Measuring the forces between magnetic dipoles 

L.E. Gayetsky and C.L. Caylor

The Physics Teacher 45 348 (2007)

We describe a simple undergraduate lab in which students determine how the force between two magnetic dipoles depends on their separation.  We consider the case where both dipoles are permanent and the case where one of the dipoles is induced by the field of the other (permanent) dipole.  Agreement with theoretically expected results is quite good. 

Sound velocity and elasticity of tetragonal lysozyme crystals by Brillouin spectroscopy

S. Speziale, C.L. Caylor, S. Kriminski, C-S. Zha, R.E. Thorne, and T.S. Duffy

Biophysical Journal 85 3202 (2003)

Quasilongitudinal sound velocities and the second-order elastic moduli of tetragonal hen egg-white lysozyme crystals were determined as a function of relative humidity (RH) by Brillouin scattering. In hydrated crystals the measured sound velocities in the [110] plane vary between 2.12 ± 0.03 km/s along the [001] direction and 2.31 ± 0.08 km/s along the [110] direction. Dehydration from 98% to 67% RH increases the sound velocities and decreases the velocity anisotropy in (110) from 8.2% to 2.0%. A discontinuity in velocity and an inversion of the anisotropy is observed with increasing dehydration providing support for the existence of a structural transition below 88% RH. Brillouin linewidths can be described by a mechanical model in which the phonon is coupled to a relaxation mode of hydration water with a single relaxation time of 55 ± 5 ps. At equilibrium hydration (98% RH) the longitudinal moduli C11 + C12 + 2C66 = 12.81 ± 0.08 GPa, C11 = 5.49 ± 0.03 GPa, and C33 = 5.48 ± 0.05 GPa were directly determined. Inversion of the measured sound velocities in the [110] plane constrains the combination C44 + 1/2 C13 to 2.99 ± 0.05 GPa. Further constraints on the elastic tensor are obtained by combining the Brillouin quasilongitudinal results with axial compressibilities determined from high-pressure x-ray diffraction. We constrain the adiabatic bulk modulus to the range 2.7–5.3 GPa.

Flash-cooling and annealing of protein crystals

S. Kriminski, C. L. Caylor, M. C. Nonato, K. D. Finkelstein, and R. E. Thorne

Acta Crystallographica D 58 459 (2002)

Flash-cooling and annealing of macromolecular crystals have been investigated using in situ X-ray imaging, diffraction-peak lineshape measurements and conventional crystallographic diffraction. The dominant mechanisms by which flash-cooling creates disorder are suggested and a fixed-temperature annealing protocol for reducing this disorder is demonstrated that should be more reliable and flexible than existing protocols. Flash-cooling tetragonal lysozyme crystals degrades diffraction resolution and broadens the distributions of lattice orientations (mosaicity) and lattice spacings. The diffraction resolution strongly correlates with the width of the lattice-spacing distribution. Annealing at fixed temperatures of 253 and 233 K consistently reduces the lattice-spacing spread and improves the resolution for annealing times up to similar to 30 s. X-ray images show that this improvement arises from the formation of well ordered domains with characteristic sizes >10 mm and narrower mosaicities than the crystal as a whole. Flash-cooled triclinic crystals of lysozyme, which have a smaller water content than the tetragonal form, diffract to higher resolution with smaller mosaicities and exhibit pronounced ordered domain structure even before annealing. It is suggested that differential thermal expansion of the protein lattice and solvent may be the primary cause of flash-cooling-induced disorder. Mechanisms by which annealing at T << 273 K reduce this disorder are discussed.

Measuring the elastic properties of protein crystals by Brillouin scattering

C. L. Caylor, S. Speziale, S. Kriminski, T. Duffy, C. S. Zha, and R. E. Thorne

Journal of Crystal Growth 232 498 (2001)

We report preliminary measurements of the elastic properties of tetragonal lysozyme crystals using Brillouin scattering. This microscopic, non-contact technique is ideally suited for study of fragile, optically transparent macromolecular crystals. Brillouin scattering should allow much more complete characterization of crystal elasticity, and provide a novel probe of intermolecular interactions, conformation changes, and defect formation.

