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At least 19 records

Optimizing Batch Crystallization with Model-based Design of Experiments

Poster for Foundations of Computer Aided Process Design (FOCAPD) 2024 describing the formality of model-based design of experiments for batch crystallization. This paper focuses on the implementation of model-based design of experiments for parameter precision, enabled by Pyomo.DoE, a package in Python. Specifically, this work outlines an identifiability analysis for the estimability of the model parameters in a batch crystallization system.

Lynch, Hailey↗

Optimizing Batch Crystallization with Model-based Design of Experiments

Adaptive and self-optimizing intelligent systems such as digital twins are increasingly important in science and engineering. Digital twins utilize mathematical models to provide added precision to decision-making. However, physics-informed models are challenging to build, calibrate, and validate with existing data science methods. Model-based design of experiments (MBDoE) is a popular framework for optimizing data collection to maximize parameter precision in mathematical models and digital twins. In this work, we apply MBDoE, facilitated by the open-source package Pyomo.DoE, to train and validate mathematical models for batch crystallization. We quantitatively examined the estimability of the model parameters for experiments with different cooling rates. This analysis provides a quantitative explanation for the heuristic of using multiple experiments at different cooling rates.

Lynch, Hailey↗

The Effect of Temperature and Solution pH on Tetragonal Lysozyme Nucleation Kinetics

Part of the challenge of macromolecular crystal growth for structure determination is obtaining an appropriate number of crystals with a crystal volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over one week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions, Duplicate experiments indicate the reproducibility of the technique, Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable however, was pH, where crystal numbers changed by two orders of magnitude over the pH range 4.0 to 5.2. Crystal size varied also with solution conditions, with the largest crystals being obtained at pH 5.2. Having optimized the crystallization conditions, a batch of crystals were prepared under exactly the same conditions and fifty of these crystals were analyzed by x-ray techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗

High density protein crystal growth

A protein crystal growth assembly including a crystal growth cell and further including a cell body having a top side and a bottom side and a first aperture defined therethrough, the cell body having opposing first and second sides and a second aperture defined therethrough. A cell barrel is disposed within the cell body, the cell barrel defining a cavity alignable with the first aperture of the cell body, the cell barrel being rotatable within the second aperture. A reservoir is coupled to the bottom side of the cell body and a cap having a top side is disposed on the top side of the cell body. The protein crystal growth assembly may be employed in methods including vapor diffusion crystallization, liquid to liquid crystallization, batch crystallization, and temperature induction batch mode crystallization.

Rouleau, Robyn↗

The Effect of Temperature and Solution pH on the Nucleation of Tetragonal Lysozyme Crystals

Part of the challenge of macromolecular crystal growth for structure determination is obtaining crystals with a volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature, and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over 1 week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable, however, was pH; crystal numbers changed by two orders of magnitude over the pH range 4.0-5.2. Crystal size also varied with solution conditions, with the largest crystals obtained at pH 5.2. Having optimized the crystallization conditions, we prepared a batch of crystals under the same initial conditions, and 50 of these crystals were analyzed by x-ray diffraction techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗

The Effect of Solution Parameters on Lysozyme Nucleation Rates and Crystal Quality

In the pursuit of strongly diffracting high quality macromolecule crystals of suitable volume, this study investigates how the formation of macromolecules in solution and their growth characteristics effect crystal volume and diffracting quality. We systematically investigated the effect of solution conditions on lysozyme nucleation rates and the volume of crystals produced. Batch crystallization plates were used in combination with a video microscope system to measure nucleation rates and crystal volume. As expected from classical nucleation theory, crystal numbers were found to increase with increases in temperature and supersaturation. Small changes in solution pH, at constant supersaturation values were found, however, to dramatically effect the number of crystals nucleated in the wells varying from 1000s to 10s in the pH range 4.0 to 5.2. Having optimized the conditions required to produce an appropriate number of crystals of a suitable volume for X-ray analysis, a large number of uniform crystals were produced under exactly the same conditions. In the X-ray analysis of more than 50 such crystals there was found a wide variation in crystal lattice parameters and data quality. The variation in X-ray quality crystal samples is thought to be related to the growth rate variation caused by growth rate dispersion seen in lysozyme crystal growth experiments.

