Rotational and translational motions of human spermatozoa: angle dependence of dynamic laser light scattering

We have studied how the dynamic components of laser light scattered from human spermatozoa depend on the scattering angle. This was done by investigating the halfwidth of the intensity autocorrelation function. A model of the spermatozoa as freely rotating and translating linear objects was adequate to describe the scattered light. Rotational motions determined the halfwidth of the intensity autocorrelation function at very small scattering angles and contribution from translational motions was dominant at scattering angles larger than 20 degrees. The contribution from translational motions increased with increasing scattering angle. We found a nearly linear relationship between the translation speed and the rotation frequency. However, the ratio between the two properties varied more than expected from the methodological error. Therefore we introduced a propelling efficacy as a concept to describe the swimming efficiency. This property might contain important information about the swim characteristics.Abbreviations ACF Autocorrelation function - _1/2 halfwidth - RGD Rayleigh-Gans-Debye - SD Standard deviation Correspondence to: P. Thyberg     

Small-angle X-ray scattering of reduced ribonuclease A: effects of solution conditions and comparisons with a computational model of unfolded proteins

The disulfide-reduced form of bovine ribonuclease A, with the Cys thiols irreversibly blocked, was characterized by small-angle x-ray scattering. To help resolve the conflicting results and interpretations from previous studies of this model unfolded protein, we measured scattering profiles using a range of solution conditions and compared them with the profiles predicted by a computational model for a random-coil polypeptide. Analysis of the simulated and experimental profiles reveals that scattering intensities at intermediate angles, corresponding to interatomic distances in the range of 5-20 Å, are particularly sensitive to changes in solvation and can be used to assess the internal scaling behavior of the polypeptide chain, expressed as a mass fractal dimension, D_m. This region of the scattering curve is also much less sensitive to experimental artifacts than is the very small angle regime (the Guinier region) that has been more typically used to characterize unfolded proteins. The experimental small-angle x-ray scattering profiles closely matched those predicted by the computational model assuming relatively small solvation energies. The scaling behavior of the polypeptide approaches that of a well-solvated polymer under conditions where it has a large net charge and at high urea concentrations. At lower urea concentrations and neutral pH, the behavior of the chain approaches that expected for θ-conditions, where the effects of slightly unfavorable interactions with solvent balance those of excluded volume, leading to scaling behavior comparable to that of an idealized random walk chain. Though detectable, the shift toward more compact conformations at lower urea concentrations does not correspond to a transition to a globule state and is associated with little or no reduction in conformational entropy. This type of collapse, therefore, is unlikely to greatly reduce the conformational search for the native state.     

New method for incorporating solvent influence into the evaluation of X-ray scattering intensity of proteins in solution

A new method, the surface integration method, is presented for taking into account the influence of solvent on the intensity of X-ray scattered from proteins in solution. It requires no averaging numerically over the solute orientation. The solvent is modeled by a continuous medium with electrons of uniform density. This method is applied to amino acids, peptides and native proteins to confirm its effectiveness. The solvent influence on the normalized scattering intensity I(K) I(0) is more noticeable for larger solutes and at larger scattering angles, where I(K) is the intensity of scattered X-ray with the magnitude of scattering vector K.     

Fractal dimension of humic acids

Small-angle neutron scattering experiments have been made on solutions of humic acid aggregates with an acidity corresponding to pH 5.0 and at 0.1 M ionic strength. We observe power-law decay of the intensity over one decade of the scattering vector, Q, indicating that the aggregates are fractal. We explain the normalized intensity in the entire Q-range by assuming that the humic acid particles can be described by building units of a radial size, 25 Å, aggregated into clusters with an average radius of 400–500 Å. For humic acids obtained from two different sources, we determine the fractal dimension, D = 2.3 ± 0.1. For small values of Q, the measured data of one of the samples extend into the Guinier range giving an average radius of gyration of 320 ± 20 Å. Correspondence to: R. Österberg     

Interpretation of small angle x-ray scattering from starch on the basis of fractals

Using small-angle X-ray scattering, the behaviour of corn and potato starches during gelatinization, swelling, and rétrogradation was investigated. The scattering patterns were analysed on the basis of the fractal concept. The main scattering source from low moisture starches could be interpreted as a ‘surface fractal’ obeying a power law with an exponent of ca —4. When the starch swelled, the surface fractal characteristic was recognised only at very low angles, and on heating it disappeared at ca 80 °C. For gelatinised starches, the whole scattering pattern obeyed the power law with the power around -2.0. This result suggests that the physical arrangement of gelatinised starch molecules is a ‘mass fractal’, i.e. a self-similar structure, in nature. Further, it was found that the scattering of the retrograded starch showed a shoulder like peak superimposed the background scattering representing the mass fractal. The corresponding Bragg spacing was estimated to be 31˜15nm.     

