Mechanisms and Points of Control in the Spread of Inflammation: A Mathematical Investigation

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.

Diffusive mediator feedbacks control the health-to-disease transition of skin inflammation

The spatiotemporal dynamics of inflammation provide vital insights into the understanding of skin inflammation. Skin inflammation primarily depends on the regulatory feedback between pro- and anti-inflammatory mediators. Healthy skin exhibits fading erythema. In contrast, diseased skin exhibits expanding erythema with diverse patterns, which are clinically classified into five types: circular, annular, arcuate, gyrate, and polycyclic. Inflammatory diseases with expanding erythema are speculated to result from the overproduction of pro-inflammatory mediators. However, the mechanism by which feedback selectively drives the transition from a healthy fading erythema to each of the five types of diseased expanding erythema remains unclear. This study theoretically elucidates the imbalanced production between pro- and anti-inflammatory mediators and prospective treatment strategies for each expanding pattern. Our literature survey showed that eleven diseases exhibit some of the five expanding erythema, thereby suggesting a common spatiotemporal regulation underlying different patterns and diseases. Accordingly, a reaction-diffusion model incorporating mediator feedback reproduced the five observed types of diseased expanding and healthy fading patterns. Importantly, the fading pattern transitioned to the arcuate, gyrate, and polycyclic patterns when the productions of anti-inflammatory and pro-inflammatory mediators were lower and higher, respectively than in the healthy condition. Further depletion of anti-inflammatory mediators caused a circular pattern, whereas further overproduction of pro-inflammatory mediators caused an annular pattern. Mechanistically, the bistability due to stabilization of the diseased state exhibits circular and annular patterns, whereas the excitability exhibits the gyrate, polycyclic, arcuate, and fading patterns as the threshold of pro-inflammatory mediator concentration relative to the healthy state increases. These dynamic regulations of diffusive mediator feedback provide effective treatment strategies for mediator production wherein skins recover from each expanding pattern toward a fading pattern. Thus, these strategies can estimate disease severity and risk based on erythema patterns, paving the way for developing noninvasive and personalized treatments for inflammatory skin diseases.

Is Pulmonary Inflammation a Valid Predictor of Particle Induced Lung Pathology? The Case of Amorphous and Crystalline silicas

Although inflammation is a normal and beneficial response, it is also a key event in the pathology of many chronic diseases, including pulmonary and systemic particle-induced disease. In addition, inflammation is now considered as the key response in standard settings for inhaled particles and a critical endpoint in OECD-based sub-acute/ chronic animal inhalation testing protocols. In this paper, we discuss that whilst the role of inflammation in lung disease is undeniable, it is when inflammation deviates from normal parameters that adversity occurs. We introduce the importance of the time course and in particular, the reversibility of inflammation in the progression towards tissue remodelling and neoplastic changes as commonly seen in rat inhalation studies. For this purpose, we used chronic inhalation studies with synthetic amorphous silicas (SAS) and reactive crystalline silica (RCS) as a source of data to describe the time-course of inflammation towards and beyond adversity. Whilst amorphous silicas induce an acute but reversible inflammatory response, only RCS induces a persistent, progressive response after cessation of exposure, resulting in fibrosis and carcinogenicity in rodents and humans. This suggests that the use of inflammation as a fixed endpoint at the cessation of exposure may not be a reliable predictor of particle-induced lung pathology. We therefore suggest extending the current OECD testing guidelines with a recovery period, that allows inflammation to resolve or progress into altered structure and function, such as fibrosis.