Dynamic responses of tetragonal lysozyme crystals to changes in relative humidity:  implications for post-growth crystal treatments

I. Dobrianov, S. Kriminski, C. L. Caylor, S. G. Lemay, C. Kimmer, A. Kisselev, K. D. Finkelstein, and R. E. Thorne

Acta Crystallographica D 57 61 (2001)

The dynamic response of tetragonal lysozyme crystals to dehydration has been characterized in situ using a combination of X-ray topography, high-resolution diffraction lineshape measurements and conventional crystallographic diffraction. For dehydration from 98% relative humidity (r.h.) to above 89%, mosaicity and diffraction resolution show little change and X-ray topographs remain featureless. Lattice constants decrease rapidly but the lattice-constant distribution within the crystal remains very narrow, indicating that water concentration gradients remain very small. Near 88% r.h., the c-axis lattice parameter decreases abruptly, the steady-state mosaicity and diffraction resolution degrade sharply and topographs develop extensive contrast. This transformation exhibits metastability and hysteresis. At fixed r.h. < 88% it is irreversible, but the original order can be almost completely restored by rehydration. These results suggest that this transformation is a first-order structural transition involving an abrupt loss of crystal water. The front between transformed and untransformed regions may propagate inward from the crystal surface and the resulting stresses along the front may degrade mosaicity. Differences in crystal size, shape and initial perfection may produce the observed variations in degradation timescale. Consequently, the success of more general post-growth treatments may often involve identifying procedures that either avoid lattice transitions, minimize disorder created during such transitions or maintain the lattice in an ordered metastable state.

Evidence for dipole surface orientational order at critical interfaces

A. Mukhopadhyay, C. L. Caylor, and B.M. Law

Physical Review E 61 R1036 (2000)

At the critical interface of dipolar systems, theory predicts that the amplitude of the surface orientational order α2(z) ~ m*4d2v(z)/dz2, where m* is a reduced dipole moment and v(z) is the local composition z within the interface.  We find quantitative agreement with these predictions for two different critical binary liquid mixtures composed of a highly polar and a nonpolar component.

Macromolecular impurities and disorder in protein crystals

C.L. Caylor, I. Dobrianov, S.G. Lemay, C. Kimmer, S. Kriminski, K.D. Finkelstein, W. Zipfel, W.W. Webb, B.R. Thomas, A.A. Chernov, and R.E. Thorne

Proteins: Structure, Function, and Genetics 36 270 (1999)

The mechanisms by which macromolecular impurities degrade the diffraction properties of protein crystals have been investigated using X-ray topography, high-resolution diffraction line shape measurements, crystallographic data collection, chemical analysis, and two-photon excitation fluorescence microscopy. Hen egg-white lysozyme crystals grown from solutions containing a structurally unrelated protein (ovotransferrin) and a related protein (turkey egg-white lysozyme) can exhibit significantly broadened mosaicity due to formation of cracks and dislocations but have overall B factors and diffraction resolutions comparable to those of crystals grown from uncontaminated lysozyme. Direct fluorescence imaging of the three-dimensional impurity distribution shows that impurities incorporate with different densities in sectors formed by growth on different crystal faces, and that impurity densities in the crystal core and along boundaries between growth sectors can be much larger than in other parts of the crystal. These nonuniformities create stresses that drive formation of the defects responsible for the mosaic broadening. Our results provide a rationale for the use of seeding to obtain high-quality crystals from heavily contaminated solutions and have implications for the use of crystallization for protein purification.

