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OBJECTIVE: Healthy subjects and patients with rheumatoid arthritis (RA) exhibit circadian rhythms of the neuroendocrine-immune system. Understanding circadian dynamics is complex due to the nonlinear behavior of the neuroendocrine-immune network. This study was undertaken to seek and test a mathematical model for studying this network. METHODS: We established a quantitative computational model to simulate nonlinear interactions between key factors in the neuroendocrine-immune system, such as plasma tumor necrosis factor (TNF), plasma cortisol (and adrenal cholesterol store), and plasma noradrenaline (NA) (and presynaptic NA store). RESULTS: The model was nicely fitted with measured reference data on healthy subjects and RA patients. Although the individual circadian pacemakers of cortisol, NA, and TNF were installed without a phase shift, the relative phase shift between these factors evolved as a consequence of the modeled network interactions. Combined long-term and short-term TNF increase (the 'RA model') increased cortisol plasma levels for only a few days, and cholesterol stores started to become markedly depleted. This nicely demonstrated the phenomenon of inadequate cortisol secretion relative to plasma TNF levels, as a consequence of adrenal deficiency. Using the RA model, treatment with glucocorticoids between midnight and 2:00 AM was found to have the strongest inhibitory effect on TNF secretion, which supports recent studies on RA therapy. Long-term reduction of TNF levels by simulation of anti-TNF therapy normalized cholesterol stores under 'RA' conditions. CONCLUSION: These first in silico studies of the neuroendocrine-immune system in rheumatology demonstrate that computational biology in medicine, making use of large collections of experimental data, supports understanding of the pathophysiology of complex nonlinear systems. [ABSTRACT FROM AUTHOR]

The product of an axialvector and a scalar current and its relation to the chiral-odd distribution function h1 is discussed in the framework of the renormalon approach. Using a bag-model calculation for h1, we calculate its intrinsic uncertainty due to renormalon poles. The result is given as a function of Bjorken- x as well as for the first moments separately. [ABSTRACT FROM AUTHOR]

Control of cell proliferation is critical for the lymphocyte life cycle. However, little is known about how stage-specific alterations in cell cycle behavior drive proliferation dynamics during T cell development. Here, we employed in vivo dual-nucleoside pulse labeling combined with the determination of DNA replication over time as well as fluorescent ubiquitination-based cell cycle indicator mice to establish a quantitative high-resolution map of cell cycle kinetics of thymocytes. We developed an agent-based mathematical model of T cell developmental dynamics. To generate the capacity for proliferative bursts, cell cycle acceleration followed a "stretch model" characterized by the simultaneous and proportional contraction of both G1 and S phases. Analysis of cell cycle phase dynamics during regeneration showed tailored adjustments of cell cycle phase dynamics. Taken together, our results highlight intrathymic cell cycle regulation as an adjustable system to maintain physiologic tissue homeostasis and foster our understanding of dysregulation of the T cell developmental program., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Emerging infectious diseases and climate change are two of the major challenges in 21st century. Although over the past decades, highly-resolved mathematical models have contributed in understanding dynamics of infectious diseases and are of great aid when it comes to finding suitable intervention measures, they may need substantial computational effort and produce significant CO 2 emissions. Two popular modeling approaches for mitigating infectious disease dynamics are agent-based and population-based models. Agent-based models (ABMs) offer a microscopic view and are thus able to capture heterogeneous human contact behavior and mobility patterns. However, insights on individual-level dynamics come with high computational effort that scales with the number of agents. On the other hand, population-based models (PBMs) using e.g. ordinary differential equations (ODEs) are computationally efficient even for large populations due to their complexity being independent of the population size. Yet, population-based models are restricted in their granularity as they assume a (to some extent) homogeneous and well-mixed population. To manage the trade-off between computational complexity and level of detail, we propose spatial- and temporal-hybrid models that use ABMs only in an area or time frame of interest. To account for relevant influences to disease dynamics, e.g., from outside, due to commuting activities, we use population-based models, only adding moderate computational costs. Our hybridization approach demonstrates significant reduction in computational effort by up to 98% - without losing the required depth in information in the focus frame. The hybrid models used in our numerical simulations are based on two recently proposed models, however, any suitable combination of ABM and PBM could be used, too. Concluding, hybrid epidemiological models can provide insights on the individual scale where necessary, using aggregated models where possible, thereby making a contribution to green computing., Competing Interests: All authors declare to not have any conflict of interest., (© 2025 The Authors.)

