- Model invalidation
- Kinetic models
- Differential equations
- Smooth principal components analysis
- Cross validation
- Forecast analysis
Kinetic models can present mechanistic descriptions of molecular processes within a cell. They can be used to predict the dynamics of metabolite production, signal transduction or transcription of genes. Although there has been tremendous effort in constructing kinetic models for different biological systems, not much effort has been put into their validation. In this study, we introduce the concept of resampling methods for the analysis of kinetic models and present a statistical model invalidation approach.
We based our invalidation approach on the evaluation of a kinetic model’s predictive power through cross validation and forecast analysis. As a reference point for this evaluation, we used the predictive power of an unsupervised data analysis method which does not make use of any biochemical knowledge, namely Smooth Principal Components Analysis (SPCA) on the same test sets. Through a simulations study, we showed that too simple mechanistic descriptions can be invalidated by using our SPCA-based comparative approach until high amount of noise exists in the experimental data. We also applied our approach on an eicosanoid production model developed for human and concluded that the model could not be invalidated using the available data despite its simplicity in the formulation of the reaction kinetics. Furthermore, we analysed the high osmolarity glycerol (HOG) pathway in yeast to question the validity of an existing model as another realistic demonstration of our method.
With this study, we have successfully presented the potential of two resampling methods, cross validation and forecast analysis in the analysis of kinetic models’ validity. Our approach is easy to grasp and to implement, applicable to any ordinary differential equation (ODE) type biological model and does not suffer from any computational difficulties which seems to be a common problem for approaches that have been proposed for similar purposes. Matlab files needed for invalidation using SPCA cross validation and our toy model in SBML format are provided at http://www.bdagroup.nl/content/Downloads/software/software.php.