Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus

The influence of circadian rhythms on CD8+ T cell activation upon vaccination: A mathematical modeling perspective

Circadian rhythms have been implicated in the modulation of many physiological processes, including those associated with the immune system. For example, these rhythms influence CD8+ T cell responses within the adaptive immune system. The mechanism underlying this immune-circadian interaction, however, remains unclear, particularly in the context of vaccination. Here, we devise a molecularly-explicit gene regulatory network model of early signaling in the naïve CD8+ T cell activation pathway, comprised of three axes (or subsystems) labeled ZAP70, LAT and CD28, to elucidate the molecular details of this immune-circadian mechanism and its relation to vaccination. This is done by coupling the model to a periodic forcing function to identify the molecular players targeted by circadian rhythms, and analyzing how these rhythms subsequently affect CD8+ T cell activation under differing levels of T cell receptor (TCR) phosphorylation, which we designate as vaccine load. By performing both bifurcation and parameter sensitivity analyses on the model at the single cell and ensemble levels, we find that applying periodic forcing on molecular targets within the ZAP70 axis is sufficient to create a day-night discrepancy in CD8+ T cell activation in a manner that is dependent on the bistable switch inherent in CD8+ T cell early signaling. We also demonstrate that the resulting CD8+ T cell activation is dependent on the strength of the periodic coupling as well as on the level of TCR phosphorylation. Our results show that this day-night discrepancy is not transmitted to certain downstream molecules within the LAT subsystem, such as mTORC1, suggesting a secondary, independent circadian regulation on that protein complex. We also corroborate experimental results by showing that the circadian regulation of CD8+ T cell primarily acts at a baseline, pre-vaccination state, playing a facilitating role in priming CD8+ T cells to vaccine inputs according to the time of day. By applying an ensemble level analysis using bifurcation theory and by including several hypothesized molecular targets of this circadian rhythm, we further demonstrate an increased variability between CD8+ T cells (due to heterogeneity) induced by its circadian regulation, which may allow an ensemble of CD8+ T cells to activate at a lower vaccine load, improving its sensitivity. This modeling study thus provides insights into the immune targets of the circadian clock, and proposes an interaction between vaccine load and the influence of circadian rhythms on CD8+ T cell activation.

A microscale 3D organ on a chip for recapitulating reciprocal neuroendocrine crosstalk between the hypothalamus and the pituitary gland

Conventional 2D or even recently developed 3Din vitroculture models for hypothalamus and pituitary gland cannot successfully recapitulate reciprocal neuroendocrine communications between these two pivotal neuroendocrine tissues known to play an essential role in controlling the body's endocrine system, survival, and reproduction. In addition, most currentvitroculture models for neuroendocrine tissues fail to properly reflect their complex multicellular structure. In this context, we developed a novel microscale chip platform, termed the 'hypothalamic-pituitary (HP) axis-on-a-chip,' which integrates various cellular components of the hypothalamus and pituitary gland with biomaterials such as collagen and hyaluronic acid. We used non-toxic blood coagulation factors (fibrinogen and thrombin) as natural cross-linking agents to increase the mechanical strength of biomaterials without showing residual toxicity to overcome drawbacks of conventional chemical cross-linking agents. Furthermore, we identified and verified SERPINB2 as a reliable neuroendocrine toxic marker, with its expression significantly increased in both hypothalamus and pituitary gland cells following exposure to various types of toxins. Next, we introduced SERPINB2-fluorescence reporter system into loaded hypothalamic cells and pituitary gland cells within each chamber of the HP axis on a chip, respectively. By incorporating this SERPINB2 detection system into the loaded hypothalamic and pituitary gland cells within our chip platform, Our HP axis-on-chip platform can better mimic reciprocal neuroendocrine crosstalk between the hypothalamus and the pituitary gland in the brain microenvironments with improved efficiency in evaluating neuroendocrine toxicities of certain drug candidates.

PASCAR: a multiscale framework to explore the design space of constitutive and inducible CAR T cells

CAR T cells are engineered to bind and destroy tumor cells by targeting overexpressed surface antigens. However, healthy cells expressing lower abundances of these antigens can also be lysed by CAR T cells. Various CAR T cell designs increase tumor cell elimination, whereas reducing damage to healthy cells. However, these efforts are costly and labor-intensive, constraining systematic exploration of potential hypotheses. We develop a protein abundance structured population dynamic model for CAR T cells (PASCAR), a framework that combines multiscale population dynamic models and multi-objective optimization approaches with data from cytometry and cytotoxicity assays to systematically explore the design space of constitutive and tunable CAR T cells. PASCAR can quantitatively describe in vitro and in vivo results for constitutive and inducible CAR T cells and can successfully predict experiments outside the training data. Our exploration of the CAR design space reveals that optimal CAR affinities in the intermediate range of dissociation constants effectively reduce healthy cell lysis, whereas maintaining high tumor cell-killing rates. Furthermore, our modeling offers guidance for optimizing CAR expressions in synthetic notch CAR T cells. PASCAR can be extended to other CAR immune cells.

Temporal Pattern of the Emergence of a Mutant Virus Escaping Cross-Immunity and Stochastic Extinction Within a Host

A high mutation rate of the RNA virus results in the emergence of novel mutants that may escape the immunity activated by the original (wild-type) strain. However, many of them go extinct because of the stochasticity due to the small initial number of infected cells. In a previous paper, we studied the probability of escaping stochastic extinction when the novel mutant has a faster rate of infection and when it is resistant to a drug that suppresses the wild-type virus. In this study, we examine the effect of escaping the immune reaction of the host. Based on a continuous-time branching process with time-dependent rates, we conclude the chance for a mutant strain to be established [Formula: see text] decreases with time [Formula: see text] since the wild-type infection when the mutant is produced. The number of novel mutants that can escape extinction risk has a peak soon after the wild-type infection. The number of novel escape mutations produced per patient in the early phase of host infection is small both for very strong and very weak immune responses, and it attains its maximum value when immune activity is of an intermediate strength.

