Mathematical modeling in autoimmune diseases: from theory to clinical application

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

Alopecia areata: Current understanding of the pathophysiology and update on therapeutic approaches, featuring the Japanese Dermatological Association guidelines

Alopecia areata (AA) is a relatively common nonscarring hairloss disease characterized by an autoimmune response to anagen hair follicles (HFs). Accumulated evidence suggests that collapse of the HF immune privilege subsequent to triggering events, represented by viral infection, leads to autoimmune response in which autoreactive cytotoxic CD8+NKG2D+ T cells mainly target exposed HF autoantigens. AA had been recognized as type 1 inflammatory disease, but recent investigations have suggested some roles of type 2- and Th17-associated mediators in AA pathogenesis. The significance of psychological stress in AA pathogenesis is less emphasized nowadays, but psychological comorbidities, such as depression and anxiety, attract greater interest in AA management. In this regard, the disease severity may not solely be evaluated by the extent of hair loss. Use of trichoscopy markedly improved the resolution of the diagnosis and evaluation of the phase of AA, which is indispensable for the optimization of treatment. For the standardization of AA management, the establishment of guidelines/expert consensus is pivotal. Indeed, the Japanese Dermatological Association (JDA) and other societies and expert groups have published guidelines/expert consensus reports, which mostly recommend intralesional/topical corticosteroid administration and contact immunotherapy as first-line treatments, depending on the age, disease severity, and activity of AA. The uniqueness of the JDA guidelines can be found in their descriptions of intravenous corticosteroid pulse therapy, antihistamines, and other miscellaneous domestically conducted treatments. Considering the relatively high incidence of spontaneous regression in mild AA and its intractability in severe subsets, the importance of course observation is also noted. Evidenced-based medicine for AA is currently limited, however, novel therapeutic approaches, represented by JAK inhibitors, are on their way for clinical application. In this review, the latest understanding of the etiopathogenesis and pathophysiology, and update on therapeutic approaches with future perspectives are summarized for AA, following the current version of the JDA AA management guidelines.

Regulatory network analysis defines unique drug mechanisms of action and facilitates patient-drug matching in alopecia areata clinical trials

Not all therapeutics are created equal in regards to individual patients. The problem of identifying which compound will work best with which patient is a significant burden across all disease contexts. In the context of autoimmune diseases such as alopecia areata, several formulations of JAK/STAT inhibitors have demonstrated efficacy in clinical trials. All of these compounds demonstrate different rates of response, and here we observed that this coincided with different molecular effects on patients undergoing treatment. Using these data, we have developed a computational model that is capable of predicting which patient-drug pairs have the highest likelihood of response. We achieved this by integrating inferred mechanism of action data and gene regulatory networks derived from an independent patient cohort with baseline patient data prior to beginning treatment.

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

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.

Clues that mitochondria are involved in the hair cycle clock: MPZL3 regulates entry into and progression of murine hair follicle cycling

The molecular nature of the hair cycle clock (HCC), the intrinsic oscillator system that drives hair follicle (HF) cycling, remains incompletely understood; therefore, all relevant key players need to be identified. Here, we present evidence that implicates myelin protein zero-like 3 (MPZL3), a multifunctional nuclear-encoded mitochondrial protein known to be involved in epidermal differentiation, in HCC regulation. By analysing global Mpzl3 knockout (-/-) mice, we show that in the absence of functional MPZL3, mice commence HF cycling with retarded first catagen-telogen transition after normal postnatal HF morphogenesis. However, Mpzl3 -/- mice subsequently display strikingly accelerated HF cycling, i.e. a precocious telogen-to-anagen transition during the second hair cycle, compared to controls, suggesting that MPZL3 inhibits anagen entry. We also show that intrafollicular MPZL3 protein expression fluctuates in a hair cycle-dependent manner. In telogen HFs, MPZL3 is localized to the secondary hair germ, an epicentre of hair cycle regulation, where it partially co-localizes with P-cadherin. In early anagen HF, MPZL3 is localized immediately distal to the proximal hair matrix. These findings introduce the novel concept that mitochondria are more actively involved in hair cycle control than previously recognized and that MPZL3 plays a central role in the HCC.

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.