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Parameter estimation in biochemical systems models with alternating regression.

Chou IC, Martens H, Voit EO - Theor Biol Med Model (2006)

Bottom Line: It is therefore necessary to develop improved methods that are effective, fast, and scalable.Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well.In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

View Article: PubMed Central - HTML - PubMed

Affiliation: The Wallace H. Coulter Department of Biomedical Engineering at Georgia Institute of Technology and Emory University, 313 Ferst Drive, Atlanta, GA 30332, USA. gtg392p@mail.gatech.edu

ABSTRACT

Background: The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable.

Results: We show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear inverse problem of estimating parameter values into iterative steps of linear regression. We show with several artificial examples that the method works well in many cases. In cases of no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations.

Conclusion: Alternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

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Related in: MedlinePlus

Test system with four dependent variables. (a) time courses computed with initial values in Eq. (12) (use dataset 1 in Table S1); (b) corresponding dynamics of slopes. Typical units might be concentrations (e.g., in mM) plotted against time (e.g., in minutes), but the example could as well run on an hourly scale and with variables of a different nature.
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Figure 2: Test system with four dependent variables. (a) time courses computed with initial values in Eq. (12) (use dataset 1 in Table S1); (b) corresponding dynamics of slopes. Typical units might be concentrations (e.g., in mM) plotted against time (e.g., in minutes), but the example could as well run on an hourly scale and with variables of a different nature.

Mentions: The system is first used to create artificial datasets that differ in their initial conditions (Table S1 of Additional file1). In a biological setting, these may mimic different stimulus-response experiments on the same system. For example, they could represent different nutrient conditions in a growth experiment. Figure 2 shows the branched pathway, along with a selection of time course data (dataset 1) and slopes.


Parameter estimation in biochemical systems models with alternating regression.

Chou IC, Martens H, Voit EO - Theor Biol Med Model (2006)

Test system with four dependent variables. (a) time courses computed with initial values in Eq. (12) (use dataset 1 in Table S1); (b) corresponding dynamics of slopes. Typical units might be concentrations (e.g., in mM) plotted against time (e.g., in minutes), but the example could as well run on an hourly scale and with variables of a different nature.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1586003&req=5

Figure 2: Test system with four dependent variables. (a) time courses computed with initial values in Eq. (12) (use dataset 1 in Table S1); (b) corresponding dynamics of slopes. Typical units might be concentrations (e.g., in mM) plotted against time (e.g., in minutes), but the example could as well run on an hourly scale and with variables of a different nature.
Mentions: The system is first used to create artificial datasets that differ in their initial conditions (Table S1 of Additional file1). In a biological setting, these may mimic different stimulus-response experiments on the same system. For example, they could represent different nutrient conditions in a growth experiment. Figure 2 shows the branched pathway, along with a selection of time course data (dataset 1) and slopes.

Bottom Line: It is therefore necessary to develop improved methods that are effective, fast, and scalable.Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well.In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

View Article: PubMed Central - HTML - PubMed

Affiliation: The Wallace H. Coulter Department of Biomedical Engineering at Georgia Institute of Technology and Emory University, 313 Ferst Drive, Atlanta, GA 30332, USA. gtg392p@mail.gatech.edu

ABSTRACT

Background: The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable.

Results: We show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear inverse problem of estimating parameter values into iterative steps of linear regression. We show with several artificial examples that the method works well in many cases. In cases of no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations.

Conclusion: Alternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure.

Show MeSH
Related in: MedlinePlus