Analysis of fractal properties of globular protein surfaces by means of small-angle x-ray scattering]

The "cube method" [M. Yu. Pavlov, B. A. Fedorov, Biopolymers, 22, 1507, 1983] has been used to calculate the intensity of the large-angle X-ray scattering from the volumes of several globular proteins. In the logarithmic plots of the scattered intensity curves from three of these proteins, there is a linear region at scattering angles corresponding to Bragg distances of from about 6.3 A to 21 A. This linear region possibly may be due to the fractal properties of the surfaces of these proteins on length scoles from 6.3 A to 21 A, and the fractal dimensions corresponding to the power-law scattering at these scattering angles have been evaluated.     

Rotation isomerization of side chains of globular proteins and its effect on the x-ray scattering curves of proteins in a solution

A new method has been developed for averaging the intensity of X-ray diffuse scattering of proteins by different conformations of side groups. The method is based on the algorithm allowing to calculate statistical weights of rotation isomers of side chains. It is shown that for protein structures obtained from high resolution crystallographic data, conformations of the majority of surface groups correspond to rotation isomers with the greatest statistical weight. It has been found that for medium size proteins (with molecular weight varying from 15,000 to 30,000 dalton) whose structure has been determined at high resolution, the influence of rotation isomerization of side chains on the scattering indicatrices does not exceed 5%. The influence of side chains mobility on the scattering curves of large proteins is also small. For these two classes of proteins the rotation isomerization of side groups can be ignored when interpreting significant (exceeding 10%) divergences between experimental and theoretical scattering curves.     

Dynamic light scattering study of suspensions of purple membrane

Purple membrane from Halobacterium halobium in suspensions has been studied by quasielastic light scattering. The intensity correlation functions of polarized scattered light were measured at various K2 values (K being the magnitude of the scattering vector), and the first cumulant Gamma of the field correlation function G1(tau) was obtained by a cumulant expansion method. The apparent diffusion coefficient Gamma /K2 did not increase monotonically with K2 values and showed a distinct anomaly in an intermediate range of K. A theoretical formulation of G1(tau) for a disc and an extremely oblate ellipsoidal shell of revolution (S. Fujime and K. Kubota, Biophys. Chem. 23 (1985) 1) was applied to the analysis of the spectra, and characteristic features of experimental spectra were well reproduced. It was suggested that a strong interference effect between scattered rays on Gamma /K2 should be attributed to a slight noncircular shape of the purple membrane and that a contribution to Gamma /K2 from membrane flexibility should be taken into account. This study will provide experimental evidence of the feasibility of membrane studies by dynamic light scattering.     

The differential scattering of circularly polarized light by chloroplasts and evaluation of their true circular dichroism

Chloroplasts isolated from pea leaves display an intense circular dichroism in the range 600 to 720nm. Circularly polarized light is also differentially scattered by chloroplasts, and this effect can be confused with circular dichroism. By using an instrumental modification it was possible to distinguish, and record separately, the ellipticities of the transmitted light (circular dichroism) and of the scattered light in the same c.d. instrument. By means of a light-scattering apparatus, the intensity of unpolarized light scattered by chloroplasts was measured as a function of wavelength and of angle. This measurement allowed the aforementioned ellipticities to be corrected for mutual interference. At a concentration of 4mug of chlorophyll/ml (the optimum practical concentration of chloroplasts at which there was no significant interaction of scattering and absorption effects) spectra of true circular dichroism (circular differential absorption) and circular differential scattering were obtained. The former showed maxima, positive at 688nm and negative at 676nm, with an intensity Deltatheta=8.3m degrees .litre.(mg of chlorophyll)(-1).cm(-1). The latter had a maximum at 683nm with an intensity of +47m degrees with respect to the solvent baseline; this value is independent of the concentration of chloroplasts in dilute suspensions. It is suggested that the intense circular dichroism of chloroplasts reflects specific chlorophyll-chlorophyll interactions in the light-harvesting pigment. The advantages of this method for determining the c.d. of scattering suspensions over those of other investigators are discussed.     

