Limits...
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), Université 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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Lipniacki's model a) Testing quasistationarity: nonreduced trajectories (solid), quasi-stationarity trajectories (crosses). b) Trajectories of models in the hierarchy. c) Cytoplasmatic part of the signalling mechanism: terminal species (blue), intermediate species quasi-stationary (pink) non-oscillating (green), simple submechanisms (blue). This part of the network contains three critical parameters for the damping time. Sustained oscillations were obtained by decreasing the constant k3 ten times with respect to the value used in [53] (equivalently, this can be obtained by decreasing k9, or by increasing k4).
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Figure 3: Lipniacki's model a) Testing quasistationarity: nonreduced trajectories (solid), quasi-stationarity trajectories (crosses). b) Trajectories of models in the hierarchy. c) Cytoplasmatic part of the signalling mechanism: terminal species (blue), intermediate species quasi-stationary (pink) non-oscillating (green), simple submechanisms (blue). This part of the network contains three critical parameters for the damping time. Sustained oscillations were obtained by decreasing the constant k3 ten times with respect to the value used in [53] (equivalently, this can be obtained by decreasing k9, or by increasing k4).

Mentions: Fast, quasi-stationary species are generally difficult to detect. For instance, the strong production condition (cT) = (1), although informative for understanding of the dynamics, can not be used in practice. Furthermore, small concentration is not a necessary condition for quasi-stationarity. Therefore, our practical method for detection of fast, quasi-stationary species is based on the direct checking of Eqs.(22), (23) (see Fig 3a and the Results section for an example).


Robust simplifications of multiscale biochemical networks.

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

Lipniacki's model a) Testing quasistationarity: nonreduced trajectories (solid), quasi-stationarity trajectories (crosses). b) Trajectories of models in the hierarchy. c) Cytoplasmatic part of the signalling mechanism: terminal species (blue), intermediate species quasi-stationary (pink) non-oscillating (green), simple submechanisms (blue). This part of the network contains three critical parameters for the damping time. Sustained oscillations were obtained by decreasing the constant k3 ten times with respect to the value used in [53] (equivalently, this can be obtained by decreasing k9, or by increasing k4).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Lipniacki's model a) Testing quasistationarity: nonreduced trajectories (solid), quasi-stationarity trajectories (crosses). b) Trajectories of models in the hierarchy. c) Cytoplasmatic part of the signalling mechanism: terminal species (blue), intermediate species quasi-stationary (pink) non-oscillating (green), simple submechanisms (blue). This part of the network contains three critical parameters for the damping time. Sustained oscillations were obtained by decreasing the constant k3 ten times with respect to the value used in [53] (equivalently, this can be obtained by decreasing k9, or by increasing k4).
Mentions: Fast, quasi-stationary species are generally difficult to detect. For instance, the strong production condition (cT) = (1), although informative for understanding of the dynamics, can not be used in practice. Furthermore, small concentration is not a necessary condition for quasi-stationarity. Therefore, our practical method for detection of fast, quasi-stationary species is based on the direct checking of Eqs.(22), (23) (see Fig 3a and the Results section for an example).

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), Université 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
Related in: MedlinePlus