Structure of myosin subfragment 1 from low-angle X-ray scattering

The X-ray scattering pattern produced by a solution of myosin subfragment 1 has been measured to a resolution (Bragg spacing) of 2 nm. We find that for subfragment 1 (S1) prepared by limited papain digestion in the presence of ethylenediaminetetraacetate the radius of gyration is 3.28 +/- 0.06 nm, the volume is 151 +/- 6 nm3, the surface area is 330 +/- 15 nm2, and the length of the maximum chord is 12.0 +/- 1.0 nm. The theoretical scattering patterns from several objects of uniform electron density have been calculated and compared with the observed scattering produced by S1. The recent three-dimensional electron micrograph reconstruction of S1-decorated actin by J. Seymour and E. O'Brien (private communication) generated the calculated pattern that best fit the observed scattering. This fit strongly suggests that this reconstruction resembles subfragment 1. The good correspondence between an S1 structure derived when S1 is attached to actin and a study of free S1 in solution strongly suggests that binding to actin does not grossly distort the shape of S1. This is consistent with the notion that S1 changes its orientation on actin, rather than its shape, in order to generate the contractile force in muscle.     

Birefringence of Protein Solutions and Biological Systems. I

The quantitative interpretation of birefringence of biological structures such as muscle requires a knowledge of intrinsic birefringence of the components. The intrinsic birefringence of fibrous structures as determined by variation of solvent index is positive while the intrinsic birefringence of proteins in solution is negative as calculated by the Peterlin-Stuart theory. As a first step in clarifying this discrepancy the basis of the Peterlin-Stuart theory has been re-examined. The theory has been recalculated from the standpoint of light scattering and extended to particles whose length is not small compared to the wavelength. The birefringence of a system of particles possessing a shell with index different from the bulk solvent has been obtained in order to interpret measurements in mixed solvents.     

X-ray small angle scattering study of chromatin as a function of fiber length

This work investigates the structure of native calf thymus chromatin as a function of fiber length and isolation procedures by using X-ray small angle scattering technique. Two methods of chromatin isolation have been compared in order to better understand the differences reported by various authors in terms of chromatin high order structure. In addition to these experimental results the effects of shearing have also been studied. In order to explain the differences among these chromatin preparations we built several models of chromatin fibers (represented as a chain of spherical subunits) assuming increasing level of condensation at increasing salt concentrations. For all these fiber models the corresponding theoretical X-ray scattering curves have been calculated and these results have been used to explain the influence of fiber length on the scattering profiles of chromatin. The comparison between experimental and theoretical curves confirms that the high molecular weight chromatin-DNA prepared by hypotonic swelling of nuclei (without enzymatic digestion) displays a partially folded structure even at low ionic strength, whereas the low molecular weight chromatin-DNA prepared by a brief nuclease digestion appears very weakly folded at the same ionic conditions.     

Rod-like cholesterol micelles in aqueous solution studied using polarized and depolarized dynamic light scattering.

Micelles of cholesterol in aqueous solution have been investigated using polarized and depolarized dynamic light scattering. They are shown to be highly extended and characterized by a narrow size distribution. It is shown that a rod-like model is applicable with length, L = 580 nm. Determination of the rotational diffusion coefficient by analysis of the autocorrelation function gave a value of theta = 150 s-1, which is close to the calculated value for the rod with this dimension. Depolarized dynamic light scattering measurements as a function of angle gave a value of 110 s-1.     

Chromatin model calculations: Arrays of spherical nu bodies.

Chromatin fibers consists of globular nucleohistone particles (designated nu bodies) along the length of the chromatin DNA with approximately 6-to7-fold compaction of the DNA within the nu bodies. We have calculated theoretical small-angle x-ray scattering curves and have compared these with experimental data in the literature. Several models predict maxima at the correct angles. The first maximum (approximately 110 degrees A) results from interparticle interference, while both the spatial arrangement and the structure factor the nu bodies can contribute to the additional small-angle maxima. These calculations suggest models which can account for the electron microscopic observation that chromatin is seen as either approximately 100-or approximately 200-to 250 degrees A-diameter fibers, depending on the solvent conditions. They also account for the limited orientability of the x-ray pattern from pulled chromatin fibers.     

Calculations of scattered light from rigid polymers by Shifrin and Rayleigh-Debye approximations.

