Teaching light scattering spectroscopy: the dimension and shape of tobacco mosaic virus.

The tobacco mosaic virus is used as a model molecular assembly to illustrate the basic potentialities of light scattering techniques (both static and dynamic) to undergraduates. The work has two objectives: a pedagogic one (introducing light scattering to undergraduate students) and a scientific one (stabilization of the virus molecular assembly structure by the nucleic acid). Students are first challenged to confirm the stabilization of the cylindrical shape of the virus by the nucleic acid, at pH and ionic strength conditions where the coat proteins alone do not self-assemble. The experimental intramolecular scattering factor is compared with the theoretical ones for several model geometries. The data clearly suggest that the geometry is, in fact, a rod. Comparing the experimental values of gyration radius and hydrodynamic radius with the theoretical expectations further confirms this conclusion. Moreover, the rod structure is maintained over a wider range of pH and ionic strength than that valid for the coat proteins alone. The experimental values of the diffusion coefficient and radius of gyration are compared with the theoretical expectations assuming the dimensions detected by electron microscopy techniques. In fact, both values are in agreement (length approximately 300 nm, radius approximately 20 nm).     

Prediction of the viscosity radius and the size exclusion chromatography behavior of PEGylated proteins

Size exclusion chromatography (SEC) was used to determine the viscosity radii of equivalent spheres for proteins covalently grafted with poly(ethylene glycol) (PEG). The viscosity radius of such PEGylated proteins was found to depend on the molecular weight of the native protein and the total weight of grafted PEG but not on PEG molecular weight, or PEG-to-protein molar grafting ratio. Results suggest grafted PEG's form a dynamic layer over the surface of proteins. The geometry of this layer results in a surface area-to-volume ratio approximately equal to that of a randomly coiled PEG molecule of equivalent total molecular weight. Two simple methods are given to predict the viscosity radius of PEGylated proteins. Both methods accurately predicted (3% absolute error) the viscosity radii of various PEG-proteins produced using three native proteins, alpha-lactalbumin (14.2 kDa MW), beta-lactoglobulin dimer (37.4 kDa MW), and bovine serum albumin (66.7 kDa MW), three PEG reagents (2400, 5600, and 22500 MW), and molar grafting ratios of 0 to 8. Accurate viscosity radius prediction allows calculation of the distribution coefficient, K(av), for PEG-proteins in SEC. The suitability of a given SEC step for the analytical or preparative fractionation of different PEGylated protein mixtures may therefore be assessed mathematically. The methods and results offer insight to several factors related to the production, purification, and uses of PEGylated proteins.     

Solution properties of targacanthin (water-soluble part of gum tragacanth exudate from Astragalus gossypinus)

Solution properties of tragacanthin (the water-soluble part of gum tragacanth) were studied by gel permeation chromatography (GPC) combined with multi-angle light scattering and viscometry at 25 degrees C. Photon correlation spectroscopy was used to determine the hydrodynamic radius. Ultrasonic degradation was applied to obtain biopolymer fractions of different molecular weights. The dependence of intrinsic viscosity [eta] and radius of gyration (s2)z(1/2) on weight average molecular mass M(w) for this biopolymer were found to be [eta] = 9.077 x 10(-5) M(w)(0.87) (dL g(-1)) and (s2)z(1/2) in the range of M(w) from 1.8 x 10(5) to 1.6 x 10(6). The conformational parameters of tragacanthin were calculated to be 1111 nm for molar mass per unit contour length (M(L)), 26 nm for persistence length (q) and 1.87 ratio of R(g)/R(h). It was found that the Smidsr?d parameter B, the empirical stiffness parameter was 0.013, which is lower than that of several polysaccharides indicating the stiff backbone for tragacanthin. The rheological behavior of aqueous solutions of gum tragacanth and its insoluble and soluble fractions (bassorin and tragacanthin, respectively) were studied. For concentrations equal to 1%, at 25 degrees C and in the absence of salt, bassorin solution showed the highest viscosity and shear thinning behaviour. Power law and Williamson models were used to describe the rheological behaviour of bassorin and tragacanthin, respectively. Oscillatory shear experiments showed a gel like structure for the bassorin but for tragacanthin the oscillatory data were as would be expected for semi-dilute to concentrated solution of entangled, random coil polymers. NaCl changed the steady and oscillatory rheological properties of both fractions and in this way the final viscosity of bassorin was even less than tragacanthin. The calculated activation energy for bassorin and tragacanthin indicated a more rapid decrease in viscosity with temperature for tragacanthin. The plot of eta(sp,0) versus C[eta] revealed that the transition from dilute to semi-dilute regime occurs at C*[eta] = 2.82 for tragacanthin.     

