists, including reports focused on biomedical science. Far less attention has been paid to the graduate curriculum and the particular challenges of the diversity of specialization within the life sciences. We propose an innovative approach to quantitative education that goes beyond recommendations of a course or set of courses or activities, derived from analysis of the expectations for students in particular programs. Due to the plethora of quantitative methods, it is infeasible to expect that biomedical PhD students can be exposed to more than a minority of the quantitative concepts and techniques employed in modern biology. We collected key recent papers suggested by the faculty in biomedical science programs, chosen to include important scientific contributions that the faculty consider appropriate for all students in the program to be able to read with confidence. The quantitative concepts and methods inherent in these papers were then analyzed and categorized to provide a rational basis for prioritization of those concepts to be emphasized in the education program. This novel approach to prioritization of quantitative skills and concepts provides an effective method to drive curricular focus based upon program-specific faculty input for science programs of all types. The results of our particular application to biomedical science training highlight the disconnect between typical undergraduate quantitative education for life science students, focused on continuous mathematics, and the concepts and skills in graphics, statistics, and discrete mathematics that arise from priorities established by biomedical science faculty. There was little reference in the key recent papers chosen by faculty to classic mathematical areas such as calculus which make up a large component of the formal undergraduate mathematics training of graduate students in biomedical areas.

Mathematical modeling suggests cytotoxic T lymphocytes control growth of B16 tumor cells in collagin-fibrin gels by cytolytic and non-lytic mechanisms

Cytotoxic T lymphocytes (CTLs) are important in controlling some viral infections, and therapies involving transfer of large numbers of cancer-specific CTLs have been successfully used to treat several types of cancers in humans. While molecular mechanisms of how CTLs kill their targets are relatively well understood we still lack solid quantitative understanding of the kinetics and efficiency at which CTLs kill their targets in different conditions. Collagen-fibrin gel-based assays provide a tissue-like environment for the migration of CTLs, making them an attractive system to study the cytotoxicity in vitro. Budhu et al. [1] systematically varied the number of peptide (SIINFEKL)- pulsed B16 melanoma cells and SIINFEKL-specific CTLs (OT-1) and measured remaining targets at different times after target and CTL co-inoculation into collagen-fibrin gels. The authors proposed that their data were consistent with a simple model in which tumors grow exponentially and are killed by CTLs at a per capita rate proportional to the CTL density in the gel. By fitting several alternative mathematical models to these data we found that this simple "exponential-growth-mass-action-killing" model does not precisely fit the data. However, determining the best fit model proved difficult because the best performing model was dependent on the specific dataset chosen for the analysis. When considering all data that include biologically realistic CTL concentrations ( E ≤ 10 ⁷ cell/ml) the model in which tumors grow exponentially and CTLs suppress tumor's growth non-lytically and kill tumors according to the mass-action law (SiGMA model) fitted the data with best quality. Results of power analysis suggested that longer experiments (∼ 3 - 4 days) with 4 measurements of B16 tumor cell concentrations for a range of CTL concentrations would best allow to discriminate between alternative models. Taken together, our results suggest that interactions between tumors and CTLs in collagen-fibrin gels are more complex than a simple exponential-growth- mass-action killing model and provide support for the hypothesis that CTLs impact on tumors may go beyond direct cytotoxicity.

Correlation between speed and turning naturally arises for sparsely sampled cell movements

Mechanisms regulating cell movement are not fully understood. One feature of cell movement that determines how far cells displace from an initial position is persistence, the ability to perform movements in a direction similar to the previous movement direction. Persistence is thus determined by turning angles (TA) between two sequential displacements and can be characterized by an average TA or persistence time. Recent studies documenting T cell movement in zebrafish found that a cell's average speed and average TA are negatively correlated, suggesting a fundamental cell-intrinsic program whereby cells with a lower TA (and larger persistence time) are intrinsically faster (or faster cells turn less). In this paper we confirm the existence of the correlation between turning and speed for six different datasets on 3D movement of CD8 T cells in murine lymph nodes or liver. Interestingly, the negative correlation between TA and speed was observed in experiments in which liver-localized CD8 T cells rapidly displace due to floating with the blood flow, suggesting that other mechanisms besides cell-intrinsic program may be at play. By simulating correlated random walks using two different frameworks (one based on the von Mises-Fisher (vMF) distribution and another based on the Ornstein-Uhlenbeck (OU) process) we show that the negative correlation between speed and turning naturally arises when cell trajectories are sub-sampled, i.e. when the frequency of sampling is lower than frequency at which cells typically make movements. This effect is strongest when the sampling frequency is of the order of magnitude of the inverse of persistence time of cells and when cells vary in persistence time. The effect arises in part due to the sensitivity of estimated cell speeds to the frequency of imaging whereby less frequent imaging results in slower speeds. Interestingly, by using estimated persistence times for cells in two of our datasets and simulating cell movements using the OU process, we could partially reproduce the experimentally observed correlation between TA and speed without a cell-intrinsic program linking the two processes. Our results thus suggest that sub-sampling may contribute to (and perhaps fully explains) the observed correlation between speed and turning at least for some cell trajectory data and emphasize the role of sampling frequency in the inference of critical cellular parameters of cell motility such as speeds.

Interactions with Asialo-Glycoprotein Receptors and Platelets Are Dispensable for CD8+ T Cell Localization in the Murine Liver

Liver-resident CD8⁺ T cells can play critical roles in the control of pathogens, including Plasmodium and hepatitis B virus. Paradoxically, it has also been proposed that the liver may act as the main place for the elimination of CD8⁺ T cells at the resolution of immune responses. We hypothesized that different adhesion processes may drive residence versus elimination of T cells in the liver. Specifically, we investigated whether the expression of asialo-glycoproteins (ASGPs) drives the localization and elimination of effector CD8⁺ T cells in the liver, while interactions with platelets facilitate liver residence and protective function. Using murine CD8⁺ T cells activated in vitro, or in vivo by immunization with Plasmodium berghei sporozoites, we found that, unexpectedly, inhibition of ASGP receptors did not inhibit the accumulation of effector cells in the liver, but instead prevented these cells from accumulating in the spleen. In addition, enforced expression of ASGP on effector CD8⁺ T cells using St3GalI-deficient cells lead to their loss from the spleen. We also found, using different mouse models of thrombocytopenia, that severe reduction in platelet concentration in circulation did not strongly influence the residence and protective function of CD8⁺ T cells in the liver. These data suggest that platelets play a marginal role in CD8⁺ T cell function in the liver. Furthermore, ASGP-expressing effector CD8⁺ T cells accumulate in the spleen, not the liver, prior to their destruction.

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.

