A branching stochastic evolutionary model of the B-cell repertoire.

We propose a stochastic framework to describe the evolution of the B-cell repertoire during germinal center (GC) reactions. Our model is formulated as a multitype age-dependent branching process with time-varying immigration. The immigration process captures the mechanism by which founder B cells initiate clones by gradually seeding GC over time, while the branching process describes the temporal evolution of the composition of these clones. The model assigns a type to each cell to represent attributes of interest. Examples of attributes include the binding affinity class of the B cells, their clonal family, or the nucleotide sequence of the heavy and light chains of their receptors. The process is generally non-Markovian. We present its properties, including as t → ∞ when the process is supercritical, the most relevant case to study expansion of GC B cells. We introduce temporal alpha and beta diversity indices for multitype branching processes. We focus on the dynamics of clonal dominance, highlighting its non-stationarity, and the accumulation of somatic hypermutations in the context of sequential immunization. We evaluate the impact of the ongoing seeding of GC by founder B cells on the dynamics of the B-cell repertoire, and quantify the effect of precursor frequency and antigen availability on the timing of GC entry. An application of the model illustrates how it may help with interpretation of BCR sequencing data.

Measles Infection Dose Responses: Insights from Mathematical Modeling.

How viral infections develop can change based on the number of viruses initially entering the body. The understanding of the impacts of infection doses remains incomplete, in part due to challenging constraints, and a lack of research. Gaining more insights is crucial regarding the measles virus (MV). The higher the MV infection dose, the earlier the peak of acute viremia, but the magnitude of the peak viremia remains almost constant. Measles is highly contagious, causes immunosuppression such as lymphopenia, and contributes substantially to childhood morbidity and mortality. This work investigated mechanisms underlying the observed wild-type measles infection dose responses in cynomolgus monkeys. We fitted longitudinal data on viremia using maximum likelihood estimation, and used the Akaike Information Criterion (AIC) to evaluate relevant biological hypotheses and their respective model parameterizations. The lowest AIC indicates a linear relationship between the infection dose, the initial viral load, and the initial number of activated MV-specific T cells. Early peak viremia is associated with high initial number of activated MV-specific T cells. Thus, when MV infection dose increases, the initial viremia and associated immune cell stimulation increase, and reduce the time it takes for T cell killing to be sufficient, thereby allowing dose-independent peaks for viremia, MV-specific T cells, and lymphocyte depletion. Together, these results suggest that the development of measles depends on virus-host interactions at the start and the efficiency of viral control by cellular immunity. These relationships are additional motivations for prevention, vaccination, and early treatment for measles.

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes.

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

A multiscale spatial modeling framework for the germinal center response.

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymphoid organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events, including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanistic and applied research questions on the adaptive humoral immune response in the future.

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model.

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Construction and validation of a novel immunological model to predict prognosis in pancreatic ductal adenocarcinoma.

Pancreatic ductal adenocarcinoma (PDAC) is a highly aggressive cancer, with limited treatment options. In this study, we investigated the role of immune cell infiltration in PDAC progression and constructed an immune-related predictive model for patients with PDAC based on the International Cancer Genome Consortium (ICGC) cohort. Related algorithms have been used to assess the immune microenvironment. Least Absolute Shrinkage and Selection Operator (LASSO) Cox analysis was used to construct the model, and receiver operating characteristic and decision curve analysis analyses were conducted to evaluate its diagnostic and prognostic efficacy. The results demonstrated a correlation between high immune infiltration and better prognosis in PDAC. The immune-related prognostic model (IPM) identified four genes through LASSO Cox analysis, with the high IPM group being associated with a worse prognosis. Cox regression analysis confirmed that IPM is an independent risk factor for PDAC. Validation through analysis of The Cancer Genome Atlas cohort and our own individual tumor samples revealed a similar trend to that observed in the ICGC cohort. Finally, a nomogram incorporating age and IPM demonstrated efficacy in the prognostic evaluation of patients with PDAC. In conclusion, we developed a novel immune-related prognosis prediction model for PDAC that offers new possibilities for the measurement of immunotherapy and prognostic assessment of patients.