Judge, R. A.↗

A Few Good Crystals Please

Part of the challenge of macromolecular crystal growth for structure determination is obtaining an appropriate number of crystals with a crystal volume suitable for X-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of solution conditions on the nucleation rate and final crystal size of two crystal systems; tetragonal lysozyme and glucose isomerase. Batch crystallization plates were prepared at given solution concentration and incubated at set temperatures over one week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Duplicate experiments indicate the reproducibility of the technique. Results for each system showing the effect of supersaturation, incubation temperature and solution pH on nucleation rates will be presented and discussed. In the case of lysozyme, having optimized solution conditions to produce an appropriate number of crystals of a suitable size, a batch of crystals were prepared under exactly the same conditions. Fifty of these crystals were analyzed by x-ray techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗

The Effect of Solution Conditions on the Nucleation Kinetics of Tetragonal Lysozyme Crystals

An understanding of protein crystal nucleation rates and the effect of solution conditions upon them, is fundamental to the preparation of protein crystals of the desired size and shape for X-ray diffraction analysis. The ability to predict the effect of supersaturation, temperature, pH and precipitant concentration on the number and size of crystals formed is of great benefit in the pursuit of protein structure analysis. In this study we experimentally examine the effect of supersaturation, temperature, pH and sodium chloride concentration on the nucleation rate of tetragonal chicken egg white lysozyme crystals. In order to do this batch crystallization plates were prepared at given solution concentrations and incubated at three different temperatures over the period of one week. The number of crystals per well with their size and dimensions were recorded and correlated against solution conditions. Duplicate experiments indicate the reproducibility of the technique. Although it is well known that crystal numbers increase with increasing supersaturation, large changes in crystal number were also correlated against solution conditions of temperature, pH and salt concentration over the same supersaturation ranges. Analysis of these results enhance our understanding of the effect of solution conditions such as the dramatic effect that small changes in charge and ionic strength can have on the number of tetragonal lysozyme crystals that form and grow in solution.

Judge, Russell A.↗

Protein Crystals and their Growth

Recent results on binding between protein molecules in crystal lattice, crystal-solution surface energy, elastic properties and strength and spontaneous crystal cracking are reviewed and discussed in the first half of this paper (Sea 2-4). In the second par&, some basic approaches to solubility of proteins are followed by overview on crystal nucleation and growth (Sec 5). It is argued that variability of mixing in batch crystallization may be a source for scattering of crystal number ultimately appearing in the batch. Frequency at which new molecules join crystal lattice is measured by kinetic coefficient and related to the observable crystal growth rate. Numerical criteria to discriminate diffusion and kinetic limited growth are discussed on this basis in Sec 7. In Sec 8, creation of defects is discussed with the emphasis on the role of impurities and convection on macromolecular crystal I;erfection.

Chernov, A. A.↗

Physics of Biocrystals and Their Growth

Recent results on binding between protein molecules in crystal lattice, crystal-solution surface energy, elastic properties and strength and spontaneous crystal cracking are reviewed and discussed in the first half of the paper (Sections 2-5). In the second part, some basic approaches to solubility of proteins is followed by overview on crystal nucleation and growth (Section 6). It is argued that variability of mixing in batch crystallization may be a source scattering of crystal number ultimately appearing in the batch (Section 7). Frequency at which new molecules join crystal lattice is related to the observable crystal growth rate. Numerical criteria to discriminate diffusion and kinetic limited growth are discussed on this basis in Section 8. In Section 9, creation of defects is discussed with the emphasis on the role of impurities and convection in macromolecular crystal perfection.

Chernov, A.↗

Does Warming a Lysozyme Solution Cook Ones Data?