In the realm of infectious disease control, accurate modeling of the transmission dynamics is pivotal. As human mobility and commuting patterns are key components of communicable disease spread, we introduce a novel travel time aware metapopulation model. Our model aims to enhance estimations of disease transmission. By providing more reliable assessments on the efficacy of interventions, curtailing personal rights or human mobility behavior through interventions can be minimized. The proposed model is an advancement over traditional compartmental models, integrating explicit transmission on travel and commute, a factor available in agent-based models but often neglected with metapopulation models. Our approach employs a multi-edge graph ODE-based (Graph-ODE) model, which represents the intricate interplay between mobility and disease spread. This granular modeling is particularly important when assessing the dynamics in densely connected urban areas or when heterogeneous structures across entire countries have to be assessed. The given approach can be coupled with any kind of ODE-based model. In addition, we propose a novel multi-layer waning immunity model that integrates waning of different paces for protection against mild and severe courses of the disease. As this is of particular interest for late-phase epidemic or endemic scenarios, we consider the late-phase of SARS-CoV-2 in Germany. The results of this work show that accounting for resolved mobility significantly influences the pattern of outbreaks. The improved model provides a refined tool for predicting outbreak trajectories and evaluating intervention strategies in relation to mobility by allowing us to assess the transmission that result on traveling. The insights derived from this model can serve as a basis for decisions on the implementation or suspension of interventions, such as mandatory masks on public transportation. Eventually, our model contributes to maintaining mobility as a social good while reducing exuberant disease dynamics potentially driven by travel activities., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Zunker et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Identifying immune modulators that impact neutralizing antibody responses against severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) is of great relevance. We postulated that high serum concentrations of soluble angiotensin-converting enzyme 2 (sACE2) might mask the spike and interfere with antibody maturation toward the SARS-CoV-2-receptor-binding motif (RBM). We tested 717 longitudinal samples from 295 COVID-19 patients and showed a 2- to 10-fold increase of enzymatically active sACE2 (a-sACE2), with up to 1 μg/mL total sACE2 in moderate and severe patients. Fifty percent of COVID-19 sera inhibited ACE2 activity, in contrast to 1.3% of healthy donors and 4% of non-COVID-19 pneumonia patients. A mild inverse correlation of a-sACE2 with RBM-directed serum antibodies was observed. In silico , we show that sACE2 concentrations measured in COVID-19 sera can disrupt germinal center formation and inhibit timely production of high-affinity antibodies. We suggest that sACE2 is a biomarker for COVID-19 and that soluble receptors may contribute to immune suppression informing vaccine design., Competing Interests: The Max Delbrück Center for Molecular Medicine in the Helmholtz Association and the Charité - Universitätsmedizin Berlin have filed three patent applications in connection with this work on which M.L., F.K., L.E.S., and K.D.L.R. (EP21155584.2); C.V.G. and K.D.L.R. (EP22164013.9); and M.L., C.R., C.V.G., and K.D.L.R. (EP21194414.5) are inventors., (© 2024 The Authors.)

