An accurate numerical model for calculating the equilibration rate of a hanging-drop experiment

Diller, David J.; Hól, Wim G. J.

doi:10.1107/s0907444998014589

Cited by 13 publications

(16 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of these, save possibly the last, are experimentally optimized (solution composition) or controllable parameters. Diller & Hol (1999) developed a numerical model for the vapor diffusion process, the results of which are in close agreement with the available experimental data to that time. The model showed that there was an approximately linear dependence of the equilibration time with the droplet to reservoir distance and upon the initial droplet size.…”

Section: Introductionsupporting

confidence: 71%

“…Note that the equilibration rates at best are only approximately double for an order of magnitude change in the volume ratio. From the model of Diller & Hol (1999), a 10 fold increase in droplet volume results in an approximately 5 fold increase in the equilibration time. B decreasing the reservoir volume we effectively move it further from the droplet, which again would increase the equilibration time.…”

Section: Resultsmentioning

confidence: 99%

“…Previous researchers studied the effects of varying the crystallization droplet size while keeping the reservoir solution volume constant. It was experimentally and theoretically shown that equilibration rates decrease approximately linearly with a decrease in the drop volume (Mikol et al, 1990;Diller & Hol, 1999). A qualitative survey of recent crystallization reports shows that most initial crystallization droplet volumes are in the 2 -4 µl range, being composed of 50 % each of macromolecule and reservoir solutions.…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Vapor diffusion, nucleation rates and the reservoir to crystallization volume ratio

Forsythe

Maxwell²,

Pusey³

2002

Acta Crystallogr D Biol Cryst

View full text Add to dashboard Cite

In a classical vapor diffusion crystallization, the protein solution is mixed in a 1:1 ratio with the reservoir solution, containing one or more precipitant species, after which the two are placed in an enclosed chamber. As the vapor pressure is lower for the reservoir solution, due to its higher solute concentration, there is a net transfer of water through the vapor phase from the protein droplet to the reservoir. In theory, the initial conditions in the droplet are such that the protein is in either a metastable or undersaturated state with respect to crystal nucleation. The loss of water serves to both concentrate the protein and the precipitant concentrations within the drop, bringing the protein past the metastable point to nucleation. The equilibration rate is a function of the precipitant(s) used, their concentration, the temperature, the distance between the two surfaces, and the droplet to reservoir volume ratio. For a given reservoir volume smaller droplets equilibrate faster, the rate being inversely linear with the droplet volume. In attempts to maximize the number of crystallization trials, and as crystals in the 100 -200 µm size range are sufficient, it has currently become standard practice to use starting droplet volumes of 2 -4 µl, with reservoir volumes typically in the 200 to 500 µl range. The equilibration rates are maximized, and for most common salt concentrations and higher concentrations of polyethylene glycol (PEG) and 2-methyl-2,4-pentanediol (MPD) one can reasonably estimate that equilibration has occurred within 3 to 6 days at room temperature. Crystals appearing after this time are essentially grown under batch conditions. We experimentally find that altering the reservoir to droplet volume ratio, by changing the reservoir volume, from 50:1 (high ratio) to 5:1 (low ratio), on average increases the equilibration time by approximately 50 % when tested with solutions of 50% MPD, 1.5 M NaCl, or 30 % PEG400. However, experiments with two proteins, chicken egg white lysozyme and concanavalin a, showed an unexpected trend of slightly faster nucleation and larger crystals in the lowest ratio experiments.

show abstract

Section: Introductionsupporting

confidence: 71%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Vapor diffusion, nucleation rates and the reservoir to crystallization volume ratio

Forsythe

Maxwell²,

Pusey³

2002

Acta Crystallogr D Biol Cryst

View full text Add to dashboard Cite

show abstract

“…The limitation of this type of equations is on their restricted applicability, which is confined to the set of conditions at which the empirical parameters were determined. In a different approach, numerical methods were employed to describe the equilibration of hanging drop experiments reported in literature; the software program “Drop” was presented as being based on the FM and SM but with fewer geometric assumptions, and was reported to adequately describe the experimental data [8].…”

Section: Introductionmentioning

confidence: 99%

Understanding Water Equilibration Fundamentals as a Step for Rational Protein Crystallization

