Modelling and Simulation of the Dynamics of the Antigen-Specific T Cell Response Using Variable Structure Control Theory

Abstract

Experimental and mathematical studies in immunology have revealed that the dynamics of the programmed T cell response to vigorous infection can be conveniently modelled using a sigmoidal or a discontinuous immune response function. This paper hypothesizes strong synergies between this existing work and the dynamical behaviour of engineering systems with a variable structure control (VSC) law. These findings motivate the interpretation of the immune system as a variable structure control system. It is shown that dynamical properties as well as conditions to analytically assess the transition from health to disease can be developed for the specific T cell response from the theory of variable structure control. In particular, it is shown that the robustness properties of the specific T cell response as observed in experiments can be explained analytically using a VSC perspective. Further, the predictive capacity of the VSC framework to determine the T cell help required to overcome chronic Lymphocytic Choriomeningitis Virus (LCMV) infection is demonstrated. The findings demonstrate that studying the immune system using variable structure control theory provides a new framework for evaluating immunological dynamics and experimental observations. A modelling and simulation tool results with predictive capacity to determine how to modify the immune response to achieve healthy outcomes which may have application in drug development and vaccine design.

Dynamical conditions for the containment of HIV infection by CD8+ T Cells — A variable structure control approach

“…As in [3], [4], the framework of sliding mode control is utilized to investigate the performance of the specific T cell response. Here, a sliding manifold representing the immunological objective of the HIV-specific CD8+ T cell response is defined and a reachability condition is formulated to ensure that immunity is achieved.…”

“…A variety of control techniques have been considered to analyse HIV dynamics in vivo [9], [1], [25], [6]. Evaluating the condition for the containment of HIV infection by the HIV-specific CD8+ T cell response using a Variable Structure Control (VSC) approach is supported by the following observations:1-the dynamics of the CD8+ T cell response has been shown to behave as a switched control system in [3]. 2-The double saturation function modelling cytolytic mechanism in [16] reveals that the structure of the killing action changes during the infection.…”

Control theory helps to resolve the measles paradox

“…Viral infections such as measles disturb biological feedback and impair immune reponses by destroying immune cells [ 10 , 12 , 18 ]. Virus-specific immune responses operate as a feedback control to clear viral particles and destroy infected cells [ 10 , 21 , 26 ]. Thus, the feedback between viruses and immune cells predominantly determines clinical outcomes in the absence of treatment [ 18 , 22 , 26 , 27 ].…”

“…Virus-specific immune responses operate as a feedback control to clear viral particles and destroy infected cells [ 10 , 21 , 26 ]. Thus, the feedback between viruses and immune cells predominantly determines clinical outcomes in the absence of treatment [ 18 , 22 , 26 , 27 ]. Indeed, it is important to understand how immunological feedback controls viral infections.…”

“…Here, control theory is used to explain different outcomes observed during acute morbillivirus infections. Analysis is completed for a particular mathematical form of feedback, sliding mode control [ 23 , 24 , 26 ], which is consistent with viral clearance [ 27 , 29 ]. The control analysis delivers fundamental mathematical conditions to exhibit viral clearance and immunosuppression (lymphopenia) during acute morbillivirus infections.…”