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 mathematical model for HIV dynamics with multiple infections: implications for immune escape.

Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.

Lyapunov functionals for a general time-delayed virus dynamic model with different CTL responses.

A time-delayed virus dynamic model is proposed with general monotonic incidence, different nonlinear CTL (cytotoxic T lymphocyte) responses [CTL elimination function pyg1(z) and CTL stimulation function cyg2(z)], and immune impairment. Indeed, the different CTL responses pose challenges in obtaining the dissipativeness of the model. By constructing appropriate Lyapunov functionals with some detailed analysis techniques, the global stability results of all equilibria of the model are obtained. By the way, we point out that the partial derivative fv(x,0) is increasing (but not necessarily strictly) in x>0 for the general monotonic incidence f(x,v). However, some papers defaulted that the partial derivative was strictly increasing. Our main results show that if the basic reproduction number R0≤1, the infection-free equilibrium E0 is globally asymptotically stable (GAS); if CTL stimulation function cyg2(z)=0 for z=0 and the CTL threshold parameter R1≤1

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes.

The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle's invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays.

An immuno-epidemiological model with waning immunity after infection or vaccination.

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.

Modelling the Impact of NETosis During the Initial Stage of Systemic Lupus Erythematosus.

The development of autoimmune diseases often takes years before clinical symptoms become detectable. We propose a mathematical model for the immune response during the initial stage of Systemic Lupus Erythematosus which models the process of aberrant apoptosis and activation of macrophages and neutrophils. NETosis is a type of cell death characterised by the release of neutrophil extracellular traps, or NETs, containing material from the neutrophil's nucleus, in response to a pathogenic stimulus. This process is hypothesised to contribute to the development of autoimmunogenicity in SLE. The aim of this work is to study how NETosis contributes to the establishment of persistent autoantigen production by analysing the steady states and the asymptotic dynamics of the model by numerical experiment.

Stability of a diffusive-delayed HCV infection model with general cell-to-cell incidence function incorporating immune response and cell proliferation.

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay.

Decoding systems immunological model of sphingolipids with IL-6/IL-17/IL-23 axes in L. major infection.

IL-6, IL-17, IL-23 and IL-1ß are the crucial cytokines controlling inflammatory and immune response during L. major infection. During cutaneous leishmaniasis, an important T helper cell type CD4+ Th17 subset plays a deterministic role in lesion formation through channelling infected macrophages and production of IL-1ß, IL-6, IL-23 and IFN-γ. Ceramide derived sphingosine precursors may assist in pro-inflammatory cytokine response. However, the role of these metabolites in inflammation with pleiotropic pro-inflammatory cytokines in L. major infection is unknown. The present study indicates IL-6/IL-17/IL-23 and SPHK1-S1P-S1PRs signaling axes with the overexpression of SATB1 aiding in disease progression. Targeting SATB1 might modulate the secretion of pro-inflammatory cytokines and abnormal immune functioning, thereby killing the intracellular parasite. Systems immunological methods assisted in a step towards identifying the key to the mystery of crucial components and serving as an approach for therapeutic intervention in L. major infection.

CircRNA-Based Cervical Cancer Prognosis Model, Immunological Validation and Drug Prediction.

