Considerations of coherent scattering and electron binding in incoherent scattering, in computation of dose deposition in tissue from low-energy photon beams

Two different sets of Monte Carlo computations were carried out for the study of dose penetration of monoenergetic, low-energy (10 to 100 keV) photon beams incident on slabs of tissue. One program took into account coherent scattering and considered electron binding when finding the angle of scattering during incoherent scattering; the other simpler program, customarily used at higher energies, largely ignored these effects. For calculations at the source photon energy of 100 keV, it was found that there was negligible difference in dose distribution in the slab between the more and less complex type of calculations. The same thing was found to be true for the 30 and 10-keV source photon energies only for shallow penetration distances; and at deeper penetrations the simple approach tended to overestimate the dose appreciably. It is concluded that for penetration of low-energy photon beams into tissue, accurate calculational results cannot be assured with the neglect of coherent scattering effects and electron binding considerations in determining the scattering angles except for shallow depths of penetration.     

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.     

Model computations on the differential scattering of circularly polarized light (CIDS) by dense macromolecular particles

Circular intensity differential scattering (CIDS) patterns have been calculated for two general types of chiral arrangements. The calculations were done using the second Born approximation. The geometries considered are (a) a linear array of anisotropic scattering groups with a spiraling orientation (a twisted ladder) and (b) a helical array of scattering groups with arbitrary anisotropy and orientation. The CIDS expressions for the first of these models (twisted ladder) reduces to a simple analytical form and clearly illustrates many properties of CIDS patterns. The second geometry (helix) is more general. Calculations were done for oriented scatterers and for rotationally averaged scatterers as would be found in solution.     

Isotopic light scattering of lipid vesicles. Water permeation and effect of alpha-tocopherol

The influence of the index of refraction of the solvent on light scattering properties of lecithin bilayer vesicles is described. Large vesicles (diameter 300 nm) are considered where one lamella separates the intravesicular compartment from the external medium. Stationary and transient cases are distinguished with special emphasis on the isotopic substitution of the solvent, i.e. H2O vs. D2O. Theoretical calculations based on the Mie theory of light-scattering are in accord with results from experiments. The two stationary cases considered serve to calibrate the numerical calculations and illustrate the capability of the method. Transient experiments allow the determination of permeation rates; in particular the D2O/H2O permeability coefficients can be obtained. Single component vesicular lecithin bilayers and ones containing tocopherol are compared. In the crystalline state the incorporation of tocopherol increases the fluidity of the lipid bilayer in parallel with the water permeation rate.     

A study of the kinetics and mechanism of ADP-triggered platelet aggregation

The time-course of ADP-triggered aggregation of human blood platelets has been followed by sensitive right-angle light scattering intensity measurements as a function of the platelet and fibrinogen concentrations. Rayleigh-Gans light scattering theory has been combined with the Smoluchowski aggregation model to predict the dependence of the right-angle scattering intensity on particle size and concentration as well as the time-dependent changes during aggregation. The validity of the calculations was confirmed by measuring the scattering intensity with suspensions of polystyrene microspheres of known radius, as well as the time-dependent changes in the 90 degrees scattering intensity during aggregation of these particles. However, in contrast to the predictions of the model, the time-course of the scattering intensity changes during platelet aggregation was characterized by single exponential decay with a rate constant which reached a limiting value of 0.017 s-1 at high platelet concentrations. The value of kagg was also independent of the fibrinogen concentration over a 30-fold range. Covalently cross-linked fibrinogen dimers and Fragment D-inhibited fibrin protofibrils yielded aggregation rates that agreed with those measured with fibrinogen. The results indicate that the rate of platelet aggregation is not limited by either the rate of fibrinogen binding or the frequency of platelet-platelet collisions under these conditions.     

The DFPase from Loligo vulgaris in sugar surfactant-based bicontinuous microemulsions: structure, dynamics, and enzyme activity

The enzyme diisopropyl fluorophosphatase (DFPase) from the squid Loligo vulgaris is of great interest because of its ability to catalyze the hydrolysis of highly toxic organophosphates. In this work, the enzyme structure in solution (native state) was studied by use of different scattering methods. The results are compared with those from hydrodynamic model calculations based on the DFPase crystal structure. Bicontinuous microemulsions made of sugar surfactants are discussed as host systems for the DFPase. The microemulsion remains stable in the presence of the enzyme, which is shown by means of scattering experiments. Moreover, activity assays reveal that the DFPase still has high activity in this complex reaction medium. To complement the scattering experiments cryo-SEM was also employed to study the microemulsion structure.     

