The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Nucleosomes, linker DNA, and linker histone form a unique structural motif that directs the higher-order folding and compaction of chromatin

The compaction level of arrays of nucleosomes may be understood in terms of the balance between the self-repulsion of DNA (principally linker DNA) and countering factors including the ionic strength and composition of the medium, the highly basic N termini of the core histones, and linker histones. However, the structural principles that come into play during the transition from a loose chain of nucleosomes to a compact 30-nm chromatin fiber have been difficult to establish, and the arrangement of nucleosomes and linker DNA in condensed chromatin fibers has never been fully resolved. Based on images of the solution conformation of native chromatin and fully defined chromatin arrays obtained by electron cryomicroscopy, we report a linker histone-dependent architectural motif beyond the level of the nucleosome core particle that takes the form of a stem-like organization of the entering and exiting linker DNA segments. DNA completes ≈1.7 turns on the histone octamer in the presence and absence of linker histone. When linker histone is present, the two linker DNA segments become juxtaposed ≈8 nm from the nucleosome center and remain apposed for 3–5 nm before diverging. We propose that this stem motif directs the arrangement of nucleosomes and linker DNA within the chromatin fiber, establishing a unique three-dimensional zigzag folding pattern that is conserved during compaction. Such an arrangement with peripherally arranged nucleosomes and internal linker DNA segments is fully consistent with observations in intact nuclei and also allows dramatic changes in compaction level to occur without a concomitant change in topology.

Pulling a single chromatin fiber reveals the forces that maintain its higher-order structure

Single chicken erythrocyte chromatin fibers were stretched and released at room temperature with force-measuring laser tweezers. In low ionic strength, the stretch-release curves reveal a process of continuous deformation with little or no internucleosomal attraction. A persistence length of 30 nm and a stretch modulus of ≈5 pN is determined for the fibers. At forces of 20 pN and higher, the fibers are modified irreversibly, probably through the mechanical removal of the histone cores from native chromatin. In 40–150 mM NaCl, a distinctive condensation-decondensation transition appears between 5 and 6 pN, corresponding to an internucleosomal attraction energy of ≈2.0 kcal/mol per nucleosome. Thus, in physiological ionic strength the fibers possess a dynamic structure in which the fiber locally interconverting between “open” and “closed” states because of thermal fluctuations.

Blind separation of auditory event-related brain responses into independent components

Averaged event-related potential (ERP) data recorded from the human scalp reveal electroencephalographic (EEG) activity that is reliably time-locked and phase-locked to experimental events. We report here the application of a method based on information theory that decomposes one or more ERPs recorded at multiple scalp sensors into a sum of components with fixed scalp distributions and sparsely activated, maximally independent time courses. Independent component analysis (ICA) decomposes ERP data into a number of components equal to the number of sensors. The derived components have distinct but not necessarily orthogonal scalp projections. Unlike dipole-fitting methods, the algorithm does not model the locations of their generators in the head. Unlike methods that remove second-order correlations, such as principal component analysis (PCA), ICA also minimizes higher-order dependencies. Applied to detected—and undetected—target ERPs from an auditory vigilance experiment, the algorithm derived ten components that decomposed each of the major response peaks into one or more ICA components with relatively simple scalp distributions. Three of these components were active only when the subject detected the targets, three other components only when the target went undetected, and one in both cases. Three additional components accounted for the steady-state brain response to a 39-Hz background click train. Major features of the decomposition proved robust across sessions and changes in sensor number and placement. This method of ERP analysis can be used to compare responses from multiple stimuli, task conditions, and subject states.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

A Polymer Model for the Structural Organization of Chromatin Loops and Minibands in Interphase Chromosomes

A quantitative model of interphase chromosome higher-order structure is presented based on the isochore model of the genome and results obtained in the field of copolymer research. G1 chromosomes are approximated in the model as multiblock copolymers of the 30-nm chromatin fiber, which alternately contain two types of 0.5- to 1-Mbp blocks (R and G minibands) differing in GC content and DNA-bound proteins. A G1 chromosome forms a single-chain string of loop clusters (micelles), with each loop ∼1–2 Mbp in size. The number of ∼20 loops per micelle was estimated from the dependence of geometrical versus genomic distances between two points on a G1 chromosome. The greater degree of chromatin extension in R versus G minibands and a difference in the replication time for these minibands (early S phase for R versus late S phase for G) are explained in this model as a result of the location of R minibands at micelle cores and G minibands at loop apices. The estimated number of micelles per nucleus is close to the observed number of replication clusters at the onset of S phase. A relationship between chromosomal and nuclear sizes for several types of higher eukaryotic cells (insects, plants, and mammals) is well described through the micelle structure of interphase chromosomes. For yeast cells, this relationship is described by a linear coil configuration of chromosomes.

Spatially independent activity patterns in functional MRI data during the Stroop color-naming task

A method is given for determining the time course and spatial extent of consistently and transiently task-related activations from other physiological and artifactual components that contribute to functional MRI (fMRI) recordings. Independent component analysis (ICA) was used to analyze two fMRI data sets from a subject performing 6-min trials composed of alternating 40-sec Stroop color-naming and control task blocks. Each component consisted of a fixed three-dimensional spatial distribution of brain voxel values (a “map”) and an associated time course of activation. For each trial, the algorithm detected, without a priori knowledge of their spatial or temporal structure, one consistently task-related component activated during each Stroop task block, plus several transiently task-related components activated at the onset of one or two of the Stroop task blocks only. Activation patterns occurring during only part of the fMRI trial are not observed with other techniques, because their time courses cannot easily be known in advance. Other ICA components were related to physiological pulsations, head movements, or machine noise. By using higher-order statistics to specify stricter criteria for spatial independence between component maps, ICA produced improved estimates of the temporal and spatial extent of task-related activation in our data compared with principal component analysis (PCA). ICA appears to be a promising tool for exploratory analysis of fMRI data, particularly when the time courses of activation are not known in advance.