Liver Environment-Imposed Constraints Diversify Movement Strategies of Liver-Localized CD8 T Cells

Pathogen-specific CD8 T cells face the problem of finding rare cells that present their cognate Ag either in the lymph node or in infected tissue. Although quantitative details of T cell movement strategies in some tissues such as lymph nodes or skin have been relatively well characterized, we still lack quantitative understanding of T cell movement in many other important tissues, such as the spleen, lung, liver, and gut. We developed a protocol to generate stable numbers of liver-located CD8 T cells, used intravital microscopy to record movement patterns of CD8 T cells in livers of live mice, and analyzed these and previously published data using well-established statistical and computational methods. We show that, in most of our experiments, Plasmodium-specific liver-localized CD8 T cells perform correlated random walks characterized by transiently superdiffusive displacement with persistence times of 10-15 min that exceed those observed for T cells in lymph nodes. Liver-localized CD8 T cells typically crawl on the luminal side of liver sinusoids (i.e., are in the blood); simulating T cell movement in digital structures derived from the liver sinusoids illustrates that liver structure alone is sufficient to explain the relatively long superdiffusive displacement of T cells. In experiments when CD8 T cells in the liver poorly attach to the sinusoids (e.g., 1 wk after immunization with radiation-attenuated Plasmodium sporozoites), T cells also undergo Lévy flights: large displacements occurring due to cells detaching from the endothelium, floating with the blood flow, and reattaching at another location. Our analysis thus provides quantitative details of movement patterns of liver-localized CD8 T cells and illustrates how structural and physiological details of the tissue may impact T cell movement patterns.

A New Method Based on the von Mises-Fisher Distribution Shows that a Minority of Liver-Localized CD8 T Cells Display Hard-To-Detect Attraction to Plasmodium-Infected Hepatocytes

Malaria is a disease caused by Plasmodium parasites, resulting in over 200 million infections and 400,000 deaths every year. A critical step of malaria infection is when sporozoites, injected by mosquitoes, travel to the liver and form liver stages. Malaria vaccine candidates which induce large numbers of malaria-specific CD8 T cells in mice are able to eliminate all liver stages, preventing fulminant malaria. However, how CD8 T cells find all parasites in 48 h of the liver stage lifespan is not well understood. Using intravital microscopy of murine livers, we generated unique data on T cell search for malaria liver stages within a few hours after infection. To detect attraction of T cells to an infection site, we used the von Mises-Fisher distribution in 3D, similar to the 2D von Mises distribution previously used in ecology. Our results suggest that the vast majority (70-95%) of malaria-specific and non-specific liver-localized CD8 T cells did not display attraction towards the infection site, suggesting that the search for malaria liver stages occurs randomly. However, a small fraction (15-20%) displayed weak but detectable attraction towards parasites which already had been surrounded by several T cells. We found that speeds and turning angles correlated with attraction, suggesting that understanding mechanisms that determine the speed of T cell movement in the liver may improve the efficacy of future T cell-based vaccines. Stochastic simulations suggest that a small movement bias towards the parasite dramatically reduces the number of CD8 T cells needed to eliminate all malaria liver stages, but to detect such attraction by individual cells requires data from long imaging experiments which are not currently feasible. Importantly, as far as we know this is the first demonstration of how activated/memory CD8 T cells might search for the pathogen in nonlymphoid tissues a few hours after infection. We have also established a framework for how attraction of individual T cells towards a location in 3D can be rigorously evaluated.

Intravital imaging experiments track CD8 T cells searching for Plasmodium liver stages, but do the imaging frequency and duration impact the detection of CD8 T cell bias?

Vaccine-induced CD8 T cells can provide sterilizing protection by killing Plasmodium sporozoites in mice, but how do they find those parasites? We recently showed that most liver-localized CD8 T cells search for infected hepatocytes randomly, with some cells displaying bias toward the infection site only when there is already a CD8 T cell cluster present. Our initial intravital microscopy experiments minimized tissue damage from laser exposure by using low imaging frequency (volume/1.5–2min) and were fairly lengthy (1–2h). In these experiments, activated CD8 T cells displayed Brownian-like turns and slow average calculated speeds of 1–3 um/min. Recently, we performed new experiments in which we recorded the movement of CD8 T cells at a higher frequency (volume/0.2min) at the cost of shorter experiments (30min). Interestingly, observed speeds ranged between 5 and 18 um/min, suggesting that the calculated speed of CD8 T cells depends on the details of the experiment. Further testing found that imaging frequency impacts the estimated average speed per cell: reducing the imaging frequency from 0.2min to 2min can reduce the average calculated cell speed 5-fold, partially explaining the discrepancy between our datasets’ speeds. Nonetheless, the new data still suggest that some CD8 T cells display attraction towards the infection site only when there is a cluster of CD8 T cells already present. Taken together, our results highlight the impact of details of intravital imaging experiments on inferred parameters of T cell movement in complex environments.

Liver-localized CD8 T cells do not need Levy walks to be efficient killers

Pathogen-specific CD8 T cells face the problem of finding rare cells that present their cognate antigen either in the lymph node or infected tissue. To optimize the search for rare targets it has been proposed that T cells might perform a random walk with long displacements called Levy walks enabling superdiffusive behavior and shorter search times which may be evolutionary selected. We examined the behavior of activated CD8 T cells in the liver where both the movement of the cells and the underlying structural constraints can be clearly defined. We show that Plasmodium-specific liver-localized CD8 T cells perform short displacement, Brownian-like walks and yet display transiently superdiffusive displacement, the cardinal feature of efficient Levy walks. Because liver-localized CD8 T cells are mainly associated with liver sinusoids, simulations of Brownian or Levy walkers in structures derived from the liver sinusoids illustrate that structure together with preferred forward movement results in superdiffusive movement. Interestingly, Brownian walkers require less time to find a rare target when T cells search for the infection in physiologically-derived liver structures. Our results strongly suggest that observed patterns of movement of CD8 T cells are likely to result from a combination of a cell-intrinsic movement program, physical constraints imposed by the environmental structures, and other environmental cues. Future work needs to focus on quantifying the relative contributions of these factors to the overall observed movement patterns of biological agents.

Impact of Oseltamivir Treatment on Influenza A and B Virus Dynamics in Human Volunteers

Influenza viruses infect millions of humans every year causing an estimated 400,000 deaths globally. Due to continuous virus evolution current vaccines provide only limited protection against the flu. Several antiviral drugs are available to treat influenza infection, and one of the most commonly used drugs is oseltamivir (Tamiflu). While the mechanism of action of oseltamivir as a neuraminidase inhibitor is well-understood, the impact of oseltamivir on influenza virus dynamics in humans has been controversial. Many clinical trials with oseltamivir have been done by pharmaceutical companies such as Roche but the results of these trials until recently have been provided as summary reports or papers. Typically, such reports included median virus shedding curves for placebo and drug-treated influenza virus infected volunteers often indicating high efficacy of the early treatment. However, median shedding curves may be not accurately representing drug impact in individual volunteers. Importantly, due to public pressure clinical trials data testing oseltamivir efficacy has been recently released in the form of redacted PDF documents. We digitized and re-analyzed experimental data on influenza virus shedding in human volunteers from three previously published trials: on influenza A (1 trial) or B viruses (2 trials). Given that not all volunteers exposed to influenza viruses actually start virus shedding we found that impact of oseltamivir on the virus shedding dynamics was dependent on (i) selection of volunteers that were infected with the virus, and (ii) the detection limit in the measurement assay; both of these details were not well-articulated in the published studies. By assuming that any non-zero viral measurement is above the limit of detection we could match previously published data on median influenza A virus (flu A study) shedding but not on influenza B virus shedding (flu B study B) in human volunteers. Additional analyses confirmed that oseltamivir had an impact on the duration of shedding and overall shedding (defined as area under the curve) but this result varied by the trial. Interestingly, treatment had no impact on the rates at which shedding increased or declined with time in individual volunteers. Additional analyses showed that oseltamivir impacted the kinetics of the end of viral shedding, and in about 20-40% of volunteers that shed the virus treatment had no impact on viral shedding duration. Our results suggest an unusual impact of oseltamivir on influenza viruses shedding kinetics and caution about the use of published median data or data from a few individuals for inferences. Furthermore, we call for the need to publish raw data from critical clinical trials that can be independently analyzed.

