An Adaptive Control Scheme for Interleukin-2 Therapy

Abstract

Regulatory T cells (Treg) are suppressor cells that control self-reactive and excessive effector conventional T helper cell (Tconv) responses. Breakdown of the balance between Tregs and Tconvs is a hallmark of autoimmune and inflammatory diseases. Interleukin-2 (IL-2) is a growth factor for both populations and subtle leverage to restore the healthy immune balance in IL-2 therapy. By using a mechanistic mathematical model, we introduced an adaptive control strategy to design the minimal therapeutic IL-2 dosage required to increase and stabilize Treg population and restrict inflammatory response. This adaptive protocol allows for dose adjustments based on the feedback of the immune kinetics of the patient. Our simulation results showed that a minimal Treg population was required to restrict the transient side effect of IL-2 injections on the effector Tconv response. In silico results suggested that a combination of IL-2 and adoptive Treg transfer therapies can limit this side effect.

Keywords: Biological Sciences; Immunology; Mathematical Bioscience.

Graphical abstract

Figure 1

Scheme of the T Cell Response Model and Adaptive Dosing IL-2 Therapy IL-2 concentration and the population of two T-cell subsets, Tconvs and Tregs, are the immune variables considered in the mathematical model (1). Naïve Tconvs and resting Tregs originated from thymic selection are under homeostatic turnover in the periphery. Upon Ag stimulation provided by APCs, naïve Tconvs and resting Tregs become activated. In contrast to activated Tconvs, activated Tregs do not secrete IL-2, but both activated populations proliferate in dependence on the presence of IL-2. Activated Tregs suppress activated Tconvs in a cell contact–dependent and cytokine-driven manner. In contrast to Tregs, activated Tconvs undergo Fas-induced apoptosis by interacting with each other (fratricide). All cells undergo natural cell death and IL-2 is degraded. In the context of IL-2 therapy, the control unit provides the next optimal IL-2 dose according to a feedback from the current status of the immune variables. The control unit calculates the IL-2 dose that is needed to keep T-cell numbers and systemic IL-2 concentration in a predefined range (clinical constraints). Adoptive Treg transfer is the therapeutic process of increasing Treg numbers in the immune system by transiently transferring Tregs to the individual.

Figure 2

Immune Response with and without IL-2 Therapy The T-cell response model, Equation (1), was numerically solved in the presence (red) and absence (black) of IL-2 injections. The values of (A) Tconvs, (B) Tregs, and (C) IL-2 concentration were normalized to their maximum value in the absence of IL-2 injections. For IL-2 therapy, constant doses of 0.5 (arbitrary unit) are administered every unit of time ($\delta =1$). The initial conditions are set to zero.

Figure 3

IL-2 Therapy Combined with Adoptive Treg Transfer Equation (1) was solved for the cases of IL-2 therapy alone (black) and in combination with different levels of adoptive Tregs transfer at $t=0$ (colors). The values of (A) Tconvs, (B) Tregs, and (C) IL-2 concentration were normalized to their maximum value for the case of IL-2 therapy alone. The administration frequency is 1. Low, medium, and high adoptive Tregs correspond to initial values of R of 0.01, 0.04, and 0.5, respectively.

Figure 4

Adaptive IL-2 Dosing Strategy The kinetics of (A) Tconvs, (B) Tregs, (C) IL-2, and (D) IL-2 dose is shown for fixed (black) and adaptive dose IL-2 therapy (red), each applied at every time unit ($\delta =1$) and combined with adoptive Treg transfer ($R(t=0)=0.5$). The physiological range was $\mathcal{X}=\{\left(\mathrm{0,0,0}\right)<(T,R,I)<\left(\mathrm{40,30,2}\right)\}$ and the therapeutic target window was ${\mathcal{X}}^{Tar}=\{\left(\mathrm{0,19,0}\right)<(T,R,I)<\left(\mathrm{1,22,1}\right)\}$. IL-2 doses were constrained to $\mathcal{U}=\{0<d_{IL-2}<0.7\}$. For the fixed-dose therapy, the maximum allowed dose (i.e., 0.7) was administered. The calculated adaptive doses successfully enforced variables to the therapeutic target window (horizontal dashed lines). The kinetics of (E) Tconvs, (F) Tregs, (G) IL-2, and (H) IL-2 dose is shown for different IL-2 injection frequencies δ of 1, 2, and 5 time units, corresponding to high, medium, and low frequency, respectively. The control unit selects the corresponding suitable doses in each case. The value of Tconvs, Tregs, and IL-2 is normalized to its maximum value for the uncontrolled case (without IL-2 therapy, Figure 2, black curves). For low frequencies, higher doses are required. Therefore, the maximum allowed IL-2 dose was increased to 2.5 to make the optimization problem feasible. The IL-2 dose is normalized to the dose in (D) fixed-dose value and (H) maximum dose value in low frequency.