T cell activation: a queueing theory analysis at low agonist density

¹ University of warwick
² University of Ruhuna

^* To whom correspondence should be addressed. E-mail: njb{at}maths.warwick.ac.uk.

Submitted on May 17, 2005
Revised on August 16, 2005
Accepted on 17 April 2006

	Abstract

We analyse a simple linear triggering model of the T cell receptor (TCR) within the framework of queueing theory, TCRs entering the queue upon full activation, and exit by down regulation. We fit our model to four experimentally characterised activation criteria and analyse their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the time scale of downregulation; thus the calcium spike (30s) has low specificity but a sensitivity to single peptide MHC ligands while the cytokine threshold (1hr) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation, for example under stochasticity in the ligand number in the cell:cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hrs), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proof reading scheme). Therefore through a combination of thresholds and signal integration a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that threshold mechanisms are employed to establish the conditions for efficient signal integration, ie coordinate the formation of a stable contact interface.

Key Words: Markov chains, exit time, immunology, threshold models, triggering