Introduction: A protective humoral response to pathogens requires the development of high affinity antibodies in germinal centers (GC). The combination of antigens available during immunization has a strong impact on the strength and breadth of the antibody response. Antigens can display various levels of immunogenicity, and a hierarchy of immunodominance arises when the GC response to an antigen dampens the response to other antigens. Immunodominance is a challenge for the development of vaccines to mutating viruses, and for the development of broadly neutralizing antibodies. The extent by which antigens with different levels of immunogenicity compete for the induction of high affinity antibodies and therefore contribute to immunodominance is not known., Methods: Here, we perform in silico simulations of the GC response, using a structural representation of antigens with complex surface amino acid composition and topology. We generate antigens with complex domains of different levels of immunogenicity and perform simulations with combinations of these domains., Results: We found that GC dynamics were driven by the most immunogenic domain and immunodominance arose as affinity maturation to less immunogenic domain was inhibited. However, this inhibition was moderate since the less immunogenic domain exhibited a weak GC response in the absence of the most immunogenic domain. Less immunogenic domains reduced the dominance of GC responses to more immunogenic domains, albeit at a later time point., Discussion: The simulations suggest that increased vaccine valency may decrease immunodominance of the GC response to strongly immunogenic domains and therefore, act as a potential strategy for the natural induction of broadly neutralizing antibodies in GC reactions., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Robert, Arulraj and Meyer-Hermann.)

The selection of high-affinity B cells and the production of high-affinity antibodies are mediated by T follicular helper cells (Tfhs) within germinal centres (GCs). Therein, somatic hypermutation and selection enhance B cell affinity but risk the emergence of self-reactive B cell clones. Despite being outnumbered compared to their helper counterpart, the ablation of T follicular regulatory cells (Tfrs) results in enhanced dissemination of self-reactive antibody-secreting cells (ASCs). The specific mechanisms by which Tfrs exert their regulatory action on self-reactive B cells are largely unknown. We developed computer simulations to investigate how Tfrs regulate either selection or differentiation of B cells to prevent auto-reactivity. We observed that Tfr-induced apoptosis of self-reactive B cells during the selection phase impedes self-reactivity with physiological Tfr numbers, especially when Tfrs can access centrocyte-enriched GC areas. While this aided in selecting non-self-reactive B cells by restraining competition, higher Tfr numbers distracted non-self-reactive B cells from receiving survival signals from Tfhs. Thus, the location and number of Tfrs must be regulated to circumvent such Tfr distraction and avoid disrupting GC evolution. In contrast, when Tfrs regulate differentiation of selected centrocytes by promoting recycling to the dark zone phenotype of self-reactive GC resident pre-plasma cells (GCPCs), higher Tfr numbers were required to impede the circulation of self-reactive ASCs (s-ASCs). On the other hand, Tfr-engagement with GCPCs and subsequent apoptosis of s-ASCs can control self-reactivity with low Tfr numbers, but does not confer selection advantage to non-self-reactive B cells. The simulations predict that to restrict auto-reactivity, natural redemption of self-reactive B cells is insufficient and that Tfrs should increase the mutation probability of self-reactive B cells., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Schips, Mitra, Bandyopadhyay and Meyer-Hermann.)

The magnitude and quality of the germinal center (GC) response decline with age, resulting in poor vaccine-induced immunity in older individuals. A functional GC requires the co-ordination of multiple cell types across time and space, in particular across its two functionally distinct compartments: the light and dark zones. In aged mice, there is CXCR4-mediated mislocalization of T follicular helper (T FH ) cells to the dark zone and a compressed network of follicular dendritic cells (FDCs) in the light zone. Here we show that T FH cell localization is critical for the quality of the antibody response and for the expansion of the FDC network upon immunization. The smaller GC and compressed FDC network in aged mice were corrected by provision of T FH cells that colocalize with FDCs using CXCR5. This demonstrates that the age-dependent defects in the GC response are reversible and shows that T FH cells support stromal cell responses to vaccines., (© 2023. The Author(s).)