Rapid characterization of protein molecular weights and hydrodynamic structures by quasielastic laser-light scattering

Two methods for the characterization of protein molecular weights from their diffusion coefficients are discussed. These measurements can be made quickly and reliably at low concentrations using quasielastic light-scattering techniques. First, an empirical calibration of the diffusion coefficient at infinite dilution of denatured random coils against molecular weight is reported. The second method combines the measurement of D₀ with the intrinsic viscosity [η]. This D₀–[η] relationship proves to be very insensitive to polymers structure or solvent type. The data indicate that the ratio of the hydrodynamic radius measured by viscosity to the hydrodynamic radius measured by diffusion is about 15% smaller than that predicted by theoretical models. The nature of the molecular-weight average obtained for polydisperse systems is defined for a Schulz distribution. These hydrodynamic methods have also been used to demonstrate the presence of chain branching in the glycoprotein ovomucoid. In addition, a method is proposed by which the effective segment length and an excluded volume parameter for random coils may be evaluated for diffusion measurements.     

Nonionic polysaccharides as calibration standards for aqueous size exclusion chromatography

Size exclusion chromatography may be used to determine molecular size or mass of solutes. The validity of the method depends on the correct choice of macromolecular standards used to calibrate the chromatographic column. This calibration is an experimental determination of the relationship between the molecular dimensions and the peak migration velocity of the solute, in practice often presented as a semi-logarithmic plot of log(MW) vs elution volume, but more fundamentally expressed as the dependence of for example, the Stokes radius (R_S), or the viscosity radius (R_η) on the chromatographic partition coefficient, K_SEC. The validity of this calibration rests on the absence of enthalpic interactions between the standards and the stationary phase and the ability to determine the standards' molecular dimensions and/or mass in a nonambiguous way. Nonionic polysaccharides are ideal for this purpose, and furthermore provide an excellent paradigm for studying the role of molecular architecture in the relationship between K_SEC and R_η or R_S.     

Molecular size and shape of beta-connectin, an elastic protein of striated muscle

Connectin is an elastic protein of vertebrate striated muscle, and consists of doublet components, alpha and beta (also called titins 1 and 2). In the present study, beta-connectin isolated in the native state was investigated in order to characterize its molecular size and shape. The molecular weight was approximately 2.1 X 10(6) (SDS gel electrophoresis) or 2.7 X 10(6) (sedimentation equilibrium). The sedimentation coefficient (SO20, w) was 17S in 0.1 M phosphate buffer, pH 7.0. The intrinsic viscosity measured in an Ostwald-type viscometer was 1.8 dl/g. However, the viscosity was greatly dependent on the velocity gradient, and at a very low velocity gradient of 0.0007 s-1, a solution of connectin (0.3 mg/ml) showed a viscosity value of 17,000 cp. Flow birefringence measurements suggested a length distribution ranging from 300 to 450 nm. Electron microscopic observations revealed that connectin is a long flexible filament and the peaks of frequency of length distribution were at 150, 300, 450, and 600 nm. It was tentatively assumed that the connectin molecule is 300-400 nm long and 34-38 nm wide. It is likely that beta-connectin is derived from alpha-connectin, which has an apparent molecular weight of 2.8 X 10(6).     

