The intestinal microbiota play a critical role in human health and disease, maintaining metabolic and immune/inflammatory health, synthesizing essential vitamins and amino acids and maintaining intestinal barrier integrity. The aim of this paper is to develop a mathematical model to describe the complex interactions between the microbiota, vitamin D/vitamin D receptor (VDR) pathway, epithelial barrier and immune response in order to understand better the effects of supplementation with probiotics and vitamin D. This is motivated by emerging data indicating the beneficial effects of vitamin D and probiotics individually and when combined. We propose a system of ordinary differential equations determining the time evolution of intestinal bacterial populations, concentration of the VDR:1,25(OH)$_{2}$D complex in epithelial and immune cells, the epithelial barrier and the immune response. The model shows that administration of probiotics and/or vitamin D upregulates the VDR complex, which enhances barrier function and protects against intestinal inflammation. The model also suggests co-supplementation to be superior to individual supplements. We explore the effects of inflammation on the populations of commensal and pathogenic bacteria and the vitamin D/VDR pathway and discuss the value of gathering additional experimental data motivated by the modelling insights.

Background: Emerging evidence links the gut microbiome to chronic pain processing. Inulin, a prebiotic fibre, modulates the gut microbiome, while physiotherapy-supported exercise (PSE) improves pain and function. We evaluated the effects of inulin supplementation with and without PSE on knee osteoarthritis (OA) pain. Methods: In a 2 × 2 factorial RCT, 117 community-dwelling adults with knee OA received 6 weeks of: (A) 20 g/day inulin, (B) digital PSE (Joint Academy™), (C) inulin +PSE, or (D) 10 g/day maltodextrin. Primary outcome: pain (Numerical Rating Scale). Secondary: 30 s sit-to-stand (30-CST), timed up and go (TUG), grip strength, and quantitative sensory testing. Serum short-chain fatty acids (SCFAs) and glucagon-like peptide-1 (GLP-1) were measured. The study was not powered to detect synergistic interaction. Results: A total of 117 participants (58.1% female; mean ± SD age = 67.5 ± 9.4 years; BMI = 29.5 ± 5.3 kg/m²; NRS = 3.96 ± 2.67) completed the trial. Pain improved with inulin (baseline-adjusted between-group mean difference (Δ) = −1.11 [95%CI −2.18, −0.04], p = 0.045) and PSE (Δ = −1.55 [95%CI −2.52, −0.58], p = 0.002) compared to placebo, with no synergistic effect. PSE improved TUG (p = 0.02) and 30-CST (p = 0.0004), while inulin improved grip strength (p = 0.002), pressure pain thresholds (p = 0.009) and temporal summation (p = 0.025) compared to placebo and had significantly lower dropout rates (3.6%) compared with PSE (21% p < 0.01). Only inulin increased SCFA butyrate (p = 0.0248) and GLP-1 (p = 0.0109), and higher GLP-1 was associated with improved grip strength, suggesting a gut–muscle link. Conclusions: Inulin and PSE each produced meaningful pain reductions. Only inulin improved pain sensitivity and grip strength, the latter paralleled by increased GLP-1, and had much higher rates of retention compared to PSE.

The relationship between the intestinal microbiota and human health during ageing is an area of increasing interest due to increasing health challenges experienced by ageing populations. This paper develops a mathematical model describing the age-related biological changes associated with alterations to the microbiota, vitamin D levels, immunosenescence and inflammageing to determine the likely impact of manipulating the intestinal microbiota with dietary components. Age-dependent parameters are incorporated into a previously developed model to determine the evolution of intestinal bacterial populations, vitamin D receptor:1,25 dihydroxyvitamin D levels, epithelial barrier integrity and immune response with increasing age. Results suggest an age-related decline in both innate and adaptive immunity, weakening of the intestinal barrier, elevation in systemic inflammation and reduced serum vitamin D, resulting in individuals over 60 years old becoming vitamin D deficient (<50 nmol/L). Numerical simulations indicate that administration of probiotics and/or vitamin D supplements upregulates the VDR complex at all ages, which helps restore epithelial barrier function, particularly in older adults in whom the intestinal barrier has been compromised. The greatest benefit is derived from co-supplementation with probiotics and age-dependent doses of vitamin D. Finally, the value of gathering additional experimental data motivated by the modelling insights is discussed.

