Finite-Amplitude Instability in Growth Step Trains with Overlapping Step Supply Fields
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Engineering topics
Publications and source records attributed to Rosenberger, F..
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We have experimentally studied the effects of solution flow on the growth kinetics of the protein lysozyme. To this end, we have expanded our interferometry setup by a novel crystallization cell and solution recirculation system. This combination permits monitoring of interface morphology and kinetics with a depth resolution of 200 A at bulk flow rates of up to 2000 micron/s. Particular attention was paid to the prevention of protein denaturation that is often associated with the pumping of protein solutions. We found that at bulk flow rates it less than 250 microns/s the average growth rate and step velocity, R(sub avg) and upsilon(sub avg) increase with increasing it. This can be quantitatively understood in terms of the enhanced, convective solute supply to the interface. With high-purity solutions, it u greater than 250 microns/s lead to growth deceleration, and, at low supersaturations sigma, to growth cessation. When solutions containing approx. 1% of other protein impurities were used, growth deceleration occurred at any u greater than 0 and cessation in the low sigma experiments was reached at about half the it causing cessation with pure solution. The flow-induced changes in R(sub avg) and upsilon(sub avg) including growth cessation, were reversible and reproducible, independent of the direction of the u-changes and solution purity. Hence, we attribute the deceleration to the convection-enhanced supply of impurities to the interface, which at higher flow rates overpowers the effects of enhanced interfacial solute concentration. Most importantly, we found that convective transport leads to a significant reduction in kinetics fluctuations, in agreement with our earlier expectations for the lysozyme system. This supports our hypothesis that these long-term fluctuations represent an intrinsic response feature of the coupled bulk transport-interfacial kinetics system in the mixed growth control regime.
Hen egg-white lysozyme (HEWL) is widely used as a model protein, although its purity has not been adequately characterized by modern biochemical techniques. We have identified and quantified the protein heterogeneities in three commercial HEWL preparations by sodium dodecyl sulfate polyacrylamide gel electrophoresis with enhanced silver staining, reversed-phase fast protein liquid chromatography (FPLC) and immunoblotting with comparison to authentic protein standards. Depending on the source, the contaminating proteins totalled 1-6%(w/w) and consisted of ovotransferrin, ovalbumin, HEWL dimers, and polypeptides with approximate M(sub r) of 39 and 18 kDa. Furthermore, we have obtained gram quantities of electrophoretically homogeneous [> 99.9%(w/w)] HEWL by single-step semi-preparative scale cation-exchange FPLC with a yield of about 50%. Parallel studies of crystal growth kinetics, salt repartitioning and crystal perfection with this highly purified material showed fourfold increases in the growth-step velocities and significant enhancement in the structural homogeneity of HEWL crystals.
Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.
In earlier sodium dodecylsulfate polyacylamide gel electrophoresis (SDS-PAGE) studies it has been found that commonly utilized commercial hen egg-white lysozyme (HEWL) preparations contained 0.2-0.4 mol% covalently bound dimers. Here it is shown, using high-performance capillary electrophoresis (HPCE), that HEWL contains, in addition, two differently charged monomers in comparable amounts. To explore the origin of these microheterogeneous contaminants, purified HEWL (PHEWL) has been oxidized with hydrogen peroxide (0.0026-0.88 M) at various pH levels between 4.5 and 12.0. Optical densitometry of oxidized PHEWL (OHEWL) bands in SDS PAGE gels shows that hydrogen peroxide at 0.88 M in acetate buffer pH 4.5 increased the amount of dimers about sixfold over that in commercial HEWL. OHEWL had, in addition to one of the two monomer forms found in HEWL and PHEWL, three other differently charged monomer forms, each of them representing about 25% of the preparation. SDS-PAGE analysis of OHEWL yielded two closely spaced dimer bands with M(sub r) = 28 000 and 27 500. In addition, larger HEWL oligomers with M, = 1.7 million and 320 000 were detected by gel-filtration fast protein liquid chromatography with multiangle laser light scattering detection. Non-dissociating PAGE in large pore size gels at pH 4.5 confirmed the presence of these large oligomers in HEWL and OHEWL. Increased microheterogeneity resulted in substantial effects on crystal growth and nucleation rate. On addition of 10 microgram(exp -1) mg ml(exp -1) OHEWL to 32 mg ml(exp -1) HEWL crystallizing solutions, both the number and size of forming crystals decreased roughly proportionally to the concentration of the added microheterogeneity. The same effect was observed in HEWL solutions on addition of 0.03-9,3 M Hydrogen peroxide. Repartioning of the dimer during crystallzation aat various temperatures between 277 and 293 K was analyzed by SDS-PAGE. The crystals contained <= 25 % weight by volume of the oligomers in the solution, with no apparent temperature dependence of the repartioning.
