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Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

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Title: Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction
Authors: Beguerisse Diaz, M
Desikan, R
Barahona, M
Item Type: Journal Article
Abstract: Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal-gain cascades (i.e., when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.
Issue Date: 31-Aug-2016
Date of Acceptance: 5-Aug-2016
URI: http://hdl.handle.net/10044/1/38843
DOI: https://dx.doi.org/10.1098/rsif.2016.0409
ISSN: 1742-5689
Publisher: Royal Society, The
Journal / Book Title: Journal of the Royal Society Interface
Volume: 13
Issue: 121
Copyright Statement: © 2016 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.
Sponsor/Funder: Biotechnology and Biological Sciences Research Council (BBSRC)
Engineering & Physical Science Research Council (EPSRC)
James S. McDonnell Foundation
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: BB/G020434/1
EP/I017267/1
220020349
EP/N014529/1
Keywords: activation cascades
model reduction
ordinary differential equation models
signal transduction
q-bio.MN
math.DS
math.OC
q-bio.QM
General Science & Technology
MD Multidisciplinary
Notes: 18 pages, 6 figures
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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