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.

A high-density immunoblotting methodology for quantification of total protein levels and phosphorylation modifications

The components of many signaling pathways have been identified and there is now a need to conduct quantitative data-rich temporal experiments for systems biology and modeling approaches to better understand pathway dynamics and regulation. Here we present a modified Western blotting method that allows the rapid and reproducible quantification and analysis of hundreds of data points per day on proteins and their phosphorylation state at individual sites. The approach is of particular use where samples show a high degree of sample-to-sample variability such as primary cells from multiple donors. We present a case study on the analysis of >800 phosphorylation data points from three phosphorylation sites in three signaling proteins over multiple time points from platelets isolated from ten donors, demonstrating the technique's potential to determine kinetic and regulatory information from limited cell numbers and to investigate signaling variation within a population. We envisage the approach being of use in the analysis of many cellular processes such as signaling pathway dynamics to identify regulatory feedback loops and the investigation of potential drug/inhibitor responses, using primary cells and tissues, to generate information about how a cell's physiological state changes over time.

The resolution of inflammation: a mathematical model of neutrophil and macrophage interactions

There is growing interest in inflammation due to its involvement in many diverse medical conditions, including Alzheimer's disease, cancer, arthritis and asthma. The traditional view that resolution of inflammation is a passive process is now being superceded by an alternative hypothesis whereby its resolution is an active, anti-inflammatory process that can be manipulated therapeutically. This shift in mindset has stimulated a resurgence of interest in the biological mechanisms by which inflammation resolves. The anti-inflammatory processes central to the resolution of inflammation revolve around macrophages and are closely related to pro-inflammatory processes mediated by neutrophils and their ability to damage healthy tissue. We develop a spatially averaged model of inflammation centring on its resolution, accounting for populations of neutrophils and macrophages and incorporating both pro- and anti-inflammatory processes. Our ordinary differential equation model exhibits two outcomes that we relate to healthy and unhealthy states. We use bifurcation analysis to investigate how variation in the system parameters affects its outcome. We find that therapeutic manipulation of the rate of macrophage phagocytosis can aid in resolving inflammation but success is critically dependent on the rate of neutrophil apoptosis. Indeed our model predicts that an effective treatment protocol would take a dual approach, targeting macrophage phagocytosis alongside neutrophil apoptosis.