Molecular dynamics decomposition of temperature-dependent elastic neutron scattering by a protein solution

Molecular dynamics simulations are performed of bovine pancreatic trypsin inhibitor in a cryosolution over a range of temperatures from 80 to 300 K and the origins identified of elastic dynamic neutron scattering from the solution. The elastic scattering and mean-square displacement calculated from the molecular dynamics trajectories are in reasonable agreement with experiments on a larger protein in the same solvent. The solvent and protein contributions to the scattering from the simulation model are determined. At lower temperatures (< approximately 200 K) or on shorter timescales ( approximately 10 ps) the scattering contributions are proportional to the isotopic nuclear scattering cross-sections of each component. However, for T > 200 K marked deviations from these cross-sections are seen due to differences in the dynamics of the components of the solution. Rapid activation of solvent diffusion leads to the variation with temperature of the total elastic intensity being determined largely by that of the solvent. At higher temperatures (>240 K) and longer times ( approximately 100 ps) the protein makes the only significant contribution to the scattering, the solvent scattering having moved out of the accessible time-space window. Decomposition of the protein mean-square displacement shows that the observed dynamical transition in the solution at 200-220 K involves activation of both internal motions and external whole-molecule rotational and translational diffusion. The proportion that the external dynamics contributes to the protein mean-square displacement increases to approximately 30 and 60% at 300 K on the 10- and 100-ps timescales, respectively.     

The correlation of human erythrocyte shape with dark-field light scattering intensity]

This study was concerned with the quantitative evaluation of dark field light scattering by sedimented erythrocytes of banked human blood samples. Due to considerable variability of both appearance and amount of scattered light the discocyte group had to be subdivided into discocyte I and discocyte II. The mean intensity of scattered light increased about three fold from discocyte II to echinocytes I, II, III, sphaeroechinocyte, and sphaerocyte. On the other hand the average light scattering intensity of discocytes I exceeded that of discocytes II about 2.5 times, with individual data varying over a wide range. There was a rapid disappearing of discocytes I correlated with time of storage. Therefore it is concluded that discocytes I represent the initial stage of erythrocytes transforming under banking conditions.     

Contribution of solvent water to the solution X-ray scattering profile of proteins

A theoretical framework is presented to analyze how solvent water contributes to the X-ray scattering profile of protein solution. Molecular dynamics simulations were carried out on pure water and an aqueous solution of myoglobin to determine the spatial distribution of water molecules in each of them. Their solution X-ray scattering (SXS) profiles were numerically evaluated with obtained atomic-coordinate data. It is shown that two kinds of contributions from solvent water must be considered to predict the SXS profile of a solution accurately. One is the excluded solvent scattering originating in exclusion of water molecules from the space occupied by solutes. The other is the hydration effect resulting from formation of a specific distribution of water around solutes. Explicit consideration of only two molecular layers of water is practically enough to incorporate the hydration effect. Care should be given to using an approximation in which an averaged electron density distribution is assumed for the structure factor because it may predict profiles considerably deviating from the correct profile at large K.     

Stimulated Brillouin scattering in the field of a two-dimensionally localized pumping wave

Stimulated Brillouin scattering of electromagnetic waves in the field of a two-dimensionally localized pump wave at arbitrary scattering angles in the regime of forward scattering is analyzed. Spatial variations in the amplitudes of interacting waves are studied for different values of the pump field and different dimensions of the pump wave localization region. The intensity of scattered radiation is determined as a function of the scattering angle and the dimensions of the pump wave localization region. It is shown that the intensity increases with increasing scattering angle.     

Determination of second virial coefficient of proteins using a dual-detector cell for simultaneous measurement of scattered light intensity and concentration in SEC-HPLC

A method is proposed for the measurement of the B22 value of proteins in aqueous solutions in flow-mode that utilizes a novel fabricated dual-detector cell, which simultaneously measures protein concentration and the corresponding scattered light intensity at 90 degrees , after the protein elutes from a size-exclusion column. Each data point on the chromatograms obtained from the light scattering detector and the concentration (ultraviolet) detector is converted to Rayleigh's ratio, Rtheta, and concentration, c, respectively. The B22 value is calculated from the slope of the Debye plot (Kc/Rtheta versus c) generated from a range of concentrations obtained from these chromatograms for a single protein injection. It is shown that this method provides reliable determination of the B22 values for such proteins as lysozyme, chymotrypsinogen, and chymotrypsin in various solution conditions that agree well with those reported in literature.     

