Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

Periodicity of strong nucleosome positioning sites around the chicken adult beta-globin gene may encode regularly spaced chromatin.

Positioned nucleosomes contribute to both the structure and the function of the chromatin fiber and can play a decisive role in controlling gene expression. We have mapped, at high resolution, the translational positions adopted by limiting amounts of core histone octamers reconstituted onto 4.4 kb of DNA comprising the entire chicken adult beta-globin gene, its enhancer, and flanking sequences. The octamer displays extensive variation in its affinity for different positioning sites, the range exhibited being about 2 orders of magnitude greater than that of the initial binding of the octamer. Strong positioning sites are located 5' and 3' of the globin gene and in the second intron but are absent from the coding regions. These sites exhibit a periodicity (approximately 200 bp) similar to the average spacing of nucleosomes on the inactive beta-globin gene in vivo, which could indicate their involvement in packaging the gene into higher-order chromatin structure. Overlapping, alternative octamer positioning sites commonly exhibit spacings of 20 and 40 bp, but not of 10 bp. These short-range periodicities could reflect features of the core particle structure contributing to the pronounced sequence-dependent manner in which the core histone octamer interacts with DNA.

Periodicity of polar and nonpolar amino acids is the major determinant of secondary structure in self-assembling oligomeric peptides.

The tendency of a polypeptide chain to form alpha-helical or beta-strand secondary structure depends upon local and nonlocal effects. Local effects reflect the intrinsic propensities of the amino acid residues for particular secondary structures, while nonlocal effects reflect the positioning of the individual residues in the context of the entire amino acid sequence. In particular, the periodicity of polar and nonpolar residues specifies whether a given sequence is consistent with amphiphilic alpha-helices or beta-strands. The importance of intrinsic propensities was compared to that of polar/nonpolar periodicity by a direct competition. Synthetic peptides were designed using residues with intrinsic propensities that favored one or the other type of secondary structure. The polar/nonpolar periodicities of the peptides were designed either to be consistent with the secondary structure favored by the intrinsic propensities of the component residues or in other cases to oppose these intrinsic propensities. Characterization of the synthetic peptides demonstrated that in all cases the observed secondary structure correlates with the periodicity of the peptide sequence--even when this secondary structure differs from that predicted from the intrinsic propensities of the component amino acids. The observed secondary structures are concentration dependent, indicating that oligomerization of the amphiphilic peptides is responsible for the observed secondary structures. Thus, for self-assembling oligomeric peptides, the polar/nonpolar periodicity can overwhelm the intrinsic propensities of the amino acid residues and serves as the major determinant of peptide secondary structure.

Fluctuation analysis of rotational speeds of the bacterial flagellar motor.

We measured the dependence of the variance in the rotation rate of tethered cells of Escherichia coli on the mean rotation rate over a regime in which the motor generates constant torque. This dependence was compared with that of broken motors. In either case, motor torque was augmented with externally applied torque. We show that, in contrast to broken motors, functioning motors in this regime do not freely rotationally diffuse and that the variance measurements are consistent with the predicted values of a stepping mechanism with exponentially distributed waiting times (a Poisson stepper) that steps approximately 400 times per revolution.