Modeling the effector - regulatory T cell cross-regulation reveals the intrinsic character of relapses in Multiple Sclerosis

Abstract

Background: The relapsing-remitting dynamics is a hallmark of autoimmune diseases such as Multiple Sclerosis (MS). Although current understanding of both cellular and molecular mechanisms involved in the pathogenesis of autoimmune diseases is significant, how their activity generates this prototypical dynamics is not understood yet. In order to gain insight about the mechanisms that drive these relapsing-remitting dynamics, we developed a computational model using such biological knowledge. We hypothesized that the relapsing dynamics in autoimmunity can arise through the failure in the mechanisms controlling cross-regulation between regulatory and effector T cells with the interplay of stochastic events (e.g. failure in central tolerance, activation by pathogens) that are able to trigger the immune system.

Results: The model represents five concepts: central tolerance (T-cell generation by the thymus), T-cell activation, T-cell memory, cross-regulation (negative feedback) between regulatory and effector T-cells and tissue damage. We enriched the model with reversible and irreversible tissue damage, which aims to provide a comprehensible link between autoimmune activity and clinical relapses and active lesions in the magnetic resonances studies in patients with Multiple Sclerosis. Our analysis shows that the weakness in this negative feedback between effector and regulatory T-cells, allows the immune system to generate the characteristic relapsing-remitting dynamics of autoimmune diseases, without the need of additional environmental triggers. The simulations show that the timing at which relapses appear is highly unpredictable. We also introduced targeted perturbations into the model that mimicked immunotherapies that modulate effector and regulatory populations. The effects of such therapies happened to be highly dependent on the timing and/or dose, and on the underlying dynamic of the immune system.

Conclusion: The relapsing dynamic in MS derives from the emergent properties of the immune system operating in a pathological state, a fact that has implications for predicting disease course and developing new therapies for MS.

Figure 1

The relapsing-remitting dynamics of Multiple Sclerosis. A) Disease subtype classification based in the presence of relapses: relapsing-remitting (RR), secondary-progressive (SP), primary-progressive (PP) and progressive-relapsing (PR); B) Representative patient with MS whom underwent monthly MRI for 48 months. Number of contrast enhancing lesions (CEL; left Y axis), disability (measured with the EDSS scale; right Y axis) and presence of clinical relapses counterpart (no scale)

Figure 2

Model of the adaptive immune system. The model of the adaptive immune system is comprised of four parts: 1) the generation of Teff and Treg cells from thymus; 2) T-cell activation by APCs; 3) the cross-regulation modeled by the Teff-Treg loop; and 4) T cell activation and memory populations in the tissue. The Teff-Treg loop is composed of a negative feedback between the two populations (Teff in red and Treg in blue). The model can be found in the additional files, and the parameters and initial conditions are listed in Table 1.

Figure 3

Simulations of the computational model in healthy and autoimmune state. Plots show representative simulations of the antigen-specific activated-Teff (red) and Treg (blue) population in log scale over 5 years. By changing the parameters of the Teff-Treg loop, we were able to reproduce two dynamics:A)Healthy state in which the Teff and Treg populations fluctuate at low levels indicating that the system is not generating an immune response, nor immunopathology;B) Autoimmune dynamics due to a failure in the cross-regulation (Teff-Treg loop), provoking the expansion and contraction of activated Teff cells. C, D) Simulations of tissue damage: reversible damage (blue), irreversible damage (red) and total damage (black): C) In healthy configuration the functioning of the immune system (blue line) do not induce significant tissue damage (black line); D) in autoimmune configuration the peaks of activated Teff induce tissue dysfunction and damage (red line), leading to the relapsing dynamics (back line).

Figure 4

State-space analysis of the Teff-Treg loop. The state-space analysis was done with the simplified T-cell population model (eq. 2). The X axis represents the activated Treg population and the Y axis activated Teff cells. A)By plotting both populations with different levels of α_R the equilibrium point moves to higher numbers of Teff cells, remaining practically the number of Treg cells in the same point.B)State-space plot corresponding to the two extreme values for α_R: 0.21 and 2.0, showing an abrupt change in the dynamics.

Figure 5

Prediction of relapses for clinical datasets A) Simulations of CEL time series: simulations of the reversible damage in months (in blue) from the computational model reproduce the dynamics of CEL dataset from patients with MS (in red); B) Pearson's correlation coefficients between CEL series and reversible damage. Each correlation distribution was obtained by comparing 2,000 simulated series and each patient series.

Figure 6

Modeling Treg cell therapy. A)Healthy configurations: while the system is moving clockwise on a spiral trajectory that moves towards the equilibrium point, the model was perturbed with an impulse of Treg cells (only a portion of the trajectory is shown for clarity). The perturbation was introduced near to the maximum possible value of activated Treg. After the impulse, the system jumps to a more distant spiral, where the new maximum value reached by the activated Teff is greater than that on the initial trajectory. B)In the healthy configuration reversible and irreversible damage result almost imperceptible. C) Autoimmune configuration: while the Teff-Treg loop is driving an autoimmune regime, the model was perturbed with the same impulse as above. The effect of the perturbation was qualitative similar to that in the healthy regime, but not quantitatively, showing the hypersensitivity of this kind of regime in the model. D)Both reversible and irreversible damage resulted evident when the system was working under autoimmune conditions.