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.

Mössbauer and electron paramagnetic resonance studies of chloroperoxidase following mechanism-based inactivation with allylbenzene

We have used Mössbauer and electron paramagnetic resonance (EPR) spectroscopy to study a heme-N-alkylated derivative of chloroperoxidase (CPO) prepared by mechanism-based inactivation with allylbenzene and hydrogen peroxide. The freshly prepared inactivated enzyme (“green CPO”) displayed a nearly pure low-spin ferric EPR signal with g = 1.94, 2.15, 2.31. The Mössbauer spectrum of the same species recorded at 4.2 K showed magnetic hyperfine splittings, which could be simulated in terms of a spin Hamiltonian with a complete set of hyperfine parameters in the slow spin fluctuation limit. The EPR spectrum of green CPO was simulated using a three-term crystal field model including g-strain. The best-fit parameters implied a very strong octahedral field in which the three 2T2 levels of the (3d)5 configuration in green CPO were lowest in energy, followed by a quartet. In native CPO, the 6A1 states follow the 2T2 ground state doublet. The alkene-mediated inactivation of CPO is spontaneously reversible. Warming of a sample of green CPO to 22°C for increasing times before freezing revealed slow conversion of the novel EPR species to two further spin S = ½ ferric species. One of these species displayed g = 1.82, 2.25, 2.60 indistinguishable from native CPO. By subtracting spectral components due to native and green CPO, a third species with g = 1.86, 2.24, 2.50 could be generated. The EPR spectrum of this “quasi-native CPO,” which appears at intermediate times during the reactivation, was simulated using best-fit parameters similar to those used for native CPO.

Sequence dependent hypermutation of the immunoglobulin heavy chain in cultured B cells

The variable (V) regions of immunoglobulin heavy and light chains undergo high rates of somatic mutation during the immune response. Although point mutations accumulate throughout the V regions and their immediate flanking sequences, analysis of large numbers of mutations that have arisen in vivo reveal that the triplet AGC appears to be most susceptible to mutation. We have stably transfected B cell lines with γ2a heavy chain constructs containing TAG nonsense codons in their V regions that are part of either a putative (T)AGC hot spot or a (T)AGA non-hot spot motif. Using an ELISA spot assay to detect revertants and fluctuation analysis to determine rates of mutation, the rate of reversion of the TAG nonsense codon has been determined for different motifs in different parts of the V region. In the NSO plasma cell line, the (T)AGC hot spot motif mutates at rates of ≈6 × 10−4/bp per generation and ≈3 × 10−5/bp per generation at residues 38 and 94 in the V region. At each of these locations, the (T)AGC hot spot motif is 20–30 times more likely to undergo mutation than the (T)AGA non-hot spot motif. Moreover, the AGA non-hot spot motif mutates at as high a rate as the hot spot motif when it is located adjacent to hot spot motifs, suggesting that more extended sequences influence susceptibility to mutation.

Simultaneous two-photon excitation of distinct labels for dual-color fluorescence crosscorrelation analysis

Confocal fluorescence correlation spectroscopy as a time-averaging fluctuation analysis combining maximum sensitivity with high statistical confidence has proved to be a very versatile and powerful tool for detection and temporal investigation of biomolecules at ultralow concentrations on surfaces, in solutions, and in living cells. To probe the interaction of different molecular species for a detailed understanding of biologically relevant mechanisms, crosscorrelation studies on dual or multiple fluorophore assays with spectrally distinct excitation and emission are particularly promising. Despite the considerable improvement of detection specificity provided by fluorescence crosscorrelation analysis, few applications have so far been reported, presumably because of the practical challenges of properly aligning and controlling the stability of the experimental setup. In this work, we demonstrate that two-photon excitation combined with dual-color fluorescence correlation spectroscopy can be the key to simplifying simultaneous investigations of multiple fluorescent species significantly on a single-molecule scale. Two-photon excitation allows accession of common fluorophores of largely distinct emission by the same excitation wavelength, because differences in selection rules and vibronic coupling can induce considerable shifts between the one-photon and two-photon excitation spectra. The concept of dual-color two-photon fluorescence crosscorrelation analysis is introduced and experimentally demonstrated with an established assay probing the selective cleavage of dual-labeled DNA substrates by restriction endonuclease EcoRI.

Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Gene genealogies and population variation in plants

Early in the development of plant evolutionary biology, genetic drift, fluctuations in population size, and isolation were identified as critical processes that affect the course of evolution in plant species. Attempts to assess these processes in natural populations became possible only with the development of neutral genetic markers in the 1960s. More recently, the application of historically ordered neutral molecular variation (within the conceptual framework of coalescent theory) has allowed a reevaluation of these microevolutionary processes. Gene genealogies trace the evolutionary relationships among haplotypes (alleles) with populations. Processes such as selection, fluctuation in population size, and population substructuring affect the geographical and genealogical relationships among these alleles. Therefore, examination of these genealogical data can provide insights into the evolutionary history of a species. For example, studies of Arabidopsis thaliana have suggested that this species underwent rapid expansion, with populations showing little genetic differentiation. The new discipline of phylogeography examines the distribution of allele genealogies in an explicit geographical context. Phylogeographic studies of plants have documented the recolonization of European tree species from refugia subsequent to Pleistocene glaciation, and such studies have been instructive in understanding the origin and domestication of the crop cassava. Currently, several technical limitations hinder the widespread application of a genealogical approach to plant evolutionary studies. However, as these technical issues are solved, a genealogical approach holds great promise for understanding these previously elusive processes in plant evolution.

Expression Studies of the Zeaxanthin Epoxidase Gene in Nicotiana plumbaginifolia1

Abscisic acid (ABA) is a plant hormone involved in the control of a wide range of physiological processes, including adaptation to environmental stress and seed development. In higher plants ABA is a breakdown product of xanthophyll carotenoids (C40) via the C15 intermediate xanthoxin. The ABA2 gene of Nicotiana plumbaginifolia encodes zeaxanthin epoxidase, which catalyzes the conversion of zeaxanthin to violaxanthin. In this study we analyzed steady-state levels of ABA2 mRNA in N. plumbaginifolia. The ABA2 mRNA accumulated in all plant organs, but transcript levels were found to be higher in aerial parts (stems and leaves) than in roots and seeds. In leaves ABA2 mRNA accumulation displayed a day/night cycle; however, the ABA2 protein level remained constant. In roots no diurnal fluctuation in mRNA levels was observed. In seeds the ABA2 mRNA level peaked around the middle of development, when ABA content has been shown to increase in many species. In conditions of drought stress, ABA levels increased in both leaves and roots. A concomitant accumulation of ABA2 mRNA was observed in roots but not in leaves. These results are discussed in relation to the role of zeaxanthin epoxidase both in the xanthophyll cycle and in the synthesis of ABA precursors.

Circadian-Regulated Transcription of the psbD Light-Responsive Promoter in Wheat Chloroplasts1

The level of mRNAs derived from the plastid-encoded psbD light-responsive promoter (LRP) is controlled by a circadian clock(s) in wheat (Triticum aestivum). The circadian oscillations in the psbD LRP mRNA level persisted for at least three cycles in continuous light and for one cycle in continuous dark, with maxima in subjective morning and minima in subjective early night. In vitro transcription in chloroplast extracts revealed that the circadian cycles in the psbD LRP mRNA level were dominantly attributed to the circadian-regulated transcription of the psbD LRP. The effects of various mutations introduced into the promoter region on the psbD LRP activity in vitro suggest the existence of two positive elements located between −54 and −36, which generally enhance the transcription activity, and an anomalous core promoter structure lacking the functional “−35” element, which plays a crucial role in the circadian fluctuation and light dependency of psbD LRP transcription activity.

Local densities orthogonal to beta-sheet amide planes: patterns of packing in globular proteins.