Exploring the constituent mechanisms of hepatitis: a dynamical systems approach

Hepatitis is the term used to describe inflammation in the liver. It is associated with a high rate of mortality, but the underlying disease mechanisms are not completely understood and treatment options are limited. We present a mathematical model of hepatitis that captures the complex interactions between hepatocytes (liver cells), hepatic stellate cells (cells in the liver that produce hepatitis-associated fibrosis) and the immune components that mediate inflammation. The model is in the form of a system of ordinary differential equations. We use numerical techniques and bifurcation analysis to characterize and elucidate the physiological mechanisms that dominate liver injury and its outcome to a healthy or unhealthy, chronic state. This study reveals the complex interactions between the multiple cell types and mediators involved in this complex disease and highlights potential problems in targeting inflammation in the liver therapeutically.

Delicate regulation of IL-1β-mediated inflammation by cyclophilin A

The inflammatory response is tightly regulated, but its regulatory principles are still incompletely understood. Cyclophilin A (CypA) has long been considered as a pro-inflammatory factor. Here, we discover how CypA precisely regulates interleukin-1β (IL-1β)-mediated inflammatory responses. In lipopolysaccharide-treated mice, CypA deficiency initially inhibits and then promotes lung inflammation, which is closely related to IL-1β production. Mechanistically, CypA not only facilitates pro-IL-1β processing by increasing Smurf1-mediated K63-linked ubiquitination in an ATP-dependent manner but also accelerates pro-IL-1β degradation, depending on Smurf1-mediated K48-linked ubiquitination. Moreover, in IL-1β-treated mice, CypA exacerbates lung injury by enhancing cytokine production. It also upregulates the ILK/AKT pathway by inhibiting Cyld-mediated K63-linked ILK deubiquitination, which promotes the epithelial-mesenchymal transition (EMT) to facilitate lung repair. Collectively, CypA promotes inflammation activation by increasing IL-1β production and then promotes inflammation resolution by enhancing redundant pro-IL-1β degradation and IL-1β-induced EMT, indicating the complex and delicate regulation of inflammatory response.

New translational and experimental insights into the role of pro-resolving lipid mediators in inflammatory bowel disease

The resolution of inflammation is an active process, guided by specialized pro-resolution lipid mediators (SPMs). These mediators originate from polyunsaturated fatty acids, such as omega-3. Sufficient evidence suggests that the beneficial effects attributed to omega-3 are, at least in part, the result of the immunomodulatory action of the SPMs, which act systemically by overcoming inflammation and repairing tissue damage, without suppressing the immune response. Recent studies suggest that an imbalance in the synthesis and/or activity of these compounds may be associated with the pathogenesis of several inflammatory conditions, such as inflammatory bowel disease (IBD). Thus, this review highlights the advances made in recent years with regard to the endo-genous synthesis and the biological role of lipoxins, resolvins, protectins, and maresins, as well as their precursors, in the regulation of inflammation; and provides an update on the participation of these mediators in the development and evolution of IBD and the therapeutic approaches that these immunomodulating substances are involved in this context.

Effects of Lipopolysaccharide-Binding Protein (LBP) Single Nucleotide Polymorphism (SNP) in Infections, Inflammatory Diseases, Metabolic Disorders and Cancers

Inflammation, which is induced by the immune response, is recognized as the driving factor in many diseases, including infections and inflammatory diseases, metabolic disorders and cancers. Genetic variations in pivotal genes associated with the immune response, particularly single nucleotide polymorphisms (SNPs), may account for predisposition and clinical outcome of diseases. Lipopolysaccharide (LPS)-binding protein (LBP) functions as an enhancer of the host response to LPS, the main component of the outer membrane of gram-native bacteria. Given the crucial role of LBP in inflammation, we will review the impact of SNPs in the LBP gene on infections and inflammatory diseases, metabolic disorders and cancers.