Observation of correlated X-ray scattering at atomic resolution

Tools to study disordered systems with local structural order, such as proteins in solution, remain limited. Such understanding is essential for e.g. rational drug design. Correlated X-ray scattering (CXS) has recently attracted new interest as a way to leverage next-generation light sources to study such disordered matter. The CXS experiment measures angular correlations of the intensity caused by the scattering of X-rays from an ensemble of identical particles, with disordered orientation and position. Averaging over 15 496 snapshot images obtained by exposing a sample of silver nanoparticles in solution to a micro-focused synchrotron radiation beam, we report on experimental efforts to obtain CXS signal from an ensemble in three dimensions. A correlation function was measured at wide angles corresponding to atomic resolution that matches theoretical predictions. These preliminary results suggest that other CXS experiments on disordered ensembles—such as proteins in solution—may be feasible in the future.     

Explaining the Non-Newtonian Character of Aggregating Monoclonal Antibody Solutions Using Small-Angle Neutron Scattering

A monoclonal antibody solution displays an increase in low shear rate viscosity upon aggregation after prolonged incubation at 40°C. The morphology and interactions leading to the formation of the aggregates responsible for this non-Newtonian character are resolved using small-angle neutron scattering. Our data show a weak repulsive barrier before proteins aggregate reversibly, unless a favorable contact with high binding energy occurs. Two types of aggregates were identified after incubation at 40°C: oligomers with radius of gyration ∼10 nm and fractal submicrometer particles formed by a slow reaction-limited aggregation process, consistent with monomers colliding many times before finding a favorable strong interaction site. Before incubation, these antibody solutions are Newtonian liquids with no increase in low shear rate viscosity and no upturn in scattering at low wavevector, whereas aggregated solutions under the same conditions have both of these features. These results demonstrate that fractal submicrometer particles are responsible for the increase in low shear rate viscosity and low wavevector upturn in scattered intensity of aggregated antibody solutions; both are removed from aggregated samples by filtering.     

Explaining the Non-Newtonian Character of Aggregating Monoclonal Antibody Solutions Using Small-Angle Neutron Scattering

A monoclonal antibody solution displays an increase in low shear rate viscosity upon aggregation after prolonged incubation at 40°C. The morphology and interactions leading to the formation of the aggregates responsible for this non-Newtonian character are resolved using small-angle neutron scattering. Our data show a weak repulsive barrier before proteins aggregate reversibly, unless a favorable contact with high binding energy occurs. Two types of aggregates were identified after incubation at 40°C: oligomers with radius of gyration ∼10 nm and fractal submicrometer particles formed by a slow reaction-limited aggregation process, consistent with monomers colliding many times before finding a favorable strong interaction site. Before incubation, these antibody solutions are Newtonian liquids with no increase in low shear rate viscosity and no upturn in scattering at low wavevector, whereas aggregated solutions under the same conditions have both of these features. These results demonstrate that fractal submicrometer particles are responsible for the increase in low shear rate viscosity and low wavevector upturn in scattered intensity of aggregated antibody solutions; both are removed from aggregated samples by filtering.     

Synchrotron radiation SAXS of 11S soya globulin

Small-angle X-ray scattering using the Daresbury synchrotron source has been employed to obtain scattering curves from a 5% solution of the 11S soya globulin. The high intensity of the source allowed exposure times to be reduced by up to 1000 times compared with those for a conventional X-ray generator. Submaxima at higher angles were recorded which have not been reported previously. This improved resolution appears to result from reduced aggregation and/or denaturation of the protein due to the very short exposure times. Such detail in the scattering curve should be of importance for structural modelling of the proteins, particularly in the case of the 11S soya globulin for which intact individual subunits cannot be isolated.     

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.     

Prediction of the three-dimensional structure of the rap-1A protein from its homology to theras-gene-encoded p21 protein

rap-1A, an anti-oncogene-encoded protein, is aras-p21-like protein whose sequence is over 80% homologous to p21 and which interacts with the same intracellular target proteins and is activated by the same mechanisms as p21, e.g., by binding GTP in place of GDP. Both interact with effector proteins in the same region, involving residues 32–47. However, activated rap-1A blocks the mitogenic signal transducing effects of p21. Optimal sequence alignment of p21 and rap-1A shows two insertions of rap-1A atras positions 120 and 138. We have constructed the three-dimensional structure of rap-1A bound to GTP by using the energy-minimized three-dimensional structure ofras-p21 as the basis for the modeling using a stepwise procedure in which identical and homologous amino acid residues in rap-1A are assumed to adopt the same conformation as the corresponding residues in p21. Side-chain conformations for homologous and nonhomologous residues are generated in conformations that are as close as possible to those of the corresponding side chains in p21. The entire structure has been subjected to a nested series of energy minimizations. The final predicted structure has an overall backbone deviation of 0.7 å from that ofras-p21. The effector binding domains from residues 32–47 are identical in both proteins (except for different side chains of different residues at position 45). A major difference occurs in the insertion region at residue 120. This region is in the middle of another effector loop of the p21 protein involving residues 115–126. Differences in sequence and structure in this region may contribute to the differences in cellular functions of these two proteins.     