Antibody affinity maturation depends on the formation of germinal centers (GCs) in lymph nodes. This process generates a massive number of apoptotic B cells, which are removed by a specialized subset of phagocytes, known as tingible body macrophages (TBMs). Although defects in these cells are associated with pathological conditions, the identity of their precursors and the dynamics of dying GC B cell disposal remained unknown. Here, we demonstrate that TBMs originate from pre-existing lymph node-resident precursors that enter the lymph node follicles in a GC-dependent manner. Intravital imaging shows that TBMs are stationary cells that selectively phagocytose GC B cells via highly dynamic protrusions and accommodate the final stages of B cell apoptosis. Cell-specific depletion and chimeric mouse models revealed that GC B cells drive TBM formation from bone marrow-derived precursors stationed within lymphoid organs prior to the immune challenge. Understanding TBM dynamics and function may explain the emergence of various antibody-mediated autoimmune conditions., (© 2023 Gurwicz et al.)

Sequencing of B-cell and T-cell immune receptor repertoires helps us to understand the adaptive immune response, although it only provides information about the clonotypes (lineages) and their frequencies and not about, for example, their affinity or antigen (Ag) specificity. To further characterize the identified clones, usually with special attention to the particularly abundant ones (dominant), additional time-consuming or expensive experiments are generally required. Here, we present an extension of a multiscale model of the germinal center (GC) that we previously developed to gain more insight in B-cell repertoires. We compare the extent that these simulated repertoires deviate from experimental repertoires established from single GCs, blood, or tissue. Our simulations show that there is a limited correlation between clonal abundance and affinity and that there is large affinity variability among same-ancestor (same-clone) subclones. Our simulations suggest that low-abundance clones and subclones, might also be of interest since they may have high affinity for the Ag. We show that the fraction of plasma cells (PCs) with high B-cell receptor (BcR) mRNA content in the GC does not significantly affect the number of dominant clones derived from single GCs by sequencing BcR mRNAs. Results from these simulations guide data interpretation and the design of follow-up experiments., (© 2023. The Author(s).)

A variety of B cell clones seed the germinal centers, where a selection stringency expands the fitter clones to generate higher affinity antibodies. However, recent experiments suggest that germinal centers often retain a diverse set of B cell clones with a range of affinities and concurrently carry out affinity maturation. Amid a tendency to flourish germinal centers with fitter clones, how several B cell clones with differing affinities can be concurrently selected remains poorly understood. Such a permissive selection may allow non-immunodominant clones, which are often rare and of low-affinity, to somatically hypermutate and result in a broad and diverse B cell response. How the constituent elements of germinal centers, their quantity and kinetics may modulate diversity of B cells, has not been addressed well. By implementing a state-of-the-art agent-based model of germinal center, here, we study how these factors impact temporal evolution of B cell clonal diversity and its underlying balance with affinity maturation. While we find that the extent of selection stringency dictates clonal dominance, limited antigen availability on follicular dendritic cells is shown to expedite the loss of diversity of B cells as germinal centers mature. Intriguingly, the emergence of a diverse set of germinal center B cells depends on high affinity founder cells. Our analysis also reveals a substantial number of T follicular helper cells to be essential in balancing affinity maturation with clonal diversity, as a low number of T follicular helper cells impedes affinity maturation and also contracts the scope for a diverse B cell response. Our results have implications for eliciting antibody responses to non-immunodominant specificities of the pathogens by controlling the regulators of the germinal center reaction, thereby pivoting a way for vaccine development to generate broadly protective antibodies., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Garg, Mitra, Schips, Bandyopadhyay and Meyer-Hermann.)

We develop a novel approach integrating epidemiological and economic models that allows data-based simulations during a pandemic. We examine the economically optimal opening strategy that can be reconciled with the containment of a pandemic. The empirical evidence is based on data from Germany during the SARS-CoV-2 pandemic. Our empirical findings reject the view that there is necessarily a conflict between health protection and economic interests and suggest a non-linear U-shape relationship: it is in the interest of public health and the economy to balance non-pharmaceutical interventions in a manner that further reduces the incidence of infections. Our simulations suggest that a prudent strategy that leads to a reproduction number of around 0.75 is economically optimal. Too restrictive policies cause massive economic costs. Conversely, policies that are too loose lead to higher death tolls and higher economic costs in the long run. We suggest this finding as a guide for policy-makers in balancing interests of public health and the economy during a pandemic., (© 2022. The Author(s).)