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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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Summary of convergence patterns of AR. Panel A: all variables are initially used as regressors and constraints are imposed afterwards; Panel B: regression with the "union" of variables of both terms; Panel C: only those variables that are known to appear in the production or degradation term, respectively, are used as regressors. Row (a): speed of convergence; the color bars represent the numbers of iterations needed to converge to the optimum solution; Rows (b) and (c): 2D view of the error surface superimposed with convergence trajectories with different initial values of β and h; the color bars represent the value of log(SSE). The intersections of dotted lines indicate the optimum values of parameters β and h.
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Figure 3: Summary of convergence patterns of AR. Panel A: all variables are initially used as regressors and constraints are imposed afterwards; Panel B: regression with the "union" of variables of both terms; Panel C: only those variables that are known to appear in the production or degradation term, respectively, are used as regressors. Row (a): speed of convergence; the color bars represent the numbers of iterations needed to converge to the optimum solution; Rows (b) and (c): 2D view of the error surface superimposed with convergence trajectories with different initial values of β and h; the color bars represent the value of log(SSE). The intersections of dotted lines indicate the optimum values of parameters β and h.

Mentions: Figure 3 combines results from several sets of initial guesses of βi and hij (the results of the second phase of AR are not shown, but are analogous). The data for this illustration consist of observations on the first variable of datasets 4, 5 and 6 (see Table S1 in the Additional file1). These are processed simultaneously as three sets of algebraic equations at 50 time points. Thus, the parameters α1, g13, β1, and h11of the equation


Parameter estimation in biochemical systems models with alternating regression.

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

Summary of convergence patterns of AR. Panel A: all variables are initially used as regressors and constraints are imposed afterwards; Panel B: regression with the "union" of variables of both terms; Panel C: only those variables that are known to appear in the production or degradation term, respectively, are used as regressors. Row (a): speed of convergence; the color bars represent the numbers of iterations needed to converge to the optimum solution; Rows (b) and (c): 2D view of the error surface superimposed with convergence trajectories with different initial values of β and h; the color bars represent the value of log(SSE). The intersections of dotted lines indicate the optimum values of parameters β and h.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Summary of convergence patterns of AR. Panel A: all variables are initially used as regressors and constraints are imposed afterwards; Panel B: regression with the "union" of variables of both terms; Panel C: only those variables that are known to appear in the production or degradation term, respectively, are used as regressors. Row (a): speed of convergence; the color bars represent the numbers of iterations needed to converge to the optimum solution; Rows (b) and (c): 2D view of the error surface superimposed with convergence trajectories with different initial values of β and h; the color bars represent the value of log(SSE). The intersections of dotted lines indicate the optimum values of parameters β and h.
Mentions: Figure 3 combines results from several sets of initial guesses of βi and hij (the results of the second phase of AR are not shown, but are analogous). The data for this illustration consist of observations on the first variable of datasets 4, 5 and 6 (see Table S1 in the Additional file1). These are processed simultaneously as three sets of algebraic equations at 50 time points. Thus, the parameters α1, g13, β1, and h11of the equation

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