Ultra-low Dose Aerosol Infection of Mice with Mycobacterium tuberculosis More Closely Models Human Tuberculosis

Tuberculosis (TB) is a heterogeneous disease manifesting in a subset of individuals infected with aerosolized Mycobacterium tuberculosis (Mtb). Unlike human TB, murine infection results in uniformly high lung bacterial burdens and poorly organized granulomas. To develop a TB model that more closely resembles human disease, we infected mice with an ultra-low dose (ULD) of between 1-3 founding bacteria, reflecting a physiologic inoculum. ULD-infected mice exhibited highly heterogeneous bacterial burdens, well-circumscribed granulomas that shared features with human granulomas, and prolonged Mtb containment with unilateral pulmonary infection in some mice. We identified blood RNA signatures in mice infected with an ULD or a conventional Mtb dose (50-100 CFU) that correlated with lung bacterial burdens and predicted Mtb infection outcomes across species, including risk of progression to active TB in humans. Overall, these findings highlight the potential of the murine TB model and show that ULD infection recapitulates key features of human TB.

Treatment timing shifts the benefits of short and long antibiotic treatment over infection

Antibiotics are the major tool for treating bacterial infections. Rising antibiotic resistance, however, calls for a better use of antibiotics. While classical recommendations favor long and aggressive treatments, more recent clinical trials advocate for moderate regimens. In this debate, two axes of 'aggression' have typically been conflated: treatment intensity (dose) and treatment duration. The third dimension of treatment timing along each individual's infection course has rarely been addressed. By using a generic mathematical model of bacterial infection controlled by immune response, we examine how the relative effectiveness of antibiotic treatment varies with its timing, duration and antibiotic kill rate. We show that short or long treatments may both be beneficial depending on treatment onset, the target criterion for success and on antibiotic efficacy. This results from the dynamic trade-off between immune response build-up and resistance risk in acute, self-limiting infections, and uncertainty relating symptoms to infection variables. We show that in our model early optimal treatments tend to be 'short and strong', while late optimal treatments tend to be 'mild and long'. This suggests a shift in the aggression axis depending on the timing of treatment. We find that any specific optimal treatment schedule may perform more poorly if evaluated by other criteria, or under different host-specific conditions. Our results suggest that major advances in antibiotic stewardship must come from a deeper empirical understanding of bacterial infection processes in individual hosts. To guide rational therapy, mathematical models need to be constrained by data, including a better quantification of personal disease trajectory in humans. Lay summary: Bacterial infections are becoming more difficult to treat worldwide because bacteria are becoming resistant to the antibiotics used. Addressing this problem requires a better understanding of how treatment along with other host factors impact antibiotic resistance. Until recently, most theoretical research has focused on the importance of antibiotic dosing on antibiotic resistance, however, duration and timing of treatment remain less explored. Here, we use a mathematical model of a generic bacterial infection to study three aspects of treatment: treatment dose/efficacy (defined by the antibiotic kill rate), duration, and timing, and their impact on several infection endpoints. We show that short and long treatment success strongly depends on when treatment begins (defined by the symptom threshold), the target criterion to optimize, and on antibiotic efficacy. We find that if administered early in an infection, "strong and short" therapy performs better, while if treatment begins at higher bacterial densities, a "mild and long" course of antibiotics is favored. In the model host immune defenses are key in preventing relapses, controlling antibiotic resistant bacteria and increasing the effectiveness of moderate intervention. In order to improve rational treatments of human infections, we call for a better quantification of individual disease trajectories in bacteria-immunity space.

Experimental determination of the force of malaria infection reveals a non-linear relationship to mosquito sporozoite loads

Plasmodium sporozoites are the infective stage of the malaria parasite. Though this is a bottleneck for the parasite, the quantitative dynamics of transmission, from mosquito inoculation of sporozoites to patent blood-stage infection in the mammalian host, are poorly understood. Here we utilize a rodent model to determine the probability of malaria infection after infectious mosquito bite, and consider the impact of mosquito parasite load, blood-meal acquisition, probe-time, and probe location, on infection probability. We found that infection likelihood correlates with mosquito sporozoite load and, to a lesser degree, the duration of probing, and is not dependent upon the mosquito’s ability to find blood. The relationship between sporozoite load and infection probability is non-linear and can be described by a set of models that include a threshold, with mosquitoes harboring over 10,000 salivary gland sporozoites being significantly more likely to initiate a malaria infection. Overall, our data suggest that the small subset of highly infected mosquitoes may contribute disproportionally to malaria transmission in the field and that quantifying mosquito sporozoite loads could aid in predicting the force of infection in different transmission settings.

Malaria is a leading cause of death in many parts of the world. Infection is initiated when infected Anopheles mosquitoes inject sporozoites as they look for blood. Though transmission is a bottleneck for the parasite and thus a good point for intervention, many aspects of transmission remain poorly understood. In this study, using a rodent model of malaria, we found that the majority of infective bites do not result in malaria infection. Furthermore, we found that the bites of mosquitoes with heavy parasite burdens are significantly more likely to result in blood stage infection. These data have important implications for designing interventions targeting transmission stages of the malaria parasite as they suggest that reducing parasite loads, even without completely eliminating them, could be effective against disease spread. We also found that mosquitoes that probe but do not succeed in finding blood are equally likely to initiate infection, an important finding for human vaccine trials. Overall this work contributes to our understanding of the epidemiology of malaria and should aid in the development of malaria elimination strategies.

Liver-resident CD8 T cells do not need Levy walks to be efficient killers

Movement strategies by which antigen-specific CD8 T cells search for sites of infection are not fully understood. It was recently suggested that activated CD8 T cells, specific for Toxoplasma gondii, perform generalized Levy walks in murine brains; that is cells perform a local search and then displace randomly to distant locations. Several theoretical studies found that Levy walkers are an order of magnitude more efficient at finding rare targets than Brownian walkers. We investigated movement patterns of Plasmodium-specific liver-resident CD8 T cells using intravital microscopy. Based on the distribution of movement lengths Trm cells performed Brownian walks and yet displayed superdiffusive (Levy-like) behavior, i.e., on average they displaced further from the initial position than that predicted by the standard diffusion theory. Mapping out structure of liver sinusoids revealed that superdiffiusive nature of T cell walks in the liver is likely due to small branching angles of the sinusoids, instructing T cells to move directly. By simulating T cells moving as Brownian or Levy walkers in free space or physiologically constrained liver sinusoids we showed that structure may override the intrinsic pattern of cell movement. Interestingly, while Levy walkers indeed required less time than Brownian walkers to find rare targets when search was done in space with no constrains, on average, this advantage disappeared when search was done in the liver. Our results, thus, suggest that observed patterns of movement of T cells in the liver are likely to arise as a combination of cell-intrinsic search patterns and environmental constrains, and that evolutionary benefits of Levy walks may be limited in biologically-relevant environments.