We show that the commonly used Rayleigh-Debye method for calculating light scattering can lead to significant errors when used for describing scattering from dilute solutions of long rigid polymers, errors that can be overcome by use of the easily applied Shifrin approximation. In order to show the extent of the discrepancies between the two methods, we have performed calculations at normal incidence both for polarized and unpolarized incident light with the scattering intensity determined as a function of polarization angle and of scattering angle, assuming that the incident light is in a spectral region where the absorption of hemoglobin is small. When the Shifrin method is used, the calculated intensities using either polarized or unpolarized scattered light give information about the alignment of polymers, a feature that is lost in the Rayleigh-Debye approximation because the effect of the asymmetric shape of the scatterer on the incoming polarized electric field is ignored. Using sickle hemoglobin polymers as an example, we have calculated the intensity of light scattering using both approaches and found that, for totally aligned polymers within parallel planes, the difference can be as large as 25%, when the incident electric field is perpendicular to the polymers, for near forward or near backward scattering (0 degrees or 180 degrees scattering angle), but becomes zero as the scattering angle approaches 90 degrees. For randomly oriented polymers within a plane, or for incident unpolarized light for either totally oriented or randomly oriented polymers, the difference between the two results for near forward or near backward scattering is approximately 15%.     

Differential scattering of circularly polarized light as a unique probe of polynucleosome superstructures. A simulation by multiple scattering of dipoles

A theoretical approach to modeling Circular Intensity Differential Scattering (CIDS) of native chromatin as multiple scattering of dipoles is discussed without the Born approximation. The model can explain the experimental data in the literature. It is shown that CIDS contains more structural information than does total light scattering and to a good approximation is independent of the length of the scattering molecules. Finally, CIDS in conjunction with traditional light scattering measurements should aid in discriminating between various alternative models of higher order chromatin structure now being proposed. Generalization of this theoretical study to other complex biomolecular structures, is also briefly discussed.     

Disposition of ceramide in model lipid membranes determined by neutron diffraction

The lipid matrix present in the uppermost layer of the skin, the stratum corneum, plays a crucial role in the skin barrier function. The lipids are organized into two lamellar phases. To gain more insight into the molecular organization of one of these lamellar phases, we performed neutron diffraction studies. In the diffraction pattern, five diffraction orders were observed attributed to a lamellar phase with a repeat distance of 5.4 nm. Using contrast variation, the scattering length density profile could be calculated showing a typical bilayer arrangement. To obtain information on the arrangement of ceramides in the unit cell, a mixture that included a partly deuterated ceramide was also examined. The scattering length density profile of the 5.4-nm phase containing this deuterated ceramide demonstrated a symmetric arrangement of the ceramides with interdigitating acyl chains in the center of the unit cell.     

Neutron scattering analysis of bacterial lipopolysaccharide phase structure. Changes at high pH

The aggregate structure of lipopolysaccharide isolated from an Re strain of Escherichia coli was examined at different pH values using small angle neutron scattering. At pH values of 6 and 7.4, angle-averaged scattering of the sodium salt of this isolate was consistent with randomly coiled tubular micelles approximately 100 A in diameter. At pH 9.1, however, Kratky analysis of the scattering data was distinctly different and consistent with pairing of uniform tubular micelle sections of length 1440 and 110 A in diameter. Contrast variation measurements of the micelles yielded an average micellar weight of the sample at pH 9.1 of approximately 1.11 X 10(7) daltons and suggested that the aggregates were tubular micelles of size and length similar to that derived from the scattering intensity data. Anisotropic scattering patterns of samples under shear indicated a rigidification of the micelles as the pH was increased to 9.1 and the temperature decreased from 25 to 10 degrees C. The rotational diffusion constants deduced from the observed shear anisotropy indicate that the structure at pH 9.1 must have smallest and largest dimensions which differ by at least an order of magnitude, ruling out spherical or moderately ellipsoidal structures. Analysis of the shear rate needed to induce anisotropic scattering indicated that the stiffness length of the micelles at pH 9.1 was approximately 1000 A and decreased at higher and lower pH values.     

Sarcomere length dispersion in single skeletal muscle fibers and fiber bundles.

Light diffraction patterns produced by single skeletal muscle fibers and small fiber bundles of Rana pipiens semitendinosus have been examined at rest and during tetanic contraction. The muscle diffraction patterns were recorded with a vidicon camera interfaced to a minicomputer. Digitized video output was analyzed on-line to determine mean sarcomere length, line intensity, and the distribution of sarcomere lengths. The occurrence of first-order line intensity and peak amplitude maxima at approximately 3.0 mum is interpreted in terms of simple scattering theory. Measurements made along the length of a singel fiber reveal small variations in calculated mean sarcomere length (SD about 1.2%) and its percent dispersion (2.1% +/- 0.8%). Dispersion in small multifiber preparations increases approximately linearly with fiber number (about 0.2% per fiber) to a maximum of 8-10% in large bundles. Dispersion measurements based upon diffraction line analysis are comparable to SDs calculated from length distribution histograms obtained by light micrography of the fiber. First-order line intensity decreases by about 40% during tetanus; larger multifibered bundles exhibit substantial increases in sarcomere dispersion during contraction, but single fibers show no appreciable dispersion change. These results suggest the occurrence of asynchronous static or dynamic axial disordering of thick filaments, with a persistence in long range order of sarcomere spacing during contraction in single fibers.     

