Topological and kinetic determinants of the modal matrices of dynamic models of metabolism.
Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of met...
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doaj-71a238d681964bd7a612368d711300412020-11-25T01:20:09ZengPublic Library of Science (PLoS)PLoS ONE1932-62032017-01-011212e018988010.1371/journal.pone.0189880Topological and kinetic determinants of the modal matrices of dynamic models of metabolism.Bin DuDaniel C ZielinskiBernhard O PalssonLarge-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.http://europepmc.org/articles/PMC5739448?pdf=render |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bin Du Daniel C Zielinski Bernhard O Palsson |
spellingShingle |
Bin Du Daniel C Zielinski Bernhard O Palsson Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. PLoS ONE |
author_facet |
Bin Du Daniel C Zielinski Bernhard O Palsson |
author_sort |
Bin Du |
title |
Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
title_short |
Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
title_full |
Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
title_fullStr |
Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
title_full_unstemmed |
Topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
title_sort |
topological and kinetic determinants of the modal matrices of dynamic models of metabolism. |
publisher |
Public Library of Science (PLoS) |
series |
PLoS ONE |
issn |
1932-6203 |
publishDate |
2017-01-01 |
description |
Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions. |
url |
http://europepmc.org/articles/PMC5739448?pdf=render |
work_keys_str_mv |
AT bindu topologicalandkineticdeterminantsofthemodalmatricesofdynamicmodelsofmetabolism AT danielczielinski topologicalandkineticdeterminantsofthemodalmatricesofdynamicmodelsofmetabolism AT bernhardopalsson topologicalandkineticdeterminantsofthemodalmatricesofdynamicmodelsofmetabolism |
_version_ |
1725135287348101120 |