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.

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

Stretched and overwound DNA forms a Pauling-like structure with exposed bases

We investigate structural transitions within a single stretched and supercoiled DNA molecule. With negative supercoiling, for a stretching force >0.3 pN, we observe the coexistence of B-DNA and denatured DNA from σ ≈ −0.015 down to σ = −1. Surprisingly, for positively supercoiled DNA (σ > +0.037) stretched by 3 pN, we observe a similar coexistence of B-DNA and a new, highly twisted structure. Experimental data and molecular modeling suggest that this structure has ≈2.62 bases per turn and an extension 75% larger than B-DNA. This structure has tightly interwound phosphate backbones and exposed bases in common with Pauling’s early DNA structure [Pauling, L. & Corey, R. B. (1953), Proc. Natl. Acad. Sci. USA 39, 84–97] and an unusual structure proposed for the Pf1 bacteriophage [Liu, D. J. & Day, L. A. (1994) Science 265, 671–674].

Resistance to endotoxic shock and reduced neutrophil migration in mice deficient for the Src-family kinases Hck and Fgr

Signal transduction through the leukocyte integrins is required for the processes of firm adhesion, activation, and chemotaxis of neutrophils during inflammatory reactions. Neutrophils isolated from knockout mice that are deficient in the expression of p59/61hck (Hck) and p58c-fgr (Fgr), members of the Src-family of protein tyrosine kinases, have been shown to be defective in adhesion mediated activation. Cells from these animals have impaired induction of respiratory burst and granule secretion following plating on surfaces that crosslink β2 and β3 integrins. To determine if the defective function of hck−/−fgr−/− neutrophils observed in vitro also results in impaired inflammatory responses in vivo, we examined responses induced by lipopolysaccharide (LPS) injection in these animals. The hck−/−fgr−/− mice showed marked resistance to the lethal effects of high-dose LPS injection despite the fact that high levels of serum tumor necrosis factor α and interleukin 1α were detected. Serum chemistry analysis revealed a marked reduction in liver and renal damage in mutant mice treated with LPS, whereas blood counts showed a marked neutrophilia that was not seen in wild-type animals. Direct examination of liver sections from mutant mice revealed reduced neutrophil migration into the tissue. These data demonstrate that defective integrin signaling in neutrophils, caused by loss of Hck and Fgr tyrosine kinase activity, results in impaired inflammation-dependent tissue injury in vivo.

Dynamical principles in biological processes: A model of charge migration in proteins and DNA

The generalized master equations (GMEs) that contain multiple time scales have been derived quantum mechanically. The GME method has then been applied to a model of charge migration in proteins that invokes the hole hopping between local amino acid sites driven by the torsional motions of the floppy backbones. This model is then applied to analyze the experimental results for sequence-dependent long-range hole transport in DNA reported by Meggers et al. [Meggers, E., Michel-Beyerle, M. E., & Giese, B. (1998) J. Am. Chem. Soc. 120, 12950–12955]. The model has also been applied to analyze the experimental results of femtosecond dynamics of DNA-mediated electron transfer reported by Zewail and co-workers [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014–6019]. The initial events in the dynamics of protein folding have begun to attract attention. The GME obtained in this paper will be applicable to this problem.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.

Blood flow and oxygen delivery to human brain during functional activity: Theoretical modeling and experimental data

Coupling of cerebral blood flow (CBF) and cerebral metabolic rate for oxygen (CMRO2) in physiologically activated brain states remains the subject of debates. Recently it was suggested that CBF is tightly coupled to oxidative metabolism in a nonlinear fashion. As part of this hypothesis, mathematical models of oxygen delivery to the brain have been described in which disproportionately large increases in CBF are necessary to sustain even small increases in CMRO2 during activation. We have explored the coupling of CBF and oxygen delivery by using two complementary methods. First, a more complex mathematical model was tested that differs from those recently described in that no assumptions were made regarding tissue oxygen level. Second, [15O] water CBF positron emission tomography (PET) studies in nine healthy subjects were conducted during states of visual activation and hypoxia to examine the relationship of CBF and oxygen delivery. In contrast to previous reports, our model showed adequate tissue levels of oxygen could be maintained without the need for increased CBF or oxygen delivery. Similarly, the PET studies demonstrated that the regional increase in CBF during visual activation was not affected by hypoxia. These findings strongly indicate that the increase in CBF associated with physiological activation is regulated by factors other than local requirements in oxygen.