The use of three ferguson-plot-based calculation methods to determine the molecular mass of proteins as illustrated by molecular mass assessment of rat-plasma carboxylesterases ES-1, ES-2, and ES-14.

The molecular masses of three rat-plasma carboxylesterases (ES-1, ES-2, and ES-14) were estimated by transverse-gradient polyacrylamide gel electrophoresis and subsequent application of Ferguson-plot-based calculation methods. Two electrophoretic buffer systems were used and the data subjected to either weighted or unweighted regression analysis. The Tris-boric acid buffer system produced significantly higher retardation coefficients than the Tris-glycine system. Molecular mass estimates were significantly higher with the Tris-glycine buffer system. Unweighted instead of weighted analysis produced significantly higher molecular mass estimates. Molecular mass estimates also depended on the calculation method, that is, the choice of calibration relationship with molecular size as a function of retardation coefficient. Three commonly used calibration relationships were compared. On the basis of their accuracy, both the weighted log[retardation coefficient] versus log[molecular mass] plot and the square root of retardation coefficient versus molecular radius were found suitable, provided that the Tris-boric acid buffer was used for electrophoresis. Using the former calibration relationship, the molecular masses of rat-plasma ES-1, ES-2, and ES-14 were 55.5, 61.1, and 65.3 kDa, respectively.     

Conformation study on poly(L-tyrosine) in dimethyl formamide by small-angle X-ray scattering

The size and shape parameters of poly(L -tyrosine) in dimethyl formamide were investigated with fractionated samples of different molecular weight by small-angle X-ray scattering. The molecular weight, the radius of gyration of the molecule as a whole, the radius of gyration of the cross section, the mass per unit length, and the length of helix molecule were determined. The molecular conformations proposed by Applequist and Pao for poly(L -tyrosine) were compared with the experimental results obtained. It was concluded that poly(L -tyrosine) exists in a form of the right-handed α-helix in dimethyl formamide.     

A General Method for Modeling Macromolecular Shape in Solution: A Graphical (II-G) Intersection Procedure for Triaxial Ellipsoids

A general method for modeling macromolecular shape in solution is described involving measurements of viscosity, radius of gyration, and the second thermodynamic virial coefficient. The method, which should be relatively straightforward to apply, does not suffer from uniqueness problems, involves shape functions that are independent of hydration, and models the gross conformation of the macromolecule in solution as a general triaxial ellipsoid. The method is illustrated by application to myosin, and the relevance and applicability of ellipsoid modeling to biological structures is discussed.     

Isolation and physical characterization of an exocellular polysaccharide

The physical properties of a polysaccharide produced by the lactic acid bacterium Lactococcus lactis subsp. cremoris strain NIZO B40 were investigated. Separation of the polysaccharide from most low molar mass compounds in the culture broth was performed by filtration processes. Residual proteins and peptides were removed by washing with a mixture of formic acid, ethanol, and water. Gel permeation chromatography (GPC) was used to size fractionate the polysaccharide. Fractions were analyzed by multiangle static light scattering in aqueous 0.10 M NaNO3 solutions from which a number- (Mn) and weight-averaged (Mw) molar mass of (1.47 +/- 0.06).10(3) and (1.62 +/- 0.07).10(3) kg/mol, respectively, were calculated so that Mw/Mn approximately 1.13. The number-averaged radius of gyration was found to be 86 +/- 2 nm. From dynamic light scattering an apparent z-averaged diffusion coefficient was obtained. Upon correcting for the contributions from intramolecular modes by extrapolating to zero wave vector a hydrodynamic radius of 86 +/- 4 nm was calculated. Theoretical models for random coil polymers show that this z-averaged hydrodynamic radius is consistent with the z-averaged radius of gyration, 97 +/- 3 nm, as found with GPC.     

