A simple mathematical model helps to explain the immunodominance of CD8 T cells in influenza A virus infections

Predicting Influenza A Virus Infection in the Lung from Hematological Data with Machine Learning

The tracking of pathogen burden and host responses with minimally invasive methods during respiratory infections is central for monitoring disease development and guiding treatment decisions. Utilizing a standardized murine model of respiratory influenza A virus (IAV) infection, we developed and tested different supervised machine learning models to predict viral burden and immune response markers, i.e., cytokines and leukocytes in the lung, from hematological data. We performed independently in vivo infection experiments to acquire extensive data for training and testing of the models. We show here that lung viral load, neutrophil counts, cytokines (such as gamma interferon [IFN-γ] and interleukin 6 [IL-6]), and other lung infection markers can be predicted from hematological data. Furthermore, feature analysis of the models showed that blood granulocytes and platelets play a crucial role in prediction and are highly involved in the immune response against IAV. The proposed in silico tools pave the path toward improved tracking and monitoring of influenza virus infections and possibly other respiratory infections based on minimally invasively obtained hematological parameters. IMPORTANCE During the course of respiratory infections such as influenza, we do have a very limited view of immunological indicators to objectively and quantitatively evaluate the outcome of a host. Methods for monitoring immunological markers in a host's lungs are invasive and expensive, and some of them are not feasible to perform. Using machine learning algorithms, we show for the first time that minimally invasively acquired hematological parameters can be used to infer lung viral burden, leukocytes, and cytokines following influenza virus infection in mice. The potential of the framework proposed here consists of a new qualitative vision of the disease processes in the lung compartment as a noninvasive tool.

Host-pathogen kinetics during influenza infection and coinfection: insights from predictive modeling

Influenza virus infections are a leading cause of morbidity and mortality worldwide. This is due in part to the continual emergence of new viral variants and to synergistic interactions with other viruses and bacteria. There is a lack of understanding about how host responses work to control the infection and how other pathogens capitalize on the altered immune state. The complexity of multi-pathogen infections makes dissecting contributing mechanisms, which may be non-linear and occur on different time scales, challenging. Fortunately, mathematical models have been able to uncover infection control mechanisms, establish regulatory feedbacks, connect mechanisms across time scales, and determine the processes that dictate different disease outcomes. These models have tested existing hypotheses and generated new hypotheses, some of which have been subsequently tested and validated in the laboratory. They have been particularly a key in studying influenza-bacteria coinfections and will be undoubtedly be useful in examining the interplay between influenza virus and other viruses. Here, I review recent advances in modeling influenza-related infections, the novel biological insight that has been gained through modeling, the importance of model-driven experimental design, and future directions of the field.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection

Myriad experiments have identified an important role for CD8⁺ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8⁺ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8⁺ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8⁺ T cells may receive significantly more benefit from induction of additional effector CD8⁺ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

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.

A spatial model of the efficiency of T cell search in the influenza-infected lung

Emerging strains of influenza, such as avian H5N1 and 2009 pandemic H1N1, are more virulent than seasonal H1N1 influenza, yet the underlying mechanisms for these differences are not well understood. Subtle differences in how a given strain interacts with the immune system are likely a key factor in determining virulence. One aspect of the interaction is the ability of T cells to locate the foci of the infection in time to prevent uncontrolled expansion. Here, we develop an agent based spatial model to focus on T cell migration from lymph nodes through the vascular system to sites of infection. We use our model to investigate whether different strains of influenza modulate this process. We calibrate the model using viral and chemokine secretion rates we measure in vitro together with values taken from literature. The spatial nature of the model reveals unique challenges for T cell recruitment that are not apparent in standard differential equation models. In this model comparing three influenza viruses, plaque expansion is governed primarily by the replication rate of the virus strain, and the efficiency of the T cell search-and-kill is limited by the density of infected epithelial cells in each plaque. Thus for each virus there is a different threshold of T cell search time above which recruited T cells are unable to control further expansion. Future models could use this relationship to more accurately predict control of the infection.

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.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

How sticky should a virus be? The impact of virus binding and release on transmission fitness using influenza as an example

Budding viruses face a trade-off: virions need to efficiently attach to and enter uninfected cells while newly generated virions need to efficiently detach from infected cells. The right balance between attachment and detachment-the right amount of stickiness-is needed for maximum fitness. Here, we design and analyse a mathematical model to study in detail the impact of attachment and detachment rates on virus fitness. We apply our model to influenza, where stickiness is determined by a balance of the haemagglutinin (HA) and neuraminidase (NA) proteins. We investigate how drugs, the adaptive immune response and vaccines impact influenza stickiness and fitness. Our model suggests that the location in the 'stickiness landscape' of the virus determines how well interventions such as drugs or vaccines are expected to work. We discuss why hypothetical NA enhancer drugs might occasionally perform better than the currently available NA inhibitors in reducing virus fitness. We show that an increased antibody or T-cell-mediated immune response leads to maximum fitness at higher stickiness. We further show that antibody-based vaccines targeting mainly HA or NA, which leads to a shift in stickiness, might reduce virus fitness above what can be achieved by the direct immunological action of the vaccine. Overall, our findings provide potentially useful conceptual insights for future vaccine and drug development and can be applied to other budding viruses beyond influenza.

