A note on estimation of dynamics of multiple gene expression based on singular value decomposition

Recently, data on multiple gene expression at sequential time points were analyzed, using singular value decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model we formulate a non-linear optimization problem and present how to solve it numerically using standard MATLAB procedures. We use publicly available data to test the approach. For reader's convenience, we provide a straightforward, ready-to-use, procedure in MATLAB, which employs its standard features to analyze data of this kind. Then, we investigate the sensitivity of the method to missing measurements and its possibilities to reconstruct missing data. Also, we discuss the possible consequences of data regularization, called sometimes 'polishing', on the outcome of analysis, especially when model is to be used for prediction purposes. Summarizing we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics but may also lead to unexpected difficulties, like overfitting problems.