Projecting gene expression trajectories through inducing differential equations from microarray time series experiments

Microarray technologies are enabling measurements of gene expression levels at large scales. Applications of microarrays in medicine, biological engineering and agriculture often depend on quantitative studies of time-series data. For drug delivery, fed batch reactors and crop growth, time series analysis is essential in optimizing controlled biological processes. In particular, it is useful to project discrete time series data into continuous dynamic trajectories with a global gene expression model. Time series microarray data were fitted with differential equations based on Singular Value Decomposition. Using the data from two different organisms, Saccharomyces Cerevisiae and Drosophila melanogaster the local predictive accuracy was assessed with cross-fold validation across all experiments. The equations were integrated and inspected visually. The algorithm for inducing differential equations was found to produce a good fit both globally and locally.