Abstract
Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a number of important roles in the function of immune cells. It belongs to the Src family of kinases which are known to undergo autophosphorylation. It turns out that this leads to a remarkable variety of dynamical behaviour which can occur during their activation. We prove that in the presence of autophosphorylation one phenomenon, bistability, already occurs in a mathematical model for a protein with a single phosphorylation site. We further show that a certain model of Lck exhibits oscillations. Finally, we discuss the relations of these results to models in the literature which involve Lck and describe specific biological processes, such as the early stages of T cell activation and the stimulation of T cell responses resulting from the suppression of PD-1 signalling which is important in immune checkpoint therapy for cancer.
Original language | English |
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Article number | 64 |
Journal | Bulletin of Mathematical Biology |
Volume | 83 |
Issue number | 6 |
Early online date | 1 May 2021 |
DOIs | |
Publication status | Published - 30 Jun 2021 |
Bibliographical note
Funding Information:Acknowledgements LMK acknowledges support from the European Union Horizon 2020 research and innovation programmes under the Marie Skłodowska-Curie Grant Agreement No. 777826 (NoMADS), the Cantab Capital Institute for the Mathematics of Information and Magdalene College, Cambridge (Nevile Research Fellowship).
Funding
Acknowledgements LMK acknowledges support from the European Union Horizon 2020 research and innovation programmes under the Marie Skłodowska-Curie Grant Agreement No. 777826 (NoMADS), the Cantab Capital Institute for the Mathematics of Information and Magdalene College, Cambridge (Nevile Research Fellowship).
Keywords
- Bifurcation
- Dynamics
- Phosphorylation
- Src kinase
- T cells
ASJC Scopus subject areas
- General Neuroscience
- Immunology
- General Mathematics
- General Biochemistry,Genetics and Molecular Biology
- General Environmental Science
- Pharmacology
- General Agricultural and Biological Sciences
- Computational Theory and Mathematics