Open Access Research article

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

Nieves Vélez de Mendizábal12, Jorge Carneiro3, Ricard V Solé4, Joaquín Goñi1, Jean Bragard1, Ivan Martinez-Forero1, Sara Martinez-Pasamar5, Jorge Sepulcre1, Javier Torrealdea2, Francesca Bagnato6, Jordi Garcia-Ojalvo7 and Pablo Villoslada5*

Author Affiliations

1 Division of Neurosciences, CIMA - University of Navarra. Avenida Pio XII 55, 31008 Pamplona, Spain

2 Computer Science and Artificial Intelligence Department, University of the Basque Country, Paseo de Manuel Lardizábal, 1, 20018 San Sebastian, Spain

3 Theoretical Immunology Group, Instituto Gulbenkian de Ciencia, Rua da Quinta Grande 6, 2780-156 Oeiras, Portugal

4 Complex Systems Lab, Universitat Pompeu Fabra, Carrer del Dr. Aiguader, 88, 08003 Barcelona, Spain

5 Center for Neuroimmunology, Department of Neurosciences. Institute of Biomedical Research August Pi Sunyer (IDIBAPS) - Hospital Clinic of Barcelona. Villarroel 170, 08036 Barcelona, Spain

6 Neuroimmunology Branch, National Institute of Neurological Diseases and Stroke. 9000 Rockville Pike, Bethesda, MD. USA

7 Departament de Física i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Rambla Sant Nebridi s/n, 08222 Terrasa, Spain

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BMC Systems Biology 2011, 5:114  doi:10.1186/1752-0509-5-114

Published: 15 July 2011

Additional files

Additional file 1:

Model equations for Vensim software as text. It contains all the equations, auxiliary variable definitions and parameter values of the model (doc file).

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Additional file 2:

The model in Vensim software code. It contains the model. It's ready to run using the Vensim software (mdl file). Vensim can be downloaded from http://www.vensim.com/ webcite

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Additional file 3:

Dataset CEL from patients with MS Data from 9 patients with RRMS who underwent monthly MRI with gadolinium for 48 months. It showed the number of CELs for each consecutive month on the MRI, the Expanded Disability Status Scale (EDSS) for measuring clinical disability and the presence of clinical relapses (excel file).

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Additional file 4:

Figure S1. Clinical heterogeneity: Influence of timing on the generation of self-reacting T-cells in the dynamics of the immune system. Four simulations (over 5 years) of the same model (same parameters and initial conditions) are presented for four different seeds generating the naïve Teff and Treg populations. We used a parameter configuration that allows the generation of autoimmune dynamics (αR = 0.25). Left: Dynamics of activated Teff cells. Right: Evolution along time of the reversible, irreversible and total damage.

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Additional file 5:

Figure S2. Sensitivity analysis of the model A. At individual level: The figure shows the sensitivity analysis when changing the Teff and Treg proliferation rates for four different seeds. The X axis corresponds to the maximum Treg proliferation rate, αR, and the Y axis to the maximum Teff proliferation rate αE. The Z axis shows the average relapse intensity reached by activated-Teff cells during a 5 year simulation (Z axis). Each blanket corresponds to a different seed. B. At global level: We realize 200 different simulations per each pair of proliferation rates; Average of 200 different "A" blankets.

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Additional file 6:

Figure S3. The effect of perturbing the Te-Treg loop with a pulse of Treg and Te cells. The system, under autoimmune configuration, was perturbed at different times (sectors) with different intensity pulses of Treg/Te cells and the graphs display the phase space of the Te-Tr loop. The number of activated-Treg cells is plotted on the X axis and the number of the activated-Te cells on the Y axis. Both populations move clockwise along a spiral path to the equilibrium point in the absence of perturbations. Because the Te and Treg populations fluctuate under a negative feedback control, there are four feasible dynamic states. Sector I: both activated Te and Treg populations are growing. Sector II: the activated-Treg population is growing and the activated-Te population is diminishing. Sector III: the activated-Treg population is diminishing and activated-Te population is growing. Sector IV: the activated-Te population is growing and activated-Tr population is diminishing. The trajectory before the perturbation is depicted in black and after in red. Treg impulses: A. A small Treg perturbation in sector I leads to a jump to a closer trajectory. B. A large Treg perturbation in sector I leads to a jump to a more distant trajectory. C. a small Treg perturbation in sector IV leads to a jump to a closer trajectory. D. a large Treg perturbation in sector IV leads to a jump to a more distant trajectory. Any other perturbation in sector II and III, irrespective of its intensity, will move the system to another more distant trajectory (data not shown). Te impulses: E. A small Te perturbation in sector IV leads to a jump to a closer trajectory. F. a large Te perturbation in sector IV leads to a jump to a more distant trajectory. G. A small Te perturbation in sector III leads to a jump to a closer trajectory. H. A large Te perturbation in sector III leads to a jump to a more distant trajectory. Any other perturbation in sector I and II will move the system to a more distant trajectory, irrespective of its intensity (data not shown).

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