Inelastic neutron scattering analysis of picosecond internal protein dynamics. Comparison of harmonic theory with experiment

The experimental inelastic neutron scattering spectrum of a protein, the bovine pancreatic trypsin inhibitor (BPTI), in a powder sample is presented together with the generalized density of states, G(omega), as a function of the frequency, omega, derived from the scattering data. The experimental results are compared with calculations from two different normal mode analyses of BPTI. One of these, based on an improved model, gives a calculated spectrum and density of states in general agreement with those obtained experimentally; the other, based on an earlier model, shows considerable disagreement. The important improvements in the newer normal mode analysis are the explicit treatment of all atoms (non-polar as well as polar hydrogens are included) and a modified truncation scheme for the long-range electrostatic interactions. The fact that the inelastic neutron scattering measurements can distinguish between the two theoretical models makes clear their utility for the analysis of protein dynamics.     

Sensitivity of muscle force estimations to changes in muscle input parameters using nonlinear optimization approaches.

The purpose of this study was to analyze the sensitivity of muscle force calculations to changes in muscle input parameters. Force sharing between two synergistic muscles was derived analytically for a one-degree-of-freedom system using three nonlinear optimization approaches. Changes in input parameters that are within normal anatomical variations often caused changes in muscular forces exceeding 100 percent. These results indicate that errors in muscle force calculations may depend as much on inadequate muscle input parameters as they may on the choice of the objective and constraint functions of the optimization approach.     

Nonlinear Optical Properties of Large-Sized Gold Nanorods

The nonlinear optical properties of single gold nanorods (GNRs) with a large diameter of ～200 nm and a long length of ～800 nm were investigated by using a focused femtosecond (fs) laser light with tunable wavelength. While the linear and nonlinear optical properties of small-sized GNRs have been extensively studied, the nonlinear optical properties of large-sized GNRs and the effects of high-order surface plasmon resonances remain unexplored. Second harmonic generation (SHG) or/and two-photon-induced luminescence (TPL) were observed in the nonlinear response spectra, and their dependences on excitation wavelength and polarization were examined. The scattering and absorption spectra of the small- and large-sized GNRs were compared by using the discrete dipole approximation method. It was found that the extinction of large-sized GNRs is dominated by scattering rather than absorption, which is dominant in small-sized GNRs. In addition, it was revealed that the excitation wavelength-dependent SHG of a GNR is governed by the linear scattering of the GNR and the maximum SHG is achieved at the valley of the scattering spectrum. In comparison, the excitation wavelength dependence of TPL is determined by the absorption spectrum of the GNR. The polarization-dependent SHG of a GNR exhibits a strong dependence on the dimension of the GNR, and it may appear as bipolar distributions parallel or perpendicular to the long axis of the GNR or multipole distributions.     

Effect of Oxidation on the Structure of Human Low- and High-Density Lipoproteins

This work presents a controlled study of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) structural changes due to in vitro oxidation with copper ions. The changes were studied by small-angle x-ray scattering (SAXS) and dynamic light scattering (DLS) techniques in the case of LDL and by SAXS, DLS, and Z-scan (ZS) techniques in the case of HDL. SAXS data were analyzed with a to our knowledge new deconvolution method. This method provides the electron density profile of the samples directly from the intensity scattering of the monomers. Results show that LDL particles oxidized for 18 h show significant structural changes when compared to nonoxidized particles. Changes were observed in the electrical density profile, in size polydispersity, and in the degree of flexibility of the APO-B protein on the particle. HDL optical results obtained with the ZS technique showed a decrease of the amplitude of the nonlinear optical signal as a function of oxidation time. In contrast to LDL results reported in the literature, the HDL ZS signal does not lead to a complete loss of nonlinear optical signal after 18 h of copper oxidation. Also, the SAXS results did not indicate significant structural changes due to oxidation of HDL particles, and DLS results showed that a small number of oligomers formed in the sample oxidized for 18 h. All experimental results for the HDL samples indicate that this lipoprotein is more resistant to the oxidation process than are LDL particles.     

Size and structure of antigen-antibody complexes. Electron microscopy and light scattering studies

Size parameters of model antigen-antibody (Ag-Ab) complexes formed by the interaction of bovine serum albumin (BSA) and pairs of monoclonal anti-BSA antibodies (mAb) were evaluated by quasielastic light scattering, classical light scattering, and electron microscopy (EM). Mean values for the hydrodynamic radius, radius of gyration, and molecular weight were determined by light scattering. Detailed information regarding the molecular weight distribution and the presence of cycles or open chains was obtained with EM. Average molecular weights were calculated from the EM data, and the Porod-Kratky wormlike chain theory was used to model the conformational behavior of the Ag-mAb complexes. Ag-mAb complexes prepared from three different mAb pairs displayed significantly different properties as assessed by each of the techniques employed. Observations and size parameter calculations from EM photomicrographs were consistent with the results from light scattering. The differences observed between the mab pairs would not have been predicted by idealized thermodynamic models. These results suggest that the geometric constraints imposed by the individual epitope environment and/or the relative epitope location are important in determining the average size of complexes and the ratio of linear to cyclic complexes.     

