Research

Overview

The main focus of the research in our laboratory is to generate quantitative understanding of the influence of immunity on the within-host dynamics and evolution of infectious diseases. Our primary tool in this approach is mathematical modeling where we combine models with experimental data. The research in the lab currently focused to study within-host dynamics and immune response to Plasmodium parasites (causative agents of malaria) and Mycobacterium tuberculosis (causative agent of tuberculosis). In particular, our research aims to understand how Plasmodium sporozoites establish infection in a new host, and how vaccine-induced immunity such as sporozoite-specific antibodies and CD8 T cells interfere with the infection process. In collaborations with numerous experimental groups, we parameterize data from intravital microscopy experiments to study the infection process and immune response to malaria. Our research also aims to study how Mycobacterium tuberculosis establishes the infection and disseminates in the lung and to extrapulmonary sites. Dissemination of bacteria is tracked using an ultra-low-dose infection of mice and the use of barcoded strains of Mtb. Additional areas of research include mathematical modeling of T-lymphocyte recirculation in the whole body, regulation of bacterial cell division, virus cooperativity at infection of cells and when spreading in plants.

Research Areas

Mathematical/Computational Immunology

Our expertise is in building and analyzing mathematical models of pathogen-host interactions, and in fitting the models to experimental data (typically available from our experimental collaborators). Typically, by rigorously comparing mathematical models with data we aim at discriminating between alternative mechanisms inherent in functioning of the immune system and within-host dynamics of pathogens. We focus on mechanisms of how pathogens (malaria parasites, Mycobacterium tuberculosis, HIV) cause disease and how host immunity may be preventing the disease and/or eliminating the infection. Some examples of how we apply mathematical models in immunology include:

Selected Publications

Rajakaruna, Harshana, James H O’Connor, Ian A Cockburn, and Vitaly Ganusov V. (2022) 2022. “Liver Environment-Imposed Constraints Diversify Movement Strategies of Liver-Localized CD8 T Cells.”. Journal of Immunology (Baltimore, Md. : 1950) 208 (5): 1292-1304. https://doi.org/10.4049/jimmunol.2100842.

Publisher's Version

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.
Aleshnick, Maya, Vitaly Ganusov V, Gibran Nasir, Gayane Yenokyan, and Photini Sinnis. (2020) 2020. “Experimental Determination of the Force of Malaria Infection Reveals a Non-Linear Relationship to Mosquito Sporozoite Loads.”. PLoS Pathogens 16 (5): e1008181. https://doi.org/10.1371/journal.ppat.1008181.

Publisher's Version

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.
McDaniel, Margaret M, Nitin Krishna, Winode G Handagama, Shigetoshi Eda, and Vitaly Ganusov V. (2016) 2016. “Quantifying Limits on Replication, Death, and Quiescence of Mycobacterium Tuberculosis in Mice.”. Frontiers in Microbiology 7: 862. https://doi.org/10.3389/fmicb.2016.00862.

Publisher's Version

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.

Statistics and Data Analysis in Immunology

We employ rigorous methods of data analysis, data visualization, and how mathematical models are fitted to data. One of the key philosophical achievements of our group is formulation of “strong inference of mathematical modeling in biology”. In strong inference we propose the cycle of mathematical modeling in biology by 1) testing alternative models in how well they describe experimental data, 2) determining reasons of why best fit model(s) fit the data well and why other models failed to describe the data, and 3) propose experiments to discriminate between remaining best fit models. We also recently proposed how mathematical modeling can be used to improve experimental design by selecting the number of experiments and specific time points for measurement to increase the ability to discriminate between alternative models (a.k.a. power analysis).

Selected Publications

Rajakaruna, Harshana, and Vitaly Ganusov V. (2022) 2022. “Mathematical Modeling to Guide Experimental Design: T Cell Clustering As a Case Study.”. Bulletin of Mathematical Biology 84 (10): 103. https://doi.org/10.1007/s11538-022-01063-x.

Publisher's Version

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.
Zenkov, Viktor S, James H O’Connor, Ian A Cockburn, and Vitaly Ganusov V. (2021) 2021. “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.”. Frontiers in Bioinformatics 1: 770448. https://doi.org/10.3389/fbinf.2021.770448.

Publisher's Version

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.
Ganusov, Vitaly, V. (2016) 2016. “Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.”. Frontiers in Microbiology 7: 1131. https://doi.org/10.3389/fmicb.2016.01131.

Publisher's Version

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.