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.

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

Understanding the mechanisms that control the body’s response to inflammation is of key importance, due to its involvement in myriad medical conditions, including cancer, arthritis, Alzheimer’s disease and asthma. While resolving inflammation has historically been considered a passive process, since the turn of the century the hunt for novel therapeutic interventions has begun to focus upon active manipulation of constituent mechanisms, particularly involving the roles of apoptosing neutrophils, phagocytosing macrophages and anti-inflammatory mediators. Moreover, there is growing interest in how inflammatory damage can spread spatially due to the motility of inflammatory mediators and immune cells. For example, impaired neutrophil chemotaxis is implicated in causing chronic inflammation under trauma and in ageing, while neutrophil migration is an attractive therapeutic target in ailments such as chronic obstructive pulmonary disease. We extend an existing homogeneous model that captures interactions between inflammatory mediators, neutrophils and macrophages to incorporate spatial behaviour. Through bifurcation analysis and numerical simulation, we show that spatially inhomogeneous outcomes can present close to the switch from bistability to guaranteed resolution in the corresponding homogeneous model. Finally, we show how aberrant spatial mechanisms can play a role in the failure of inflammation to resolve and discuss our results within the broader context of seeking novel inflammatory treatments.

Defining vitamin D status using multi-metabolite mathematical modelling: A pregnancy perspective

Vitamin D deficiency is linked to adverse pregnancy outcomes such as pre-eclampsia (PET) but remains defined by serum measurement of 25-hydroxyvitamin D3 (25(OH)D3) alone. To identify broader changes in vitamin D metabolism during normal and PET pregnancies we developed a relatively simple but fully parametrised mathematical model of the vitamin D metabolic pathway. The data used for parametrisation were serum vitamin D metabolites analysed for a cross-sectional group of women (n = 88); including normal pregnant women at 1 st (NP1, n = 25) and 3rd trimester (NP3, n = 21) and pregnant women with PET (n = 22), as well as non-pregnant female controls (n = 20). To account for the effects various metabolites have upon each other, data were analysed using an ordinary differential equation model of the vitamin D reaction network. Information obtained from the model was then also applied to serum vitamin D metabolome data (n = 50) obtained from a 2nd trimester pregnancy cohort, of which 25 prospectively developed PET. Statistical analysis of the data alone showed no significant difference between NP3 and PET for serum 25(OH)D3 and 24,25(OH)₂D3 concentrations. Conversely, a statistical analysis informed by the reaction network model revealed that a better indicator of PET is the ratios of vitamin D metabolites in late pregnancy. Assessing the potential predicative value, no significant difference between NP3 and PET cases at 15 weeks gestation was found. Mathematical modelling offers a novel strategy for defining the impact of vitamin D metabolism on human health. This is particularly relevant within the context of pregnancy, where major changes in vitamin D metabolism occur across gestation, and dysregulated metabolism is evidenced in women with established PET.

Localized redox relays as a privileged mode of cytoplasmic hydrogen peroxide signaling

Hydrogen peroxide (H₂O₂) is a key signaling agent. Its best characterized signaling actions in mammalian cells involve the early oxidation of thiols in cytoplasmic phosphatases, kinases and transcription factors. However, these redox targets are orders of magnitude less H₂O₂-reactive and abundant than cytoplasmic peroxiredoxins. How can they be oxidized in a signaling time frame? Here we investigate this question using computational reaction-diffusion models of H₂O₂ signaling. The results show that at H₂O₂ supply rates commensurate with mitogenic signaling a H₂O₂ concentration gradient with a length scale of a few tenths of μm is established. Even near the supply sites H₂O₂ concentrations are far too low to oxidize typical targets in an early mitogenic signaling time frame. Furthermore, any inhibition of the peroxiredoxin or increase in H₂O₂ supply able to drastically increase the local H₂O₂ concentration would collapse the concentration gradient and/or cause an extensive oxidation of the peroxiredoxins I and II, inconsistent with experimental observations. In turn, the local concentrations of peroxiredoxin sulfenate and disulfide forms exceed those of H₂O₂ by several orders of magnitude. Redox targets reacting with these forms at rate constants much lower than that for, say, thioredoxin could be oxidized within seconds. Moreover, the spatial distribution of the concentrations of these peroxiredoxin forms allows them to reach targets within 1 μm from the H₂O₂ sites while maintaining signaling localized. The recruitment of peroxiredoxins to specific sites such as caveolae can dramatically increase the local concentrations of the sulfenic and disulfide forms, thus further helping these species to outcompete H₂O₂ for the oxidation of redox targets. Altogether, these results suggest that H₂O₂ signaling is mediated by localized redox relays whereby peroxiredoxins are oxidized to sulfenate and disulfide forms at H₂O₂ supply sites and these forms in turn oxidize the redox targets near these sites.

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2-Cys peroxiredoxins impose strong cytoplasmic and transmembrane H₂O₂ gradients.

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Maximal cytoplasmic H₂O₂ concentrations are insufficient to oxidize Tyr phosphatases.

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Prx inhibition modestly increases maximal H₂O₂ concentration, blunts gradients.

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Sulfenate and disulfide Prx strongly exceed H₂O₂ concentrations, are also localized.

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Prx recruitment causes modest local H₂O₂ depletion, helps Prx outcompete H₂O₂.