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.

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.

T follicular helper cells in human efferent lymph retain lymphoid characteristics

T follicular helper cells (Tfh), a subset of CD4+ T cells, provide requisite help to B cells in the germinal centers (GC) of lymphoid tissue. GC Tfh are identified by high expression of the chemokine receptor CXCR5 and the inhibitory molecule PD-1. Although more accessible, blood contains lower frequencies of CXCR5+ and PD-1+ cells that have been termed circulating Tfh (cTfh). However, it remains unclear whether GC Tfh exit lymphoid tissues and populate this cTfh pool. To examine exiting cells, we assessed the phenotype of Tfh present within the major conduit of efferent lymph from lymphoid tissues into blood, the human thoracic duct. Unlike what was found in blood, we consistently identified a CXCR5-bright PD-1-bright (CXCR5BrPD-1Br) Tfh population in thoracic duct lymph (TDL). These CXCR5BrPD-1Br TDL Tfh shared phenotypic and transcriptional similarities with GC Tfh. Moreover, components of the epigenetic profile of GC Tfh could be detected in CXCR5BrPD-1Br TDL Tfh and the transcriptional imprint of this epigenetic signature was enriched in an activated cTfh subset known to contain vaccine-responding cells. Together with data showing shared TCR sequences between the CXCR5BrPD-1Br TDL Tfh and cTfh, these studies identify a population in TDL as a circulatory intermediate connecting the biology of Tfh in blood to Tfh in lymphoid tissue.

Characterizing the movement strategy of CD8+ T cells in finding malaria parasites in the liver

Movement strategies by which antigen-specific CD8+ T cells search for sites of infection in peripheral tissues are not fully understood. Measurable quantities, such as the distance traveled per unit of time, that follow Lévy statistics are common in nature, for example, in bacterial and higher animal foraging; in mussels, marine predators, monkeys. A recent study has shown that moving according to Lévy flights enables CD8+ T cells in the brain to find “rare targets” (Toxoplasma gondii-infected cells) in an order of magnitude more efficiently than using Brownian and other walking strategies. It has been, thus, suggested that such efficient strategy of T cell searching for infection may have been evolutionarily selected. However, T cells in the brain (or other tissues) are often constrained by the structure of the physical environment in which cells move. Whether the emerged statistical pattern of T cell movement is due to a cell-intrinsic program or a consequence of environmental constrains is, thus, unknown. Here, we address this question by using intravital imaging of movement of Plasmodium-specific CD8+ T cells in murine livers and mathematical modeling and analyses of the generated data. We investigate whether the physical structure of the movement paths in the liver plays a role in shaping the walking strategy of T cells in finding malaria parasites. Here, we map out liver sinusoids in 3D using intravital microscopy and use simulations to parameterize the alternative walking models by fitting them to empirical data having no references to the physical structure. Our preliminary data suggest that constraints imposed by the structure of liver sinusoids significantly impact the moving pattern of the T cells.

Activated Plasmodium-specific CD8 T cells find liver stages mostly randomly

Malaria is a major infectious disease, with 500,000 people dying every year. Malaria infection starts when an infected mosquito injects malaria sporozoites during feeding which migrate to the liver and form liver stages. Elimination of liver stages is a major feature of CD8 T cell-based malaria vaccines. It is established that vaccines inducing high numbers of memory CD8 T cells are capable of eliminating all liver stages, preventing clinical malaria. However, how CD8 T cells are capable of doing that in the 48-hour liver stage in mice remains unclear. One possibility is that as sporozoites invade hepatocytes from the blood, they induce local inflammation, acting as an attraction signal for T cells. We performed experiments in which fluorescent-labeled Plasmodium sporozoites and Plasmodium-specific and non-specific CD8 T cells were tracked in mouse livers using intravital microscopy. To analyze the data we used three metrics to measure attraction of T cells to the infection site based either on angles or distances from a T cell to the parasite. We found that for the majority of imaged T cells, there is no evidence of attraction to the parasite, indicating that in this experimental system, vaccine-induced CD8 T cells locate the infection site randomly. By modeling T cells searching for the infection site and utilizing experimentally measured speeds of T cell movement in the liver, we found that if enough memory CD8 T cells are present in the liver, all parasites can be found within 48 hours after sporozoite injection. Taken together, our results suggest that memory CD8 T cells in the liver perform the search for infection randomly, precluding the need to find specific signals and receptors of T cell attraction to the infection site.

Cutting Edge: IL-1R1 Mediates Host Resistance to Mycobacterium tuberculosis by Trans-Protection of Infected Cells

IL-1R1 deficiency in mice causes severe susceptibility to Mycobacterium tuberculosis Mice and macrophage cultures lacking IL-1R1 display increased bacterial growth, suggesting that phagocytes may require IL-1R1-dependent antimicrobial signals to limit intracellular M. tuberculosis replication directly. However, the myeloid-cell-intrinsic versus -extrinsic requirements for IL-1R1 to control M. tuberculosis infection in mice have not been directly addressed. Using single-cell analysis of infected cells, competitive mixed bone marrow chimeras, and IL-1R1 conditional mutant mice, we show in this article that IL-1R1 expression by pulmonary phagocytes is uncoupled from their ability to control intracellular M. tuberculosis growth. Importantly, IL-1R1-dependent control was provided to infected cells in trans by both nonhematopoietic and hematopoietic cells. Thus, IL-1R1-mediated host resistance to M. tuberculosis infection does not involve mechanisms of cell-autonomous antimicrobicidal effector functions in phagocytes but requires the cooperation between infected cells and other cells of hematopoietic or nonhematopoietic origin to promote bacterial containment and control of infection.

Tracking HIV-1 recombination to resolve its contribution to HIV-1 evolution in natural infection

Recombination in HIV-1 is well documented, but its importance in the low-diversity setting of within-host diversification is less understood. Here we develop a novel computational tool (RAPR (Recombination Analysis PRogram)) to enable a detailed view of in vivo viral recombination during early infection, and we apply it to near-full-length HIV-1 genome sequences from longitudinal samples. Recombinant genomes rapidly replace transmitted/founder (T/F) lineages, with a median half-time of 27 days, increasing the genetic complexity of the viral population. We identify recombination hot and cold spots that differ from those observed in inter-subtype recombinants. Furthermore, RAPR analysis of longitudinal samples from an individual with well-characterized neutralizing antibody responses shows that recombination helps carry forward resistance-conferring mutations in the diversifying quasispecies. These findings provide insight into molecular mechanisms by which viral recombination contributes to HIV-1 persistence and immunopathogenesis and have implications for studies of HIV transmission and evolution in vivo.

Recombination contributes to HIV evolution in patients, but its identification can be difficult. Here, the authors develop a computational tool called RAPR to track recombination in patients, identify recombination hot spots, and show contribution of recombination to antibody escape.

Clustering of CD8 T cells around malaria-infected hepatocytes is rapid and is driven by antigen-specific T 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. In mice, vaccine-induced CD8 T cells are capable of locating and eliminating all liver stages in 48 hours, thus preventing the blood-stage disease. 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 Py-infected cells, 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 T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific T cells) are attracted to the clusters, we found no evidence that non-specific 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 T cells, thus illustrating high efficiency of T cells in locating their targets in complex peripheral organs such as the liver. Our analysis thus clarifies details of the formation of clusters of antigen-specific CD8 T cells in the liver.

