Fitting ordinary differential equations to short time course data.
Ordinary differential equations (ODEs) are widely used to model many systems in physics, chemistry, engineering and biology. Often one wants to compare such equations with observed time course data, and use this to estimate parameters. Surprisingly, practical algorithms for doing this are relatively poorly developed, particularly in comparison with the sophistication of numerical methods for solving both initial and boundary value problems for differential equations, and for locating and analysing bifurcations. A lack of good numerical fitting methods is particularly problematic in the context of systems biology where only a handful of time points may be available. In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are high and the number of data points is low. It employs a spline-based collocation scheme and alternates linear least squares minimization steps with repeated estimates of the noise-free values of the variables. This is reminiscent of expectation-maximization methods widely used for problems with nuisance parameters or missing data.
Brewer
Daniel
D
Institute of Child Health, University College London, 30 Guilford Street, London WC1N 1EH, UK.
Barenco
Martino
M
Callard
Robin
R
Hubank
Michael
M
Stark
Jaroslav
J
D000465:Algorithms; D064007:Ataxia Telangiectasia Mutated Proteins; D018797:Cell Cycle Proteins / Q000502:physiology; D019295:Computational Biology; D004268:DNA-Binding Proteins / Q000502:physiology; D003627:Data Interpretation, Statistical; D016158:Genes, p53; D016014:Linear Models; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D017346:Protein Serine-Threonine Kinases / Q000502:physiology; D051736:Proto-Oncogene Proteins c-mdm2 / Q000502:physiology; D049490:Systems Biology / Q000706:statistics & numerical data*; D013997:Time Factors; D016159:Tumor Suppressor Protein p53 / Q000502:physiology; D025521:Tumor Suppressor Proteins / Q000502:physiology
D018797:Cell Cycle Proteins; D004268:DNA-Binding Proteins; D016159:Tumor Suppressor Protein p53; D025521:Tumor Suppressor Proteins; D051736:Proto-Oncogene Proteins c-mdm2; D064007:Ataxia Telangiectasia Mutated Proteins; D017346:Protein Serine-Threonine Kinases