A mechanistic model of thymocyte dynamics: a quantitative tool for predicting drug effects on thymic function
Victoria Kulesh (1,2,3), Kirill Peskov (1,2,3), Gabriel Helmlinger (4), Gennady Bocharov (3,5,6)
(1) Research Center of Model-Informed Drug Development, I.M. Sechenov First Moscow State Medical University, Moscow, Russia, (2) Modeling and Simulation Decisions FZ - LLC, Dubai, UAE, (3) Marchuk Institute of Numerical Mathematics RAS, Moscow, Russia, (4) Biorchestra Co., Ltd., Cambridge, Massachusetts, USA, (5) Institute for Computer Science and Mathematical Modelling, I.M. Sechenov First Moscow State Medical University, 119991 Moscow, Russia. (6) Moscow Center of Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
Objectives: The thymus is a primary lymphoid organ whereby thymocytes differentiate into functional T cells through a process of thymopoiesis. Each thymus lobe consists of two main regions – the outer cortex and the inner medulla – defining cell developmental origin, selection and maturation processes. The most important features of thymus function reside in the orchestrated staging of thymocyte differentiation processes and the phenomenon of age-related thymus involution, whereby the number of mature T cells leaving the thymus gradually decreases with age [1]. There is currently no consensus among existing mechanistic quantitative models of thymopoiesis and thymus function, in terms of practical use to address research challenges in either fundamental or applied immunology [2]. Establishing a mechanistic model of thymocyte dynamics that incorporates multi-scale modeling of T cell turnover is therefore deemed important, to quantitatively explore immune cell dynamics in cases of, e.g., infectious, autoimmune, and other diseases.
The key objective of this study was to develop a quantitative, mechanistic mathematical model of thymocyte dynamics which explicitly integrates essential biological details such as thymus spatial structure and homeostasis, as well as age-related thymic involution, in order to evaluate changes in thymic function under pathological conditions and in response to therapeutic immunomodulatory drugs.
Methods: A systematic literature search was conducted in PubMed and Google Scholar, to identify all relevant sources with experimental and clinical data on thymocyte dynamics, derive physiological ranges of thymocyte subpopulations, and define physiologically admissible parameter ranges. Parameter calibration was performed by identifying plausible parameter sets which satisfied conditions of quasi steady-state thymocyte levels within physiological ranges [3]. A partial rank correlation coefficient (PRCC) global sensitivity analysis was performed [4]. The predictive power of the newly developed model was assessed via independent cross-validation of thymic function in healthy subjects, multiple sclerosis (MS) patients, and patients on fingolimod treatment. Model development and analysis were performed using the R Statistics software, version 4.0.2.
Results: A mechanistic model of thymocyte dynamics was developed. The model consisted of ODEs describing the homeostasis of DN, DP, SP4 and SP8 subpopulations of thymocytes, while taking into account the carrying capacity of the thymic cortex and medulla using a maximal allowable number of thymocytes in these niches. Thymus involution was captured by an age-dependent function describing the maximal number of thymocytes in the thymic cortex and medulla. All generalized parameter estimates were consistent with experimentally derived estimates of thymocyte kinetics. Quasi steady-state values for the DN, DP, SP4 and SP8 subpopulations, with the proposed set of parameters values, were ~2.72*109, ~2.12*1010, ~7.45*109 and ~2.79*109, respectively, in full agreement with experimentally derived physiological ranges for these variables (respectively, [1.3*109; 3.4*109], [1.2*1010; 3.2*1010], [6.3*109; 1.7*1010] and [2.3*109; 6.0*109]. Thymic function was most impacted by the egress, proliferation, differentiation and death rates of SP4 cells (PRCC > 0.5). Predictive model simulations showed that Grade 4 lymphopenia was expected to develop after ~19 years of continuous fingolimod intake by initially 20-year old MS patients and quantitatively explained the decrease in relapse risk with age after fingolimod discontinuation, owing to decreased thymic output with age.
Conclusions: The proposed mechanistic model of thymocyte dynamics accurately described thymic output as a function of age and may be used to explore various scenarios of patho-physiological conditions, pharmacological interventions, and personalized therapeutic treatment regimens relevant to patients as well as new drug development programs. This model may also serve as a base for further developing an immune system quantitative systems pharmacology model leading to a Drug-Disease modeling platform, to support the development of novel therapies and the setting of dosing regimens of existing and new drugs in autoimmune and infectious diseases.
References:
[1] Haynes BF, Sempowski GD, Wells AF, Hale LP. The Human Thymus during Aging. Immunol Res. 2000 Dec 1;22(2):253–61.
[2] Robert PA, Kunze-Schumacher H, Greiff V, Krueger A. Modeling the Dynamics of T-Cell Development in the Thymus. Entropy. 2021;23(4).
[3] Allen R, Rieger T, Musante C. Efficient Generation and Selection of Virtual Populations in Quantitative Systems Pharmacology Models. CPT Pharmacomet Syst Pharmacol. 2016 Mar 1;5(3):140–6.
[4] Marino S, Hogue IB, Ray CJ, Kirschner DE. A Methodology for Performing Global Uncertainty and Sensitivity Analysis in Systems Biology. J Theor Biol. 2008 Sep 7;254(1):178–96.