Time Intervals in Sequence Sampling, Not Data Modifications, Have a Major Impact on Estimates of HIV Escape Rates

The ability of human immunodeficiency virus (HIV) to avoid recognition by humoral and cellular immunity (viral escape) is well-documented, but the strength of the immune response needed to cause such a viral escape remains poorly quantified. Several previous studies observed a more rapid escape of HIV from CD8 T cell responses in the acute phase of infection compared to chronic infection. The rate of HIV escape was estimated with the help of simple mathematical models, and results were interpreted to suggest that CD8 T cell responses causing escape in acute HIV infection may be more efficient at killing virus-infected cells than responses that cause escape in chronic infection, or alternatively, that early escapes occur in epitopes mutations in which there is minimal fitness cost to the virus. However, these conclusions were challenged on several grounds, including linkage and interference of multiple escape mutations due to a low population size and because of potential issues associated with modifying the data to estimate escape rates. Here we use a sampling method which does not require data modification to show that previous results on the decline of the viral escape rate with time since infection remain unchanged. However, using this method we also show that estimates of the escape rate are highly sensitive to the time interval between measurements, with longer intervals biasing estimates of the escape rate downwards. Our results thus suggest that data modifications for early and late escapes were not the primary reason for the observed decline in the escape rate with time since infection. However, longer sampling periods for escapes in chronic infection strongly influence estimates of the escape rate. More frequent sampling of viral sequences in chronic infection may improve our understanding of factors influencing the rate of HIV escape from CD8 T cell responses.

Kinetics of HIV-Specific CTL Responses Plays a Minimal Role in Determining HIV Escape Dynamics

Cytotoxic T lymphocytes (CTLs) have been suggested to play an important role in controlling human immunodeficiency virus (HIV-1 or simply HIV) infection. HIV, due to its high mutation rate, can evade recognition of T cell responses by generating escape variants that cannot be recognized by HIV-specific CTLs. Although HIV escape from CTL responses has been well documented, factors contributing to the timing and the rate of viral escape from T cells have not been fully elucidated. Fitness costs associated with escape and magnitude of the epitope-specific T cell response are generally considered to be the key in determining timing of HIV escape. Several previous analyses generally ignored the kinetics of T cell responses in predicting viral escape by either considering constant or maximal T cell response; several studies also considered escape from different T cell responses to be independent. Here, we focus our analysis on data from two patients from a recent study with relatively frequent measurements of both virus sequences and HIV-specific T cell response to determine impact of CTL kinetics on viral escape. In contrast with our expectation, we found that including temporal dynamics of epitope-specific T cell response did not improve the quality of fit of different models to escape data. We also found that for well-sampled escape data, the estimates of the model parameters including T cell killing efficacy did not strongly depend on the underlying model for escapes: models assuming independent, sequential, or concurrent escapes from multiple CTL responses gave similar estimates for CTL killing efficacy. Interestingly, the model assuming sequential escapes (i.e., escapes occurring along a defined pathway) was unable to accurately describe data on escapes occurring rapidly within a short-time window, suggesting that some of model assumptions must be violated for such escapes. Our results thus suggest that the current sparse measurements of temporal CTL dynamics in blood bear little quantitative information to improve predictions of HIV escape kinetics. More frequent measurements using more sensitive techniques and sampling in secondary lymphoid tissues may allow to better understand whether and how CTL kinetics impacts viral escape.

Severe Tuberculosis in Humans Correlates Best with Neutrophil Abundance and Lymphocyte Deficiency and Does Not Correlate with Antigen-Specific CD4 T-Cell Response

It is generally thought that Mycobacterium tuberculosis (Mtb)-specific CD4⁺ Th1 cells producing IFN-γ are essential for protection against tuberculosis (TB). In some studies, protection has recently been associated with polyfunctional subpopulation of Mtb-specific Th1 cells, i.e., with cells able to simultaneously secrete several type 1 cytokines. However, the role for Mtb-specific Th1 cells and their polyfunctional subpopulations during established TB disease is not fully defined. Pulmonary TB is characterized by a great variability of disease manifestations. To address the role for Mtb-specific Th1 responses during TB, we investigated how Th1 and other immune cells correlated with particular TB manifestations, such as the degree of pulmonary destruction, TB extent, the level of bacteria excretion, clinical disease severity, clinical TB forms, and “Timika X-ray score,” an integrative parameter of pulmonary TB pathology. In comparison with healthy Mtb-exposed controls, TB patients (TBP) did not exhibit deficiency in Mtb-specific cytokine-producing CD4⁺ cells circulating in the blood and differed by a polyfunctional profile of these cells, which was biased toward the accumulation of bifunctional TNF-α⁺IFN-γ⁺IL-2⁻ lymphocytes. Importantly, however, severity of different TB manifestations was not associated with Mtb-specific cytokine-producing cells or their polyfunctional profile. In contrast, several TB manifestations were strongly correlated with leukocyte numbers, the percent or the absolute number of lymphocytes, segmented or band neutrophils. In multiple alternative statistical analyses, band neutrophils appeared as the strongest positive correlate of pulmonary destruction, bacteria excretion, and “Timika X-ray score.” In contrast, clinical TB severity was primarily and inversely correlated with the number of lymphocytes in the blood. The results suggest that: (i) different TB manifestations may be driven by distinct mechanisms; (ii) quantitative parameters and polyfunctional profile of circulating Mtb-specific CD4⁺ cells play a minor role in determining TB severity; and (iii) general shifts in production/removal of granulocytic and lymphocytic lineages represent an important factor of TB pathogenesis. Mechanisms leading to these shifts and their specific role during TB are yet to be determined but are likely to involve changes in human hematopoietic system.

Immunologic and Virologic Mechanisms for Partial Protection from Intravenous Challenge by an Integration-Defective SIV Vaccine

The suppression of viral loads and identification of selection signatures in non-human primates after challenge are indicators for effective human immunodeficiency virus (HIV)/simian immunodeficiency virus (SIV) vaccines. To mimic the protective immunity elicited by attenuated SIV vaccines, we developed an integration-defective SIV (idSIV) vaccine by inactivating integrase, mutating sequence motifs critical for integration, and inserting the cytomegalovirus (CMV) promoter for more efficient expression in the SIVmac239 genome. Chinese rhesus macaques were immunized with idSIV DNA and idSIV particles, and the cellular and humoral immune responses were measured. After the intravenous SIVmac239 challenge, viral loads were monitored and selection signatures in viral genomes from vaccinated monkeys were identified by single genome sequencing. T cell responses, heterologous neutralization against tier-1 viruses, and antibody-dependent cellular cytotoxicity (ADCC) were detected in idSIV-vaccinated macaques post immunization. After challenge, the median peak viral load in the vaccine group was significantly lower than that in the control group. However, this initial viral control did not last as viral set-points were similar between vaccinated and control animals. Selection signatures were identified in Nef, Gag, and Env proteins in vaccinated and control macaques, but these signatures were different, suggesting selection pressure on viruses from vaccine-induced immunity in the vaccinated animals. Our results showed that the idSIV vaccine exerted some pressure on the virus population early during the infection but future modifications are needed in order to induce more potent immune responses.

