A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Perturbation of the T cell repertoire in rheumatoid arthritis

Aberrations in the T cell repertoire with the emergence of oligoclonal populations have been described in patients with rheumatoid arthritis (RA). However, the extent of the repertoire perturbations as well as the underlying mechanisms are not known. We now have examined the diversity of the peripheral CD4 T cell repertoire by determining the frequencies of arbitrarily selected T cell receptor (TCR) β-chain sequences. Healthy individuals displayed a highly diverse repertoire, with a median frequency of individual TCR β-chain sequences of 1 in 2.4 × 107 CD4 T cells. In RA patients, the median TCR β-chain frequency was increased 10-fold, indicating marked contraction of the repertoire (P < 0.001). The loss in TCR diversity was not limited to CD4 memory T cells but also involved the compartment of naive T cells, suggesting that it reflected an abnormality in T cell repertoire formation and not a consequence of antigen recognition in the synovium. Also, control patients with chronic inflammatory disease such as hepatitis C expressed a diverse repertoire indistinguishable from that of normals. Telomere length studies indicated an increased replicative history of peripheral CD4 T cells in RA patients, suggesting an enhanced turnover within the CD4 compartment. Compared with age-matched controls, terminal restriction fragment sizes were 1.7 kilobases shorter (P < 0.001). These data demonstrate an altered CD4 T cell homeostasis in RA that may contribute to the autoimmune response as well as to the immunodeficiency in these patients.

Selective Perturbation of Apical Membrane Traffic by Expression of Influenza M2, an Acid-activated Ion Channel, in Polarized Madin–Darby Canine Kidney Cells

The function of acidification along the endocytic pathway is not well understood, in part because the perturbants used to modify compartmental pH have global effects and in some cases alter cytoplasmic pH. We have used a new approach to study the effect of pH perturbation on postendocytic traffic in polarized Madin–Darby canine kidney (MDCK) cells. Influenza M2 is a small membrane protein that functions as an acid-activated ion channel and can elevate the pH of the trans-Golgi network and endosomes. We used recombinant adenoviruses to express the M2 protein of influenza virus in polarized MDCK cells stably transfected with the polymeric immunoglobulin (Ig) receptor. Using indirect immunofluorescence and immunoelectron microscopy, M2 was found to be concentrated at the apical plasma membrane and in subapical vesicles; intracellular M2 colocalized partly with internalized IgA in apical recycling endosomes as well as with the trans-Golgi network marker TGN-38. Expression of M2 slowed the rate of IgA transcytosis across polarized MDCK monolayers. The delay in transport occurred after IgA reached the apical recycling endosome, consistent with the localization of intracellular M2. Apical recycling of IgA was also slowed in the presence of M2, whereas basolateral recycling of transferrin and degradation of IgA were unaffected. By contrast, ammonium chloride affected both apical IgA and basolateral transferrin release. Together, our data suggest that M2 expression selectively perturbs acidification in compartments involved in apical delivery without disrupting other postendocytic transport steps.

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.

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.

Avicins: Triterpenoid saponins from Acacia victoriae (Bentham) induce apoptosis by mitochondrial perturbation

Anticancer agents target various subcellular components and trigger apoptosis in chemosensitive cells. We have recently reported the tumor cell growth inhibitory properties of a mixture of triterpenoid saponins obtained from an Australian desert tree (Leguminosae) Acacia victoriae (Bentham). Here we report the purification of this mixture into two biologically pure components called avicins that contain an acacic acid core with two acyclic monoterpene units connected by a quinovose sugar. We demonstrate that the mixture of triterpenoid saponins and avicins induce apoptosis in the Jurkat human T cell line by affecting the mitochondrial function. Avicin G induced cytochrome c release within 30–120 min in whole cells and within a minute in the cell-free system. Caspase inhibitors DEVD or zVAD-fmk had no effect on cytochrome c release, suggesting the direct action of avicin G on the mitochondria. Activation of caspase-3 and total cleavage of poly(ADP-ribose) polymerase (PARP) occurred between 2 and 6 h posttreatment with avicins by zVAD-fmk. Interestingly, in the treated cells no significant changes in the membrane potential preceded or accompanied cytochrome c release. A small decrease in the generation of reactive oxygen species (ROS) was measured. The study of these evolutionarily ancient compounds may represent an interesting paradigm for the application of chemical ecology and chemical biology to human health.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

High-Temperature Perturbation of Starch Synthesis Is Attributable to Inhibition of ADP-Glucose Pyrophosphorylase by Decreased Levels of Glycerate-3-Phosphate in Growing Potato Tubers1

