A Mathematical Model of the Effects of Aging on Naive T Cell Populations and Diversity

Mathematical Characterization of Private and Public Immune Receptor Sequences

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

Immunosenescence in Aging-Related Vascular Dysfunction

The immunosenescence-related disproportion in T lymphocytes may have important consequences for endothelial dysfunction, which is a key event in vascular aging. The study was designed to assess the prognostic values of the inflammatory-immune profile to better predict and prevent vascular diseases associated with old age. Eighty individuals aged 70.9 ± 5.3 years were allocated to a low- (LGI) or high-grade inflammation (HGI) group based on CRP (<3 or ≥3 mg/L) as a conventional risk marker of cardiovascular diseases. Significant changes in inflammatory and endothelium-specific variables IL-1β, IL-6, TNFα, oxLDL, H2O2, NO, 3-nitrotyrosine, and endothelial progenitor cells (OR 7.61, 95% CI 2.56−29.05, p < 0.0001), confirmed their interplay in vascular inflammation. The flow-cytometry analysis demonstrated a high disproportion in T lymphocytes CD4+ and CD8+ between LGI and HGI groups. CRP was <3 mg/mL for the CD4/CD8 ratio within the reference values ≥ 1 or ≤2.5, unlike for the CD4/CD8 ratio < 1 and >2.5. The odds ratios for the distribution of CD4+ (OR 5.98, 95% CI 0.001−0.008, p < 0.001), CD8+ (OR 0.23, 95% CI 0.08−0.59, p < 0.01), and CD8CD45RO+ T naïve cells (OR 0.27, 95% CI 0.097−0.695, p < 0.01) and CD4/CD8 (OR 5.69, 95% CI 2.07−17.32, p < 0.001) indicated a potential diagnostic value of T lymphocytes for clinical prognosis in aging-related vascular dysfunction.

Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian

Background and objective

Cancer Immunoediting (CI) describes the cellular-level interaction between tumor cells and the Immune System (IS) that takes place in the Tumor Micro-Environment (TME). CI is a highly dynamic and complex process comprising three distinct phases (Elimination, Equilibrium and Escape) wherein the IS can both protect against cancer development as well as, over time, promote the appearance of tumors with reduced immunogenicity. Herein we present an agent-based model for the simulation of CI in the TME, with the objective of promoting the understanding of this process.

Methods

Our model includes agents for tumor cells and for elements of the IS. The actions of these agents are governed by probabilistic rules, and agent recruitment (including cancer growth) is modeled via logistic functions. The system is formalized as an analogue of the Ising model from statistical mechanics to facilitate its analysis. The model was implemented in the Netlogo modeling environment and simulations were performed to verify, illustrate and characterize its operation.

Results

A main result from our simulations is the generation of emergent behavior in silico that is very difficult to observe directly in vivo or even in vitro. Our model is capable of generating the three phases of CI; it requires only a couple of control parameters and is robust to these. We demonstrate how our simulated system can be characterized through the Ising-model energy function, or Hamiltonian, which captures the “energy” involved in the interaction between agents and presents it in clear and distinct patterns for the different phases of CI.

Conclusions

The presented model is very flexible and robust, captures well the behaviors of the target system and can be easily extended to incorporate more variables such as those pertaining to different anti-cancer therapies. System characterization via the Ising-model Hamiltonian is a novel and powerful tool for a better understanding of CI and the development of more effective treatments. Since data of CI at the cellular level is very hard to procure, our hope is that tools such as this may be adopted to shed light on CI and related developing theories.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04731-w.

How Naive T-Cell Clone Counts Are Shaped By Heterogeneous Thymic Output and Homeostatic Proliferation

The specificity of T cells is that each T cell has only one T cell receptor (TCR). A T cell clone represents a collection of T cells with the same TCR sequence. Thus, the number of different T cell clones in an organism reflects the number of different T cell receptors (TCRs) that arise from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution, are important factors in immune functions. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. We describe the heterogeneous steady-state population of naive T cells (those that have not yet been antigenically triggered) by using a mean-field model of a regulated birth-death-immigration process. After accounting for random sampling, we investigate how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or “clone counts”). By using reasonable physiological parameter values and fitting predicted clone counts to experimentally sampled clone abundances, we show that realistic levels of heterogeneity in immigration rates cause very little change to predicted clone-counts, but that modest heterogeneity in proliferation rates can generate the observed clone abundances. Our analysis provides constraints among physiological parameters that are necessary to yield predictions that qualitatively match the data. Assumptions of the model and potentially other important mechanistic factors are discussed.