Gelatinization of starch in excess water: beyond the melting of lamellar crystallites. A combined wide- and small-angle X-ray scattering study

The gelatinization of waxy rice, regular rice, and potato starch suspensions (66% w/w moisture) was investigated by real-time small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) during heating and by fast ramp differential scanning calorimetry (DSC). The high-angle tail of the SAXS patterns suggested the transition from surface to mass fractal structures in the DSC gelatinization range. Amylose plays a major role in determining the dimensions of the self-similar structures that develop during this process as the characteristic power-law scattering behavior extends to lower scattering angles for regular than for waxy starches. Crystallinity of A-type starches is lost in the temperature region roughly corresponding to the DSC gelatinization range. At the end of the gelatinization endotherm, the B-type potato starch showed residual crystallinity (WAXD), while SAXS-patterns exhibited features of remaining lamellar stacks. Results indicate that the melting of amylopectin crystallites during gelatinization is accompanied by the (exothermic) formation of amorphous networks.     

Prediction of the three-dimensional structure of the rap-1A protein from its homology to theras-gene-encoded p21 protein

rap-1A, an anti-oncogene-encoded protein, is aras-p21-like protein whose sequence is over 80% homologous to p21 and which interacts with the same intracellular target proteins and is activated by the same mechanisms as p21, e.g., by binding GTP in place of GDP. Both interact with effector proteins in the same region, involving residues 32–47. However, activated rap-1A blocks the mitogenic signal transducing effects of p21. Optimal sequence alignment of p21 and rap-1A shows two insertions of rap-1A atras positions 120 and 138. We have constructed the three-dimensional structure of rap-1A bound to GTP by using the energy-minimized three-dimensional structure ofras-p21 as the basis for the modeling using a stepwise procedure in which identical and homologous amino acid residues in rap-1A are assumed to adopt the same conformation as the corresponding residues in p21. Side-chain conformations for homologous and nonhomologous residues are generated in conformations that are as close as possible to those of the corresponding side chains in p21. The entire structure has been subjected to a nested series of energy minimizations. The final predicted structure has an overall backbone deviation of 0.7 å from that ofras-p21. The effector binding domains from residues 32–47 are identical in both proteins (except for different side chains of different residues at position 45). A major difference occurs in the insertion region at residue 120. This region is in the middle of another effector loop of the p21 protein involving residues 115–126. Differences in sequence and structure in this region may contribute to the differences in cellular functions of these two proteins.     

Structural changes and aggregation of human influenza virus

The pH-induced change in the structure and aggregation state of the PR-8 and X-31 strains of intact human influenza virus has been studied in vitro. Reducing the pH from 7.4 to 5.0 produces a large increase in the intensity of light scattered to low angles. A modest increase in the polydispersity parameter from cumulants fits to the dynamic light scattering correlograms accompanies the increase, as does a change in how that parameter varies with scattering angle. These trends imply that the virus particles are not uniform, even at pH 7.4, and tend to aggregate as pH is reduced. The scattering profiles (angular dependence of intensity) never match those of isolated, spherical particles of uniform size, but the deviations from that simple model remain modest at pH 7.4. At pH 5.0, scattering profiles calculated for aggregates of uniformly sized spheres come much closer to matching the experimental data than those computed for isolated particles. Although these observations indicate that acid-induced aggregation develops over a period of minutes to hours after acidification, a nearly instantaneous increase in hydrodynamic size is the first response of intact virus particles to lower pH.     