2008

View full text Add to dashboard Cite

BackgroundVapor diffusion is the most widely used technique for protein crystallization and the rate of water evaporation plays a key role on the quality of the crystals. Attempts have been made in the past to solve the mass transfer problem governing the evaporation process, either analytically or by employing numerical methods. Despite these efforts, the methods used for protein crystallization remain based on trial and error techniques rather than on fundamental principles.Methodology/Principal FindingsHere we present a new theoretical model which describes the hanging drop method as a function of the different variables that are known to influence the evaporation process. The model is extensively tested against experimental data published by other authors and considering different crystallizing conditions. Aspects responsible for the discrepancies between the existing theories and the measured evaporation kinetics are especially discussed; they include the characterization of vapor-liquid equilibrium, the role of mass transfer within the evaporating droplet, and the influence of the droplet-reservoir distance.Conclusions/SignificanceThe validation tests show that the proposed model can be used to predict the water evaporation rates under a wide range of experimental conditions used in the hanging drop vapor-diffusion method, with no parameter fitting or computational requirements. This model combined with protein solubility data is expected to become a useful tool for a priori screening of crystallization conditions.

show abstract

“…Nanodrop crystallization trials reduce the required protein sample size, allowing for more complete exploration of crystallization parameter space, as well as for improved rates of drop equilibration (18) and successful crystal production. Faster crystal formation permits faster feedback, and, perhaps more surprisingly, can lead to improved crystal quality due to decreased decomposition and degradation.…”

Section: Expressmentioning

confidence: 99%

Industrializing Structural Biology

Stevens

Wilson

2001

Science

View full text Add to dashboard Cite

S ince Riientgen's discovery of x-rays, crystallography has been the method of choice to determine molecular structure (1, 2). The utility of this technique toward proteins was f i i demonstrated in 1960 with the determination of the myoglobin structure (3) and has since been applied to much more complex macromolecular structures and assemblies, such as viruses (4, 5), membrane proteins (6), and the ribosome (7,8). The gradual accumulation of structures has allowed a more complete representation of three-dimensional (3D) protein folds, enabling more successful homology modeling of unknown structures (9). Breakthroughs in genome sequencing projects have underscored the need for concomitant advances in structural biology if we hope to determine the extent of protein folding-space and elucidate how an assembly of proteins constitutes a cellular organism. As a result, structural genornics programs have sprung up both nationally and internationally, with significant funding from the National Institutes of Health in the United States (www.nigms.nih.gov).Determining protein structures on a genome-wide scale is a formidable task. Traditionally, each target gene is cloned into an expression vector, expressed with the use of a single set of conditions, and the resulting protein is then purified. With this protein in hand, a number of basic screens for crystallization are used, followed by further screening, if necessary, to optimize crystal quality. Lastly, the best crystal(s) are used for diffraction analysis. Such isolated investigations on individual proteins are being replaced with parallel sample processing approaches for structure determination in both the public and private sectors. Public efforts, at least in the United States, are being directed toward elucidating the universe of protein structural families. In the private sector, structural data are also being harnessed for biochemical function prediction and as initial 3D templates in drug discovery programs.Using conventional methods, the throughput of rnacromolecular 3D structure determination can be improved only by increasing the person-hours of work. As a consequence, academic and industrybased researchers have initiated research and development progmns to develop high-throughput (HT) structure determination process pipelines, as diagrammed in the figure. The stage is now being set for the industrialization of structural biology in much the same way that Henry Ford revolutionized the auto industry. Structures will no longer be determined one at a time. "Assembly line" structure determination approaches are being developed that can cope with HT. Large multiinstitutional conglomerates of expertise have coalesced into factorylike consortiums to provide the wide range of methodologies needed to convert gene sequences into validated protein structures.HT structural biology requires development of methods and reagents to streamline and automate the process of protein structure determination. Given the large number of gene sequences, their protein products, and co...

show abstract

An accurate numerical model for calculating the equilibration rate of a hanging-drop experiment

Cited by 13 publications

References 21 publications

Vapor diffusion, nucleation rates and the reservoir to crystallization volume ratio

Vapor diffusion, nucleation rates and the reservoir to crystallization volume ratio

Understanding Water Equilibration Fundamentals as a Step for Rational Protein Crystallization

Industrializing Structural Biology

Contact Info

Product

Resources

About