Innate immunity does not contribute to the resistance of mice from different vendors to P. yoelii infection

Nearly 500,000 individuals die annually from Plasmodium infections. Factors contributing to susceptibility to Plasmodium infections remain poorly understood. It was recently observed that C57BL/6 mice from different vendors (NCI, Harlem, Taconic, Jackson) have different susceptibility to Plasmodium yoelii infection: Jackson/Taconic mice generally have lower peak parasitemia in the blood and better survival than NIC/Harlem mice (Villarino et al. PNAS 2016). Bioinformatic analysis suggested that high mortality of susceptible mice could arise due to a higher expression of basigin, a protein required by Plasmodium falciparum to invade red blood cells in humans (Stough et al. Front Microbiol 2017). We applied a series of mathematical models of different levels of complexity to experimental data on P. yoelii dynamics in mice from these 4 vendors. Our analysis suggests that there are no statistically significant differences in the P. yoelii dynamics during the first 10–14 days post infection, and that the estimated rates of parasite replication were independent of the vendor type. In contrast, we found large differences in parameters for Plasmodium-specific adaptive immune response suggesting that resistant mice mounted a faster and a more efficient response. Our results thus suggest that higher expression of basigin is unlikely to explain higher susceptibility of NCI/Harlem mice to P. yoelii infection and that innate immunity controlling parasite replication during the first 2 weeks of infection unlikely to be different between susceptible and resistant mice. In contrast, a faster generation of the adaptive immunity in resistant mice was likely to be responsible for better parasite control.

Up-regulation of LFA-1 allows liver-resident memory T cells to patrol and remain in the hepatic sinusoids

Liver-resident CD8+ T cells are highly motile cells that patrol the vasculature and provide protection against liver pathogens. A key question is: how can these liver CD8+ T cells be simultaneously present in the circulation and tissue-resident? Because liver-resident T cells do not express CD103 - a key integrin for T cell residence in epithelial tissues - we investigated other candidate adhesion molecules. Using intra-vital imaging we found that CD8+ T cell patrolling in the hepatic sinusoids is dependent upon LFA-1-ICAM-1 interactions. Interestingly, liver-resident CD8+ T cells up-regulate LFA-1 compared to effector-memory cells, presumably to facilitate this behavior. Finally, we found that LFA-1 deficient CD8+ T cells failed to form substantial liver-resident memory populations following Plasmodium or LCMV immunization. Collectively, our results demonstrate that it is adhesion through LFA-1 that allows liver-resident memory CD8+ T cells to patrol and remain in the hepatic sinusoids.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Quantifying Limits on Replication, Death, and Quiescence of Mycobacterium tuberculosis in Mice

When an individual is exposed to Mycobacterium tuberculosis (Mtb) three outcomes are possible: bacterial clearance, active disease, or latent infection. It is generally believed that most individuals exposed to Mtb become latently infected and carry the mycobacteria for life. How Mtb is maintained during this latent infection remains largely unknown. During an Mtb infection in mice, there is a phase of rapid increase in bacterial numbers in the murine lungs within the first 3 weeks, and then bacterial numbers either stabilize or increase slowly over the period of many months. It has been debated whether the relatively constant numbers of bacteria in the chronic infection result from latent (dormant, quiescent), non-replicating bacteria, or whether the observed Mtb cell numbers are due to balance between rapid replication and death. A recent study of mice, infected with a Mtb strain carrying an unstable plasmid, showed that during the chronic phase, Mtb was replicating at significant rates. Using experimental data from this study and mathematical modeling we investigated the limits of the rates of bacterial replication, death, and quiescence during Mtb infection of mice. First, we found that to explain the data the rates of bacterial replication and death could not be constant and had to decrease with time since infection unless there were large changes in plasmid segregation probability over time. While a decrease in the rate of Mtb replication with time since infection was expected due to depletion of host's resources, a decrease in the Mtb death rate was counterintuitive since Mtb-specific immune response, appearing in the lungs 3–4 weeks after infection, should increase removal of bacteria. Interestingly, we found no significant correlation between estimated rates of Mtb replication and death suggesting the decline in these rates was driven by independent mechanisms. Second, we found that the data could not be explained by assuming that bacteria do not die, suggesting that some removal of bacteria from lungs of these mice had to occur even though the total bacterial counts in these mice always increased over time. Third and finally, we showed that to explain the data the majority of bacterial cells (at least ~60%) must be replicating in the chronic phase of infection further challenging widespread belief of nonreplicating Mtb in latency. Our predictions were robust to some changes in the structure of the model, for example, when the loss of plasmid-bearing cells was mainly due to high fitness cost of the plasmid. Further studies should determine if more mechanistic models for Mtb dynamics are also able to accurately explain these data.

CD4 T Cell-Derived IFN-γ Plays a Minimal Role in Control of Pulmonary Mycobacterium tuberculosis Infection and Must Be Actively Repressed by PD-1 to Prevent Lethal Disease

IFN-γ–producing CD4 T cells are required for protection against Mycobacterium tuberculosis (Mtb) infection, but the extent to which IFN-γ contributes to overall CD4 T cell-mediated protection remains unclear. Furthermore, it is not known if increasing IFN-γ production by CD4 T cells is desirable in Mtb infection. Here we show that IFN-γ accounts for only ~30% of CD4 T cell-dependent cumulative bacterial control in the lungs over the first six weeks of infection, but >80% of control in the spleen. Moreover, increasing the IFN-γ–producing capacity of CD4 T cells by ~2 fold exacerbates lung infection and leads to the early death of the host, despite enhancing control in the spleen. In addition, we show that the inhibitory receptor PD-1 facilitates host resistance to Mtb by preventing the detrimental over-production of IFN-γ by CD4 T cells. Specifically, PD-1 suppressed the parenchymal accumulation of and pathogenic IFN-γ production by the CXCR3⁺KLRG1^-CX3CR1^- subset of lung-homing CD4 T cells that otherwise mediates control of Mtb infection. Therefore, the primary role for T cell-derived IFN-γ in Mtb infection is at extra-pulmonary sites, and the host-protective subset of CD4 T cells requires negative regulation of IFN-γ production by PD-1 to prevent lethal immune-mediated pathology.

The development of novel tuberculosis vaccines has been hindered by the poor understanding of the mechanisms of host-protection. It has been long-held that IFN-γ is the principle effector of CD4 T cell-mediated resistance to Mtb infection, but Mtb-specific CD4 T cells produce low amounts of IFN-γ in vivo, leading to the possibility that increasing IFN-γ production by Th1 cells might enhance control of Mtb infection. However, the precise contribution of IFN-γ to CD4 T cell-dependent protection and the outcome of increasing IFN-γ production by CD4 T cells have not been evaluated. Here we show that IFN-γ accounts for only ~30% of the cumulative CD4 T cell-mediated reduction in lung bacterial loads over the first 1.5 months of infection. Moreover, we find that increasing the per capita production of IFN-γ by CD4 T cells leads to the early death of the host. Lastly, we show that suppression of CD4 T cell-derived IFN-γ by the inhibitory receptor PD-1 is essential to prevent lethal disease. Therefore, poor control Mtb infection does not result from defective production of IFN-γ, and strategies to selectively boost it are unwarranted. Furthermore, identifying the primary mechanisms of CD4 T cell-dependent control of Mtb infection should be a priority.