BACKGROUND: Cervical cancer (CC) is a common cancer in female, which is associated with problems like poor prognosis. Circular RNA (circRNA) is a kind of competing endogenous RNA (ceRNA) that has an important role in regulating microRNA (miRNA) in many cancers. The regulatory mechanisms of CC immune microenvironment and the transcriptome level remain to be fully explored. METHODS: In this study, we constructed the ceRNA network through the interaction data and expression matrix of circRNA, miRNA and mRNA. Meanwhile, based on the gene expression matrix, CIBERSORT algorithm was used to reveal contents of tumor-infiltrating immune cells (TIICs). Then, we screened prognostic markers based on ceRNA network and immune infiltration and constructed two nomograms. In order to find immunological differences between the high- and low-risk CC samples, we examined multiple immune checkpoints and predicted the effect of PD-L1 ICI immunotherapy. In addition, the sensitive therapeutics for high-risk patients were screened, and the potential agents with anti-CC activity were predicted by Connective Map (CMap). RESULTS: We mapped a ceRNA network including 5 circRNAs, 17 miRNAs and 129 mRNAs. From the mRNA nodes of the network six genes and two kind of cells were identified as prognostic makers for CC. Among them, there was a significant positive correlation between CD8+ T cells and SNX10 gene. The results of TIDE and single sample GSEA (ssGSEA) showed that T cells CD8 do play a key role in inhibiting tumor progression. Further, our study screened 24 drugs that were more sensitive to high-risk CC patients and several potential therapeutic agents for reference. CONCLUSIONS: Our study identified several circRNA-miRNA-mRNA regulatory axes and six prognostic genes based on the ceRNA network. In addition, through TIIC, survival analysis and a series of immunological analyses, T cells were proved to be good prognostic markers, besides play an important role in the immune process. Finally, we screened 24 potentially more effective drugs and multiple potential drug compounds for high- and low-risk patients.

The adaptation model of immunity: Is the goal of central tolerance to eliminate defective T cells or self-reactive T cells?

The self-non-self model and the danger model are designed to understand how an immune response is induced. These models are not meant to predict if an immune response may succeed or fail in destroying/controlling its target. However, these immunological models rely on either self-antigens or self-dendritic cells for understanding of central tolerance, which have been discussed by Fuchs and Matzinger in response to Al-Yassin. In an attempt to address some questions that these models are facing when it comes to understanding central tolerance, I propose that the goal of negative selection in the thymus is to eliminate defective T cells but not self-reactive T cells. Therefore, any escape from negative selection could increase lymphopenia because of the depletion of defective naïve T cells outside the thymus, as seen in the elderly.

Universal antigen encoding of T cell activation from high-dimensional cytokine dynamics.

Systems immunology lacks a framework with which to derive theoretical understanding from high-dimensional datasets. We combined a robotic platform with machine learning to experimentally measure and theoretically model CD8+ T cell activation. High-dimensional cytokine dynamics could be compressed onto a low-dimensional latent space in an antigen-specific manner (so-called "antigen encoding"). We used antigen encoding to model and reconstruct patterns of T cell immune activation. The model delineated six classes of antigens eliciting distinct T cell responses. We generalized antigen encoding to multiple immune settings, including drug perturbations and activation of chimeric antigen receptor T cells. Such universal antigen encoding for T cell activation may enable further modeling of immune responses and their rational manipulation to optimize immunotherapies.

Malnutrition and Dietary Habits Alter the Immune System Which May Consequently Influence SARS-CoV-2 Virulence: A Review.

COVID-19, resulting from the SARS-CoV-2 virus, is a major pandemic that the world is fighting. SARS-CoV-2 primarily causes lung infection by attaching to the ACE2 receptor on the alveolar epithelial cells. However, the ACE2 receptor is also present in intestinal epithelial cells, suggesting a link between nutrition, virulence and clinical outcomes of COVID-19. Respiratory viral infections perturb the gut microbiota. The gut microbiota is shaped by our diet; therefore, a healthy gut is important for optimal metabolism, immunology and protection of the host. Malnutrition causes diverse changes in the immune system by repressing immune responses and enhancing viral vulnerability. Thus, improving gut health with a high-quality, nutrient-filled diet will improve immunity against infections and diseases. This review emphasizes the significance of dietary choices and its subsequent effects on the immune system, which may potentially impact SARS-CoV-2 vulnerability.