Pre-Existing Hypertension Is Related with Disproportions in T-Lymphocytes in Older Age

Age-related immune deficiencies increase the risk of comorbidities and mortality. This study evaluated immunosenescence patterns by flow cytometry of naïve and memory T cell subpopulations and the immune risk profile (IRP), expressed as the CD4/CD8 ratio and IgG CMV related to comorbidities. The disproportions in naïve and memory T cells, as well as in the CD4/CD8 ratio, were analysed in 99 elderly individuals (71.9 ± 5.8 years) diagnosed with hypertension (n = 51) or without hypertension (n = 48), using an eight-parameter flow cytometer. The percentage of CD4+ T lymphocytes was significantly higher in hypertensive than other individuals independently from CMV infections, with approximately 34% having CD4/CD8 > 2.5, and only 4% of the elderly with hypertension having CD4/CD8 < 1. The elderly with a normal BMI demonstrated the CD4/CD8 ratio ≥ 1 or ≤ 2.5, while overweight and obese participants showed a tendency to an inverted CD4/CD8 ratio. CD4/CD8 ratio increased gradually with age and reached the highest values in participants aged >75 years. The decline in CD4+ naïve T lymphocytes was more prominent in IgG CMV+ men when compared to IgG CMV+ women. The changes in naïve and memory T lymphocyte population, CD4/CD8, and CMV seropositivity included in IRP are important markers of health status in the elderly that are dependent on hypertension.

Lifestyle exercise attenuates immunosenescence; flow cytometry analysis

Background

Interaction of physical activity and overall immune profile is very complex and depends on the intensity, duration and frequency of undertaken physical activity, the exposure to cytomegalovirus (CMV) infection and the age-related changes in the immune system. Daily physical activity, which particularly influences immunity, declines dramatically with age. Therefore, the aim of the study was to explain whether physical activity sustained throughout life can attenuate or reverse immunosenescence.

Methods

Ninety-nine older adults (60–90 years) were recruited for the study. According to the 6-min walk test (6WMT), the Åstrand-Ryhming bike test (VO₂max) and Community Healthy Activities Model Program for Seniors (CHAMPS) questionnaire, the individuals were classified as physically active (n = 34) and inactive (n = 20) groups. The analysis of T lymphocytes between active vs. inactive participants was performed using eight-parameter flow cytometry.

Results

Analysis of the baseline peripheral naïve and memory T lymphocytes showed a significant relationship of lifestyle exercise with the CD4/CD8 ratio. Above 50% of physically active participants demonstrated the CD4/CD8 ratio ≥ 1 or ≤ 2.5 contrary to the inactive group who showed the ratio < 1. The older adults with the result of 6WMT > 1.3 m/s and VO₂max > 35 mL/kg/min had a significantly higher CD4⁺CD45RA⁺ T lymphocyte percentage and also a higher ratio of CD4⁺CD45RA⁺/CD4⁺CD45RO⁺. Interestingly, in active older adults with IgG CMV⁺ (n = 30) the count of CD4⁺CD45RA⁺ T lymphocytes was higher than in the inactive group with IgG CMV⁺ (n = 20).

Conclusion

Based on the flow cytometry analysis, we concluded that lifestyle exercise could lead to rejuvenation of the immune system by increasing the percentage of naïve T lymphocytes or by reducing the tendency of the inverse CD4/CD8 ratio.

Dynamics of thymus function and T cell receptor repertoire breadth in health and disease

T cell recognition of unknown antigens relies on the tremendous diversity of the T cell receptor (TCR) repertoire; generation of which can only occur in the thymus. TCR repertoire breadth is thus critical for not only coordinating the adaptive response against pathogens but also for mounting a response against malignancies. However, thymic function is exquisitely sensitive to negative stimuli, which can come in the form of acute insult, such as that caused by stress, infection, or common cancer therapies; or chronic damage such as the progressive decline in thymic function with age. Whether it be prolonged T cell deficiency after hematopoietic cell transplantation (HCT) or constriction in the breadth of the peripheral TCR repertoire with age; these insults result in poor adaptive immune responses. In this review, we will discuss the importance of thymic function for generation of the TCR repertoire and how acute and chronic thymic damage influences immune health. We will also discuss methods that are used to measure thymic function in patients and strategies that have been developed to boost thymic function.

Diversity in biology: definitions, quantification and models

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depends on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population, before outlining the various definitions of 'diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields, including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.

Dynamics of T cell receptor distributions following acute thymic atrophy and resumption

Naive human T cells are produced and developed in the thymus, which atrophies abruptly and severely in response to physical or psychological stress. To understand how an instance of stress affects the size and "diversity" of the peripheral naive T cell pool, we derive a mean-field autonomous ODE model of T cell replenishment that allows us to track the clone abundance distribution (the mean number of different TCRs each represented by a specific number of cells). We identify equilibrium solutions that arise at different rates of T cell production, and derive analytic approximations to the dominant eigenvalues and eigenvectors of the mathematical model linearized about these equilibria. From the forms of the eigenvalues and eigenvectors, we estimate rates at which counts of clones of different sizes converge to and depart from equilibrium values-that is, how the number of clones of different sizes "adjusts" to the changing rate of T cell production. Under most physiological realizations of our model, the dominant eigenvalue (representing the slowest dynamics of the clone abundance distribution) scales as a power law in the thymic output for low output levels, but saturates at higher T cell production rates. Our analysis provides a framework for quantitatively understanding how the clone abundance distribution evolves under small changes in the overall T cell production rate.