Defining limits on efficacy of CD8 T cell-based HIV vaccines

It is generally accepted that an effective HIV vaccine should be able to induce neutralizing antibodies and memory CD8 T cells. Yet, basic features of protective CD8 T cell responses remain poorly defined. Using recently published data from a cohort of HIV-infected patients that were followed from the onset of symptoms into the chronic phase, we determined the basic quantitative in vivo features of HIV-specific CD8 T cell responses. First, we found that the number of responses recognizing different viral epitopes (immune response breadth) varied greatly between patients and on average, 8 epitopes were recognized by CD8 T cells. Surprisingly, we found that in most patients the breadth did not change significantly over the course of first year of infection suggesting that most HIV-specific T cell responses were primed in acute infection. There was a strong negative correlation between the predicted precursor frequency and the rate of expansion of epitope-specific T cells suggesting intraclonal competition. Finally, we found that the majority of CD8 T cell populations expanded and contracted in unison; however, about 20% of all CD8 T cell responses had a discordant dynamics suggesting interclonal competition. Taken together, our results suggest that effective control of HIV infection can be achieved with broad CD8 T cell response if vaccine-induced breadth is larger than that induced by a natural infection. However, broader T cell response will likely lead to interclonal competition between responses, and boosting the magnitude of epitope-specific T cell responses may reduce the expansion rate of these responses due to intraclonal competition. Our results thus suggest potential limits on the efficacy of CD8 T cell-based HIV vaccines.

Broad CTL Response in Early HIV Infection Drives Multiple Concurrent CTL Escapes

Recent studies have highlighted the ability of HIV to escape from cytotoxic T lymphocyte (CTL) responses that concurrently target multiple viral epitopes. Yet, the viral dynamics involved in such escape are incompletely understood. Previous analyses have made several strong assumptions regarding HIV escape from CTL responses such as independent or non-concurrent escape from individual CTL responses. Using experimental data from evolution of HIV half genomes in four patients we observe concurrent viral escape from multiple CTL responses during early infection (first 100 days of infection), providing confirmation of a recent result found in a study of one HIV-infected patient. We show that current methods of estimating CTL escape rates, based on the assumption of independent escapes, are biased and perform poorly when CTL escape proceeds concurrently at multiple epitopes. We propose a new method for analyzing longitudinal sequence data to estimate the rate of CTL escape across multiple epitopes; this method involves few parameters and performs well in simulation studies. By applying our novel method to experimental data, we find that concurrent multiple escapes occur at rates between 0.03 and 0.4 day⁻¹, a relatively broad range that reflects uncertainty due to sparse sampling and wide ranges of parameter values. However, we show that concurrent escape at rates 0.1–0.2 day⁻¹ across multiple epitopes is consistent with our patient datasets.

Since the early 1990s, cytotoxic T lymphocytes (CTLs) have been known to play an important role in HIV infection with CTLs targeting HIV epitopes and, in turn, HIV escapes arising through mutations in the targeted epitopes. Over the past decade, studies have shown that CTL responses concurrently target multiple HIV epitopes, yet the effect of concurrent responses on HIV dynamics and evolution is not well understood. Through an analysis of patient datasets and a novel statistical method, we show that during early HIV infection concurrent CTL responses drive concurrent HIV escapes at multiple epitopes with significant pressure, suggesting a complex picture in which HIV simultaneously explores multiple mutational pathways to escape from broad and potent CTL response.

Evaluating contribution of the cellular and humoral immune responses to the control of shedding of Mycobacterium avium spp. paratuberculosis 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.

Mathematical modeling provides kinetic details of the human immune response to vaccination

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

Plasmodium suppresses expansion of T cell responses to heterologous infections

Plasmodium remains a major pathogen causing malaria and impairing defense against other infections. Defining how Plasmodium increases susceptibility to heterologous pathogens may lead to interventions that mitigate the severity of coinfections. Previous studies proposed that reduced T cell responses during coinfections are due to diminished recruitment of naive T cells through infection-induced decreases in chemokine CCL21. We found that, although Listeria infections reduced expression of CCL21 in murine spleens, lymphocytic choriomeningitis virus (LCMV)-specific T cell responses were not impaired during Listeria + LCMV coinfection, arguing against a major role for this chemokine in coinfection-induced T cell suppression. In our experiments, Plasmodium yoelii infection led to a reduced CD8(+) T cell response to a subsequent Listeria infection. We propose an alternative mechanism whereby P. yoelii suppresses Listeria-specific T cell responses. We found that Listeria-specific T cells expanded more slowly and resulted in lower numbers in response to coinfection with P. yoelii. Mathematical modeling and experimentation revealed greater apoptosis of Listeria-specific effector T cells as the main mechanism, because P. yoelii infections did not suppress the recruitment or proliferation rates of Listeria-specific T cells. Our results suggest that P. yoelii infections suppress immunity to Listeria by causing increased apoptosis in Listeria-specific T cells, resulting in a slower expansion rate of T cell responses.

Classification of T cell movement tracks allows for prediction of cell function

Using a unique combination of visual, statistical, and data mining methods, we tested the hypothesis that an immune cell's movement pattern can convey key information about the cell's function, antigen specificity, and environment. We applied clustering, statistical tests, and a support vector machine (SVM) to assess our ability to classify different datasets of imaged flouresently labelled T cells in mouse liver. We additionally saw clusters of different movement patterns of T cells of identical antigenic specificity. We found that the movement patterns of T cells specific and non-specific for malaria parasites are differentiable with 72% accuracy, and that specific cells have a higher tendency to move towards the parasite than non-specific cells. Movements of antigen-specific T cells in uninfected mice vs. infected mice were differentiable with 69.8% accuracy. We additionally saw clusters of different movement patterns of T cells of identical antigenic specificity. We concluded that our combination of methods has the potential to advance the understanding of cell movements in vivo.

Mathematical modeling reveals kinetics of lymphocyte recirculation in the whole organism

The kinetics of recirculation of naive lymphocytes in the body has important implications for the speed at which local infections are detected and controlled by immune responses. With a help of a novel mathematical model, we analyze experimental data on migration of 51Cr-labeled thoracic duct lymphocytes (TDLs) via major lymphoid and nonlymphoid tissues of rats in the absence of systemic antigenic stimulation. We show that at any point of time, 95% of lymphocytes in the blood travel via capillaries in the lung or sinusoids of the liver and only 5% migrate to secondary lymphoid tissues such as lymph nodes, Peyer's patches, or the spleen. Interestingly, our analysis suggests that lymphocytes travel via lung capillaries and liver sinusoids at an extremely rapid rate with the average residence time in these tissues being less than 1 minute. The model also predicts a relatively short average residence time of TDLs in the spleen (2.5 hours) and a longer average residence time of TDLs in major lymph nodes and Peyer's patches (10 hours). Surprisingly, we find that the average residence time of lymphocytes is similar in lymph nodes draining the skin (subcutaneous LNs) or the gut (mesenteric LNs) or in Peyer's patches. Applying our model to an additional dataset on lymphocyte migration via resting and antigen-stimulated lymph nodes we find that enlargement of antigen-stimulated lymph nodes occurs mainly due to increased entrance rate of TDLs into the nodes and not due to decreased exit rate as has been suggested in some studies. Taken together, our analysis for the first time provides a comprehensive, systems view of recirculation kinetics of thoracic duct lymphocytes in the whole organism.