Background: Pain response to treatment in knee osteoarthritis (OA) varies substantially between individuals, but the biological factors underlying this heterogeneity remain poorly understood. We investigated whether circulating protein, transcriptional and autoantibody features were associated with variation in pain response to lifestyle interventions in people with knee OA. Methods: We performed an exploratory multi-modal analysis using participants from the INSPIRE randomised controlled trial and, for proteomic analyses, an independent WebEx cohort. Circulating inflammatory proteins were measured using Olink proximity extension assay at baseline and 6 weeks. Associations between baseline protein concentrations, longitudinal protein changes and pain response were assessed using multivariable regression, with multivariate protein patterns examined using supervised and sparse partial least squares approaches. Whole-blood transcriptomic data from INSPIRE were analysed using limma, restricted a priori to pain-associated genes represented in the Human Pain Genetics Database (HPGDB), with a responder-by-visit interaction used to assess differential longitudinal expression. Finally, exploratory IgG binding to murine satellite glial cells (SGCs) was assessed in selected INSPIRE participants with contrasting clinical responses to exercise. Results: No circulating protein or transcriptomic association remained significant after correction for multiple testing. Several nominal associations were observed in the proteomic analyses, including baseline IL-10RA and CST5 in INSPIRE and OSM and TNFSF14 in WebEx. Longitudinal changes in IL-17A and TSLP were nominally associated with improvement in pain in INSPIRE, with a similar nominal association between IL-17A and pain improvement observed in WebEx. In the transcriptomic analysis, MMP9 showed the strongest nominal association with differential longitudinal expression according to pain response under both the ΔNRS ≤ −1 (log2 fold change = 0.91, p = 0.008) and ΔNRS ≤ −2 (log2 fold change = 1.02, p = 0.004) definitions; neither association remained significant following FDR correction. Exploratory SGC-binding analysis identified markedly increased baseline IgG binding in one participant with worsening pain, but this pattern was not consistently observed among other participants with poor clinical responses. Paired analyses provided no evidence of a consistent increase in SGC-binding IgG following exercise. Conclusions: This exploratory multi-modal analysis found no robust molecular signature of the pain response that survived correction for multiple testing. Nominal associations involving several circulating proteins, including IL-10RA, IL-17A and MMP9 provide potential leads for future investigation, but these findings should be interpreted cautiously given the multiple comparisons and limited sample sizes. Exploratory autoantibody analyses likewise provided no evidence of a consistent SGC-binding signature. Larger, independently powered studies are required to determine whether these candidate molecular features are reproducibly associated with treatment-related variation in pain response.

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid (17-HDHA, a metabolite of docosahexaenoic acid (DHA)), is significantly associated with OA pain. The aim of this multidisciplinary work is to develop a mathematical model to describe the contributions of enzymatic pathways (and the genes that encode them) to the metabolism of DHA by monocytes and to the levels of the down-stream metabolites, 17-HDHA and 14-hydroxydocasahexaenoic acid (14-HDHA), motivated by novel clinical data from a study involving 30 participants with OA. The data include measurements of oxylipin levels, mRNA levels, measures of OA severity and self-reported pain scores. We propose a system of ordinary differential equations to characterise associations between the different datasets, in order to determine the homeostatic concentrations of DHA, 17-HDHA and 14-HDHA, dependent upon the gene expression of the associated metabolic enzymes. Using parameter-fitting methods, local sensitivity and uncertainty analysis, the model is shown to fit well qualitatively to experimental data. The model suggests that up-regulation of some ALOX genes may lead to the down-regulation of 17HDHA and that dosing with 17-HDHA increases the production of resolvins, which helps to down-regulate the inflammatory response. More generally, we explore the challenges and limitations of modelling real data, in particular individual variability, and also discuss the value of gathering additional experimental data motivated by the modelling insights.