Modeling T Cell Fate

Many of the pathways that underlie the diversification of naive T cells into effector and memory subsets, and the maintenance of these populations, remain controversial. In recent years a variety of experimental tools have been developed that allow us to follow the fates of cells and their descendants. In this review we describe how mathematical models provide a natural language for describing the growth, loss, and differentiation of cell populations. By encoding mechanistic descriptions of cell behavior, models can help us interpret these new datasets and reveal the rules underpinning T cell fate decisions, both at steady state and during immune responses.

Modelling of the Innate and Adaptive Immune Response to SARS Viral Infection, Cytokine Storm and Vaccination

In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose-response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.

Population-based cellular kinetic characterization of ciltacabtagene autoleucel in subjects with relapsed or refractory multiple myeloma

The aims of this work were to develop a population pharmacokinetic (PK) model for chimeric antigen receptor (CAR) transgene after single intravenous infusion administration of ciltacabtagene autoleucel in adult patients with relapsed or refractory multiple myeloma. CAR transgene level in blood were measured by quantitative polymerase chain reaction (qPCR) from 97 subjects in a phase Ib/II CARTITUDE-1 study (NCT03548207), with a targeted cilta-cel dose of 0.75 × 10⁶ (range 0.5-1.0 × 10⁶ ) CAR positive viable T-cells per kg body weight. The population PK model development was primarily guided by the current mechanistic understanding of CAR-T kinetics and the principles of building a parsimonious model. Cilta-cel PK was adequately described by a two-compartment model (with a fast and a slow apparent decline rate from each compartment, respectively) and a chain of four transit compartments with a lag time empirically representing the process from infused CAR-T cell to measurable CAR transgene. No apparent relationship was observed between cilta-cel dose (i.e., the actual number of CAR positive viable T-cells infused), given the narrow dose range, and the observed transgene level. Based on covariate search and subgroup analysis of maximum systemic CAR transgene level (C_max ) and area under curve from the first dose to day 28 (AUC_0-28d ), none of the investigated subjects' demographics, baseline characteristics, and manufactured product characteristics had significant effects on cilta-cel PK. The developed model is deemed robust and adequate for enabling subsequent exposure-safety and exposure-efficacy analyses.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

Iterative community-driven development of a SARS-CoV-2 tissue simulator

The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, intracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable "choke points" for pharmacologic interventions, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce and iteratively refine a prototype of a multiscale model of SARS-CoV-2 dynamics in lung tissue. The first prototype model was built and shared internationally as open source code and an online interactive model in under 12 hours, and community domain expertise is driving regular refinements. In a sustained community effort, this consortium is integrating data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health. More broadly, this effort is creating a reusable, modular framework for studying viral replication and immune response in tissues, which can also potentially be adapted to related problems in immunology and immunotherapy.

A Mathematical Description of the Bone Marrow Dynamics during CAR T-Cell Therapy in B-Cell Childhood Acute Lymphoblastic Leukemia

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients' experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T-cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells, and CAR T-cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T-cells, and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T-cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load, and leukemia burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.

A participant-derived xenograft model of HIV enables long-term evaluation of autologous immunotherapies

HIV-specific CD8⁺ T cells partially control viral replication and delay disease progression, but they rarely provide lasting protection, largely due to immune escape. Here, we show that engrafting mice with memory CD4⁺ T cells from HIV⁺ donors uniquely allows for the in vivo evaluation of autologous T cell responses while avoiding graft-versus-host disease and the need for human fetal tissues that limit other models. Treating HIV-infected mice with clinically relevant HIV-specific T cell products resulted in substantial reductions in viremia. In vivo activity was significantly enhanced when T cells were engineered with surface-conjugated nanogels carrying an IL-15 superagonist, but it was ultimately limited by the pervasive selection of a diverse array of escape mutations, recapitulating patterns seen in humans. By applying mathematical modeling, we show that the kinetics of the CD8⁺ T cell response have a profound impact on the emergence and persistence of escape mutations. This “participant-derived xenograft” model of HIV provides a powerful tool for studying HIV-specific immunological responses and facilitating the development of effective cell-based therapies.

Modeling and characterization of inter-individual variability in CD8 T cell responses in mice

To develop vaccines it is mandatory yet challenging to account for inter-individual variability during immune responses. Even in laboratory mice, T cell responses of single individuals exhibit a high heterogeneity that may come from genetic backgrounds, intra-specific processes (e.g. antigen-processing and presentation) and immunization protocols.

To account for inter-individual variability in CD8 T cell responses in mice, we propose a dynamical model coupled to a statistical, nonlinear mixed effects model. Average and individual dynamics during a CD8 T cell response are characterized in different immunization contexts (vaccinia virus and tumor). On one hand, we identify biological processes that generate inter-individual variability (activation rate of naive cells, the mortality rate of effector cells, and dynamics of the immunogen). On the other hand, introducing categorical covariates to analyze two different immunization regimens, we highlight the steps of the response impacted by immunogens (priming, differentiation of naive cells, expansion of effector cells and generation of memory cells). The robustness of the model is assessed by confrontation to new experimental data.

