Fundamental patterns underlying gene expression profiles: Simplicity from complexity

Analysis of previously published sets of DNA microarray gene expression data by singular value decomposition has uncovered underlying patterns or “characteristic modes” in their temporal profiles. These patterns contribute unequally to the structure of the expression profiles. Moreover, the essential features of a given set of expression profiles are captured using just a small number of characteristic modes. This leads to the striking conclusion that the transcriptional response of a genome is orchestrated in a few fundamental patterns of gene expression change. These patterns are both simple and robust, dominating the alterations in expression of genes throughout the genome. Moreover, the characteristic modes of gene expression change in response to environmental perturbations are similar in such distant organisms as yeast and human cells. This analysis reveals simple regularities in the seemingly complex transcriptional transitions of diverse cells to new states, and these provide insights into the operation of the underlying genetic networks.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Perturbations in maturation of secretory proteins and their association with endoplasmic reticulum chaperones in a cell culture model for epithelial ischemia.

The effects of ischemia on the maturation of secretory proteins are not well understood. Among several events that occur during ischemia-reperfusion are a rapid and extensive decrease in ATP levels and an alteration of cellular oxidative state. Since the normal folding and assembly of secretory proteins are mediated by endoplasmic reticulum (ER) molecular chaperones, the function of which depends on ATP and maintenance of an appropriate redox environment, ischemia might be expected to perturb folding of secretory proteins. In this study, whole animal and cultured cell models for the epithelial ischemic state were used to examine this possibility. After acute kidney ischemia, marked increases in the mRNA levels of the ER chaperones glucose-regulated protein (grp)78/immunoglobulin-binding protein (BiP), grp94, and ER protein (ERp)72 were noted. Likewise, when cellular ATP was depleted to less than 10% of control with antimycin A, mRNA levels of BiP, ERp72, and grp94 were increased in kidney and thyroid epithelial cell culture models. Since the signal for the up-regulation of these stress proteins is believed to be the accumulation of misfolded/misassembled secretory proteins in the ER, their induction after ischemia in vivo and antimycin treatment of cultured cells suggests that maturation of secretory proteins in the ER lumen might indeed be perturbed. To analyze the effects of antimycin A on the maturation of secretory proteins, we studied the fate of thyroglobulin (Tg), a large oligomeric secretory glycoprotein, the folding and assembly of which seems to require a variety of ER chaperones. Treatment of cultured thyroid epithelial cells with antimycin A greatly inhibited ( > 90%) the secretion of Tg. Sucrose density gradient analysis revealed that in antimycin A-treated cells Tg associates into large macromolecular complexes which, by immunofluorescence, appeared to localize to the ER. Furthermore, coimmunoprecipitation studies after antimycin A treatment demonstrated that Tg stably associates with BiP, grp94, and ERp72. Together, our results suggest that a key cellular lesion in ischemia is the misfolding of secretory proteins as they transit the ER, and this leads not only to increased expression of ER chaperones but also to their stable association with and the subsequent retention of at least some misfolded secretory proteins.

Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.