A variational approach to parameter estimation in ordinary differential equations

BMC Systems Biology

Jens Timmer²  Daniel Kaschek¹ 

[1] Institute of Physics, Freiburg University, Freiburg, Germany;BIOSS Centre for Biological Signalling Studies, Freiburg University, Freiburg, Germany

关键词: Statistical inference;    Ordinary differential equations;    Reaction networks;    Optimal control;    Boundary value problem;    Calculus of variations;    Parameter estimation;   

Others  :  1143715
DOI  :  10.1186/1752-0509-6-99

 received in 2011-10-25, accepted in 2012-07-25,  发布年份 2012

【 摘 要 】

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.

【 授权许可】

   
2012 Kaschek and Timmer; licensee BioMed Central Ltd.

【 图 表 】

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