基于边界特征的景观格局分析

通过边界数量的长度谱分布分析。探讨了边界数量-长度特征与景观和组分碎裂化程度之间的相互关系;基于边界的数量和累积长度计算了景观多样性,均匀度、异质性和空间复杂性,并与基于斑快面积比重的传统格局指数计算结果进行了对比分析。研究表明,研究区内的快速城市化过程导致组分界面特征复杂化,空间分布的圈层结构简化;边界总体的数量谱分布方程系数α对于景观整体碎裂化程度有良好的指示意义,基于边界特征的景观格局指数对于传统的格局分析方法可以形成有益的补充。     

Protein dynamics in solution and powder measured by incoherent elastic neutron scattering: the influence of Q-range and energy resolution

Incoherent elastic neutron scattering (IENS) has been widely used to measure intramolecular atomic mean square displacements (MSDs) of proteins in powder and in solution. The instrumental energy resolution and the wave vector transfer (Q-range) determine, respectively, the time and length scales of observable motions. In order to investigate contributions of diffusive motions to MSDs measured by this method, we calculated the elastic intensity for several simple scattering functions. We showed that continuous translational diffusion contributes to MSDs in a Q-range where the energy width of the scattering function is of the order of the instrumental energy resolution. We discuss the choice of instruments adapted to focus on intramolecular motions in the presence of solvent or global macromolecular diffusion. The concepts developed are applied to interpret experimental data from H₂O- and D₂O-hydrated proteins. Finally, analogies between the Gaussian approximation in IENS and the Guinier approximation in small-angle scattering are discussed.     

Protein dynamics from X-ray crystallography: anisotropic, global motion in diffuse scattering patterns

Understanding X-ray crystallographic diffuse scattering is likely to improve our comprehension of equilibrium collective protein dynamics. Here, using molecular dynamics (MD) simulation, a detailed analysis is performed of the origins of diffuse scattering in crystalline Staphylococcal nuclease, for which the complete diffuse scattering pattern has been determined experimentally. The hydrogen-atom contribution and the scattering range over which the scattering can be considered to be a sum of solvent and protein scattering are determined. Two models of correlated protein motion are investigated by calculating the model-derived diffuse scattering and comparing with the scattering calculated directly from MD trajectories. In one model, previously used in diffuse scattering interpretation, the atomic displacement correlations decay isotropically with increasing separation. Model correlation lengths are obtained by refining the model scattering against the simulation-derived scattering pattern, and are found to be significantly different from those correlation lengths derived directly from the MD trajectories. Furthermore, the convergence between the model-derived and MD-derived scattering is poor. The second model, in which the displacement correlations are calculated from the principal components of the MD trajectories, is capable of fully reproducing the MD-derived diffuse scattering if the approximately 50% lowest-frequency modes are included. However, a small number ( approximately 10) of lowest-frequency and largest-amplitude modes dominates the diffuse scattering and thus the correlated protein motions. A detailed analysis of the principal components is performed. In particular, the effective free energy profile associated with each principle mode is analyzed and the eigenfrequency and damping coefficient computed using a model of Brownian dynamics. Those collective modes with effective frequencies below approximately 0.5 THz, including those that determine the diffuse scattering, are overdamped.     

A physical picture of atomic motions within the Dickerson DNA dodecamer in solution derived from joint ensemble refinement against NMR and large-angle X-ray scattering data

The structure and dynamics of the Dickerson DNA dodecamer [5'd(CGCGAATTCGCG)2] in solution have been investigated by joint simulated annealing refinement against NMR and large-angle X-ray scattering data (extending from 0.25 to 3 A-1). The NMR data comprise an extensive set of hetero- and homonuclear residual dipolar coupling and 31P chemical shift anisotropy restraints in two alignment media, supplemented by NOE and 3J coupling data. The NMR and X-ray scattering data cannot be fully ascribed to a single structure representation, indicating the presence of anisotropic motions that impact the experimental observables in different ways. Refinement with ensemble sizes (Ne) of >or=2 to represent the atomic motions reconciles all the experimental data within measurement error. Cross validation against both the dipolar coupling and X-ray scattering data suggests that the optimal ensemble size required to account for the current data is 4. The resulting ensembles permit one to obtain a detailed view of the conformational space sampled by the dodecamer in solution and permit one to analyze fluctuations in helicoidal parameters, sugar puckers, and BI-BII backbone transitions and to obtain quantitative metrics of atomic motion such as generalized order parameters and thermal B factors. The calculated order parameters are in good agreement with experimental order parameters obtained from 13C relaxation measurements. Although DNA behaves as a relatively rigid rod with a persistence length of approximately 150 bp, dynamic conformational heterogeneity at the base pair level is functionally important since it readily permits optimization of intermolecular protein-DNA interactions.     