Competition for antigen between Th1 and Th2 responses determines the timing of the immune response switch during Mycobaterium avium subspecies paratuberulosis infection in ruminants

Johne's disease (JD), a persistent and slow progressing infection of ruminants such as cows and sheep, is caused by slow replicating bacilli Mycobacterium avium subspecies paratuberculosis (MAP) infecting macrophages in the gut. Infected animals initially mount a cell-mediated CD4 T cell response against MAP which is characterized by the production of interferon (Th1 response). Over time, Th1 response diminishes in most animals and antibody response to MAP antigens becomes dominant (Th2 response). The switch from Th1 to Th2 response occurs concomitantly with disease progression and shedding of the bacteria in feces. Mechanisms controlling this Th1/Th2 switch remain poorly understood. Because Th1 and Th2 responses are known to cross-inhibit each other, it is unclear why initially strong Th1 response is lost over time. Using a novel mathematical model of the immune response to MAP infection we show that the ability of extracellular bacteria to persist outside of macrophages naturally leads to switch of the cellular response to antibody production. Several additional mechanisms may also contribute to the timing of the Th1/Th2 switch including the rate of proliferation of Th1/Th2 responses at the site of infection, efficiency at which immune responses cross-inhibit each other, and the rate at which Th1 response becomes exhausted over time. Our basic model reasonably well explains four different kinetic patterns of the Th1/Th2 responses in MAP-infected sheep by variability in the initial bacterial dose and the efficiency of the MAP-specific T cell responses. Taken together, our novel mathematical model identifies factors of bacterial and host origin that drive kinetics of the immune response to MAP and provides the basis for testing the impact of vaccination or early treatment on the duration of infection.

Mycobacterium avium subsp. paratuberculosis (MAP) is the causative agent of Johne's disease, a chronic enteric disease of ruminants such as sheep and cows. Due to early culling and reduction in milk production of affected animals, MAP inflicts high economic cost to diary farms. MAP infection has a long incubation period of several years, and during the asymptomatic stage a strong cellular (T helper 1) immune response is thought to control MAP replication. Over time, Th1 response is lost and ineffective antibody response driven by Th2 cells becomes predominant. We develop the first mathematical model of helper T cell response to MAP infection to understand impact of various mechanisms on the dynamics of the switch from Th1 to Th2 response. Our results suggest that in contrast to the generally held belief, Th1/Th2 switch may be driven by the accumulation of long-lived extracellular bacteria, and therefore, may be the consequence of the disease progression of MAP-infected animals and not its cause. Our model highlights limitations of our current understanding of regulation of helper T cell responses during MAP infection and identifies areas for future experimental research.

Cellular and population plasticity of helper CD4(+) T cell responses

Vertebrates are constantly exposed to pathogens, and the adaptive immunity has most likely evolved to control and clear such infectious agents. CD4⁺ T cells are the major players in the adaptive immune response to pathogens. Following recognition of pathogen-derived antigens naïve CD4⁺ T cells differentiate into effectors which then control pathogen replication either directly by killing pathogen-infected cells or by assisting with generation of cytotoxic T lymphocytes (CTLs) or pathogen-specific antibodies. Pathogen-specific effector CD4⁺ T cells are highly heterogeneous in terms of cytokines they produce. Three major subtypes of effector CD4⁺ T cells have been identified: T-helper 1 (Th1) cells producing IFN-γ and TNF-α, Th2 cells producing IL-4 and IL-10, and Th17 cells producing IL-17. How this heterogeneity is maintained and what regulates changes in effector T cell composition during chronic infections remains poorly understood. In this review we discuss recent advances in our understanding of CD4⁺ T cell differentiation in response to microbial infections. We propose that a change in the phenotype of pathogen-specific effector CD4⁺ T cells during chronic infections, for example, from Th1 to Th2 response as observed in Mycobactrium avium ssp. paratuberculosis (MAP) infection of ruminants, can be achieved by conversion of T cells from one effector subset to another (cellular plasticity) or due to differences in kinetics (differentiation, proliferation, death) of different effector T cell subsets (population plasticity). We also shortly review mathematical models aimed at describing CD4⁺ T cell differentiation and outline areas for future experimental and theoretical research.

Mathematical modeling of escape of HIV from cytotoxic T lymphocyte responses

Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about 2-3 weeks post infection that can lower the amount of virus in the body, but which cannot eradicate the virus. How HIV establishes a chronic infection in the face of a strong immune response remains poorly understood. It has been shown that HIV is able to rapidly change its proteins via mutation to evade recognition by virus-specific cytotoxic T lymphocytes (CTLs). Typically, an HIV-infected patient will generate 4-12 CTL responses specific for parts of viral proteins called epitopes. Such CTL responses lead to strong selective pressure to change the viral sequences encoding these epitopes so as to avoid CTL recognition. Indeed, the viral population "escapes" from about half of the CTL responses by mutation in the first year. Here we review experimental data on HIV evolution in response to CTL pressure, mathematical models developed to explain this evolution, and highlight problems associated with the data and previous modeling efforts. We show that estimates of the strength of the epitope-specific CTL response depend on the method used to fit models to experimental data and on the assumptions made regarding how mutants are generated during infection. We illustrate that allowing CTL responses to decay over time may improve the fit to experimental data and provides higher estimates of the killing efficacy of HIV-specific CTLs. We also propose a novel method for simultaneously estimating the killing efficacy of multiple CTL populations specific for different epitopes of HIV using stochastic simulations. Lastly, we show that current estimates of the efficacy at which HIV-specific CTLs clear virus-infected cells can be improved by more frequent sampling of viral sequences and by combining data on sequence evolution with experimentally measured CTL dynamics.

Vertical T cell immunodominance and epitope entropy determine HIV-1 escape

HIV-1 accumulates mutations in and around reactive epitopes to escape recognition and killing by CD8+ T cells. Measurements of HIV-1 time to escape should therefore provide information on which parameters are most important for T cell-mediated in vivo control of HIV-1. Primary HIV-1-specific T cell responses were fully mapped in 17 individuals, and the time to virus escape, which ranged from days to years, was measured for each epitope. While higher magnitude of an individual T cell response was associated with more rapid escape, the most significant T cell measure was its relative immunodominance measured in acute infection. This identified subject-level or "vertical" immunodominance as the primary determinant of in vivo CD8+ T cell pressure in HIV-1 infection. Conversely, escape was slowed significantly by lower population variability, or entropy, of the epitope targeted. Immunodominance and epitope entropy combined to explain half of all the variability in time to escape. These data explain how CD8+ T cells can exert significant and sustained HIV-1 pressure even when escape is very slow and that within an individual, the impacts of other T cell factors on HIV-1 escape should be considered in the context of immunodominance.

A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU+ cells are expected to divide into BrdU+ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU+ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU+ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU+ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.