Modeling inoculum dose dependent patterns of acute virus infections

Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses. We suggest that such models should be taken as basis for future models of acute viral infections.

CD4 T-cell memory responses to viral infections of humans show pronounced immunodominance independent of duration or viral persistence

Little is known concerning immunodominance within the CD4 T-cell response to viral infections and its persistence into long-term memory. We tested CD4 T-cell reactivity against each viral protein in persons immunized with vaccinia virus (VV), either recently or more than 40 years ago, as a model self-limited viral infection. Similar tests were done with persons with herpes simplex virus 1 (HSV-1) infection as a model chronic infection. We used an indirect method capable of counting the CD4 T cells in blood reactive with each individual viral protein. Each person had a clear CD4 T-cell dominance hierarchy. The top four open reading frames accounted for about 40% of CD4 virus-specific T cells. Early and long-term memory CD4 T-cell responses to vaccinia virus were mathematically indistinguishable for antigen breadth and immunodominance. Despite the chronic intermittent presence of HSV-1 antigen, the CD4 T-cell dominance and diversity patterns for HSV-1 were identical to those observed for vaccinia virus. The immunodominant CD4 T-cell antigens included both long proteins abundantly present in virions and shorter, nonstructural proteins. Limited epitope level and direct ex vivo data were also consistent with pronounced CD4 T-cell immunodominance. We conclude that human memory CD4 T-cell responses show a pattern of pronounced immunodominance for both chronic and self-limited viral infections and that this pattern can persist over several decades in the absence of antigen.

Increasing viral dose causes a reversal in CD8+ T cell immunodominance during primary influenza infection due to differences in antigen presentation, T cell avidity, and precursor numbers

T cell responses are characterized by the phenomenon of immunodominance (ID), whereby peptide-specific T cells are elicited in a reproducible hierarchy of dominant and subdominant responses. However, the mechanisms that give rise to ID are not well understood. We investigated the effect of viral dose on primary CD8(+) T cell (T(CD8+)) ID by injecting mice i.p. with various doses of influenza A virus and assessing the primary T(CD8+) response to five dominant and subdominant peptides. Increasing viral dose enhanced the overall strength of the T(CD8+) response, and it altered the ID hierarchy: specifically, NP(366-374) T(CD8+) were dominant at low viral doses but were supplanted by PA(224-233) T(CD8+) at high doses. To understand the basis for this reversal, we mathematically modeled these T(CD8+) responses and used Bayesian statistics to obtain estimates for Ag presentation, T(CD8+) precursor numbers, and avidity. Interestingly, at low viral doses, Ag presentation most critically shaped ID hierarchy, enabling T(CD8+) specific to the more abundantly presented NP(366-374) to dominate. By comparison, at high viral doses, T(CD8+) avidity and precursor numbers appeared to be the major influences on ID hierarchy, resulting in PA(224-233) T(CD8+) usurping NP(366-374) cells as the result of higher avidity and precursor numbers. These results demonstrate that the nature of primary T(CD8+) responses to influenza A virus is highly influenced by Ag dose, which, in turn, determines the relative importance of Ag presentation, T(CD8+) avidity, and precursor numbers in shaping the ID hierarchy. These findings provide valuable insights for future T(CD8+)-based vaccination strategies.

Dynamics of stochastic mutation to immunodominance

Although a virus contains several epitopes that can be recognized by cytotoxic T lymphocytes (CTL), the immune responses against different epitopes are not uniform. Only a few CTLs (sometimes just one) will be immunodominant. Mutation of epitopes has been recognized as an important mechanism of immunodominance. Previous research has studied the influences of sporadic, discrete mutation events. In this work, we introduce a bounded noise term to account for the intrinsic stochastic nature of mutation. Monte Carlo simulations of the stochastic model show abounding complex phenomena, and patterns observed from the numerical simulations shed lights on long term trends of immunodomnance.

Modeling of influenza-specific CD8+ T cells during the primary response indicates that the spleen is a major source of effectors

The biological parameters that determine the distribution of virus-specific CD8(+) T cells during influenza infection are not all directly measurable by experimental techniques but can be inferred through mathematical modeling. Mechanistic and semimechanistic ordinary differential equations were developed to describe the expansion, trafficking, and disappearance of activated virus-specific CD8(+) T cells in lymph nodes, spleens, and lungs of mice during primary influenza A infection. An intensive sampling of virus-specific CD8(+) T cells from these three compartments was used to inform the models. Rigorous statistical fitting of the models to the experimental data allowed estimation of important biological parameters. Although the draining lymph node is the first tissue in which Ag-specific CD8(+) T cells are detected, it was found that the spleen contributes the greatest number of effector CD8(+) T cells to the lung, with rates of expansion and migration that exceeded those of the draining lymph node. In addition, models that were based on the number and kinetics of professional APCs fit the data better than those based on viral load, suggesting that the immune response is limited by Ag presentation rather than the amount of virus. Modeling also suggests that loss of effector T cells from the lung is significant and time dependent, increasing toward the end of the acute response. Together, these efforts provide a better understanding of the primary CD8(+) T cell response to influenza infection, changing the view that the spleen plays a minor role in the primary immune response.