Our approach allows to investigate immune responses in various immunization contexts, when measurements are scarce or missing, and contributes to a better understanding of inter-individual variability in CD8 T cell immune responses.

Role of subnetworks mediated by [Formula: see text], IL-23/IL-17 and IL-15 in a network involved in the pathogenesis of psoriasis

Psoriasis is a chronic inflammatory skin disease clinically characterized by the appearance of red colored, well-demarcated plaques with thickened skin and with silvery scales. Recent studies have established the involvement of a complex signalling network of interactions between cytokines, immune cells and skin cells called keratinocytes. Keratinocytes form the cells of the outermost layer of the skin (epidermis). Visible plaques in psoriasis are developed due to the fast proliferation and unusual differentiation of keratinocyte cells. Despite that, the exact mechanism of the appearance of these plaques in the cytokine-immune cell network is not clear. A mathematical model embodying interactions between key immune cells believed to be involved in psoriasis, keratinocytes and relevant cytokines has been developed. The complex network formed of these interactions poses several challenges. Here, we choose to study subnetworks of this complex network and initially focus on interactions involving [Formula: see text], IL-23/IL-17, and IL-15. These are chosen based on known evidence of their therapeutic efficacy. In addition, we explore the role of IL-15 in the pathogenesis of psoriasis and its potential as a future drug target for a novel treatment option. We perform steady state analyses for these subnetworks and demonstrate that the interactions between cells, driven by cytokines could cause the emergence of a psoriasis state (hyper-proliferation of keratinocytes) when levels of [Formula: see text], IL-23/IL-17 or IL-15 are increased. The model results explain and support the clinical potentiality of anti-cytokine treatments. Interestingly, our results suggest different dynamic scenarios underpin the pathogenesis of psoriasis, depending upon the dominant cytokines of subnetworks. We observed that the increase in the level of IL-23/IL-17 and IL-15 could lead to psoriasis via a bistable route, whereas an increase in the level of [Formula: see text] would lead to a monotonic and gradual disease progression. Further, we demonstrate how this insight, bistability, could be exploited to improve the current therapies and develop novel treatment strategies for psoriasis.

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.

Model-Based Cellular Kinetic Analysis of Chimeric Antigen Receptor-T Cells in Humans

Chimeric antigen receptor (CAR)-T cell therapy has achieved considerable success in treating B-cell hematologic malignancies. However, the challenges of extending CAR-T therapy to other tumor types, particularly solid tumors, remain appreciable. There are substantial variabilities in CAR-T cellular kinetics across CAR-designs, CAR-T products, dosing regimens, patient responses, disease types, tumor burdens, and lymphodepletion conditions. As a "living drug," CAR-T cellular kinetics typically exhibit four distinct phases: distribution, expansion, contraction, and persistence. The cellular kinetics of CAR-T may correlate with patient responses, but which factors determine CAR-T cellular kinetics remain poorly defined. Herein, we developed a cellular kinetic model to retrospectively characterize CAR-T kinetics in 217 patients from 7 trials and compared CAR-T kinetics across response status, patient populations, and tumor types. Based on our analysis results, CAR-T cells exhibited a significantly higher cell proliferation rate and capacity but a lower contraction rate in patients who responded to treatment. CAR-T cells proliferate to a higher degree in hematologic malignancies than in solid tumors. Within the assessed dose ranges (10⁷ -10⁹ cells), CAR-T doses were weakly correlated with CAR-T cellular kinetics and patient response status. In conclusion, the developed CAR-T cellular kinetic model adequately characterized the multiphasic CAR-T cellular kinetics and supported systematic evaluations of the potential influencing factors, which can have significant implications for the development of more effective CAR-T therapies.

A modeling platform for the lymphatic system

We present a physiologically-based pharmacokinetic modeling platform capable of simulating the biodistribution of different therapeutic agents, including cells, their interactions within the immune system, redistribution across lymphoid compartments, and infiltration into tumor tissues. This transport-based platform comprises a distinctive implementation of a tumor compartment with spatial heterogeneity which enables the modeling of tumors of different size, necrotic state, and agent infiltration capacity. We provide three validating and three exploratory examples that illustrate the capabilities of the proposed approach. The results show that the model can recapitulate immune cell balance across different compartments, respond to antigen stimulation, simulate immune vaccine effects, and immune cell infiltration to tumors. Based on the results, the model can be used to study problems pertinent to current immunotherapies and has the potential to assist medical techniques that rely on the transport of biological species.

A model for establishment, maintenance and reactivation of the immune response after vaccination against Ebola virus

The 2014-2016 Ebola outbreak in West Africa has triggered accelerated development of several preventive vaccines against Ebola virus. Under the EBOVAC1 consortium, three phase I studies were carried out to assess safety and immunogenicity of a two-dose heterologous vaccination regimen developed by Janssen Vaccines and Prevention in collaboration with Bavarian Nordic. To describe the immune response induced by the two-dose heterologous vaccine regimen, we propose a mechanistic ODE based model, which takes into account the role of immunological memory. We perform identifiability and sensitivity analysis of the proposed model to establish which kind of biological data are ideally needed in order to accurately estimate parameters, and additionally, which of those are non-identifiable based on the available data. Antibody concentrations data from phase I studies have been used to calibrate the model and show its ability in reproducing the observed antibody dynamics. Together with other factors, the establishment of an effective and reactive immunological memory is of pivotal importance for several prophylactic vaccines. We show that introducing a memory compartment in our calibrated model allows to evaluate the magnitude of the immune response induced by a booster dose and its long-term persistence afterwards.

