Mathematical model for glutathione dynamics in the retina

Abstract The retina is highly susceptible to the generation of toxic reactive oxygen species (ROS) that disrupt the normal operations of retinal cells. The glutathione (GSH) antioxidant system plays an important role in mitigating ROS. To perform its protective functions, GSH depends on nicotinamide adenine dinucleotide phosphate (NADPH) produced through the pentose phosphate pathway. This work develops the first mathematical model for the GSH antioxidant system in the outer retina, capturing the most essential components for formation of ROS, GSH production, its oxidation in detoxifying ROS, and subsequent reduction by NADPH. We calibrate and validate the model using experimental measurements, at different postnatal days up to PN28, from control mice and from the rd1 mouse model for the disease retinitis pigmentosa (RP). Global sensitivity analysis is then applied to examine the model behavior and identify the pathways with the greatest impact in control compared to RP conditions. The findings underscore the importance of GSH and NADPH production in dealing with oxidative stress during retinal development, especially after peak rod degeneration occurs in RP, leading to increased oxygen tension. This suggests that stimulation of GSH and NADPH synthesis could be a potential intervention strategy in degenerative mouse retinas with RP

Toward Predicting the Spatio-Temporal Dynamics of Alopecia Areata Lesions Using Partial Differential Equation Analysis

Hair loss in the autoimmune disease, alopecia areata (AA), is characterized by the appearance of circularly spreading alopecic lesions in seemingly healthy skin. The distinct spatial patterns of AA lesions form because the immune system attacks hair follicle cells that are in the process of producing hair shaft, catapults the mini-organs that produce hair from a state of growth (anagen) into an apoptosis-driven regression state (catagen), and causes major hair follicle dystrophy along with rapid hair shaft shedding. In this paper, we develop a model of partial differential equations (PDEs) to describe the spatio-temporal dynamics of immune system components that clinical and experimental studies show are primarily involved in the disease development. Global linear stability analysis reveals there is a most unstable mode giving rise to a pattern. The most unstable mode indicates a spatial scale consistent with results of the humanized AA mouse model of Gilhar et al. (Autoimmun Rev 15(7):726-735, 2016) for experimentally induced AA lesions. Numerical simulations of the PDE system confirm our analytic findings and illustrate the formation of a pattern that is characteristic of the spatio-temporal AA dynamics. We apply marginal linear stability analysis to examine and predict the pattern propagation

Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling

Abstract Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages—growth (anagen), regression (catagen) and relative quiescence (telogen)—only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al., 2015), we here present a mathematical model for AA which incorporates HF cycling and illustrates the anagen phase interruption in AA resulting from an inflammatory autoimmune response against HFs. The model couples a system describing the dynamics of autoreactive immune cells with equations modelling the hair cycle. We illustrate states of health, disease and treatment as well as transitions between them. In addition, we perform parameter sensitivity analysis to assess how different processes, such as proliferation, apoptosis and input from stem cells, impact anagen duration in healthy versus AA-affected HFs. The proposed model may help in evaluating the effectiveness of existing treatments and identifying new potential therapeutic targets

Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata

Abstract The goal of patient-specific treatment of diseases requires a connection between clinical observations with models that are able to accurately predict the disease progression. Even when realistic models are available, it is very difficult to parameterize them and often parameter estimates that are made using early time course data prove to be highly inaccurate. Inaccuracies can cause different predictions, especially when the progression depends sensitively on the parameters. In this study, we apply a Bayesian data assimilation method, where the data are incorporated sequentially, to a model of the autoimmune disease alopecia areata that is characterized by distinct spatial patterns of hair loss. Using synthetic data as simulated clinical observations, we show that our method is relatively robust with respect to variations in parameter estimates. Moreover, we compare convergence rates for parameters with different sensitivities, varying observational times and varying levels of noise. We find that this method works better for sparse observations, sensitive parameters and noisy observations. Taken together, we find that our data assimilation, in conjunction with our biologically inspired model, provides directions for individualized diagnosis and treatments

Втора научна сесия за преподаватели и студенти 3-4 Октомври 2013, Варна

Варненски медицински форум (Varna Medical Forum) V. 2, Suppl 3(2013