Size determination of cyanobacterial and higher plant photosystem II by gel permeation chromatography, light scattering, and ultracentrifugation

The oxygen-evolving photosystem II core complexes (PSIIcc) from the thermophilic cyanobacterium Thermosynechococcus elongatus (PSIIccTe) and the higher plant Spinacia oleracea (PSIIccSo) have been isolated from the thylakoid membrane by solubilization with n-dodecyl-beta-d-maltoside, purified and characterized by gel permeation chromatography (GPC), dynamic light scattering (DLS), and analytical ultracentrifugation (AUC). DLS suggests that PSIIcc from both organisms exists as a monomer in dilute solution and aggregates with increasing protein concentration. In contrast to DLS, GPC and AUC showed that PSIIcc of both organisms occur as monomers and dimers, and it became clear from our studies that calibration of GPC columns with soluble proteins leads to wrong estimates of the molecular masses of membrane proteins. At a PSIIcc protein concentration of 0.2 mg/mL, molar masses, M, of 756 +/- 18 kDa and 710 +/- 15 kDa for dimeric PSIIccTe and PSIIccSo, respectively, were determined by analytical ultracentrifugation. At very low protein concentrations, at or below 0.05 mg/mL, the dimeric form of PSIIccTe partially dissociates (20-30%) to form monomers. On the basis of these studies 3-dimensional crystals of PSIIccTe were obtained that contain dimers in the asymmetric unit [Zouni, A. et al. (2001) Nature 409, 739-743]. Using synchrotron radiation the crystals diffract to a resolution of 3.8 A, which has been improved recently to 3.2 A [Biesiadka, J., et al. (2004) Phys. Chem. Chem. Phys. 6, 4733-4736].     

Temperature dependence of the yield shear resultant and the plastic viscosity coefficient of erythrocyte membrane. Implications about molecular events during membrane failure.

Structural failure of the erythrocyte membrane in shear deformation occurs when the maximum shear resultant (force/length) exceeds a critical value, the yield shear resultant. When the yield shear resultant is exceeded, the membrane flows with a rate of deformation characterized by the plastic viscosity coefficient. The temperature dependence of the yield shear resultant and the plastic viscosity coefficient have been measured over the temperature range 10-40 degrees C. Over this range the yield shear resultant does not change significantly (+/- 15%), but the plastic viscosity coefficient changes exponentially from a value of 1.3 X 10(-2) surface poise (dyn s/cm) at 10 degrees C to a value of 6.2 X 10(-4) surface poise (SP) at 40 degrees C. The different temperature dependence of these two parameters is not surprising, inasmuch as they characterize different molecular events. The yield shear resultant depends on the number and strength of intermolecular connections within the membrane skeleton, whereas the plastic viscosity depends on the frictional interactions between molecular segments as they move past one another in the flowing surface. From the temperature dependence of the plastic viscosity, a temperature-viscosity coefficient, E, can be calculated: eta p = constant X exp(--E/RT). This quantity (E) is related to the probability that a molecular segment can "jump" to its next location in the flowing network. The temperature-viscosity coefficient for erythrocyte membrane above the elastic limit is calculated to be 18 kcal/mol, which is similar to coefficients for other polymeric materials.     

Ovomucoid domains: preparation and physico-chemical characterization

Four fragments of ovomucoid representing its individual domains and their different combinations were prepared by peptic and cyanogen bromide cleavages of the protein. The fragments corresponding to domains I + II, II + III, I and III of the parent ovomucoid molecule, were found to be homogeneous by gel filtration and polyacrylamide gel electrophoresis in presence and absence of SDS. Various physico-chemical properties of these proteins, such as molecular weight, NH2- and COOH-terminal amino acid residues, sugar content, isoionic pH, specific extinction coefficient, fluorescence emission spectra, intrinsic viscosity, frictional coefficient, Stokes radius, diffusion coefficient and geometrical mean radius were determined. Analysis of the results on trypsin inhibitory activity of ovomucoid and its different fragments suggested that only domain II is involved in the antitryptic activity of the inhibitor. Optical characteristics of these fragments indicate that they are devoid of tryptophan residues. The hydrodynamic properties suggest that intact ovomucoid and two of its fragments (domain I + II and domain II + III) are significantly different from those of typical globular proteins and are asymmetric in nature. However, the shape of the two remaining fragments representing domains I and III of the intact protein appeared to be compact and globular. Furthermore, domain II of ovomucoid has been suggested to primarily contribute towards the apparent asymmetry in the intact protein.     