Dynamics of the Humoral Immune Response to a Prime-Boost Ebola Vaccine: Quantification and Sources of Variation

The Ebola vaccine based on Ad26.ZEBOV/MVA-BN-Filo prime-boost regimens is being evaluated in multiple clinical trials. The long-term immune response to the vaccine is unknown, including factors associated with the response and variability around the response. We analyzed data from three phase 1 trials performed by the EBOVAC1 Consortium in four countries: the United Kingdom, Kenya, Tanzania, and Uganda. Participants were randomized into four groups based on the interval between prime and boost immunizations (28 or 56 days) and the sequence in which Ad26.ZEBOV and MVA-BN-Filo were administered. Consecutive enzyme-linked immunosorbent assay (ELISA) measurements of the IgG binding antibody concentrations against the Kikwit glycoprotein (GP) were available for 177 participants to assess the humoral immune response up to 1 year postprime. Using a mathematical model for the dynamics of the humoral response, from 7 days after the boost immunization up to 1 year after the prime immunization, we estimated the durability of the antibody response and the influence of different factors on the dynamics of the humoral response. Ordinary differential equations (ODEs) described the dynamics of antibody response and two populations of antibody-secreting cells (ASCs), short-lived (SL) and long-lived (LL). Parameters of the ODEs were estimated using a population approach. We estimated that half of the LL ASCs could persist for at least 5 years. The vaccine regimen significantly affected the SL ASCs and the antibody peak but not the long-term response. The LL ASC compartment dynamics differed significantly by geographic regions analyzed, with a higher long-term antibody persistence in European subjects. These differences could not be explained by the observed differences in cellular immune response.IMPORTANCE With no available licensed vaccines or therapies, the West African Ebola virus disease epidemic of 2014 to 2016 caused 11,310 deaths. Following this outbreak, the development of vaccines has been accelerated. Combining different vector-based vaccines as heterologous regimens could induce a durable immune response, assessed through antibody concentrations. Based on data from phase 1 trials in East Africa and Europe, the dynamics of the humoral immune response from 7 days after the boost immunization onwards were modeled to estimate the durability of the response and understand its variability. Antibody production is maintained by a population of long-lived cells. Estimation suggests that half of these cells can persist for at least 5 years in humans. Differences in prime-boost vaccine regimens affect only the short-term immune response. Geographical differences in long-lived cell dynamics were inferred, with higher long-term antibody concentrations induced in European participants.

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

Dependence of CD8 T Cell Response upon Antigen Load During Primary Infection : Analysis of Data from Yellow Fever Vaccination

A major question in immunology is what role antigen load plays in determining the size of the CD8 immune response. Is the amount of antigen important during recruitment, proliferation, and/or memory formation? Animal studies have shown that antigen is only strictly required early during activation of T cells, but the importance of antigen at later timepoints is unclear. Using data from 24 volunteers infected with the yellow fever vaccine virus (YFV), we analyzed the dependence of T cell proliferation upon viral load. We found that volunteers with high viral load initially have greater T cell responses, but by 28 days post-vaccination those with lower viral load are able to 'catch-up.' Using differential equation modeling we show that this pattern is consistent with viral load only affecting recruitment (i.e., programmed proliferation) as opposed to affecting recruitment and proliferation (i.e., antigen-dependent proliferation). A quantitative understanding of the dependence of T cell dynamics on antigen load will be of use to modelers studying not only vaccination, but also cancer immunology and autoimmune disorders.

Herpes simplex virus-2 dynamics as a probe to measure the extremely rapid and spatially localized tissue-resident T-cell response

Herpes simplex virus-2 infection is characterized by frequent episodic shedding in the genital tract. Expansion in HSV-2 viral load early during episodes is extremely rapid. However, the virus invariably peaks within 18 hours and is eliminated nearly as quickly. A critical feature of HSV-2 shedding episodes is their heterogeneity. Some episodes peak at 10⁸ HSV DNA copies, last for weeks due to frequent viral re-expansion, and lead to painful ulcers, while others only reach 10³ HSV DNA copies and are eliminated within hours and without symptoms. Within single micro-environments of infection, tissue-resident CD8+ T cells (T_RM ) appear to contain infection within a few days. Here, we review components of T_RM biology relevant to immune surveillance between HSV-2 shedding episodes and containment of infection upon detection of HSV-2 cognate antigen. We then describe the use of mathematical models to correlate large spatial gradients in T_RM density with the heterogeneity of observed shedding within a single person. We describe how models have been leveraged for clinical trial simulation, as well as future plans to model the interactions of multiple cellular subtypes within mucosa, predict the mechanism of action of therapeutic vaccines, and describe the dynamics of 3-dimensional infection environment during the natural evolution of an HSV-2 lesion.

Within-host modeling of blood-stage malaria

Malaria infection continues to be a major health problem worldwide and drug resistance in the major human parasite species, Plasmodium falciparum, is increasing in South East Asia. Control measures including novel drugs and vaccines are in development, and contributions to the rational design and optimal usage of these interventions are urgently needed. Infection involves the complex interaction of parasite dynamics, host immunity, and drug effects. The long life cycle (48 hours in the common human species) and synchronized replication cycle of the parasite population present significant challenges to modeling the dynamics of Plasmodium infection. Coupled with these, variation in immune recognition and drug action at different life cycle stages leads to further complexity. We review the development and progress of "within-host" models of Plasmodium infection, and how these have been applied to understanding and interpreting human infection and animal models of infection.

