Integrated Inflammatory Stress (ITIS) Model

Modelling the continuum of macrophage phenotypes and their role in inflammation

Macrophages are a type of white blood cell that play a significant role in determining the inflammatory response associated with a wide range of medical conditions. They are highly plastic, having the capacity to adopt numerous polarisation states or 'phenotypes' with disparate pro- or anti-inflammatory roles. Many previous studies divide macrophages into two categorisations: M1 macrophages are largely pro-inflammatory in nature, while M2 macrophages are largely restorative. However, there is a growing body of evidence that the M1 and M2 classifications represent the extremes of a much broader spectrum of phenotypes, and that intermediate phenotypes can play important roles in the progression or treatment of many medical conditions. In this article, we present a model of macrophage dynamics that includes a continuous description of phenotype, and hence incorporates intermediate phenotype configurations. We describe macrophage phenotype switching via nonlinear convective flux terms that scale with background levels of generic pro- and anti-inflammatory mediators. Through numerical simulation and bifurcation analysis, we unravel the model's resulting dynamics, paying close attention to the system's multistability and the extent to which key macrophage-mediator interactions provide bifurcations that act as switches between chronic states and restoration of health. We show that interactions that promote M1-like phenotypes generally result in a greater array of stable chronic states, while interactions that promote M2-like phenotypes can promote restoration of health. Additionally, our model admits oscillatory solutions reminiscent of relapsing-remitting conditions, with macrophages being largely polarised toward anti-inflammatory activity during remission, but with intermediate phenotypes playing a role in inflammatory flare-ups. We conclude by reflecting on our observations in the context of the ongoing pursuance of novel therapeutic interventions.

A systematic evaluation of the influence of macrophage phenotype descriptions on inflammatory dynamics

Macrophages play a wide range of roles in resolving the inflammatory damage that underlies many medical conditions and have the ability to adopt different phenotypes in response to different environmental stimuli. Categorising macrophage phenotypes exactly is a difficult task, and there is disparity in the literature around the optimal nomenclature to describe these phenotypes; however, what is clear is that macrophages can exhibit both pro- and anti-inflammatory behaviours dependent upon their phenotype, rendering mathematical models of the inflammatory response potentially sensitive to their description of the macrophage populations that they incorporate. Many previous models of inflammation include a single macrophage population with both pro- and anti-inflammatory functions. Here, we build upon these existing models to include explicit descriptions of distinct macrophage phenotypes and examine the extent to which this influences the inflammatory dynamics that the models emit. We analyse our models via numerical simulation in MATLAB and dynamical systems analysis in XPPAUT, and show that models that account for distinct macrophage phenotypes separately can offer more realistic steady state solutions than precursor models do (better capturing the anti-inflammatory activity of tissue resident macrophages), as well as oscillatory dynamics not previously observed. Finally, we reflect on the conclusions of our analysis in the context of the ongoing hunt for potential new therapies for inflammatory conditions, highlighting manipulation of macrophage polarisation states as a potential therapeutic target.

Characterization of differences in immune responses during bolus and continuous infusion endotoxin challenges using mathematical modelling

Endotoxin administration is commonly used to study the inflammatory response, and though traditionally given as a bolus injection, it can be administered as a continuous infusion over multiple hours. Several studies hypothesize that the latter better represents the prolonged and pronounced inflammation observed in conditions like sepsis. Yet very few experimental studies have administered endotoxin using both strategies, leaving significant gaps in determining the underlying mechanisms responsible for their differing immune responses. We used mathematical modelling to analyse cytokine data from two studies administering a 2 ng kg-1 dose of endotoxin, one as a bolus and the other as a continuous infusion over 4 h. Using our model, we simulated the dynamics of mean and subject-specific cytokine responses as well as the response to long-term endotoxin administration. Cytokine measurements revealed that the bolus injection led to significantly higher peaks for interleukin (IL)-8, while IL-10 reaches higher peaks during continuous administration. Moreover, the peak timing of all measured cytokines occurred later with continuous infusion. We identified three model parameters that significantly differed between the two administration methods. Monocyte activation of IL-10 was greater during the continuous infusion, while tumour necrosis factor α $ {\alpha} $ and IL-8 recovery rates were faster for the bolus injection. This suggests that a continuous infusion elicits a stronger, longer-lasting systemic reaction through increased stimulation of monocyte anti-inflammatory mediator production and decreased recovery of pro-inflammatory catalysts. Furthermore, the continuous infusion model exhibited prolonged inflammation with recurrent peaks resolving within 2 days during long-term (20-32 h) endotoxin administration.

