Engineering topics
Publications and source records attributed to Chernov, A. A..
High precision interferometric studies of step bunching on KDP crystal surface growing from solution moving at rates up to 1 d s . It is shown that the bunch height is limited as the bunch propagates over the surface. An hypothesis is put forward describing why the bunch height decreases as the solution flow rate increases.
Classical Burton-Cabrera-Frank theory presumes that thermal fluctuations are so fast that at any time density of kinks on a step is comparable with the reciprocal intermolecular distance, so that the step rate is about isotropic within the crystal plane. Such azimuthal isotropy is, however, often not the case: Kink density may be much lower. In particular, it was recently found on the (010) face of orthorhombic lysozyme that interkink distance may exceed 500-600 intermolecular distances. Under such conditions, Gibbs-Thomson law (GTL) may not be applicable: On a straight step segment between two corners, communication between the comers occurs exclusively by kink exchange. Annihilation between kinks of opposite sign generated at the comers results in the grain in step energy entering GTL. If the step segment length l much greater than D/v, where D and v are the kink diffusivity and propagation rate, respectively, the opposite kinks have practically no chance to annihilate and GTL is not applicable. The opposite condition of the GTL applicability, l much less than D/v, is equivalent to the requirement that relative supersaturation Delta(sub mu)/kT much less than alpha/l, where alpha is molecular size. Thus, GTL may be applied to a segment of 10(exp 3)alpha approx. 3 x 10(exp -5)cm approx 0.3 micron only if supersaturation is less than 0.1%, while practically used driving forces for crystallization are much larger. Relationships alternative to the GTL for different, but low, kink density have been discussed. They confirm experimental evidences that the Burton-Cabrera-Frank theory of spiral growth is growth rates twice as low as compared to the observed figures. Also, application of GTL results in unrealistic step energy while suggested kinetic law give reasonable figures.
Imagine a sequence of equidistant steps parallel to one another on a crystal face growing from solution. Steps may be one or part of a lattice spacing high. With such ideal morphology, the most perfect material is expected to be produced. Sometimes this happens. Much more often, however, steps form bunches, acquire wavy shapes and interlace. With time, these spontaneous perturbations may be increased in amplitude, i.e. the stepped surface becomes morphologically unstable. Interferometric studies of Y.G. Kuznetsov, L.N. Rashkovich, P.G. Vekilov and N.A. Booth and the author demonstrated that the step bunching depends at least on direction and rate of solution flow over the interface, supersaturation and presence of impurities. In particular, if solution and step flow are parallel to one another, the steps convene into bunches. If these flows are antiparallel, the bunches disappear. As the step train propagates, the overall bunch height often increases infinitely. However, we have found recently that if the flow rate is large enough, (approximately 1 meter per second), the bunch height may be limited. All these phenomena come from interaction between steps. The interaction mechanisms are still not fully understood. I plan to overview major approaches to the still unresolved problem on how these dissipative structures on growing crystal face appear and evolve.
Canavalin crystals grown from material purified and not purified by High Performance Liquid Chromatography were studied by atomic force microscopy and x-ray diffraction. After purification, resolution was improved from 2.55Angstroms to 2.22Angstroms and jagged isotropic spiral steps transformed into regular, well polygonized steps.
This is an overview of basic problems of crystal growth kinetics controlled by processes on the crystal interface with solution and melt. Included, also, are results on fundamental issues concerning morphological stability of crystal-solution interface that engage both interface kinetics and mass transport by diffusion and convection.
The crystals are built of molecules of protein, nucleic acid and their complexes, like viruses, approx. 5x10(exp 3)+ 3x10(exp 6) Da in weight and 2 + 20 nm in effective diameter. This size strongly exceeds action range of molecular forces and makes a big difference with inorganic crystals. Intermolecular contacts form patches on the biomacromolecular surface. Each patch may occupy only a small percent of the whole surface and vary from polymorph to polymorph of the same protein. Thus, under different conditions (pH, solution chemistry, temperature, any area on the macromolecular surface may form a contact. The crystal Young moduli, E approx. equals 0.1 + 0.5 GPa are more than 10 times lower than that of inorganics and the biomolecules themselves. Water within biocrystals (30-70%) is unable to flow unless typical deformation time is longer than approx. 10(exp -5)s. This explains the discrepancy between light scattering and static measurements of E. Nucleation and Growth requires typically concentrations exceeding the equilibrium ones up to 100 times - because of the new size scale results in 10 - 10(exp 3) times lower kinetic coefficients than that needed for inorganic solution growth. All phenomena observed in the latter occur with protein crystallization and are even better studied by AFM. Crystals are typically facetted. Among unexpected findings of general significance are - net molecular exchange flux at kinks is much lower than that expected from supersaturation, steps with low (< approx. 10(exp -2)) kink density at steps follow Gibbs-Thomson law only at very low supersaturations, step segment growth rate may be independent of step energy. Crystal perfection is a must of biocrystallization to achieve the major goal to find 3-D atomic structure of biomacromolecules by x-ray diffraction. Poor diffraction resolution (> 3Angstrom) makes crystallization a bottleneck for structural biology. All defects typical of small molecule crystals are found in biocrystals, but the defects responsible for poor resolution are not identified. Conformational changes are one of them. Biocrystallization in microgravity reportedly results in 20% cases of better crystals. The mechanism of how lack of convection can do this is still not clear. Lower supersaturation, self-purification &om preferentially trapped homologous impurities and step bunching are viable hypotheses.
