Modelling the self-tolerance mechanisms of T cells: An adaptive sliding mode control approach

Abstract

The response of the immune system to self or foreign tissues induce dynamics which lead to health or disease. The maintenance of the healthy state by the inhibition of undesirable responses to self tissues is a key property of the naturally occurring robust feedback mechanism seen within a healthy immune system. In this paper, Variable Structure Control (VSC) theory is used to design an adaptive sliding mode control to model the observed self-tolerance exhibited by a healthy immune system. A suitable sliding manifold and corresponding reachability condition are formulated based on knowledge of the healthy tolerance steady-state. Unlike existing candidate immune response functions, the proposed control function exhibits robust performance commensurate with the self-tolerance mechanisms of the immune system which have been observed experimentally.

Synergies between the dynamics of the immune response of T cells and the variable structure control paradigm

“…where ξ is a constant and u is the chosen control action. Consider a fixed structure design where the control gain is set to: u = k (2) and the constant parameter k is a positive or a negative scalar. The phase portrait of the system (1) with the control (2) reveals that this strategy produces unstable dynamics and the desired stable motion of the system trajectories towards the equilibrium located at the origin is not exhibited as shown in Figure 1.…”

“…Consider a fixed structure design where the control gain is set to: u = k (2) and the constant parameter k is a positive or a negative scalar. The phase portrait of the system (1) with the control (2) reveals that this strategy produces unstable dynamics and the desired stable motion of the system trajectories towards the equilibrium located at the origin is not exhibited as shown in Figure 1. In contrast to this fixed structure design, the basic philosophy of VSC consists in formulating a decision rule to switch between different control structures to achieve stable dynamics and performance requirements [14].…”

“…Collectively, the features of VSC provide several benefits and motivate the use of the VSC paradigm in various applications from engineering. These include power electronics and robotics, and most recently assist the study of the robust switched control processes that naturally occur within biology [2], [3].…”

“…sufficiently high, the stability properties are altered and the desired timings of the switching mechanisms are violated as seen in Figure 6 and Figure 7. In immunology, this relates to cases of improper immune responses [16], [17], [1], [2]. These undesirable immunological dynamics caused by biological perturbations are analogous to cases where the gain of an engineering VSCS is not sufficient to reject the effects of the disturbance and a reachability condition fails to hold [8], [14].…”