Two-photon fluorescence imaging of impurity distributions in protein crystals

C.L. Caylor, I. Dobrianov, C. Kimmer, R.E. Thorne, W. Zipfel, and W.W. Webb

Physical Review E 59 3831 (1999)

Macromolecular impurities present in solution have profound effects on the growth and quality of protein crystals used for x-ray structure determinations.  We have imaged the three-dimensional distribution of ovotransferrin impurities in crystals of the protein hen egg white lysozyme (HEWL) using two-photon excitation fluorescence microscopy.  Impurity concentrations differ between the two types of growth sectors present in tetragonal HEWL crystals and impurities preferentially incorporate along the boundaries between growth sectors.  Cracked crystals show large impurity-rich cores that are not observed in uncracked crystals.  These nonuniform impurity distributions provide insight into how and why impurities affect crystal quality.  Our results have implications for crystal growth and for protein purification.

X-ray diffraction studies of protein crystal disorder

I. Dobrianov, C. Caylor, S.G. Lemay, K.D. Finkelstein, and R.E. Thorne

Journal of Crystal Growth 196 511 (1999)

Protein crystals contain many kinds of disorder, but only a small fraction of these are likely to be important in limiting the diffraction properties of interest to crystallographers.  X-ray topography, high-angular-resolution reciprocal space measurements, and standard crystallographic data collection have been used to probe three factors that may produce diffraction-limiting disorder:  (1) solution variations during crystal growth, (2) macromolecular impurities, and (3) post-growth crystal treatments.  Variations in solution conditions that occur in widely used growth methods may lead to variations in equilibrium protein conformation and crystal packing as a crystal grows, and these may induce appreciable disorder for sensitive proteins.  Tetragonal lysozyme crystals subjected to abrupt changes in temperature, pH, or salt concentration during growth show increased disorder, consistent with this mechanism.  Macromolecular impurities can have profound effects on protein crystal quality.  A combination of diffraction measurements provides insight into the mechanisms by which particular impurities create disorder, and this insight leads to a simple approach for reducing this disorder.  Substantial degradation of diffraction properties due to conformation and lattice constant changes can occur during post-growth crystal treatments such as heavy-atom compound and drug binding.  Measurements of the time evolution of crystal disorder during controlled crystal dehydration--a simple model for such treatments--suggest that structural metastability conferred by the constraints of the crystal lattice plays an important role in determining the extent to which the diffraction properties degrade.

Critical interface of an ionic Ising mixture

C. L. Caylor, B. M. Law, P. Senanayake, V. L. Kuzmin, V. P. Romanov, and S. Wiegand

Physical Review E 56 4441 (1997)

Ellipsometric measurements at the liquid-liquid interface of a critical ionic Ising mixture yield a decrease in the ellipticity ρ̅ as the reduced temperature t is decreased (for t > 0.002) in contrast to a tβ-ν power-law divergence found for nonionic Ising mixtures. From this surprising result we infer the existence of an anisotropic interface. A model of such an interface is used to calculate theoretical ρ̅ data, which capture some of the characteristics of the experimental results.

The scaling behavior of critical adsorption in critical polymer solutions

C. L. Caylor and B. M. Law

Journal of Chemical Physics 104 2070 (1996)

The critical adsorption ellipsometric measurements of five solutions of polystyrene in cyclohexane for different polystyrene molecular weights collapse to a single universal curve when scaled as a function of nBξ /λ , where nB is the polymer solution refractive index, ξ = ξ 0N nt–ν is the correlation length, and λ is the wavelength of incident light in vacuum. From this universal feature we deduce the value of the polymerization critical exponent n = 0.258 ± 0.017. We consider both the volume fraction order parameter (φ) and a symmetrized order parameter s) together with both the renormalization group (RG) and Monte Carlo (MC) simulation forms for the surface scaling function P + (x). The symmetrized order parameter gives significantly better agreement with experiment than the volume fraction order parameter. The combination of RG and ψs provides better agreement with experiment than does the combination of MC and ψs.

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