Tisagenlecleucel Model-Based Cellular Kinetic Analysis of Chimeric Antigen Receptor-T Cells

Tisagenlecleucel is a chimeric antigen receptor–T cell therapy that facilitates the killing of CD19⁺ B cells. A model was developed for the kinetics of tisagenlecleucel and the impact of therapies for treating cytokine release syndrome (tocilizumab and corticosteroids) on expansion. Data from two phase II studies in pediatric and young adult relapsed/refractory B cell acute lymphoblastic leukemia were pooled to evaluate this model and evaluate extrinsic and intrinsic factors that may impact the extent of tisagenlecleucel expansion. The doubling time, initial decline half‐life, and terminal half‐life for tisagenlecleucel were 0.78, 4.3, and 220 days, respectively. No impact of tocilizumab or corticosteroids on the expansion rate was observed. This work represents the first mixed‐effect model‐based analysis of chimeric antigen receptor–T cell therapy and may be clinically impactful as future studies examine prophylactic interventions in patients at risk of higher grade cytokine release syndrome and the effects of these interventions on chimeric antigen receptor–T cell expansion.

Defining Kinetic Properties of HIV-Specific CD8⁺ T-Cell Responses in Acute Infection

Multiple lines of evidence indicate that CD8 + T cells are important in the control of HIV-1 (HIV) replication. However, CD8 + T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8 + T-cell responses induced during HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8 + T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8 + T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8 + T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8 + T cells in the chronic infection. The breadth of HIV-specific CD8 + T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8 + T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8 + T-cell responses and the presence of intra- and interclonal competition between multiple CD8 + T-cell responses; such competition may limit the magnitude of CD8 + T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8 + T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

Towards multiscale modeling of the CD8+ T cell response to viral infections

The CD8⁺ T cell response is critical to the control of viral infections. Yet, defining the CD8⁺ T cell response to viral infections quantitatively has been a challenge. Following antigen recognition, which triggers an intracellular signaling cascade, CD8⁺ T cells can differentiate into effector cells, which proliferate rapidly and destroy infected cells. When the infection is cleared, they leave behind memory cells for quick recall following a second challenge. If the infection persists, the cells may become exhausted, retaining minimal control of the infection while preventing severe immunopathology. These activation, proliferation and differentiation processes as well as the mounting of the effector response are intrinsically multiscale and collective phenomena. Remarkable experimental advances in the recent years, especially at the single cell level, have enabled a quantitative characterization of several underlying processes. Simultaneously, sophisticated mathematical models have begun to be constructed that describe these multiscale phenomena, bringing us closer to a comprehensive description of the CD8⁺ T cell response to viral infections. Here, we review the advances made and summarize the challenges and opportunities ahead. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Fates Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models.

Modeling the measles paradox reveals the importance of cellular immunity in regulating viral clearance

Measles virus (MV) is a highly contagious member of the Morbillivirus genus that remains a major cause of childhood mortality worldwide. Although infection induces a strong MV-specific immune response that clears viral load and confers lifelong immunity, transient immunosuppression can also occur, leaving the host vulnerable to colonization from secondary pathogens. This apparent contradiction of viral clearance in the face of immunosuppression underlies what is often referred to as the 'measles paradox', and remains poorly understood. To explore the mechanistic basis underlying the measles paradox, and identify key factors driving viral clearance, we return to a previously published dataset of MV infection in rhesus macaques. These data include virological and immunological information that enable us to fit a mathematical model describing how the virus interacts with the host immune system. In particular, our model incorporates target cell depletion through infection of host immune cells-a hallmark of MV pathology that has been neglected from previous models. We find the model captures the data well, and that both target cell depletion and immune activation are required to explain the overall dynamics. Furthermore, by simulating conditions of increased target cell availability and suppressed cellular immunity, we show that the latter causes greater increases in viral load and delays to MV clearance. Overall, this signals a more dominant role for cellular immunity in resolving acute MV infection. Interestingly, we find contrasting dynamics dominated by target cell depletion when viral fitness is increased. This may have wider implications for animal morbilliviruses, such as canine distemper virus (CDV), that cause fatal target cell depletion in their natural hosts. To our knowledge this work represents the first fully calibrated within-host model of MV dynamics and, more broadly, provides a new platform from which to explore the complex mechanisms underlying Morbillivirus infection.

Mathematical modeling of within-host Zika virus dynamics

Recent Zika virus outbreaks have been associated with severe outcomes, especially during pregnancy. A great deal of effort has been put toward understanding this virus, particularly the immune mechanisms responsible for rapid viral control in the majority of infections. Identifying and understanding the key mechanisms of immune control will provide the foundation for the development of effective vaccines and antiviral therapy. Here, we outline a mathematical modeling approach for analyzing the within-host dynamics of Zika virus, and we describe how these models can be used to understand key aspects of the viral life cycle and to predict antiviral efficacy.

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.

More or less-On the influence of labelling strategies to infer cell population dynamics

The adoptive transfer of labelled cell populations has been an essential tool to determine and quantify cellular dynamics. The experimental methods to label and track cells over time range from fluorescent dyes over congenic markers towards single-cell labelling techniques, such as genetic barcodes. While these methods have been widely used to quantify cell differentiation and division dynamics, the extent to which the applied labelling strategy actually affects the quantification of the dynamics has not been determined so far. This is especially important in situations where measurements can only be obtained at a single time point, as e.g. due to organ harvest. To this end, we studied the appropriateness of various labelling strategies as characterised by the number of different labels and the initial number of cells per label to quantify cellular dynamics. We simulated adoptive transfer experiments in systems of various complexity that assumed either homoeostatic cellular turnover or cell expansion dynamics involving various steps of cell differentiation and proliferation. Re-sampling cells at a single time point, we determined the ability of different labelling strategies to recover the underlying kinetics. Our results indicate that cell transition and expansion rates are differently affected by experimental shortcomings, such as loss of cells during transfer or sampling, dependent on the labelling strategy used. Furthermore, uniformly distributed labels in the transferred population generally lead to more robust and less biased results than non-equal label sizes. In addition, our analysis indicates that certain labelling approaches incorporate a systematic bias for the identification of complex cell expansion dynamics.

