Application of Adjoint Sensitivity Analysis to Parameter Estimation of Age-Structured Model of Cell Cycle

2016 ◽  
pp. 123-131 ◽  
Author(s):  
Michał Jakubczak ◽  
Krzysztof Fujarewicz
Keyword(s):  
Cell Cycle ◽  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Structured Model ◽  
Age Structured ◽  
Age Structured Model

scholarly journals Optimization and uncertainty analysis of ODE models using 2nd order adjoint sensitivity analysis

2018 ◽  
Author(s):  
Paul Stapor ◽  
Fabian Fröhlich ◽  
Jan Hasenauer
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Computational Efficiency ◽  
Profile Likelihood ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
State Variables ◽  
Adjoint Sensitivity ◽  
Link Type ◽  
Ode Models

AbstractMotivationParameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with the number of state variables and quadratically with the number of parameters. This limits their application to low-dimensional problems.ResultsWe introduce second order adjoint sensitivity analysis for the computation of Hessians and a hybrid optimization-integration based approach for profile likelihood computation. Second order adjoint sensitivity analysis scales linearly with the number of parameters and state variables. The Hessians are effectively exploited by the proposed profile likelihood computation approach. We evaluate our approaches on published biological models with real measurement data. Our study reveals an improved computational efficiency and robustness of optimization compared to established approaches, when using Hessians computed with adjoint sensitivity analysis. The hybrid computation method was more than two-fold faster than the best competitor. Thus, the proposed methods and implemented algorithms allow for the improvement of parameter estimation for medium and large scale ODE models.AvailabilityThe algorithms for second order adjoint sensitivity analysis are implemented in the Advance MATLAB Interface CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI/). The algorithm for hybrid profile likelihood computation is implemented in the parameter estimation toolbox (PESTO, https://github.com/ICB-DCM/PESTO/). Both toolboxes are freely available under the BSD [email protected] informationSupplementary data are available at Bioinformatics online.

Harvesting Strategies and Parameter Estimation for an Age-Structured Model

1980 ◽  
Vol 37 (2) ◽  
pp. 268-282 ◽  
Author(s):  
R. B. Deriso
Keyword(s):  
Parameter Estimation ◽  
New England ◽  
General Model ◽  
Optimal Harvesting ◽  
Parameter Estimates ◽  
Structured Model ◽  
Individual Parameter ◽  
Age Structured ◽  
Low Sensitivity ◽  
Age Structured Model

An age-structured model with knife-edge recruitment describes the dynamics of exploited, seasonally breeding populations. For management strategy, an equation is derived that characterizes the economic optimal state of exploitation of a modeled stock. A further generalization is derived to account for those species where recruitment to the mature stock occurs over many age-categories. Since the parameters all have phenomenological definitions, they can be estimated from information independent of the model. These parameters can also be estimated by regression of the model to catch and effort data. Test regressions of the general model are made on catch and effort data from three exploited fish stocks: the yellowtail flounder of New England, the Pacific halibut of Area II, and the haddock of Georges Bank; the corresponding R2 values are 0.75, 0.87, and 0.86. Although the confidence intervals for individual parameter estimates are very large, the estimates compare favorably with published parameter values. Since only certain combinations of parameters from the general model appear to have low sensitivity to small perturbations to the data, some guiding suggestions are made that may lead to an improved robustness in the statistical procedures.Key words: age-structured model, optimal harvesting strategy, spawner–recruit curves, parameter estimation

scholarly journals Scalable parameter estimation for genome-scale biochemical reaction networks

2016 ◽  
Author(s):  
Fabian Fröhlich ◽  
Barbara Kaltenbacher ◽  
Fabian J. Theis ◽  
Jan Hasenauer
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Large Scale ◽  
Chemical Species ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Adjoint Sensitivity Analysis ◽  
Biochemical Reaction Networks ◽  
Adjoint Sensitivity ◽  
Genome Scale

AbstractMechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small-and medium-scale biological processes. While the same should in principle hold for large-and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large-and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics.Author SummaryIn this manuscript, we introduce a scalable method for parameter estimation for genome-scale biochemical reaction networks. Mechanistic models for genome-scale biochemical reaction networks describe the behavior of thousands of chemical species using thousands of parameters. Standard methods for parameter estimation are usually computationally intractable at these scales. Adjoint sensitivity based approaches have been suggested to have superior scalability but any rigorous evaluation is lacking. We implement a toolbox for adjoint sensitivity analysis for biochemical reaction network which also supports the import of SBML models. We show by means of a set of benchmark models that adjoint sensitivity based approaches unequivocally outperform standard approaches for large-scale models and that the achieved speedup increases with respect to both the number of parameters and the number of chemical species in the model. This demonstrates the applicability of adjoint sensitivity based approaches to parameter estimation for genome-scale mechanistic model. The MATLAB toolbox implementing the developed methods is available from http://ICB-DCM.github.io/AMICI/.

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