Possibility of wide-angle neutron scattering in the study of proteins and nucleic acids in solutions

A method is proposed for calculating wide-angle neutron scattering curves of biopolymers at any fraction of heavy water (D2O) in solution. The method permits to accurately take into account the phenomenon of deuteroexchange. By this method neutron scattering curves of proteins and DNA have been calculated. The calculations have shown that at optimal fractions of D2O in solution the profiles of neutron scattering curves and their sensitivity to conformational rearrangements in protein molecules turned out to differ very little from those of corresponding X-ray curves. Thus the neutron scattering curves do not contain any additional information (as compared with those contained in X-ray scattering curves) on the structure of proteins in solution. On the contrary, neutron and X-ray scattering curves of DNA differ significantly at all fractions of D2O in solution and therefore the methods of wide-angle neutron and X-ray scattering could become mutually complementary in studying the structure of nucleic acids in solution.     

Effects of organic solutes on the Raman spectra of barnacle muscle fibers

The Raman spectra observed from barnacle muscle fibers are quite complex because the cytoplasm of these cells contains several proteins and solutes. An extraction procedure was used to separate organic solutes from the contractile proteins. Glycine, trimethylamine oxide, taurine, and alanine were found to contribute to the Raman spectra of barnacle muscle fibers, while spectra of lobster fibers reveal the presence of betaine in addition. We have observed that the increase in osmolarity of the intracellular fluid caused by the augmentation of the salinity of sea water (density, 1.023-1.030) in which the barnacles were kept, induces a reduction of intensity of the amide I band. To distinguish among the different parameters which are modified by the sea water salinity, observations were made on glycerinated barnacle muscle fibers. The reduction of intensity of the amide I band in the Raman spectra of glycerinated muscle fibers was also observed with the addition of taurine (0.08 M) in the external relaxing solution. Therefore, under these experimental conditions, the Raman scattering intensity in the amide I region assigned to the alpha-helix conformation (1645-1650 cm-1) is increased when the concentration of organic electrolytes is reduced. However, as no significant decrease of the scattering intensity in the 1660-1670 cm-1 region where the amide I bands of either beta-sheet or disordered conformations normally appear was observed, the increase of intensity of the amide I band centered at 1645 cm-1 is assigned to a change of orientation of alpha-helical segments of the myosin molecules. Our results suggest that organic solutes influence the position of the S-2 segments relative to the thick filaments.     

Quantitative comparison of zero-loss and conventional electron diffraction from two-dimensional and thin three-dimensional protein crystals

The scattering cross-section of atoms in biological macromolecules for both elastically and inelastically scattered electrons is approximately 100,000 times larger than that for x-ray. Therefore, much smaller (<1 microm) and thinner (<0.01 microm) protein crystals than those used for x-ray crystallography can be used to analyze the molecular structures by electron crystallography. But, inelastic scattering is a serious problem. We examined electron diffraction data from thin three-dimensional (3-D) crystals (600-750 A thick) and two-dimensional (2-D) crystals (approximately 60 A thick), both at 93 K, with an energy filtering electron microscope operated at an accelerating voltage of 200 kV. Removal of inelastically scattered electrons significantly improved intensity data statistics and R(Friedel) factor in every resolution range up to 3-A resolution. The effect of energy filtering was more prominent for thicker crystals but was significant even for thin crystals. These filtered data sets showed better intensity statistics even in comparison with data sets collected at 4 K and an accelerating voltage of 300 kV without energy filtering. Thus, the energy filter will be an effective and important tool in the structure analysis of thin 3-D and 2-D crystals, particularly when data are collected at high tilt angle.     

Anomalous Small Angle X-Ray Scattering Simulations: Proof of Concept for Distance Measurements for Nanoparticle-Labelled Biomacromolecules in Solution

Anomalous small angle X-ray scattering can in principle be used to determine distances between metal label species on biological molecules. Previous experimental studies in the past were unable to distinguish the label-label scattering contribution from that of the molecule, because of the use of atomic labels; these labels contribute only a small proportion of the total scattering signal. However, with the development of nanocrystal labels (of 50–100 atoms) there is the possibility for a renewed attempt at applying anomalous small angle X-ray scattering for distance measurement. This is because the contribution to the scattered signal is necessarily considerably stronger than for atomic labels. Here we demonstrate through simulations, the feasibility of the technique to determine the end-to-end distances of labelled nucleic acid molecules as well as other internal distances mimicking a labelled DNA binding protein if the labels are dissimilar metal nanocrystals. Of crucial importance is the ratio of mass of the nanocrystals to that of the labelled macromolecule, as well as the level of statistical errors in the scattering intensity measurements. The mathematics behind the distance determination process is presented, along with a fitting routine than incorporates maximum entropy regularisation.     