Kinetic analysis of the pre-equilibrium steps in the self-assembly of RecA protein from Escherichia coli

Total intensity light scattering is employed to investigate the self-assembly kinetics of RecA protein. Reaction conditions are employed where the kinetics of self-assembly are slow enough to yield reliable scattered intensity measurements over the range of scattering angles from 40 to 130 degrees as a function of time. From these measurements the time-dependent behavior of the weight average molecular weight, Mr, and radius of gyration, RG, of the associating protein species as a function of [MgCl2], [NaCl], [RecA], and pH was determined. The temperature dependence of RecA self-assembly was also investigated and allowed an evaluation of the activation thermodynamic parameters of association. Results reveal RecA self-assembly is bi-phasic under all conditions examined. The first phase, referred to as "filamentation" is second-order in [RecA] and occurs via a quasi linear condensation scheme with an Arrhenius activation energy of 88.6 kcal/mol. Filamentation assembly involves the uptake of one proton, one MgCl2, the release of five to six NaCls, and is driven by the release of approximately 70 water molecules. The evaluated activation parameters of the first kinetic phase are consistent with the proposition that linear self-assembly of RecA protein into ordered filaments is entropically driven. The second kinetic phase, referred to as "bundling" is greater than second-order in both [RecA] and [MgCl2], is considerably slower that filamentation assembly, and is apparently initiated by 2nd order collisions of linear filaments.     

On the distribution and packing of RNA and protein ribosomes.

From the analysis of the measured radii of gyration of the RNA (Rg = 6.6 +/- 0.3 nm) and protein (Rg = 10.2 +/- 0.5 nm) components of the 50-S subparticle of Escherichia coli ribosomes it is concluded that proteins containing a large amount of hydrodynamically bound water are located on the periphery of the tightly packed RNA. We found that the common features of the measured X-ray scattering curves of the E. coli 70-S ribosome, its 30-S and 50-S subparticles and wheat 80-S ribosomes in the region of scattering angles corresponding to scattering vectors mu from 1 to 5 nm-1 reflect features of the RNA compact packing. A hypothesis is proposed that the compact packing of RNA helices in the range of Bragg distances of 4.5--2.0 nm is a general structural feature of all ribosomal particles.     

Treatment of mobile phase particulate matter in low-angle quasi-elastic light scattering

The method of quasi-elastic laser light scattering (QLS), particularly at low forward scattering angles, has been complicated by the transient presence of Mie or large Rayleigh scattering particles which contaminate the scattering volume. These large contaminating particles have substantial effects on photon correlation spectroscopy because the presence of these larger scatterers tends to decrease the value of the apparent diffusion coefficient of the particle of interest. A method is presented which yields more accurate diffusion constants by autocorrelation of selected photon count periods representative of minimal Mie or large Rayleigh particle contamination. This method was applied to the determination of the apparent diffusion constant for four proteins—ovalbumin, chymotrypsinogen-A, bovine serum albumin, and ribonuclease-A.     

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.     

Kinetics of cold-set diffusion-limited aggregations of denatured whey protein isolate colloids

The CaCl2-induced cold-set aggregation kinetics of the denatured whey protein isolate (WPI) colloids has been investigated under dilute diffusion-limited cluster aggregation (DLCA) conditions, using small-angle light scattering. In particular, the structure factor, the scattered intensity at zero angle and the average radius of gyration have been measured for the aggregating system as a function of time. It is found that the fractal dimension of the clusters is df= 1.85, in the range typical of clusters aggregated under DLCA conditions. The aggregation kinetics in this transition region can be described by a power law relation in the initial stage of the aggregation, but the exponent of the power law is equal to 0.7, i.e., significantly larger than 1/df= 0.54, which is the typical value of the DLCA kinetics. Since it is found that the average gyration radius of the clusters has reached a value of 80 microm, leading to a cumulative volume fraction of clusters equal to 0.25, it is legitimate to expect that the process is in the region of transition from aggregation to gelation. This confirmed by the fact that, at the later stage of the aggregation, the growth of the average cluster size further accelerates with time and eventually becomes explosive, leading to gelation. The observed aggregation kinetics has been compared with that reported in the literature from DLCA Monte Carlo simulations, and a good agreement has been found with the data corresponding to the transition region from aggregation to gelation. Numerical simulations using the Smoluchowski kinetic model have also been carried out in order to support the experimental findings.     

Sinusoidal and delta function responses of visual cells of the Limulus eye

Dynamic responses of visual cells of the Limulus eye to stimuli of sinusoids and narrow pulses of light superimposed on a nonzero mean level have been obtained. Amplitudes and phase angles of averaged sinusoidal generator potential are plotted with respect to frequency of intensity modulation for different mean levels of light adaptation. At frequencies above 10 CPS, generator potential amplitudes decrease sharply and phase lag angle increases. At frequencies below 1 CPS, amplitude decreases. A maximum of amplitude in the region of 1 to 2 CPS is apparent with increased mean intensity. The generator potential responses are compared with those of differential equation models. Variation of gain with mean intensity for incremental stimuli is consistent with logarithmic sensitivity of the photoreceptor. Frequency response of the photoreceptor derived from narrow pulses of light predicts the frequency response obtained with sinusoidal stimuli, and the photoreceptor is linear for small signals in the light-adapted state.