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Robust simplifications of multiscale biochemical networks.

Radulescu O, Gorban AN, Zinovyev A, Lilienbaum A - BMC Syst Biol (2008)

Bottom Line: In these situations reduction to a common level of complexity is needed.We propose a systematic treatment of model reduction of multiscale biochemical networks.For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1.

View Article: PubMed Central - HTML - PubMed

Affiliation: IRMAR (CNRS UMR 6025), Universit├ę de Rennes 1, Rennes, France. ovidiu.radulescu@univ-rennes1.fr

ABSTRACT

Background: Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.

Results: We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-kappaB pathway.

Conclusion: Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

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Two simple examples of exactly solvable linear kinetics. a) non-branching network without cycles. b) network with a unique sink which is a cycle. On the left, ¤Ľ(i) map is shown for the network a). The order of kinetics parameters is shown both by integer numbers (ranks) and the thickness of arrows (faster reactions are thicker).
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Figure 1: Two simple examples of exactly solvable linear kinetics. a) non-branching network without cycles. b) network with a unique sink which is a cycle. On the left, ¤Ľ(i) map is shown for the network a). The order of kinetics parameters is shown both by integer numbers (ranks) and the thickness of arrows (faster reactions are thicker).

Mentions: Hierarchical linear network can be represented as a digraph and a set of orders (integer numbers) associated to each arc (reaction). The lower the order, the more rapid is the reaction (see Fig. 1). It happens that in this case the special structure of the matrix K (originated from a reaction graph) allows us to exploit the strong relation between the dynamics (1) and the topological properties of the digraph. Big advantage of the fully separated network is that the possible values of are 0, 1 and the possible values of are -1, 0, 1 with high precision [34]. Thus, if we can provide an algorithm for finding non-zero components of , , based on the network topology and the constants ordering, then this will give us a good approximation to the problem solution (2).


Robust simplifications of multiscale biochemical networks.

Radulescu O, Gorban AN, Zinovyev A, Lilienbaum A - BMC Syst Biol (2008)

Two simple examples of exactly solvable linear kinetics. a) non-branching network without cycles. b) network with a unique sink which is a cycle. On the left, ¤Ľ(i) map is shown for the network a). The order of kinetics parameters is shown both by integer numbers (ranks) and the thickness of arrows (faster reactions are thicker).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2654786&req=5

Figure 1: Two simple examples of exactly solvable linear kinetics. a) non-branching network without cycles. b) network with a unique sink which is a cycle. On the left, ¤Ľ(i) map is shown for the network a). The order of kinetics parameters is shown both by integer numbers (ranks) and the thickness of arrows (faster reactions are thicker).
Mentions: Hierarchical linear network can be represented as a digraph and a set of orders (integer numbers) associated to each arc (reaction). The lower the order, the more rapid is the reaction (see Fig. 1). It happens that in this case the special structure of the matrix K (originated from a reaction graph) allows us to exploit the strong relation between the dynamics (1) and the topological properties of the digraph. Big advantage of the fully separated network is that the possible values of are 0, 1 and the possible values of are -1, 0, 1 with high precision [34]. Thus, if we can provide an algorithm for finding non-zero components of , , based on the network topology and the constants ordering, then this will give us a good approximation to the problem solution (2).

Bottom Line: In these situations reduction to a common level of complexity is needed.We propose a systematic treatment of model reduction of multiscale biochemical networks.For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1.

View Article: PubMed Central - HTML - PubMed

Affiliation: IRMAR (CNRS UMR 6025), Universit├ę de Rennes 1, Rennes, France. ovidiu.radulescu@univ-rennes1.fr

ABSTRACT

Background: Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.

Results: We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-kappaB pathway.

Conclusion: Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

Show MeSH