Characterization of defects and/or disorder in biological macromolecular crystals presents much greater challenges than in conventional small-molecule crystals. The lack of sufficient contrast of defects is often a limiting factor in x-ray diffraction topography of protein crystals. This has seriously hampered efforts to understand mechanisms and origins of formation of imperfections, and the role of defects as essential entities in the bulk of macromolecular crystals. In this report, we employ a phase sensitive x-ray diffraction imaging approach for augmenting the contrast of defects in protein crystals.
The dynamic coupling between mass transport and incorporation of growth units into the surface of a crystal growing from solution in microgravity is used to derive quantitative information on the crystal growth kinetics. To this end, new procedures for experiment preparation, interferometric data processing and model fitting have been developed. The use of experimental data from the bulk diffusive maw transport together with a model for steady state stagnant crystal growth allows the detailed quantitative understanding of the kinetics of both the concentration depletion zone around the crystal and the growth of the crystal interface. The protein crystal used in the experiment is shown to be growing in the mixed kinetic regime (0.2 x 10(exp -6) centimeters per second less than beta R/D less than 0.9 x 10(exp -6) centimeters per second).
Surface X-ray diffraction measurements were performed on (111) growth faces of crystals of the Cellular iron-storage protein horse spleen ferritin. Crystal Trunkation Rods (CTR) were measured. A fit of the measured profile of the CTR revealed a surface roughness of 48 +/- 4.5 A and a top layer spacing contraction of 3.9 +/- 1.5%. In addition to the peak from the CTR, the rocking curves of the crystals displayed unexpected extra peaks. Multiple-scattering is demonstrated to account for them. Future applications of the method could allow the exploration of hydration effects on the growth of protein crystals.
This paper covers review of recent research on protein crystal properties, nucleation, growth and perfection. Mechanical properties of crystals built of molecules strongly exceeding the range of molecular forces are very different from conventional ones. Similar scaling is responsible for specificity of phase equilibrium for macromolecular systems of which thermodynamics is discussed. Nucleation and growth peculiarity and similarity in protein solutions as compared to inorganic solutions is addressed. Hypotheses on why and when microgravity (lack of convection) conditions may result in more perfect crystals are discussed.
This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.
No abstract available
Conventional x-ray diffraction topography is currently used to map defects in the bulk of protein crystals, but the lack of sufficient contrast is frequently a limiting factor. We experimentally demonstrate that this barrier can be circumvented using a method that combines phase sensitive and diffraction imaging principles. Details of defects revealed in tetragonal lysozyme and cubic ferritin crystals are presented and discussed. The approach enabling the detection of the phase changes of diffracted x rays should prove to be useful in the study of defect structures in a broad range of biological macromolecular crystals.
Double-axis multiple-crystal X-ray topography, rocking-curve measurements and triple-axis reciprocal-space mapping have been combined to characterize protein crystals using a laboratory source. Crystals of lysozyme and lysozyme crystals doped with acetylated lysozyme impurities were examined. It was shown that the incorporation of acetylated lysozyme into crystals of lysozyme induces mosaic domains that are responsible for the broadening and/or splitting of rocking curves and diffraction-space maps along the direction normal to the reciprocal-lattice vector, while the overall elastic lattice strain of the impurity-doped crystals does not appear to be appreciable in high angular resolution reciprocal-space maps. Multiple-crystal monochromatic X-ray topography, which is highly sensitive to lattice distortions, was used to reveal the spatial distribution of mosaic domains in crystals which correlates with the diffraction features in reciprocal space. Discussions of the influence of acetylated lysozyme on crystal perfection are given in terms of our observations.
Colorless transparent apoferritin (Mr = 450KDa) crystals have been grown from gel with Cd(2+) as precipitant in the presence of reddish brown-colored ferritin dimers (Mr = 900KDa). In agreement with our previous measurements, showing preferential trapping of dimers (distribution coefficient K = 4), the apoferritin crystals become strongly colored while the gel solution around them became nearly colorless. The depth of the depletion with respect to the colored dimer impurity allowed us to visualize the impurity depletion zone. Depletion with respect to impurity as compared to the crystallizing protein is discussed.
Hen egg white lysozyme (HEWL) was acetylated to modify molecular charge keeping the molecular size and weight nearly constant. Two derivatives, A and B, more and less acetylated, respectively, were obtained, separated, purified and added to the solution from which crystals of tetragonal HEWL crystals were grown. Amounts of the A or B impurities added were 0.76, 0.38 and 0.1 milligram per millimeter while HEWL concentration were 20, 30 and 40 milligram per milliliter. The crystals grown in 18 experiments for each impurity were dissolved and quantities of A or B additives in these crystals were analyzed by cation exchange high performance liquid chromatography. All the data for each set of 18 samples with the different impurity and regular HEWL concentrations is well described by one distribution coefficient K = 2.15 plus or minus 0.13 for A and K = 3.42 plus or minus 0.25 for B. The observed independence of the distribution coefficient on both the impurity concentration and supersaturation is explained by the dilution model described in this paper. It shows that impurity adsorption and incorporation rate is proportional to the impurity concentration and that the growth rate is proportional to the crystallizing protein in solution. With the kinetic coefficient for crystallization, beta = 5.10(exp -7) centimeters per second, the frequency at which an impurity molecule near the growing interface irreversibly joins a molecular site on the crystal was found to be 3 1 per second, much higher than the average frequency for crystal molecules. For best quality protein crystals it is better to have low microheterogeneous protein impurity concentration and high supers aturation.
No abstract available