Recently. much progress has been made in understanding the nucleation and crystallization of globular proteins, including the formation of compositional and structural crystal defects, Insight into the interactions of (screened) protein macro-ions in solution, obtained from light scattering, small angle X-ray scattering and osmotic pressure studies. can guide the search for crystallization conditions. These studies show that the nucleation of globular proteins is governed by the same principles as that of small molecules. However, failure to account for direct and indirect (hydrodynamic) protein interactions in the solutions results in unrealistic aggregation scenarios. Microscopic studies of numerous proteins reveal that crystals grow by the attachment of growth units through the same layer-spreading mechanisms as inorganic crystals. Investigations of the growth kinetics of hen-egg-white lysozyme (HEWL) reveal non-steady behavior under steady external conditions. Long-term variations in growth rates are due to changes in step-originating dislocation groups. Fluctuations on a shorter timescale reflect the non-linear dynamics of layer growth that results from the interplay between interfacial kinetics and bulk transport. Systematic gel electrophoretic analyses suggest that most HEWL crystallization studies have been performed with material containing other proteins at percent levels. Yet, sub-percent levels of protein impurities impede growth step propagation and play a role in the formation of structural/compositional inhomogeneities. In crystal growth from highly purified HEWL solutions, however, such inhomogeneities are much weaker and form only in response to unusually large changes in growth conditions. Equally important for connecting growth conditions to crystal perfection and diffraction resolution are recent advances in structural characterization through high-resolution Bragg reflection profiling and X-ray topography.
Short-duration low-gravity experiments can be conducted either in drop tubes and drop towers, or on sounding rockets and aircraft on ballistic trajectories. While these facilities offer more frequent flight opportunities and higher cost effectiveness than orbiting spacecraft, their relatively short low-gravity times are often perceived as limiting their utility to only a narrow range of applications and research areas. In this review it is shown, based on scaling laws for diffusive transport of momentum, species and heat, radiative heat transfer and capillarity-driven motion, that with proper consideration of the characteristic length scales, a host of phenomena can be meaningfully investigated during a few seconds. This usefulness of short-duration low-gravity facilities is illustrated with numerous results of recent studies of solidification, combustion, transport in multiphase systems, statics and dynamics of liquid surfaces, magnetic Benard convection, fluid management, transport properties and the graviperception in cells.
The growth and dissolution kinetics of lysozyme in a 25 ml solution bridge inside a closed growth cell was investigated. It was found that, under all growth conditions, the growth habit forming (110) and (101) faces grew through layer spreading with different growth rate dependence on supersaturation/temperature. On the other hand, (100) faces which formed only at low temperatures underwent a thermal roughening transition around 12 C.
Recently, nonaxisymmetric convection in vertical directional solidification experiments has been observed. It has been suggested that the asymmetry is due to lack of azimuthal symmetry in imposed temperature and that the flow asymmetry will decrease with increasing velocities. Motivated by these observations, we have examined the consequences of deviations from axisymmetric wall temperature conditions in a vertical differentially heated cylinder. We show that the degree of flow asymmetry depends on the ratio, between the amplitudes of the maximum aximuthal and vertical temperature differences, and that for a fixed value of this ratio the flow asymmetry increases with increasing flow velocity (Rayleigh number).
The effects of steady and time-dependent residual accelerations on representative melt and solution crystal growth systems have been investigated using numerical models. For the melt growth system, it was found that the lateral nonuniformity in crystal composition, depending on the particular operating conditions, can be very sensitive to the orientation of the steady component of the residual gravity vector down to 10 to the -6th g. Oscillatory residual accelerations (g-jitter) were found to lead to transients in the dopant distribution. For the solution growth, longtime simulations showed that at 10 to the -5th g, and the cooling rates used in Spacelab 3 experiments, diffusive transport dominates only in the beginning. Convective transport becomes increasingly significant after 3 to 5 hours, depending on the orientation of the crystal in the residual gravity field.