Fighting Cancer with Mathematics and Viruses

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

Molecular and genetic inflammation networks in major human diseases

It has been well-recognized that inflammation alongside tissue repair and damage maintaining tissue homeostasis determines the initiation and progression of complex diseases. Albeit with the accomplishment of having captured the most critical inflammation-involved molecules, genetic susceptibilities, epigenetic factors, and environmental factors, our schemata on the role of inflammation in complex diseases remain largely patchy, in part due to the success of reductionism in terms of research methodology per se. Omics data alongside the advances in data integration technologies have enabled reconstruction of molecular and genetic inflammation networks which shed light on the underlying pathophysiology of complex diseases or clinical conditions. Given the proven beneficial role of anti-inflammation in coronary heart disease as well as other complex diseases and immunotherapy as a revolutionary transition in oncology, it becomes timely to review our current understanding of the molecular and genetic inflammation networks underlying major human diseases. In this review, we first briefly discuss the complexity of infectious diseases and then highlight recently uncovered molecular and genetic inflammation networks in other major human diseases including obesity, type II diabetes, coronary heart disease, late onset Alzheimer's disease, Parkinson's disease, and sporadic cancer. The commonality and specificity of these molecular networks are addressed in the context of genetics based on genome-wide association study (GWAS). The double-sword role of inflammation, such as how the aberrant type 1 and/or type 2 immunity leads to chronic and severe clinical conditions, remains open in terms of the inflammasome and the core inflammatome network features. Increasingly available large Omics and clinical data in tandem with systems biology approaches have offered an exciting yet challenging opportunity toward reconstruction of more comprehensive and dynamic molecular and genetic inflammation networks, which hold great promise in transiting network snapshots to video-style multi-scale interplays of disease mechanisms, in turn leading to effective clinical intervention.

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.

Identification of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny

Primary immune responses generate short-term effectors and long-term protective memory cells. The delineation of the genealogy linking naive, effector, and memory cells has been complicated by the lack of phenotypes discriminating effector from memory differentiation stages. Using transcriptomics and phenotypic analyses, we identify Bcl2 and Mki67 as a marker combination that enables the tracking of nascent memory cells within the effector phase. We then use a formal approach based on mathematical models describing the dynamics of population size evolution to test potential progeny links and demonstrate that most cells follow a linear naive→early effector→late effector→memory pathway. Moreover, our mathematical model allows long-term prediction of memory cell numbers from a few early experimental measurements. Our work thus provides a phenotypic means to identify effector and memory cells, as well as a mathematical framework to investigate their genealogy and to predict the outcome of immunization regimens in terms of memory cell numbers generated.

Modelling and Simulation of the Dynamics of the Antigen-Specific T Cell Response Using Variable Structure Control Theory

Experimental and mathematical studies in immunology have revealed that the dynamics of the programmed T cell response to vigorous infection can be conveniently modelled using a sigmoidal or a discontinuous immune response function. This paper hypothesizes strong synergies between this existing work and the dynamical behaviour of engineering systems with a variable structure control (VSC) law. These findings motivate the interpretation of the immune system as a variable structure control system. It is shown that dynamical properties as well as conditions to analytically assess the transition from health to disease can be developed for the specific T cell response from the theory of variable structure control. In particular, it is shown that the robustness properties of the specific T cell response as observed in experiments can be explained analytically using a VSC perspective. Further, the predictive capacity of the VSC framework to determine the T cell help required to overcome chronic Lymphocytic Choriomeningitis Virus (LCMV) infection is demonstrated. The findings demonstrate that studying the immune system using variable structure control theory provides a new framework for evaluating immunological dynamics and experimental observations. A modelling and simulation tool results with predictive capacity to determine how to modify the immune response to achieve healthy outcomes which may have application in drug development and vaccine design.

Modelling cross-reactivity and memory in the cellular adaptive immune response to influenza infection in the host

The cellular adaptive immune response plays a key role in resolving influenza infection. Experiments where individuals are successively infected with different strains within a short timeframe provide insight into the underlying viral dynamics and the role of a cross-reactive immune response in resolving an acute infection. We construct a mathematical model of within-host influenza viral dynamics including three possible factors which determine the strength of the cross-reactive cellular adaptive immune response: the initial naive T cell number, the avidity of the interaction between T cells and the epitopes presented by infected cells, and the epitope abundance per infected cell. Our model explains the experimentally observed shortening of a second infection when cross-reactivity is present, and shows that memory in the cellular adaptive immune response is necessary to protect against a second infection.

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.

