Connecting Local and Global Sensitivities in a Mathematical Model for Wound Healing

Age-dependent ventilator-induced lung injury: Mathematical modeling, experimental data, and statistical analysis

A variety of pulmonary insults can prompt the need for life-saving mechanical ventilation; however, misuse, prolonged use, or an excessive inflammatory response, can result in ventilator-induced lung injury. Past research has observed an increased instance of respiratory distress in older patients and differences in the inflammatory response. To address this, we performed high pressure ventilation on young (2-3 months) and old (20-25 months) mice for 2 hours and collected data for macrophage phenotypes and lung tissue integrity. Large differences in macrophage activation at baseline and airspace enlargement after ventilation were observed in the old mice. The experimental data was used to determine plausible trajectories for a mathematical model of the inflammatory response to lung injury which includes variables for the innate inflammatory cells and mediators, epithelial cells in varying states, and repair mediators. Classification methods were used to identify influential parameters separating the parameter sets associated with the young or old data and separating the response to ventilation, which was measured by changes in the epithelial state variables. Classification methods ranked parameters involved in repair and damage to the epithelial cells and those associated with classically activated macrophages to be influential. Sensitivity results were used to determine candidate in-silico interventions and these interventions were most impact for transients associated with the old data, specifically those with poorer lung health prior to ventilation. Model results identified dynamics involved in M1 macrophages as a focus for further research, potentially driving the age-dependent differences in all macrophage phenotypes. The model also supported the pro-inflammatory response as a potential indicator of age-dependent differences in response to ventilation. This mathematical model can serve as a baseline model for incorporating other pulmonary injuries.

Diabetic wound healing: The impact of diabetes on myofibroblast activity and its potential therapeutic treatments

Diabetes is a systemic disease in which the body cannot regulate the amount of sugar, namely glucose, in the blood. High glucose toxicity has been implicated in the dysfunction of diabetic wound healing, following insufficient production (Type 1) or inadequate usage (Type 2) of insulin. Chronic non-healing diabetic wounds are one of the major complications of both types of diabetes, which are serious concerns for public health and can impact the life quality of patients significantly. In general, diabetic wounds are characterized by deficient chemokine production, an unusual inflammatory response, lack of angiogenesis and epithelialization, and dysfunction of fibroblasts. Increasing scientific evidence from available experimental studies on animal and cell models strongly associates impaired wound healing in diabetes with dysregulated fibroblast differentiation to myofibroblasts, interrupted myofibroblast activity, and inadequate extracellular matrix production. Myofibroblasts play an important role in tissue repair by producing and organizing extracellular matrix and subsequently promoting wound contraction. Based on these studies, hyperglycaemic conditions can interfere with cytokine signalling pathways (such as growth factor-β pathway) affecting fibroblast differentiation, alter fibroblast apoptosis, dysregulate dermal lipolysis, and enhance hypoxia damage, thus leading to damaged microenvironment for myofibroblast formation, inappropriate extracellular matrix modulation, and weakened wound contraction. In this review, we will focus on the current available studies on the impact of diabetes on fibroblast differentiation and myofibroblast function, as well as potential treatments related to the affected pathways.

Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization

A common challenge in systems biology is quantifying the effects of unknown parameters and estimating parameter values from data. For many systems, this task is computationally intractable due to expensive model evaluations and large numbers of parameters. In this work, we investigate a new method for performing sensitivity analysis and parameter estimation of complex biological models using techniques from uncertainty quantification. The primary advance is a significant improvement in computational efficiency from the replacement of model simulation by evaluation of a polynomial surrogate model. We demonstrate the method on two models of mating in budding yeast: a smaller ODE model of the heterotrimeric G-protein cycle, and a larger spatial model of pheromone-induced cell polarization. A small number of model simulations are used to fit the polynomial surrogates, which are then used to calculate global parameter sensitivities. The surrogate models also allow rapid Bayesian inference of the parameters via Markov chain Monte Carlo (MCMC) by eliminating model simulations at each step. Application to the ODE model shows results consistent with published single-point estimates for the model and data, with the added benefit of calculating the correlations between pairs of parameters. On the larger PDE model, the surrogate models allowed convergence for the distribution of 15 parameters, which otherwise would have been computationally prohibitive using simulations at each MCMC step. We inferred parameter distributions that in certain cases peaked at values different from published values, and showed that a wide range of parameters would permit polarization in the model. Strikingly our results suggested different diffusion constants for active versus inactive Cdc42 to achieve good polarization, which is consistent with experimental observations in another yeast species S. pombe.