A robust technique for two-dimensional separation of undistorted chemical-shift anisotropy powder patterns in magic-angle-spinning NMR

A robust magic-angle-spinning experiment for separating undistorted, quasi-static chemical-shift powder patterns is presented. It is derived from the technique of R. Tycko, G. Dabbagh, and P. Mirau (1989, J. Magn. Reson. 85, 265), but uses 360 degrees instead of 180 degrees pulses. In combination with a suitable phase sequence, this makes the spectral patterns very insensitive to pulse-length errors and other imperfections, as demonstrated both experimentally and theoretically. This method, termed separation of undistorted powder patterns by effortless recoupling (SUPER), can be used at standard spinning speeds, between 2.5 and 5 kHz, and with standard radiofrequency power levels (in particular, for protons, a decoupling field strength gammaB(1)/2pi of less than 80 kHz). No significant artifacts are observed even for samples extending to the ends of the radiofrequency coil. The method has been applied to samples containing various sp(2)- and sp(3)-hybridized carbon sites. Even for the methylene groups in polyethylene, a system with very strong C-H and H-H dipolar couplings and only moderate chemical-shift anisotropy (CSA), a useful CSA powder pattern has been obtained. With a CSA scaling factor of 0.155, accuracies of +/-5, +/-3, and +/-1 ppm of the principal values can be achieved for protonated aromatic carbons, unprotonated sp(2)-hybridized groups, and aliphatic sites, respectively. Examples of CSA-based assignment of COOC vs other COO or CON groups, and of aromatic vs olefinic C=C carbons are shown, for both small molecules and polymers.     

Finding the insphere of a convex polyhedron: an analytical approach

Recursive analytical formulation for calculating the insphere in an irregular convex polyhedron has been developed. Emphasis has been placed on using coordinate geometry so that the geometric theories can be used without much modification. The results have been compared with some simple geometries for which the analytical results are well known. In all cases the results are matched with analytical results up to eight decimal places. The result for one irregular prism is also presented.     

Probability and complex quantum trajectories: Finding the missing links

It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that defined a conserved probability for most of the regions in the complex space in terms of a trajectory integral, indicating a dynamical origin of quantum probability. There it was also shown that the quantum trajectories obtained are the same characteristic curves that propagate information about the conserved probability density. Though the probability density we now adopt for those regions left out in the previous work is not conserved locally, the net source of probability for such regions is seen to be zero in the example considered, allowing to make the total probability conserved. The new combined probability density agrees with the Born’s probability everywhere on the real line, as required. A major fall out of the present scheme is that it explains why in the classical limit the imaginary parts of trajectories are not observed even indirectly and particles are confined close to the real line.     

Power-law distribution of gene expression fluctuations

Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.     

Combined clustering models for the analysis of gene expression

Clustering has become one of the fundamental tools for analyzing gene expression and producing gene classifications. Clustering models enable finding patterns of similarity in order to understand gene function, gene regulation, cellular processes and sub-types of cells. The clustering results however have to be combined with sequence data or knowledge about gene functionality in order to make biologically meaningful conclusions. In this work, we explore a new model that integrates gene expression with sequence or text information.     

Emergence of the self-similar property in gene expression dynamics

Many theoretical models have recently been proposed to understand the structure of cellular systems composed of various types of elements (e.g., proteins, metabolites and genes) and their interactions. However, the cell is a highly dynamic system with thousands of functional elements fluctuating across temporal states. Therefore, structural analysis alone is not sufficient to reproduce the cell's observed behavior.In this article, we analyze the gene expression dynamics (i.e., how the amount of mRNA molecules in cell fluctuate in time) by using a new constructive approach, which reveals a symmetry embedded in gene expression fluctuations and characterizes the dynamical equation of gene expression (i.e., a specific stochastic differential equation). First, by using experimental data of human and yeast gene expression time series, we found a symmetry in short-time transition probability from time t to time t+1. We call it self-similarity symmetry (i.e., the gene expression short-time fluctuations contain a repeating pattern of smaller and smaller parts that are like the whole, but different in size). Secondly, we reconstruct the global behavior of the observed distribution of gene expression (i.e., scaling-law) and the local behavior of the power-law tail of this distribution. This approach may represent a step forward toward an integrated image of the basic elements of the whole cell.     

Finding the impedance of the organ of Corti

Measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities: V(x,f;Vu)/Vu approximately [V(x,f)/Vu]v(x,f), f less than or equal to fc(x), where the response V is the velocity of the membrane at measurement position x, Vu is the umbo velocity, f is the frequency of the stimulus, and fc(x) is the local characteristic frequency. The frequency dependence of the functions v(x,f) and V(x,f) is determined from the data, and v(x,f) and ln V(x,f) are shown to be analytic functions in the lower half of the complex frequency plane, with Re [v(x,f)] a monotonically increasing function of f at fixed x. The linear limit of basilar membrane motion is characterized by a transfer function T(x,f) = (V/V1)v/(1-v), estimated by extrapolating V(x,f;Vu)/Vu to a small membrane velocity V1.T(x,f) and ln T(x,f) are shown to be analytic functions in the lower half of the complex frequency plane. The inverse of the amplitude of the transfer function, which has both a deep dip at f approximately fc(x) and a broad shoulder at lower frequencies, bears a striking resemblance to the neural threshold tuning curve. The functional form of T(x,f) is used to deduce the equation governing the motion of a section of the organ of Corti. Each section acts like a negatively damped harmonic oscillator stabilized at time t by a feedback force proportional to the velocity at the previous time t-tau. The time delay tau is proportional to the oscillator period [tau approximately 1.75/fc(x)]. Like a laser, the organ of Corti pumps energy into harmonic traveling waves. Unlike the laser, the direction of energy flow abruptly reverses as the traveling wave approaches the point of maximum membrane velocity [fc(x) approximately f]. All accumulated wave energy is then pumped back into a small section of the organ of Corti where transduction presumably occurs. Outer hair cells are conjectured to be active elements contributing to the negative damping and feedback of the cochlear amplifier.     

Oscillatory kinetics of gene expression: Protein conversion and slow mRNA transport

The negative feedback between mRNA and regulatory-protein production may result in oscillations in the kinetics of gene expression if the mRNA-protein interplay includes protein conversion. Using a mean-field kinetic model, we show that such oscillations can be amplified due to limitations of the mRNA transport between the nucleus and cytoplasm. This effect may be dramatic for the mRNA population in the nucleus. The article is published in the original.     

Microarray-based gene expression profiles of silkworm brains

Background  

Molecular genetic studies of Bombyx mori have led to profound advances in our understanding of the regulation of development. Bombyx mori brain, as a main endocrine organ, plays important regulatory roles in various biological processes. Microarray technology will allow the genome-wide analysis of gene expression patterns in silkworm brains.     

Finding good acoustic features for parrot vocalizations: the feature generation approach

A crucial step in the understanding of vocal behavior of birds is to be able to classify calls in the repertoire into meaningful types. Methods developed to this aim are limited either because of human subjectivity or because of methodological issues. The present study investigated whether a feature generation system could categorize vocalizations of a bird species automatically and effectively. This procedure was applied to vocalizations of African gray parrots, known for their capacity to reproduce almost any sound of their environment. Outcomes of the feature generation approach agreed well with a much more labor-intensive process of a human expert classifying based on spectrographic representation, while clearly out-performing other automated methods. The method brings significant improvements in precision over commonly used bioacoustical analyses. As such, the method enlarges the scope of automated, acoustics-based sound classification.