Time-resolved synchrotron radiation X-ray solution scattering study of DNA melting

Time resolved x-ray solution scattering measurements were made during thermal denaturation of DNA from various sources in the temperature range of 20-90 degrees C. Preliminary results on the influence of fragment length, ionic strength, and origin of the DNA on the time course of the scattering are described. Interpretation is based on model calculations of the scattering patterns. The results indicate that, for long DNA fragments at very low ionic strength, the melting process is a continuous phenomenon over the whole temperature range. It is accompanied by a progressive decrease of the radius of gyration of the cross section and of the mass per unit length. For short fragments of 146 base pair nucleosomal core DNA, stiffening of the DNA appears to precede a sharp melting transition.     

Correlation Effects in the Double Proton Transfer of the Formic Acid Dimer

The role of correlation effects in the potential energy hypersurface for the double proton transfer in the hydrogen bond of the formic acid dimer has been studied at the non-empirical level. The calculations were performed in different large as well as for the first time in complete basis set at the correlation level. The possible reasons of incorrect results of quantum chemical calculations are considered.     

Algal growth dynamics under light interaction: A nonlinear evolution problem

A mathematical model for interaction of algae with light is presented. This model consists of a couple of nonlinear integro-differential equations dealing with the evolution of algae concentration due to absorption of light and the evolution of light intensity due to absorption and scattering by algae and water. The model is formulated as a nonlinear abstract Cauchy problem in a Banach space suited to describe the physical features of the problem. By using techniques and results of semigroups theory, it is proved that the system has a unique global strict solution.Work performed under the auspices of G.N.F.M. (Gruppo Nazionale per la Fisica Matematica)     

Low-energy electron penetration range in liquid water

Monte Carlo simulations of electron tracks in liquid water are performed to calculate the energy dependence of the electron penetration range at initial electron energies between 0.2 eV and 150 keV, including the subexcitation electron region (<7.3 eV). Our calculated electron penetration distances are compared with available experimental data and earlier calculations as well as with the results of simulations using newly reported amorphous ice electron scattering cross sections in the range approximately 1-100 eV.     

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%.     

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.     

Spin-dependent electronic structure near the iron atom in rubredoxin

The fine structure of X-ray absorption spectrum of Fe in rubredoxin was interpreted on the basis of the multiple scattering theory and the results of calculations of the self-consistent potential. For biological molecules, such calculations were made for the first time. It was found that the Fe-S interaction is the main factor, which determines the electronic structure of the protein active center. The changes in spectrum shape are mostly due to the spin configuration of 3d-electrons. It was shown that the dipole transition element significantly changes near the absorption edge; therefore, it is impossible to determine the distribution of unoccupied electronic p-states directly from experiment. However, the results of calculations obtained in this work are consistent with the corresponding experimental data, indicating the adequacy of the calculated densities of free electronic states.     

Effect of Oxidation on the Structure of Human Low- and High-Density Lipoproteins

This work presents a controlled study of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) structural changes due to in vitro oxidation with copper ions. The changes were studied by small-angle x-ray scattering (SAXS) and dynamic light scattering (DLS) techniques in the case of LDL and by SAXS, DLS, and Z-scan (ZS) techniques in the case of HDL. SAXS data were analyzed with a to our knowledge new deconvolution method. This method provides the electron density profile of the samples directly from the intensity scattering of the monomers. Results show that LDL particles oxidized for 18 h show significant structural changes when compared to nonoxidized particles. Changes were observed in the electrical density profile, in size polydispersity, and in the degree of flexibility of the APO-B protein on the particle. HDL optical results obtained with the ZS technique showed a decrease of the amplitude of the nonlinear optical signal as a function of oxidation time. In contrast to LDL results reported in the literature, the HDL ZS signal does not lead to a complete loss of nonlinear optical signal after 18 h of copper oxidation. Also, the SAXS results did not indicate significant structural changes due to oxidation of HDL particles, and DLS results showed that a small number of oligomers formed in the sample oxidized for 18 h. All experimental results for the HDL samples indicate that this lipoprotein is more resistant to the oxidation process than are LDL particles.     

Amylose conformation in aqueous solution: a small-angle X-ray scattering study

An investigation of the small-angle X-ray scattering properties of aqueous solutions of an amylose derivative has been carried out. Experiments have been conducted in stable and fairly concentrated polymer solutions (up to 3.2%) by using a slightly substituted carboxymethylamylose having a degree of substitution of 0.08. Scattering intensities display a maximum in the low angle range which prevents extrapolation of the angular dependence to zero angle. Data obtained in the range of scattering vector 0.01<η<0.1Å^?1 yield 8 Å as the radius of gyration of the chain cross-section and 140 dalton Å^?1 as the mass per unit length. These results are analysed in terms of the current model of amylose solution conformation and compared with the theoretical calculations of the Debye scattering function of the isolated chain.