DNA cholesteric pitch as a function of density and ionic strength

The nature of chiral interactions among chiral biopolymers, such as DNA, protein alpha-helices, and rodlike virus particles, remains elusive. In particular, a satisfactory model connecting molecular chiral interactions and the pitch of the resulting chiral mesophases is lacking. We report the measurement of short-fragment (146-bp) DNA cholesteric spherulite pitch as a function of osmotic pressure, average DNA interaxial spacing, and salt concentration. We determined cholesteric pitch and interaxial spacing by polarizing optical microscopy and x-ray scattering, respectively, from which the twist-angle between DNA molecules can be calculated. Surprisingly, we found that decreasing ionic strength resulted in weaker chiral interactions between DNA chains, as evidenced by the decrease in the twist-angle, and consequent increase in the cholesteric pitch, for a fixed interaxial spacing. We propose that this behavior can be explained by increased smearing-out of the helical charge pattern along DNA as the Debye screening length is increased.     

Anisotropic scattering by single starch granules. II. Layered granule structure

The study of anisotropy light scattering from tapioca and potato starches has continued with the recording of more detailed experimental single-granule H_v scattering patterns and, for the first time, single-granule V_v patterns. Quantitative analysis of the higher order scattering maxima to the granule morphology, permitting an analysis of the latter in terms of a lyered structure. For tapioca starch, this analysis indicates that if layering is present at all, the layer thickness is comparable to the wavelength of the incident radiation, and most likely is considerably less than 0.5 μ in thickness. On the other hand, the potato starch morphology is characterized by a relatively coarse layering with few layers and considerable difference in the anisotropy between successive layers. The models for the two starches in best agreement with experimental data are as follows: almost perfectly spherulitic anisotropic structure with very thin shell-like layers—if any—for tapioca, and alternating layers of varying anisotropy several microns in thickness and probably simultaneously present with an isotropic center, for potato starch. The V_v pattern for tapioca starch is in agreement with this model, although its information content is lower owing to the experimental difficulty of recording higher order maxima. Suggestions for further morphological study of starches are presented.     

Low angle light scattering studies on whole, half, and quarter molecules of T2 bacteriophage DNA.

Static light scattering measurements have been made at angles as low as 8 degrees on whole, half, and quarter molecules of native, T2 bacteriophage DNA in 0.195 M Na+. The fragments were obtained by high-speed stirring of the native DNA, and fractionated on methylated-albumin-kieselguhr columns. Accompanying measurements of sedimentation coefficients and intrinsic viscosities were made. Because linear extrapolations of light scattering data above 8 degrees for these samples were suspect, the measurements were analyzed by fitting curves calculated from the theory of wormlike coils to experimental curves at c = 0. Results showed that the excluded volume parameter, epsilon, must be used in analyzing the scattering curves; a reasonable value of epsilon was 0.08, in agreement with that found for T7 DNA (Harpst, J. A. 1980. Biophys. Chem. 11:295-302). The persistence length of all three DNAs in this paper was 50 +/- 5 nm, showed no dependence on molecular weight, but was somewhat below that reported previously for T7 DNA (60 nm). Theoretical curves calculated with the preceding parameters had a clear upward curvature in scattering envelopes below 8 degrees for quarter and half molecules, but such curvature was minimal for whole T2 DNA, so that linear extrapolations of experimental data above 8 degrees gave a molecular weight and root-mean-square radius which were nearly the same as those from theory. The molecular weight and radius for whole T2, derived from the comparison of theory and experiment, were 115 X 10(6) and 1,224 nm, respectively. The measurements on T2 DNA were clearly at the upper limit of current techniques.     

Small-angle neutron scattering by a strongly denatured protein: analysis using random polymer theory.

Small-angle neutron scattering profiles are presented from phosphoglycerate kinase, in the native form and strongly denatured in 4 M guanidinium chloride (GdnHCl) solution. The data are interpreted using a model in which the excess scattering density associated with the protein is represented as a finite freely jointed chain of spheres. The similarity of the model-derived scattering function to experiment increases asymptotically with the number of spheres. The improvement of the fit obtained with more than approximately 200 spheres (i.e., two residues per sphere) is insignificant. The effects of finite size of the scattering units and of scattering length variation along the polypeptide chain are examined. Improved agreement with experiment is obtained when these effects are taken into account. A method for rapid calculation of the scattering profile of a full, all-atom configuration is examined. It is found that a representation of the chain containing two scattering units per residue, placed at the backbone and side-chain scattering length centroids, reproduces the full, all-atom profile to within 2%.