Immune-inspired search strategies for robot swarms

Detection of targets distributed randomly in space is a task common to both robotic and biological systems. Lévy search has previously been used to characterize T cell search in the immune system. We use a robot swarm to evaluate the effectiveness of a Lévy search strategy and map the relationship between search parameters and target configurations. We show that the fractal dimension of the Lévy search which optimizes search efficiency depends strongly on the distribution of targets but only weakly on the number of agents involved in search. Lévy search can therefore be tuned to the target configuration while also being scalable. Implementing search behaviors observed in T cells in a robot swarm provides an effective, adaptable, and scalable swarm robotic search strategy. Additionally, the adaptability and scalability of Lévy search may explain why Lévy-like movement has been observed in T cells in multiple immunological contexts.

Modeling the dynamics of neonatal CD8+ T-cell responses

Neonates are particularly susceptible to a number of infections, and the neonatal CD8+ T cell response demonstrates differences in both the phenotype and magnitude of responses to infection compared with adults. However, the underlying basis for these differences is unclear. We have used a mathematical modeling approach to analyze the dynamics of neonatal and adult CD8+ T cell responses following in vitro stimulation and in vivo infection, which allows us to dissect key cell-intrinsic differences in expansion, differentiation and memory formation. We found that neonatal cells started dividing 8 hrs earlier and proliferated at a faster rate (0.077 day⁻¹ vs 0.105 day⁻¹) than adult cells in vitro. In addition, neonatal cells also differentiated more rapidly, as measured by the loss in CD62L and Ly6C expression. We extended our mathematical modeling to analysis of neonatal and adult CD8+ T cells responding in vivo and demonstrated that neonatal cells divide more slowly than adult cells after day 4 post-infection. However, neonatal cells differentiate more rapidly, up-regulating more KLRG-1 per division than adult cells (20% vs. 5%). The dynamics of memory formation were also found to be different, with neonatal effector cells showing increased death (1.0 day⁻¹ vs. 2.45 day⁻¹). Comparison of the division of human cord blood and adult naïve cells stimulated in vitro showed more division in cord blood derived cells, consistent with the observations in mice. This work highlights differences of the cell-intrinsic division and differentiation program in neonatal CD8+ T cells.

Integrating Antimicrobial Therapy with Host Immunity to Fight Drug-Resistant Infections: Classical vs. Adaptive Treatment

Antimicrobial resistance of infectious agents is a growing problem worldwide. To prevent the continuing selection and spread of drug resistance, rational design of antibiotic treatment is needed, and the question of aggressive vs. moderate therapies is currently heatedly debated. Host immunity is an important, but often-overlooked factor in the clearance of drug-resistant infections. In this work, we compare aggressive and moderate antibiotic treatment, accounting for host immunity effects. We use mathematical modelling of within-host infection dynamics to study the interplay between pathogen-dependent host immune responses and antibiotic treatment. We compare classical (fixed dose and duration) and adaptive (coupled to pathogen load) treatment regimes, exploring systematically infection outcomes such as time to clearance, immunopathology, host immunization, and selection of resistant bacteria. Our analysis and simulations uncover effective treatment strategies that promote synergy between the host immune system and the antimicrobial drug in clearing infection. Both in classical and adaptive treatment, we quantify how treatment timing and the strength of the immune response determine the success of moderate therapies. We explain key parameters and dimensions, where an adaptive regime differs from classical treatment, bringing new insight into the ongoing debate of resistance management. Emphasizing the sensitivity of treatment outcomes to the balance between external antibiotic intervention and endogenous natural defenses, our study calls for more empirical attention to host immunity processes.

Strategic Priming with Multiple Antigens can Yield Memory Cell Phenotypes Optimized for Infection with Mycobacterium tuberculosis: A Computational Study

Lack of an effective vaccine results in 9 million new cases of tuberculosis (TB) every year and 1.8 million deaths worldwide. Although many infants are vaccinated at birth with BCG (an attenuated M. bovis), this does not prevent infection or development of TB after childhood. Immune responses necessary for prevention of infection or disease are still unknown, making development of effective vaccines against TB challenging. Several new vaccines are ready for human clinical trials, but these trials are difficult and expensive; especially challenging is determining the appropriate cellular response necessary for protection. The magnitude of an immune response is likely key to generating a successful vaccine. Characteristics such as numbers of central memory (CM) and effector memory (EM) T cells responsive to a diverse set of epitopes are also correlated with protection. Promising vaccines against TB contain mycobacterial subunit antigens (Ag) present during both active and latent infection. We hypothesize that protection against different key immunodominant antigens could require a vaccine that produces different levels of EM and CM for each Ag-specific memory population. We created a computational model to explore EM and CM values, and their ratio, within what we term Memory Design Space. Our model captures events involved in T cell priming within lymph nodes and tracks their circulation through blood to peripheral tissues. We used the model to test whether multiple Ag-specific memory cell populations could be generated with distinct locations within Memory Design Space at a specific time point post vaccination. Boosting can further shift memory populations to memory cell ratios unreachable by initial priming events. By strategically varying antigen load, properties of cellular interactions within the LN, and delivery parameters (e.g., number of boosts) of multi-subunit vaccines, we can generate multiple Ag-specific memory populations that cover a wide range of Memory Design Space. Given a set of desired characteristics for Ag-specific memory populations, we can use our model as a tool to predict vaccine formulations that will generate those populations.

The memory of a killer T cell: models of CD8(+) T cell differentiation

CD8(+) T cells have an important role in protection against infections and reinfections of intra-cellular pathogens like viruses. Naive CD8(+) T cells circulating in blood or lymphoid tissues can get activated upon stimulation by cognate antigen. The activated T cells undergo rapid proliferation and can expand more than 10(4)-folds comprising largely of effector T cells. Upon antigen clearance, the CD8(+) T-cell population contracts due to apoptosis, leaving behind a small population of memory T cells. The timing and mechanisms underlying the differentiation of naive cells into effector cells and memory cells is not yet clear. In this article, we review the recent quantitative studies that support different hypotheses of CD8(+) T-cell differentiation.

Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections

Oncolytic viruses (OVs) are used to treat cancer, as they selectively replicate inside of and lyse tumor cells. The efficacy of this process is limited and new OVs are being designed to mediate tumor cell release of cytokines and co-stimulatory molecules, which attract cytotoxic T cells to target tumor cells, thus increasing the tumor-killing effects of OVs. To further promote treatment efficacy, OVs can be combined with other treatments, such as was done by Huang et al., who showed that combining OV injections with dendritic cell (DC) injections was a more effective treatment than either treatment alone. To further investigate this combination, we built a mathematical model consisting of a system of ordinary differential equations and fit the model to the hierarchical data provided from Huang et al. We used the model to determine the effect of varying doses of OV and DC injections and to test alternative treatment strategies. We found that the DC dose given in Huang et al. was near a bifurcation point and that a slightly larger dose could cause complete eradication of the tumor. Further, the model results suggest that it is more effective to treat a tumor with immunostimulatory oncolytic viruses first and then follow-up with a sequence of DCs than to alternate OV and DC injections. This protocol, which was not considered in the experiments of Huang et al., allows the infection to initially thrive before the immune response is enhanced. Taken together, our work shows how the ordering, temporal spacing, and dosage of OV and DC can be chosen to maximize efficacy and to potentially eliminate tumors altogether.

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.

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl), that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

Quantitative impact of immunomodulation versus oncolysis with cytokine-expressing virus therapeutics

The past century's description of oncolytic virotherapy as a cancer treatment involving specially-engineered viruses that exploit immune deficiencies to selectively lyse cancer cells is no longer adequate. Some of the most promising therapeutic candidates are now being engineered to produce immunostimulatory factors, such as cytokines and co-stimulatory molecules, which, in addition to viral oncolysis, initiate a cytotoxic immune attack against the tumor. This study addresses the combined effects of viral oncolysis and T-cell-mediated oncolysis. We employ a mathematical model of virotherapy that induces release of cytokine IL-12 and co-stimulatory molecule 4-1BB ligand. We found that the model closely matches previously published data, and while viral oncolysis is fundamental in reducing tumor burden, increased stimulation of cytotoxic T cells leads to a short-term reduction in tumor size, but a faster relapse. In addition, we found that combinations of specialist viruses that express either IL-12 or 4-1BBL might initially act more potently against tumors than a generalist virus that simultaneously expresses both, but the advantage is likely not large enough to replace treatment using the generalist virus. Finally, according to our model and its current assumptions, virotherapy appears to be optimizable through targeted design and treatment combinations to substantially improve therapeutic outcomes.

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.

Predicting pathogen-specific CD8 T cell immune responses from a modeling approach

The primary CD8 T cell immune response constitutes a major mechanism to fight an infection by intra-cellular pathogens. We aim at assessing whether pathogen-specific dynamical parameters of the CD8 T cell response can be identified, based on measurements of CD8 T cell counts, using a modeling approach. We generated experimental data consisting in CD8 T cell counts kinetics during the response to three different live intra-cellular pathogens: two viruses (influenza, vaccinia) injected intranasally, and one bacteria (Listeria monocytogenes) injected intravenously. All pathogens harbor the same antigen (NP68), but differ in their interaction with the host. In parallel, we developed a mathematical model describing the evolution of CD8 T cell counts and pathogen amount during an immune response. This model is characterized by 9 parameters and includes relevant feedback controls. The model outputs were compared with the three data series and an exhaustive estimation of the parameter values was performed. By focusing on the ability of the model to fit experimental data and to produce a CD8 T cell population mainly composed of memory cells at the end of the response, critical parameters were identified. We show that a small number of parameters (2-4) define the main features of the CD8 T cell immune response and are characteristic of a given pathogen. Among these parameters, two are related to the effector CD8 T cell mediated control of cell and pathogen death. The parameter associated with memory cell death is shown to play no relevant role during the main phases of the CD8 T cell response, yet it becomes essential when looking at the predictions of the model several months after the infection.

The Effect of Interference on the CD8(+) T Cell Escape Rates in HIV

In early human immunodeficiency virus (HIV) infection, the virus population escapes from multiple CD8⁺ cell responses. The later an escape mutation emerges, the slower it outgrows its competition, i.e., the escape rate is lower. This pattern could indicate that the strength of the CD8⁺ cell responses is waning, or that later viral escape mutants carry a larger fitness cost. In this paper, we investigate whether the pattern of decreasing escape rates could also be caused by genetic interference among different escape strains. To this end, we developed a mathematical multi-epitope model of HIV dynamics, which incorporates stochastic effects, recombination, and mutation. We used cumulative linkage disequilibrium measures to quantify the amount of interference. We found that nearly synchronous, similarly strong immune responses in two-locus systems enhance the generation of genetic interference. This effect, combined with a scheme of densely spaced sampling times at the beginning of infection and sparse sampling times later, leads to decreasing successive escape rate estimates, even when there were no selection differences among alleles. These predictions are supported by empirical data from one HIV-infected patient. Thus, interference could explain why later escapes are slower. Considering escape mutations in isolation, neglecting their genetic linkage, conceals the underlying haplotype dynamics and can affect the estimation of the selective pressure exerted by CD8⁺ cells. In systems in which multiple escape mutations appear, the occurrence of interference dynamics should be assessed by measuring the linkage between different escape mutations.