Bistable Mathematical Model of Neutrophil Migratory Patterns After LPS-Induced Epigenetic Reprogramming

The highly controlled migration of neutrophils toward the site of an infection can be altered when they are trained with lipopolysaccharides (LPS), with high dose LPS enhancing neutrophil migratory pattern toward the bacterial derived source signal and super-low dose LPS inducing either migration toward an intermediary signal or dysregulation and oscillatory movement. Empirical studies that use microfluidic chemotaxis-chip devices with two opposing chemoattractants showed differential neutrophil migration after challenge with different LPS doses. The epigenetic alterations responsible for changes in neutrophil migratory behavior are unknown. We developed two mathematical models that evaluate the mechanistic interactions responsible for neutrophil migratory decision-making when exposed to competing chemoattractants and challenged with LPS. The first model, which considers the interactions between the receptor densities of two competing chemoattractants, their kinases, and LPS, displayed bistability between high and low ratios of primary to intermediary chemoattractant receptor densities. In particular, at equilibrium, we observe equal receptor densities for low LPS (< 15ng/mL); and dominance of receptors for the primary chemoattractant for high LPS (> 15ng/mL). The second model, which included additional interactions with an extracellular signal-regulated kinase in both phosphorylated and non-phosphorylated forms, has an additional dynamic outcome, oscillatory dynamics for both receptors, as seen in the data. In particular, it found equal receptor densities in the absence of oscillation for super-low and high LPS challenge (< 0.4 and 1.1 376 ng/mL). Predicting the mechanisms and the type of external LPS challenge responsible for neutrophils migration toward pro-inflammatory chemoattractants, migration toward pro-tolerant chemoattractants, or oscillatory movement is necessary knowledge in designing interventions against immune diseases, such as sepsis.

Spatial considerations in the resolution of inflammation: Elucidating leukocyte interactions via an experimentally-calibrated agent-based model

Many common medical conditions (such as cancer, arthritis, chronic obstructive pulmonary disease (COPD), and others) are associated with inflammation, and even more so when combined with the effects of ageing and multimorbidity. While the inflammatory response varies in different tissue types, under disease and in response to therapeutic interventions, it has common interactions that occur between immune cells and inflammatory mediators. Understanding these underlying inflammatory mechanisms is key in progressing treatments and therapies for numerous inflammatory conditions. It is now considered that constituent mechanisms of the inflammatory response can be actively manipulated in order to drive resolution of inflammatory damage; particularly, those mechanisms related to the pro-inflammatory role of neutrophils and the anti-inflammatory role of macrophages. In this article, we describe the assembly of a hybrid mathematical model in which the spatial spread of inflammatory mediators is described through partial differential equations, and immune cells (neutrophils and macrophages) are described individually via an agent-based modelling approach. We pay close attention to how immune cells chemotax toward pro-inflammatory mediators, presenting a model for cell chemotaxis that is calibrated against experimentally observed cell trajectories in healthy and COPD-affected scenarios. We illustrate how variations in key model parameters can drive the switch from resolution of inflammation to chronic outcomes, and show that aberrant neutrophil chemotaxis can move an otherwise healthy outcome to one of chronicity. Finally, we reflect on our results in the context of the on-going hunt for new therapeutic interventions.

Inflammation is the body’s primary defence to harmful stimuli such as infections, toxins and tissue strain but also underlies a much broader range of conditions, including asthma, arthritis and cancer. The inflammatory response is key in resolving injury to facilitate recovery, and involves a range of interactions between immune cells (leukocytes, neutrophils and macrophages in particular) and inflammatory mediators. Immune cells are recruited from the blood stream in response to injury. Once in tissue, neutrophils release toxins to kill invading agents and resolve damage; however, if not carefully managed by other immune cells (mainly macrophages), their responses can increase inflammation instead of helping to resolve it. We model these interactions in response to damage using a spatial model, examining how a healthy response can prevent localised inflammation from spreading. We pay close attention to how cells migrate toward the damaged area, as many inflammatory conditions are associated with impairment of this process. We calibrate our model against experimentally-observed cell trajectories from healthy patients and patients with chronic obstructive pulmonary disease. We illustrate that a healthy outcome depends strongly upon efficient cell migration and a delicate balance between the pro- and anti-inflammatory effects of neutrophils and macrophages.