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Flow-Inducing Networks

Giordano, Giulia LU and Blanchini, Franco (2017) In IEEE Control Systems Letters 1(1). p.44-49
Abstract
We consider flow-inducing networks, a class of models that are well-suited to describe important biochemical systems, including the MAPK pathway and the interactions at the trans-Golgi network. A flow-inducing network is given by the interconnection of subsystems (modules), each associated with a stochastic state matrix whose entries depend on the state variables of other modules. This results in an overall nonlinear system; when the interactions are modeled as mass action kinetics, the overall system is bilinear. We provide preliminary results concerning the existence of single or multiple equilibria and their positivity. We also show that instability phenomena are possible and that entropy is not a suitable Lyapunov function. The... (More)
We consider flow-inducing networks, a class of models that are well-suited to describe important biochemical systems, including the MAPK pathway and the interactions at the trans-Golgi network. A flow-inducing network is given by the interconnection of subsystems (modules), each associated with a stochastic state matrix whose entries depend on the state variables of other modules. This results in an overall nonlinear system; when the interactions are modeled as mass action kinetics, the overall system is bilinear. We provide preliminary results concerning the existence of single or multiple equilibria and their positivity. We also show that instability phenomena are possible and that entropy is not a suitable Lyapunov function. The simplest non-trivial module is the duet, a second order system whose variables represent the concentrations of a species in its activated and inhibited state: under mass action kinetics assumptions, we prove that: 1) a negative loop of duets has a unique equilibrium that is unconditionally stable and 2) a positive loop of duets has either a unique stable equilibrium on the boundary or two equilibria, of which one is unstable on the boundary and one is strictly positive and stable; both properties 1) and 2) hold regardless of the number of duets in the loop. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
in
IEEE Control Systems Letters
volume
1
issue
1
pages
44 - 49
publisher
Institute of Electrical and Electronics Engineers Inc.
ISSN
2475-1456
language
English
LU publication?
yes
id
25bb2134-af8e-4b26-8798-f2602f1752a5
date added to LUP
2017-05-25 11:02:40
date last changed
2017-05-29 11:21:46
@article{25bb2134-af8e-4b26-8798-f2602f1752a5,
  abstract     = {We consider flow-inducing networks, a class of models that are well-suited to describe important biochemical systems, including the MAPK pathway and the interactions at the trans-Golgi network. A flow-inducing network is given by the interconnection of subsystems (modules), each associated with a stochastic state matrix whose entries depend on the state variables of other modules. This results in an overall nonlinear system; when the interactions are modeled as mass action kinetics, the overall system is bilinear. We provide preliminary results concerning the existence of single or multiple equilibria and their positivity. We also show that instability phenomena are possible and that entropy is not a suitable Lyapunov function. The simplest non-trivial module is the duet, a second order system whose variables represent the concentrations of a species in its activated and inhibited state: under mass action kinetics assumptions, we prove that: 1) a negative loop of duets has a unique equilibrium that is unconditionally stable and 2) a positive loop of duets has either a unique stable equilibrium on the boundary or two equilibria, of which one is unstable on the boundary and one is strictly positive and stable; both properties 1) and 2) hold regardless of the number of duets in the loop.},
  author       = {Giordano, Giulia and Blanchini, Franco},
  issn         = {2475-1456},
  language     = {eng},
  number       = {1},
  pages        = {44--49},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Control Systems Letters},
  title        = {Flow-Inducing Networks},
  volume       = {1},
  year         = {2017},
}