To investigate the short-term effect of elevated temperatures on carbon metabolism in growing potato (Solanum tuberosum L.) tubers, developing tubers were exposed to a range of temperatures between 19°C and 37°C. Incorporation of [14C]glucose (Glc) into starch showed a temperature optimum at 25°C. Increasing the temperature from 23°C or 25°C up to 37°C led to decreased labeling of starch, increased labeling of sucrose (Suc) and intermediates of the respiratory pathway, and increased respiration rates. At elevated temperatures, hexose-phosphate levels were increased, whereas the levels of glycerate-3-phosphate (3PGA) and phosphoenolpyruvate were decreased. There was an increase in pyruvate and malate, and a decrease in isocitrate. The amount of adenine diphosphoglucose (ADPGlc) decreased when tubers were exposed to elevated temperatures. There was a strong correlation between the in vivo levels of 3PGA and ADPGlc in tubers incubated at different temperatures, and the decrease in ADPGlc correlated very well with the decrease in the labeling of starch. In tubers incubated at temperatures above 30°C, the overall activities of Suc synthase and ADPGlc pyrophosphorylase declined slightly, whereas soluble starch synthase and pyruvate kinase remained unchanged. Elevated temperatures led to an activation of Suc phosphate synthase involving a change in its kinetic properties. There was a strong correlation between Suc phosphate synthase activation and the in vivo level of Glc-6-phosphate. It is proposed that elevated temperatures lead to increased rates of respiration, and the resulting decline of 3PGA then inhibits ADPGlc pyrophosphorylase and starch synthesis.

Perturbation of the Nucleus: A Novel Hog1p-independent, Pkc1p-dependent Consequence of Hypertonic Shock in Yeast

Hypertonic shock of Saccharomyces cerevisiae activates the Hog1p MAP kinase cascade. In contrast, protein kinase C (Pkc1p) and the “cell integrity” MAP kinase cascade are critical for the response to hypotonic shock. We observed that hypertonic shock transiently relocated many, but not all, nuclear and nucleolar proteins to the cytoplasm. We hypothesized that the relocation of nuclear proteins was due to activation of the Hog1p kinase cascade, yet, surprisingly, Hog1p was not required for these effects. In contrast, Pkc1p kinase activity was required, although the Pkc1p MAP kinase cascade and several factors known to lie upstream and downstream of Pkc1p were not. Moreover, sudden induction of a hyperactive form of Pkc1p was sufficient to relocate nuclear proteins. Taken together, these observations show that the scope of involvement of Pkc1p in the organization of the nucleus considerably exceeds what has been characterized previously. The relocation of nuclear proteins is likely to account for the profound inhibition of RNA synthesis that was observed during hypertonic shock.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.

Membrane lipid perturbation modifies the set point of the temperature of heat shock response in yeast.

Addition of a saturated fatty acid (SFA) induced a strong increase in heat shock (HS) mRNA transcription when cells were heat-shocked at 37 degrees C, whereas treatment with an unsaturated fatty acid (UFA) reduced or eliminated the level of HS gene transcription at 37 degrees C. Transcription of the delta 9-desaturase gene (Ole1) of Histoplasma capsulatum, whose gene product is responsible for the synthesis of UFA, is up-regulated in a temperature-sensitive strain. We show that when the L8-14C mutant of Saccharomyces cerevisiae, which has a disrupted Ole1 gene, is complemented with its own Ole1 coding region under control of its own promoter or Ole1 promoters of H. capsulatum, the level of HS gene transcription depends on the activity of the promoters. Fluorescence anisotropy of mitochondrial membranes of completed strains corresponded to the different activity of the Ole1 promoter used. We propose that the SFA/UFA ratio and perturbation of membrane lipoprotein complexes are involved in the perception of rapid temperature changes and under HS conditions disturbance of the preexisting membrane physical state causes transduction of a signal that induces transcription of HS genes.

Three distinct structural environments of a transmembrane domain in the inwardly rectifying potassium channel ROMK1 defined by perturbation.

To probe the protein environment of an ion channel, we have perturbed the structure of a transmembrane domain by substituting side chains with those of two different sizes by using site-specific mutagenesis. We have used Trp and Ala as a high- and a low-impact perturbation probe, respectively, to replace each of 18 consecutive residues within the putative second transmembrane segment, M2, of an inwardly rectifying potassium channel, ROMK1. Our rationale is that a change in the channel function as a consequence of these mutations at a particular position will reflect the structural environment of the altered side chain. Each position can then be assigned to one of three classes of environments, as grated by different levels of perturbation: very tolerant (channel functions with both Trp and Ala substitutions), tolerant (function preserved with Ala but not with Trp substitution), and intolerant (either Ala or Trp substitution destroys function). We identify the very tolerant environment as being lipid-facing, tolerant as protein-interior-facing, and intolerant as pore-facing. We observe a strikingly ordered pattern of perturbation of all three environmental classes. This result indicates that M2 is a straight alpha-helix.

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.