Some comments on the article: 'The Structure of Human-Plasma Low-Density Lipoprotein B. An X-Ray Small-Angle Scattering Study' by K. Muller, P. Laggner, O. Glatter, and G. Kostner [Eur. J. Biochem. 82, 73--90 (1978)].

In their paper, K. Muller, P. Laggner, O. Glatter and G. Kostner report X-ray scattering and density experiments on human plasma low-density lipoprotein B, performed at different solvent densities (i.e. contrast variation method). The interpretation of the experimental data lead those authors to question the use of that method and particularly the use of the characteristic scattering functions in the study of serum lipoproteins. In the present paper it is shown that several aspects of their analysis are in fact highly questionable and that the objections raised are therefore unfounded.     

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.     

Laser light-scattering studies of bull spermatozoa. I. Orientational effects.

Calculations based on the known dimensions of bull spermatozoa show that the scattered light intensity is strongly dependent upon the relative orientation of the particle to the incident beam. The magnitude of this effect of apparently much greater than for other systems where motility has been investigated by dynamic light scattering. The calculations show that the scattering source can be approximated by a small spinning mirror, and consequently the greatest light intensity at the detector results from cells swimming in a direction perpendicular to the scattering vector. The calculations are in substantial agreement with photographic observations, as well as direct measurements of the scattered intensity. Previous treatments of dynamic light scattering from swimming bull spermatozoa based on point scattering models are shown to be incorrect.     

Bilayer structure of dihexadecyl phosphate

The X-ray scattering data of dihexadecyl phosphate (DHP) were analyzed by the distance distribution function directly obtained from the scattered intensity by Fourier transformation with no prior assumption about size and shape. The detergent in aqueous solutions is a random distribution of lamellae with a thickness of 58 Å and consistent with a hollow vesicular structure of an outer diameter of 340 Å with some overall size heterogeneity. The electron density profile perpendicular to the lamellar plane indicates a bilayer as the underlying structural principle.     

Phasing macromolecular structures with UV-induced structural changes

Experimental phasing of macromolecular crystal structures relies on the accurate measurement of two or more sets of reflections from isomorphous crystals, where the scattering power of a few atoms is different for each set. Recently, it was demonstrated that X-ray-induced intensity differences can also contain phasing information, exploiting specific structural changes characteristic of X-ray damage. This method (radiation damage-induced phasing; RIP) has the advantage that it can be performed on a single crystal of the native macromolecule. However, a drawback is that X-rays introduce many small changes to both solvent and macromolecule. In this study, ultraviolet (UV) radiation has been used to induce specific changes in the macromolecule alone, leading to a larger contrast between radiation-susceptible and nonsusceptible sites. Unlike X-ray RIP, UV RIP does not require the use of a synchrotron. The method has been demonstrated for a series of macromolecules.     

An analysis of the x-ray interchain peak profile in dipalmitoylglycerophosphocholine

The primary X-ray peak profile characterizing the interchain structure in the dipalmitoylglycerophosphocholine membrane has been measured as a function of temperature. The scattering between 23 and 34.6° C is characterized by an asymmetric crystalline reflection accounting for 85% of the total intensity, the remaining 15% being liquid-like in character. At a pre-transition temperature of 34.6° C, the reflection profile becomes (nearly) symmetrical, indicating a change in tilt angle of the chains with respect to the membrane surface. This change is accompanied by an increase of 20% in the amount of liquid-like scattering, indicating that the pre-transition mechanism includes a partial melting of the chains. At the melting point, 41.5° C, the crystalline reflection disappears, and the liquid component of the scattering increases to a point where it includes all the scattered intensity. The relative values of the integrated intensities at each temperature are tabulated, and the significance of the peak widths and shapes are discussed.     

Conformational studies of BSA using laser light scattering

The usefulness of laser light scattering as a technique for determining protein conformation has been investigated by studying the self-association and drug binding of bovine serum albumin (BSA). The diffusion coefficients of BSA monomers and dimers have been measured and the ratio of these two quantities indicates that in the dimer, the subunit separation is 2.2 times the monomeric hydrodynamic radius. The binding of salicylate to BSA causes an increase in its diffusion coefficient corresponding to a reduction in the frictional drag of the solvent on the protein molecules. It has been found that data obtained using laser light scattering may be interpreted confidently only when proper care has been taken in sample preparation and the scattered intensity autocorrelation function has been appropriately analyzed.