ABSTRACT: Many gene array studies of the yeast cell cycle have been performed (Cho RJ, Campbell MJ, Winzeler EA et al. A genome-wide transcriptional analysis of the mitotic cell cycle. Mol Cell 1998;2:65-73; Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944-7; Pramila T, Wu W, Miles S et al. The Forkhead transcription factor Hcm1 regulates chromosome segregation genes and fills the S-phase gap in the transcriptional circuitry of the cell cycle. Genes Dev 2006;20:2266-78; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273-97). Largely, these studies contain elements drawn from laboratory experiments. The present investigation determines cell division cycle (CDC) genes solely from the data (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944-7). It is shown by simple reasoning that the dynamics of the approximately 6000 yeast genes are described by an approximately six-dimensional space. This leads a precisely determined cell-cycle period, along with the quality and timing of the identified CDC genes. Convincing evidence for the role of the identified genes is obtained. While these show good agreement with standard CDC gene representatives (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944-7; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273-97; de Lichtenberg U, Jensen LJ, Fausbøll A et al. Comparison of computational methods for the identification of cell cycle-regulated genes. Bioinformatics 2005;21:1164-71) several hundred newly revealed CDC genes appear, which merit attention. The present approach employs an adaptation of a method introduced to study turbulent flows (Schmid PJ. Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 2010;656:5-28), "dynamic mode decomposition" (DMD). From this, one can infer that singular value decomposition, analysis of the data entangles the underlying (gene) dynamics implicit in the data; and that DMD produces the disentangling transformation. It is the assertion of this study that a new tool now exists for the analysis of the gene array signals, and in particular for investigating the yeast cell cycle.
