Multiple steady states and the form of response functions to antigen in a model for the initiation of t-cell activation

Alan D. Rendall, Eduardo D. Sontag

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of the activating signal. In particular, there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces a maximal activation of the T cell. This suggests that mechanisms taking place in the first few minutes after activation and included in the model studied in this paper suffice to explain the optimal dissociation time seen in experiments. In this way, the results of certain simulations in the literature have been confirmed rigorously and some important features which had not previously been seen have been discovered.

Original languageEnglish (US)
Article number170821
JournalRoyal Society Open Science
Volume4
Issue number11
DOIs
StatePublished - Nov 8 2017

Fingerprint

T-cells
Response Function
Receptor
Activation
T Cell Activation
Qualitative Behavior
Phosphorylation
Cell
Damped
Model
Mathematical Model
Oscillation
Zero
Experiment
Form
Simulation

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Immunology
  • Multistationarity
  • T cells

Cite this

@article{5cd7bbd8b84b400eb51870dc679d6792,
title = "Multiple steady states and the form of response functions to antigen in a model for the initiation of t-cell activation",
abstract = "The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of the activating signal. In particular, there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces a maximal activation of the T cell. This suggests that mechanisms taking place in the first few minutes after activation and included in the model studied in this paper suffice to explain the optimal dissociation time seen in experiments. In this way, the results of certain simulations in the literature have been confirmed rigorously and some important features which had not previously been seen have been discovered.",
keywords = "Immunology, Multistationarity, T cells",
author = "Rendall, {Alan D.} and Sontag, {Eduardo D.}",
year = "2017",
month = "11",
day = "8",
doi = "10.1098/rsos.170821",
language = "English (US)",
volume = "4",
journal = "Royal Society Open Science",
issn = "2054-5703",
publisher = "The Royal Society",
number = "11",

}

Multiple steady states and the form of response functions to antigen in a model for the initiation of t-cell activation. / Rendall, Alan D.; Sontag, Eduardo D.

In: Royal Society Open Science, Vol. 4, No. 11, 170821, 08.11.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Multiple steady states and the form of response functions to antigen in a model for the initiation of t-cell activation

AU - Rendall, Alan D.

AU - Sontag, Eduardo D.

PY - 2017/11/8

Y1 - 2017/11/8

N2 - The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of the activating signal. In particular, there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces a maximal activation of the T cell. This suggests that mechanisms taking place in the first few minutes after activation and included in the model studied in this paper suffice to explain the optimal dissociation time seen in experiments. In this way, the results of certain simulations in the literature have been confirmed rigorously and some important features which had not previously been seen have been discovered.

AB - The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of the activating signal. In particular, there are cases where there is a value of the dissociation constant of the ligand from the receptor which produces a maximal activation of the T cell. This suggests that mechanisms taking place in the first few minutes after activation and included in the model studied in this paper suffice to explain the optimal dissociation time seen in experiments. In this way, the results of certain simulations in the literature have been confirmed rigorously and some important features which had not previously been seen have been discovered.

KW - Immunology

KW - Multistationarity

KW - T cells

UR - http://www.scopus.com/inward/record.url?scp=85033583782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033583782&partnerID=8YFLogxK

U2 - 10.1098/rsos.170821

DO - 10.1098/rsos.170821

M3 - Article

AN - SCOPUS:85033583782

VL - 4

JO - Royal Society Open Science

JF - Royal Society Open Science

SN - 2054-5703

IS - 11

M1 - 170821

ER -