Molecular conformation of bovine A1 basic protein, a coiling macromolecule in aqueous solution.

Aqueous solutions of bovine A1 protein, the major component of the basic protein fraction of myelin, were studied by small angle X-ray diffraction. The experimentally determined molecular weight, 17,800, is within 3% of that corresponding to the amino acid sequence, 18, 395, and the radius of gyration was found to be 46.3 A. No equivalent scattering particle of uniform electron density could be found which was compatible with all parameters evaluated from the diffraction measurements. The possibility of a coiled shape was therefore investigated using a worm-like chain model. This yielded a contour length of 439 A and a persistence length of 15.7 A. The radius of gyration of this model chain, 47.1 A, is in quite reasonable accord with the experimental value. The latter, after correction for excluded volume effects and finite chain length, yields for the characteristic ratio, ro2/nplp-2, 5.4. This may be compared with the value, 6.1, obtained after applying a correction for finite chain length to the viscosity data given by Tanford et al. for 12 proteins in 6 M guanidine hydrochloride and 0.1 M beta-mercaptoethanol. These two experimental values fall in the expected order, since the 15% glycine content of the A1 protein is considerably higher than the average for other proteins, which is about 8%. The corresponding values predicted from conformational calculations by Miller et al. for random copolymers of the L-alanine-glycine type are 5.9 (18% glycine) and 7.0 (8% glycine). We conclude that the A1 protein exists predominately, if not exclusively, as a random coil in aqueous solution.     

Molecular weight and hydrodynamic properties of a proteinase A inhibitor from baker's yeast.

The molecular weight of the proteinase A inhibitor IA3 from baker's yeast was determined by different methods. From gel-filtration experiments, a molecular weight of 19 000 was calculated for the native inhibitor, while under denaturing conditions a molecular weight of 7400 was found. From electrophoretic experiments with the native protein, a molecular weight of 9000 was calculated. A similar value was obtained from the analytical ultracentrifuge, even at a protein concentration of 12 mg/ml. The diffusion coefficient and the partial specific volume were measured and from these data the frictional ratio and the Stokes radius were calculated. These parameters indicate that the relatively high apparent molecular weight calculated from the gel-filtration experiments is caused by the assymetric shape of the inhibitor molecule rather than by an aggregation of subunits.     

Microfibrillar structure of PGG-glucan in aqueous solution as triple-helix aggregates by small angle x-ray scattering.

The conformation of polysaccharide PGG-Glucan, isolated from yeast cell walls, in aqueous solution was investigated by small angle x-ray scattering (SAXS) and multidetector gel permeation chromatography coupled with postcolumn delivery (GPC/PCD) techniques in comparison with scleroglucan. It was shown that both polysaccharides exhibit a rigid rod-like conformation in aqueous solution by SAXS experiments. The mass per unit length (M/L) and radius (R) of rod cross section of PGG-Glucan were measured to be 6300 daltons/nm and 1.89 nm, while those of scleroglucan are 2300 and 0.83, respectively. Utilizing a GPC/light scattering technique, the average aggregation number of PGG-Glucan is 9, while that of scleroglucan is around 3. From the comparison of the M/L and R of the respective rod cross sections as well as their aggregation number data, it is concluded that PGG-Glucan is composed of triple helices, which tend to aggregate as triplets in solution, whereas scleroglucan is composed of a single triple helix. The aggregation number distribution of PGG-Glucan was found to range from 1 to about 25 determined by GPC/PCD. From the observation of a Debye-Scherrer ring type of peak in the macroscopic scattering cross section of PGG-Glucan by SAXS, the existence of a small amount of ordered clusters of PGG-Glucan can be deduced. The "lattice parameter" of these ordered fasces-like clusters is consistent with the radius of the individual triple-helical rods forming a microfibrillar superstructure. These results indicate that higher aggregated forms of PGG-Glucan containing up to 8 triple helices behave as ordered fasces-like clusters. We conclude that PGG-Glucan is triple-helix aggregates formed by rigid rods stacking together side by side. We propose a molecular structural model for PGG-Glucan conformations.     

