Thousands of transcriptome data sets are available, but approaches for their use in dynamic cell response modelling are few, especially for processes affected simultaneously by two orthogonal influencing variables. We approached this problem for neuroepithelial development of human pluripotent stem cells (differentiation variable), in the presence or absence of valproic acid (signaling variable). Using few basic assumptions (sequential differentiation states of cells; discrete on/off states for individual genes in these states), and time-resolved transcriptome data, a comprehensive model of spontaneous and perturbed gene expression dynamics was developed. The model made reliable predictions (average correlation of 0.85 between predicted and subsequently tested expression values). Even regulations predicted to be non-monotonic were successfully validated by PCR in new sets of experiments. Transient patterns of gene regulation were identified from model predictions. They pointed towards activation of Wnt signaling as a candidate pathway leading to a redirection of differentiation away from neuroepithelial cells towards neural crest. Intervention experiments, using a Wnt/beta-catenin antagonist, led to a phenotypic rescue of this disturbed differentiation. Thus, our broadly applicable model allows the analysis of transcriptome changes in complex time/perturbation matrices.