Stochastic effects and bistability in T cell receptor signaling

Abstract

The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand-receptor binding kinetics) and negative and positive feedback regulation mediated respectively by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein-protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide-MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.

Elucidation of T cell signalling models

“…Thus variations in ppERK concentration would change the ability of the cell to signal. Interpretations of results in Lipniacki et al [11] give further weight to this not a positive feedback argument. Changes in Lck concentration influence pSHP1 levels far more than ppERK levels, if ppERK were in positive feedback the action of Lck would be part of the feedback loop and so would influence ppERK levels.…”

“…A set of signalling events that involve kinetic proofreading, a negative influence from SH2 domain-containing phosphatase (SHP1) and a positive influence from extracellular signal regulated kinase (ERK) have been discussed in reference to tunability in [2,5] and have been experimentally investigated in [6,7]. This system has also received much modelling attention in [7][8][9][10][11]. The important quantitative and qualitative concepts that these signalling events impose on T cell discrimination are well summarised in Chan et al [8].…”

“…To this end [7] achieves a model of 557 chemical reaction equations which are converted to 238 ordinary differential equations. Artyomov et al [9] and Lipniacki et al [11] both produce simplified versions of the concepts in the ABG model and perform stochastic analysis. [9,11] argue the importance of stochastic modelling particularly when small molecule numbers can produce bistabilities in a stochastic model that do not exist in the deterministic model.…”

“…The simplified models analysed in [8,9,11] convey an understanding of the qualitative aspects of TCR, SHP1, ERK signalling. We take this opportunity to dissect the biologically detailed ABG model with the objective of gaining clarified understanding of the biological processes that contribute to the qualitative behaviour.…”

“…Here we stochastically analyse the entire ABG model 1 by investigating behaviour at the single TCR level and progressively include components to compose the entire model. With this compositional analysis we achieve a greater understanding of the elements of the model without the simplifying assumptions of [11].…”