Dataset Information

A variational approach to parameter estimation in ordinary differential equations.

ABSTRACT:

Background

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters.

Results

The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters.

Conclusions

The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

SUBMITTER: Kaschek D

PROVIDER: S-EPMC3534504 | biostudies-literature | 2012 Aug

REPOSITORIES: biostudies-literature

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Publications

A variational approach to parameter estimation in ordinary differential equations.

Kaschek Daniel D Timmer Jens J

BMC systems biology 20120814

<h4>Background</h4>Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters.<h4>Results</h4>The approach ...[more]

PMID: 22892133

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Project description:Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation. We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.

Dataset Information

A variational approach to parameter estimation in ordinary differential equations.

Background

Results

Conclusions

Publications

A variational approach to parameter estimation in ordinary differential equations.

Similar Datasets

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