VeVaPy, a Python Platform for Efficient Verification and Validation of Systems Biology Models with Demonstrations Using Hypothalamic-Pituitary-Adrenal Axis Models

In order for mathematical models to make credible contributions, it is essential for them to be verified and validated. Currently, verification and validation (V&V) of these models does not meet the expectations of the system biology and systems pharmacology communities. Partially as a result of this shortfall, systemic V&V of existing models currently requires a lot of time and effort. In order to facilitate systemic V&V of chosen hypothalamic-pituitary-adrenal (HPA) axis models, we have developed a computational framework named VeVaPy-taking care to follow the recommended best practices regarding the development of mathematical models. VeVaPy includes four functional modules coded in Python, and the source code is publicly available. We demonstrate that VeVaPy can help us efficiently verify and validate the five HPA axis models we have chosen. Supplied with new and independent data, VeVaPy outputs objective V&V benchmarks for each model. We believe that VeVaPy will help future researchers with basic modeling and programming experience to efficiently verify and validate mathematical models from the fields of systems biology and systems pharmacology.

Mathematical analysis of the role of pituitary-adrenal interactions in ultradian rhythms of the HPA axis

The hypothalamic-pituitary-adrenal (HPA) axis is a biological system in the human body that plays an important role in controlling stress and regulating various physiological elements, including the immune system, emotions, and moods in tense situations. Over the past two decades, several ordinary or delay differential equations models of the HPA axis have been proposed. In the majority of studies presented so far, corticotropin-releasing hormone (CRH), adrenocorticotropic hormone (ACTH), and cortisol are among the main variables employed to build the HPA axis models. In the present study, based on a previously introduced hypothesis which asserts that ultradian rhythms in the HPA axis are produced by the pituitary-adrenal network alone and these rhythms can endure in the absence of CRH secretion, a simple two-dimensional delayed dynamical model of the HPA axis based on only ACTH and cortisol is introduced. The model is shown to be able to capture the ultradian (low frequency) rhythms of ACTH and cortisol released into the bloodstream. By mathematical analysis of the model using the Hopf bifurcation theorem, it is also demonstrated how oscillating solutions can emerge. Also, the model employs physiologically reasonable parameter values to exhibit how in the absence of CRH secretion, a simple model of the pituitary-adrenal interaction can be used to produce ultradian rhythms of both cortisol and ACTH hormones.

Role of enhanced glucocorticoid receptor sensitivity in inflammation in PTSD: insights from computational model for circadian-neuroendocrine-immune interactions

