Algorithms to study large metabolic network dynamics

Dima Grigoriev, Satya Samal, Sergey Vakulenko und Andreas Weber
In: Mathematical Modelling of Natural Phenomena (2015), 10:5(100-118)
 

Abstract

We consider a class of systems of differential equations with quadratic nonlinearities. This class describes important biochemical models. We show that systems of this class can realize any structurally stable dynamics. Given a low dimensional dynamics, we describe algorithms that allow to realize this dynamics by a large biochemical network. Some concrete biochemical examples are studied. Moreover, we show how a big system with random kinetic rates can simulate a number of low dimensional ones. The proposed method is applied on Calcium oscillations, extracellular signal-regulated kinase (ERK) signaling pathway and multistationary Mitogen-activated protein kinase cascade system (MAPK) models from biochemistry.

Stichwörter: attractors, Metabolic networks

Bibtex

@ARTICLE{GregorievEtAl2015a,
    author = {Grigoriev, Dima and Samal, Satya and Vakulenko, Sergey and Weber, Andreas},
     pages = {100--118},
     title = {Algorithms to study large metabolic network dynamics},
   journal = {Mathematical Modelling of Natural Phenomena},
    volume = {10},
    number = {5},
      year = {2015},
  keywords = {attractors, Metabolic networks},
  abstract = {We consider a class of systems of differential equations with quadratic nonlinearities. This class
              describes important biochemical models. We show that systems of this class can realize any
              structurally stable dynamics. Given a low dimensional dynamics, we describe algorithms that allow to
              realize this dynamics by a large biochemical network. Some concrete biochemical examples are
              studied. Moreover, we show how a big system with random kinetic rates can simulate a number of low
              dimensional ones. The proposed method is applied on Calcium oscillations, extracellular
              signal-regulated kinase (ERK) signaling pathway and multistationary Mitogen-activated protein kinase
              cascade system (MAPK) models from biochemistry.},
       doi = {10.1051/mmnp/201510507}
}