Transport and interface kinetic concepts for the design and control of inorganic crystal growth experiments are reviewed, and their applications and limitations in protein crystal growth are considered. It is suggested that the interfacial concentration gradients are steeper for faster crystallization, and that the interfacial concentration distributions for the protein and the precipitant can differ significantly. Results show that uniformity in crystal composition and steady-state conditions in growth kinetics are favored by larger sample size, since surface-tension gradients drive strong in microgravity experiments and in small samples on earth.
Experimental results and numerical data on the flow characteristics of core-driven and boundary-layer-driven regimes (CDRs) and (BLDRs) are compared to two-dimensional solutions for heated convective flow in the vertical midplane of a horizontal cylinder. The data were obtained from laser Doppler velocimetry (LDA) measurements and from three-dimensional numerical solutions. It is shown that the approximate solutions gave the correct Rayleigh-number-dependences and distributions for the velocities in the CDR and BLDR regimes. However, the transition between the CDR and the BLDR, as well as the magnitude of the distribution of velocity components, were found to be dependent on the type of two-dimensional approximation selected. In the case of CDR, core velocities were overestimated by as much as 30 percent by the two-dimensional approximations; and in the case of BLDR, the core velocities were overestimated by 40-50 percent as compared to the measured velocities. A schematic illustration of the flow patterns in the cylinder is provided.
A fundamental understanding of the conditions under which crystals can retain morphological stability, i.e., shape stability of the advancing interface, during growth from vapors was studied. Morphological stability (MS) is a necessary condition for the growth of homogeneous single crystals required for numerous device applications. For crystallization from melts, the MS concepts are well developed and are essentially based on heat and mass transfer conditions about the advancing interface. For crystallization from vapors, the MS requirements are more complex and not well understood. The added complexity arises from the fact that anisotropies in interfacial kinetics are typically stronger in crystallization from vapors than from melts. These pronounced anisotropies root in the distinctly lower atomic roughness of most vapor-solid interfaces.
The present investigation is concerned with an experimentally guided approach to the estimation of Nusselt numbers (Nu) at high Rayleigh numbers (Ra) for a cylinder with an adiabatic side wall. The Rayleigh number dependence of the Nusselt number for a horizontal cylinder with an adiabatic wall is presented in a graph. The obtained data are compared with results reported by Shih (1981). Shih has extended a three-term expansion for velocity and temperature distributions reported by Bejan and Tien (1978).
The enhancement of vapor transport across horizontal and inclined rectangular (two-dimensional) enclosures by expansive convection is studied numerically for a range in Grashof number that extends up to boundary layer flow. Comparison is made with predictions of the simplifying model and resulting analytical treatment of Klosse and Ullersma (1973) for various aspect ratios of the enclosure. The influence of varying Schmidt and Prandtl numbers is investigated. Solutions for interfacial (growth) flux and temperature distributions are given, showing practically important nonuniformities.
Theoretical and experimental work on heat and mass transport in crystal growth by closed ampoule vapor transport is reviewed. It is shown that double-diffusive phenomena, together with the three-dimensional boundary conditions of real systems lead to a complexity of the transport modes that are beyond the reach of the simplifying models currently used in the materials preparation literature. Consequences of the new insights for earth-bound vapor transport and for optimization of future space experiments are discussed.
Integrated circuit (IC) flip-flop resolving time parameters are measured by wafer probing, without need of dicing or bonding, throught the incorporation of test structures on an IC together with the flip-flop to be measured. Several delays that are fabricated as part of the test circuit, including a voltage-controlled delay with a resolution of a few picosecs, are calibrated as part of the test procedure by integrating them into, and out of, the delay path of a ring oscillator. Each of the delay values is calculated by subtracting the period of the ring oscillator with the delay omitted from the period with the delay included. The delay measurement technique is sufficiently general for other applications. The technique is illustrated for the case of the flip-flop parameters of a 5-micron feature size NMOS circuit.