The Type 1 Diabetes PhysioLab Platform: a validated physiologically based mathematical model of pathogenesis in the non-obese diabetic mouse

Abstract

Type 1 diabetes is an autoimmune disease whose clinical onset signifies a lifelong requirement for insulin therapy and increased risk of medical complications. To increase the efficiency and confidence with which drug candidates advance to human type 1 diabetes clinical trials, we have generated and validated a mathematical model of type 1 diabetes pathophysiology in a well-characterized animal model of spontaneous type 1 diabetes, the non-obese diabetic (NOD) mouse. The model is based on an extensive survey of the public literature and input from an independent scientific advisory board. It reproduces key disease features including activation and expansion of autoreactive lymphocytes in the pancreatic lymph nodes (PLNs), islet infiltration and beta cell loss leading to hyperglycaemia. The model uses ordinary differential and algebraic equations to represent the pancreas and PLN as well as dynamic interactions of multiple cell types (e.g. dendritic cells, macrophages, CD4+ T lymphocytes, CD8+ T lymphocytes, regulatory T cells, beta cells). The simulated features of untreated pathogenesis and disease outcomes for multiple interventions compare favourably with published experimental data. Thus, a mathematical model reproducing type 1 diabetes pathophysiology in the NOD mouse, validated based on accurate reproduction of results from multiple published interventions, is available for in silico hypothesis testing. Predictive biosimulation research evaluating therapeutic strategies and underlying biological mechanisms is intended to deprioritize hypotheses that impact disease outcome weakly and focus experimental research on hypotheses likely to provide insight into the disease and its treatment.

Fig. 1

Key biological components included in the type 1 diabetes PhysioLab platform. Ag, autoantigen; DC, dendritic cell; macs, macrophages.

Fig. 2

The islet CD8⁺ T cell representation: cellular lifecycle, its regulation and effector activity. Ovals (nodes) represent variables; single and double border nodes represent variables determined by ordinary differential equations (ODEs) or algebraic equations, respectively. Arrows represent relationships between nodes, where closed arrows represent a positive effect and open arrows represent a negative effect.

Fig. 3

Standard format describing the mathematical relationship between regulators and their effector function. (a) To represent a regulator potentiating a function, a dose–response relationship is represented, wherein the x-axis represents the dynamic range over which the regulator has the functional effect and the y-axis represents the fold increase observed in the presence of the regulator. The regulator dynamic range was defined by the literature. Where such data were lacking, the available data were assumed to represent a concentration maximum, and a three-log range was assumed. (b) To represent a regulator inhibiting a function a similar dose–response relationship is represented, wherein the y-axis represents the fractional inhibition imposed by the regulator (e.g. 50% inhibition = 0·5).

Fig. 6

Simulated glucose dynamics in the virtual non-obese diabetic (NOD) mouse compare favourably with individual NOD mouse data. Blue squares: female NOD mice that became hyperglycaemic during the study period (Kreuwel, unpublished). Green circles = female NOD mice that remained normoglycaemic during the study period (Kreuwel, unpublished). Red solid line: simulation result for the virtual NOD mouse, demonstrating onset of frank diabetes at approximately 19 weeks.

Fig. 5

Simulated islet leucocyte accumulation in the virtual non-obese diabetic (NOD) mouse compares favourably with published data. (a) CD4⁺ T lymphocyte fraction. (b) CD8⁺ T lymphocyte fraction. (c) B lymphocyte fraction. (d) Dendritic cell and macrophage fraction. Solid lines: simulation results for the virtual NOD mouse. Symbols: values derived from published data, where different symbols correspond to specific publications. Closed circles, [84]*; closed triangles, [13]*; closed diamonds, [30]; closed squares, [83], open circles, [16]; open triangle, [111]; open diamond, [112]*; open squares, [31]. *For these publications, data were reported for dendritic cells (DCs) or macrophages.

Fig. 4

Simulated pancreatic lymph nodes (PLN) cellular expansion in the virtual non-obese diabetic (NOD) mouse compares favourably with published data. Solid lines: simulation results for the virtual NOD mouse. Symbols: values derived from published data, where colour corresponds to cell type and symbols correspond to specific publications. Blue symbols: values for total leucocytes. Green symbols: values for CD4⁺ T lymphocytes. Red symbols: values for B lymphocytes. Turquoise symbols: values for CD8⁺ T lymphocytes. Circles, [37]; triangles, [80]; squares, [81]*; diamond, Kreuwel, unpublished*; side triangles, [82]*. *These papers provided total leucocyte data. The lymphocyte subsets were calculated using fractional composition data [84,109,110].

Fig. 7

Simulation results following treatment with liposomal dichloromethylene diphosphonate (LipCl₂MDP). (a) Simulated blood glucose traces are shown following treatment of the 3-week-old virtual mouse with 1 mg LipCl2MDP 1×/week for 17 weeks as described [86]. (b) Simulated blood glucose traces are shown following treatment of the 8-week-old virtual mouse with 2 mg LipCl2MDP 2×, 2 days apart as described [87]. Simulations run for the length of time reported in each study. (c) Analysis of simulation results following application of the 8-week protocol indicates that treatment at 8 weeks results in a precipitous decline in inflammatory dendritic cells (DCs) within infiltrated islets. Inflammatory DC numbers recover but are not sustained. (d) After in silico treatment at 8 weeks, suppressive/tolerogenic DCs also decline precipitously, but in the recovery phase the population is more stable than inflammatory DCs. Dotted lines: simulation results for the untreated virtual non-obese diabetic (NOD) mouse. Solid lines: simulation results for the treated virtual NOD mouse. Grey bars: duration of treatment with LipCl₂MDP as described in the above published reports.