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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 784512, 17 pages
Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities
Biomedical Optics Research Laboratory, Clinic of Neonatology, University Hospital Zürich, Frauenklinikstrasse 10, CH-8091 Zürich, Switzerland
Received 4 January 2012; Revised 13 April 2012; Accepted 28 June 2012
Academic Editor: Zvia Agur
Copyright © 2012 Christoph Kuhn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Supplementary material includes videos (Video 3, Video 4, Video 7, Video 9, Video 10, Video 12, Video 13) demonstrating the time development from which snap-shots were singlet out and displayed in the corresponding figures (see inside PDF) of the paper Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities by Christoph Kuhn.
Video 3: Dynamical stochastic process of multiplication and selection. Discrete limit.
Video 4: Dynamical stochastic process of multiplication and selection. Continuous limit.
Video 7: Dynamical stochastic process for initial form A and mutant B.
Video 9: Computer result of a pathogen P (with antigen A) coupled through averages to an immune system consisting of an effector E (producing antigen receptor a) and memory M. Case where pathogen is eliminated.
Video 10: Computer result of a pathogen P (with antigen A) coupled through averages to an immune system consisting of an effector E (producing antigen receptor a) and memory M. Case where the pathogen is reappearing while the immune system response is low.
Video 12: Computer result of a varying pathogen (PA with antigen A changing into PB with antigen B) coupled through averages to an immune system against antigen A consisting of an effector Ea and memory Ma and against antigen B consisting of an effector Eb and memory Mb. Partial change of pathogen PA to pathogen PB escaping immune effector Ea and with delayed immune response of effector Eb.
Figure 13: Computer result of the maturation process of T-lymphocytes. First a naive T-lymphocyte (LNaive, green) in bone marrow or thymus undergoes T-cell receptor rearrangement (β-selection). T-cells with high affinity to self-peptides MHC (LSelf, black) are eliminated (negative selection), whereas T-cells with T cell receptors that are able to bind self-peptides MHC molecules with at least a weak affinity (LMat->I, blue and LMat->A, red) survive (positive selection) and circulate in the peripheral lymphatic system. The matured T-lymphocyte, recognizing the antigen by high affinity to the antigen-loaded MHC (LMat->A, red), transforms into an effector cell and proliferates.