Division of labor between subsets of lymph node dendritic cells determines the specificity of the CD8⁺ T-cell recall response to influenza infection

Cytotoxic T lymphocytes (CTLs) are important targets for vaccines against a wide variety of infections that enter the body via mucosal tissues. To induce effective immunity these vaccines must include the most protective epitopes and elicit rapid recall responses at the site of infection. Although live attenuated viruses are sometimes used to induce cellular immunity against recurrent influenza infections, the mechanisms that determine the magnitude of the response to individual viral components are very poorly defined. Heterosubtypic infections in C57BL/6 mice illustrate an additional level of complexity, when the antigen specificity of the response shifts dramatically between primary and secondary challenge. This model provides a unique opportunity to identify the mechanisms that regulate memory CD8(+) T-cell reactivation in vivo and control the specificity of the recall response by pathogen-specific CTL. We show that multiple factors contribute to the changing pattern of immunodominance during secondary infection, including the location of the memory CD8(+) T cells at the time of reinfection and their ability to directly recognize migratory CD103(+) DCs as they arrive in the lung draining LN.

Why Do CD8+ T Cells become Indifferent to Tumors: A Dynamic Modeling Approach

CD8+ T cells have the potential to influence the outcome of cancer pathogenesis, including complete tumor eradication or selection of malignant tumor escape variants. The Simian virus 40 large T-antigen (Tag) oncoprotein promotes tumor formation in Tag-transgenic mice and also provides multiple target determinants (sites) for responding CD8+ T cells in C57BL/6 (H-2(b)) mice. To understand the in vivo quantitative dynamics of CD8+ T cells after encountering Tag, we constructed a dynamic model from in vivo-generated data to simulate the interactions between Tag-expressing cells and CD8+ T cells in distinct scenarios including immunization of wild-type C57BL/6 mice and of Tag-transgenic mice that develop various tumors. In these scenarios the model successfully reproduces the dynamics of both the Tag-expressing cells and antigen-specific CD8+ T cell responses. The model predicts that the tolerance of the site-specific T cells is dependent on their apoptosis rates and that the net growth of CD8+ T cells is altered in transgenic mice. We experimentally validate both predictions. Our results indicate that site-specific CD8+ T cells have tissue-specific apoptosis rates affecting their tolerance to the tumor antigen. Moreover, the model highlights differences in apoptosis rates that contribute to compromised CD8+ T cell responses and tumor progression, knowledge of which is essential for development of cancer immunotherapy.

A theory of immunodominance and adaptive regulation

Immunodominance refers to the phenomenon in which simultaneous T cell responses against multiple target epitopes organize themselves into distinct and reproducible hierarchies. In many cases, eliminating the response to the most dominant epitope allows responses to subdominant epitopes to expand more fully. The mechanism that drives immunodominance is still not well understood, although various hypotheses have been proposed. One of the more prevalent views is that immunodominance is driven by passive T cell competition for space on antigen presenting cells (APCs) or for access to specific MHC:epitope complexes on the surface of APCs. However, several experimental studies suggest that passive competition alone may not fully explain the robustness of immunodominance under physiological conditions or varying proportions of antigen-specific precursor T cells and APCs. These studies propose that a mechanism of active suppression among T cells gives rise to immunodominance.In this work, we present the novel hypothesis that mutual suppression of simultaneous T cell responses results from the appearance of adaptive regulatory T cells (iTregs) during the course of the overall T cell expansion. We extend the mathematical model of T cell expansion proposed in Kim et al. (Bull. Math. Biol. 2009, doi: 10.1007/s11538-009-9463-1 ) to consider multiple, concurrent T cell responses. The model is formulated as a system of independent feedback loops, in which antigen-specific T cell population produces a nonspecific feedback response. Our simulations show that the fastest response to expand gives rise to a de novo generated population of iTregs that induces a premature contraction in slower or weaker T cell responses, leading to a hierarchical expansion as observed in immunodominance. Furthermore, in some cases, removing the dominant T cell response allows previously subdominant responses to develop more fully.

A shooting algorithm for complex immunodominance control problems

Although T cells are able to recognize a wide variety of target peptides, they are often strongly focused on a few of the peptides and leave the rest of them unattended. This phenomenon of strongly biased immune response is known as immunodominance. Mathematically, an immunodominance problem can be formulated using optimal control principles as a two-point boundary-value problem. The solution of this problem is challenging especially when the control variables are bounded. In this work, we develop a numerical algorithm based on the shooting technique for bounded optimal control problems. The algorithm is applied to a group of immunodominance problems. Numerical simulations reveal that the immune system selects either a broad or a specific strategy of immunodominance based on different optimization goals. The shooting algorithm can also be utilized to solve other complex optimal control problems.