López-García, M orcid.org/0000-0003-3833-8595, Nowicka, M, Bendtsen, C et al. (3 more authors) (2018) Quantifying the phosphorylation timescales of receptor–ligand complexes: a Markovian matrix-analytic approach. Open Biology, 8 (9). 180126. ISSN 2046-2441
Abstract
Cells interact with the extracellular environment by means of receptor molecules on their surface. Receptors can bind different ligands, leading to the formation of receptor–ligand complexes. For a subset of receptors, called receptor tyrosine kinases, binding to ligand enables sequential phosphorylation of intra-cellular residues, which initiates a signalling cascade that regulates cellular function and fate. Most mathematical modelling approaches employed to analyse receptor signalling are deterministic, especially when studying scenarios of high ligand concentration or large receptor numbers. There exist, however, biological scenarios where low copy numbers of ligands and/or receptors need to be considered, or where signalling by a few bound receptor–ligand complexes is enough to initiate a cellular response. Under these conditions stochastic approaches are appropriate, and in fact, different attempts have been made in the literature to measure the timescales of receptor signalling initiation in receptor–ligand systems. However, these approaches have made use of numerical simulations or approximations, such as moment-closure techniques. In this paper, we study, from an analytical perspective, the stochastic times to reach a given signalling threshold for two receptor–ligand models. We identify this time as an extinction time for a conveniently defined auxiliary absorbing continuous time Markov process, since receptor–ligand association/dissociation events can be analysed in terms of quasi-birth-and-death processes. We implement algorithmic techniques to compute the different order moments of this time, as well as the steady-state probability distribution of the system. A novel feature of the approach introduced here is that it allows one to quantify the role played by each kinetic rate in the timescales of signal initiation, and in the steady-state probability distribution of the system. Finally, we illustrate our approach by carrying out numerical studies for the vascular endothelial growth factor and one of its receptors, the vascular endothelial growth factor receptor of human endothelial cells.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | stochastic model; receptor–ligand interaction; phosphorylation; time to signalling threshold; quasi-birth-and-death process |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Biological Sciences (Leeds) > School of Molecular and Cellular Biology (Leeds) > Cardiovascular Science (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Jul 2018 09:58 |
Last Modified: | 25 Jun 2023 21:26 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rsob.180126 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133589 |