A linear discrete dynamic system model is constructed to represent the temporal interactions among significantly expressed genes in response to bioethanol conversion inhibitor 5-hydroxymethylfurfural for ethanologenic yeast Saccharomyces cerevisiae. This study identifies the most significant linear difference equations for each gene in a network. A log-time domain interpolation addresses the non-uniform sampling issue typically observed in a time course experimental design. This system model also insures its power stability under the normal condition in the absence of the inhibitor. The statistically significant system model, estimated from time course gene expression measurements during the earlier exposure to 5-hydroxymethylfurfural, reveals known transcriptional regulations as well as potential significant genes involved in detoxification for bioethanol conversion by yeast.