Precision assessment of biofluid viscosity measurements using molecular rotors

Blood viscosity changes with many pathologic conditions, but its importance has not been fully investigated because the current methods of measurement are poorly suited for clinical applications. The use of viscosity-sensitive fluorescent molecular rotors to determine fluid viscosity in a nonmechanical manner has been investigated recently, but it is unknown how the precision of the fluorescence-based method compares to established mechanical viscometry. Human blood plasma viscosity was modulated with high-viscosity plasma expanders, dextran, pentastarch, and hetastarch. The samples were divided into a calibration and a test set. The relationship between fluorescence emission and viscosity was established using the calibration set. Viscosity of the test set was determined by fluorescence and by cone-and-plate viscometer, and the precision of both methods compared. Molecular rotor fluorescence intensity showed a power law relationship with solution viscosity. Mechanical measurements deviated from the theoretical viscosity value by less than 7.6%, while fluorescence-based measurements deviated by less than 6%. The average coefficient of variation was 6.9% (mechanical measurement) and 3.4% to 3.8% (fluorescence-based measurement, depending on the molecular rotor used). Fluorescence-based viscometry exhibits comparable precision to mechanical viscometry. Fluorescence viscometry does not apply shear and is therefore more practical for biofluids which have apparent non-Newtonian properties. In addition, fluorescence instrumentation makes very fast serial measurements possible, thus promising new areas of application in laboratory and clinical settings.     

Changes in the Shape and Surface Hydrophobicity of Ovalbumin during Its Transformation to S-Ovalbumin

Intrinsic viscosity, Stokes radius and the hydrophobic coefficient of Keshavarz and Nakai [Biochim. Biophys. Acta, 576, 269 (1979)] were measured to compare the shape and surface hydrophobicity of ovalbumin and s-ovalbumin. Both the intrinsic viscosity and Stokes radius of s- ovalbumin were smaller than those of ovalbumin, which suggests that the configuration of s- ovalbumin became more compact during the ovalbumin-s-ovalbumin transformation. The hydrophobic coefficient of s-ovalbumin was larger than that of ovalbumin, which suggests that the surface hydrophobicity of s-ovalbumin was larger than that of ovalbumin. Further, these properties were measured for ovalbumin samples obtained at various stages of ovalbumin-s-ovalbumin transformation. Changes in the shape and surface hydrophobicity of ovalbumin were not found in the first stage of ovalbumin-s-ovalbumin transformation. They changed rapidly in the last stage of the ovalbumin-s-ovalbumin transformation.     

Persistence length of DNA

In the wormlike chain (Kratky-Porod) model of DNA the stiffness of the chain is determined by the persistence length, a. The persistence length may be evaluated from light-scattering measurements of the molecular weight and the mean-square radius if the samples are not polydisperse or if the polydispersity can be quantitatively determined. The persistence length can also be evaluated with the aid of hydro dynamic theory from measurements of intrinsic viscosity and sedimentation coefficient. Data taken from the literature and from other studies by the authors are examined by these methods. The light-scattering method yields a value of a of 900 ± 200 Å the hydrodynamic data yield 600 ± 100 Å. These values are considerably larger than those obtained by most previous authors.