Although glucocorticoid resistance contributes to increased inflammation, individuals with posttraumatic stress disorder (PTSD) exhibit increased glucocorticoid receptor (GR) sensitivity along with increased inflammation. It is not clear how inflammation coexists with a hyperresponsive hypothalamic-pituitary-adrenal (HPA) axis. To understand this better, we developed and analyzed an integrated mathematical model for the HPA axis and the immune system. We performed mathematical simulations for a dexamethasone (DEX) suppression test and IC₅₀-dexamethasone for cytokine suppression by varying model parameters. The model analysis suggests that increasing the steepness of the dose-response curve for GR activity may reduce anti-inflammatory effects of GRs at the ambient glucocorticoid levels, thereby increasing proinflammatory response. The adaptive response of proinflammatory cytokine-mediated stimulatory effects on the HPA axis is reduced due to dominance of the GR-mediated negative feedback on the HPA axis. To verify these hypotheses, we analyzed the clinical data on neuroendocrine variables and cytokines obtained from war-zone veterans with and without PTSD. We observed significant group differences for cortisol and ACTH suppression tests, proinflammatory cytokines TNFα and IL6, high-sensitivity C-reactive protein, promoter methylation of GR gene, and IC_50-DEX for lysozyme suppression. Causal inference modeling revealed significant associations between cortisol suppression and post-DEX cortisol decline, promoter methylation of human GR gene exon 1F (NR3C1-1F), IC_50-DEX, and proinflammatory cytokines. We noted significant mediation effects of NR3C1-1F promoter methylation on inflammatory cytokines through changes in GR sensitivity. Our findings suggest that increased GR sensitivity may contribute to increased inflammation; therefore, interventions to restore GR sensitivity may normalize inflammation in PTSD.

Mechanistic inferences on metabolic dysfunction in posttraumatic stress disorder from an integrated model and multiomic analysis: role of glucocorticoid receptor sensitivity

Posttraumatic stress disorder (PTSD) is associated with neuroendocrine alterations and metabolic abnormalities; however, how metabolism is affected by neuroendocrine disturbances is unclear. The data from combat-exposed veterans with PTSD show increased glycolysis to lactate flux, reduced TCA cycle flux, impaired amino acid and lipid metabolism, insulin resistance, inflammation, and hypersensitive hypothalamic-pituitary-adrenal (HPA) axis. To analyze whether the co-occurrence of multiple metabolic abnormalities is independent or arises from an underlying regulatory defect, we employed a systems biological approach using an integrated mathematical model and multiomic analysis. The models for hepatic metabolism, HPA axis, inflammation, and regulatory signaling were integrated to perform metabolic control analysis (MCA) with respect to the observations from our clinical data. We combined the metabolomics, neuroendocrine, clinical laboratory, and cytokine data from combat-exposed veterans with and without PTSD to characterize the differences in regulatory effects. MCA revealed mechanistic association of the HPA axis and inflammation with metabolic dysfunction consistent with PTSD. This was supported by the data using correlational and causal analysis that revealed significant associations between cortisol suppression, high-sensitivity C-reactive protein, homeostatic model assessment of insulin resistance, γ-glutamyltransferase, hypoxanthine, and several metabolites. Causal mediation analysis indicates that the effects of enhanced glucocorticoid receptor sensitivity (GRS) on glycolytic pathway, gluconeogenic and branched-chain amino acids, triglycerides, and hepatic function are jointly mediated by inflammation, insulin resistance, oxidative stress, and energy deficit. Our analysis suggests that the interventions to normalize GRS and inflammation may help to manage features of metabolic dysfunction in PTSD.

Therapeutic effects of curcumin on sepsis and mechanisms of action: A systematic review of preclinical studies

Sepsis is a complex disease that begins with an infectious disorder and causes excessive immune responses. Curcumin is considered as an active component of turmeric that can improve the condition in sepsis due to its anti-inflammatory and antioxidant properties. PubMed, Embase, Google Scholar, Web of Science, and Scopus databases were searched. Searching was not limited to a specific publication period. Only English-language original articles, which had examined the effect of curcumin on sepsis, were included. At first, 1,098 articles were totally found, and 209 articles were selected after excluding duplicated data; 46 articles were remained due to the curcumin effects on sepsis. These included 23 in vitro studies and 23 animal studies. Our results showed that curcumin and various analogs of curcumin can have an inhibitory effect on sepsis-induced complications. Curcumin has the ability to inhibit the inflammatory, oxidative coagulation factors, and regulation of immune responses in sepsis. Despite the promising evidence of the therapeutic effects of curcumin on the sepsis complication, further studies seem necessary to investigate its effect and possible mechanisms of action in human studies.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Bridging blood cancers and inflammation: The reduced Cancitis model

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.