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Multiple steady states and the form of response functions to antigen in a model for the initiation of T cell activation
- Source :
- Royal Society Open Science, Vol 4, Iss 11 (2017), Royal Society Open Science
- Publication Year :
- 2017
-
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.
- Subjects :
- 0301 basic medicine
State variable
T cell
Molecular Networks (q-bio.MN)
Phosphatase
multistationarity
Dynamical Systems (math.DS)
Dissociation (chemistry)
immunology
03 medical and health sciences
medicine
FOS: Mathematics
Quantitative Biology - Molecular Networks
Mathematics - Dynamical Systems
lcsh:Science
Receptor
t cells
Multidisciplinary
Chemistry
T-cell receptor
92C37
Dissociation constant
030104 developmental biology
medicine.anatomical_structure
FOS: Biological sciences
Biophysics
Phosphorylation
lcsh:Q
Mathematics
Research Article
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Royal Society Open Science, Vol 4, Iss 11 (2017), Royal Society Open Science
- Accession number :
- edsair.doi.dedup.....a8741847a0ca6ab8e86b54f41d232c58