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions predominate over hydrogen bonding and solvent interactions. We observed considerable variability in packing densities within these regions, confirming that the interior packing of a protein does not result in uniform occupation of the available space. Patterns of fluctuation in packing density suggest that the regular backbone-to-backbone network of hydrogen bonds is not likely to be interrupted to maximize van der Waals interactions. However, high-density packing tends to occur toward the ends of beta-structure strands where hydrogen bonds are more likely to involve nonpolar side-chain groups or solvent molecules. These features result in internal protein folding with a central low-density core surrounded by a higher-density subsurface shell, consistent with our previous calculations regarding overall protein packing density.

Hydrated myoglobin's anharmonic fluctuations are not primarily due to dihedral transitions.

To characterize the functionally important anharmonic motions of proteins, simulations of carboxymyoglobin (MbCO) dynamics have been performed during which dihedral transitions were prohibited. Comparison of torsionally restrained and unrestrained protein dynamics simulated at three levels of hydration and at temperatures ranging from 100 to 400 K suggests that hydration "catalyzes" protein mobility by facilitating collective anharmonic motions that do not require dihedral transitions. When dihedral transitions were prohibited, dehydrated MbCO, to a good approximation, exhibited only harmonic fluctuations, whereas hydrated MbCO exhibited both harmonic and anharmonic motions. The fluctuation of helix centers of mass also remained highly anharmonic in the torsionally restrained hydrated system. Atomic mean-square fluctuation at 300 K was reduced upon prohibition of dihedral transitions by only 28% and 10% for MbCO hydrated by 350 and 3830 water molecules, respectively.

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.

Conformation, energy, and folding ability of selected amino acid sequences.

Evolutionary selection of sequences is studied with a knowledge-based Hamiltonian to find the design principle for folding to a model protein structure. With sequences selected by naive energy minimization, the model structure tends to be unstable and the folding ability is low. Sequences with high folding ability have only the low-lying energy minimum but also an energy landscape which is similar to that found for the native sequence over a wide region of the conformation space. Though there is a large fluctuation in foldable sequences, the hydrophobicity pattern and the glycine locations are preserved among them. Implications of the design principle for the molecular mechanism of folding are discussed.

Olfactory transduction is intrinsically noisy.

The sources of noise that limit olfactory signal detection were investigated in dissociated rat olfactory receptor cells. Near-threshold odorant-evoked currents exhibited large random fluctuation. However, similar fluctuations were observed in the absence of applied odorants when currents were induced by elevating the intracellular cyclic AMP concentration. This suggests that the fluctuations reflect noise intrinsic to the transduction mechanism, rather than the quantal nature of an odorant stimulus. For many odorants, this intrinsic noise may preclude the reliable detection of single odorant molecules.

Immunoglobulin variable region hypermutation in hybrids derived from a pre-B- and a myeloma cell line.

Somatic mutation of the variable (V) regions of immunoglobulin genes occurs in vivo at rates that have been estimated to be between 10(-3) and 10(-4) per bp per generation. To study this process in vitro, the 18.81 pre-B-cell line and hybrids derived by fusing 18.81 to the NSO myeloma fusion partner were transfected with a mu heavy-chain construct containing a nonsense mutation in the V region (Vn) or the constant region (Cn). Mutation was quantitated by reversion analysis using the ELISA spot assay to detect single cells secreting IgM. Fluctuation analysis revealed that V-region mutations spontaneously occurred in 18.81 cells at an average rate of 5.8 x 10(-6) per bp per cell generation and in selected 18.81-NSO hybrids at greatly increased rates of 1.6 x 10(-3) to 5.8 x 10(-4) per bp per generation. The Vn construct also reverted frequently in transgenic mice, indicating that it contained sufficient information to mutate at high rates both in vivo and in vitro. Sequence analysis of reverted genes revealed that reversion was due to point mutations. Since the rates and nature of the mutations that are occurring in these transfected genes are similar to those reported in vivo, it should be possible to use this system to identify the cis-acting sequences and trans-acting factors that are responsible for V-region somatic hypermutation.