Chicken egg white lysozyme has a well characterized thermally driven phase transition. Between pH 4.0 and 5.2, the transition temperature, as defined by the point where the tetragonal and orthorhombic solubility are equal, is a function of the pH, salt (precipitant) type and concentration, and most likely of the buffer concentration as well. This phase transition can be carried out with protein solution alone, prior to the initiation of the crystallization process. We have now measured the kinetics of this process and investigated its reversibility. An aliquot of a stock protein solution is held at a given temperature, and at periodic intervals used to set up batch crystallization experiments. The batch solutions were incubated at 20 C until macroscopic crystals were obtained, at which point the number of crystals in each well were counted. The transition effects increased with temperature, slowly falling off at 30 C with a half time (time to approx. 1/2 the t = 0 number of crystals) of approx. 5 hours, and an estimated half time of approx. 0.5 hours at 43 C. Further, the process was not reversible by simple cooling. After holding a lysozyme solution at 37 C (prior to addition of precipitant) for 16 hours, then cooling and holding it at 4 C, no return to the pre-warmed nucleation kinetics are observed after at least 4 weeks. Thus every thermal excursion above the phase transition point results in a further decrease in the nucleation rate of that solution, the extent being a function of the time and temperature. Orthorhombic lysozyme crystals apparently do not undergo the flow-induced growth cessation of tetragonal lysozyme crystals. We have previously shown that putting the protein in the orthorhombic form does not affect the averaged face growth kinetics, only nucleation, for tetragonal crystals. We may be able to use this differential behavior to elucidate how flow affects tile lysozyme crystal growth process.

Pusey, Marc↗

Crystallization of Chicken Egg-White Lysozyme from Ammonium Sulfate

Chicken egg-white lysozyme was crystallized from ammonium sulfate over the pH range 4.0-7.8, with protein concentrations from 100 to 150 mg/ml. Crystals were obtained by vapor-diffusion or batch-crystallization methods. The protein crystallized in two morphologies with an apparent morphology dependence on temperature and protein concentration. In general, tetragonal crystals could be grown by lowering the protein concentration or temperature. Increasing the temperature or protein concentration resulted in the growth of orthorhombic crystals. Representative crystals of each morphology were selected for X-ray analysis. The tetragonal crystals belonged to the P4(sub 3)2(sub 1)2 space group with crystals grown at ph 4.4 having unit-cell dimensions of a = b = 78.7 1, c=38.6 A and diffracting to beyond 2.0 A. The orthorhombic crystals, grown at pH 4.8, were of space group P2(sub 1)2(sub 1)2 and had unit-cell dimensions of a = 30.51, b = 56.51 and c = 73.62 A.

Forsythe, Elizabeth L.↗

The Feasibility of Bulk Crystallization as an Industrial Purification and Production Technique for Proteins

Bulk crystallization in stirred vessels is used industrially for the recovery and purification of many inorganic and organic materials. Although much has been written on the crystallization of proteins for X-ray diffraction analysis, very little has been reported on the application of bulk crystallization in stirred vessels. In this study, a 1-liter, seeded, stirred, batch crystallizer was used with ovalbumin as a model protein to test the feasibility of this crystallization method as a recovery and purification process for proteins. Results were obtained for ovalbumin solubility, nucleation thresholds, crystal breakage and crystal growth kinetics in bulk solution under a range of operating conditions of pH and ammonium sulphate concentration (Judge et al., 1996). Experiments were also performed to determine the degree of purification that can be achieved by the crystallization of ovalbumin from a mixture of proteins. The effect of the presence of these proteins upon the ovalbumin crystal growth kinetics was also investigated (Judge et al., 1995). All of these aspects are essential for the design of bulk crystallization processes which have not previously been reported for proteins. Results from a second study that investigated the effect of structurally different proteins on the solubility, crystal growth rates and crystal purity of chicken egg white lysozyme are also presented (Judge et al., 1997). In this case face growth rates were measured using lysozyme purified by liquid chromatography and the effect of the addition of specific protein impurities were observed on the (110) and (101) crystal faces. In these two studies the results are presented to show the feasibility and purifying ability of crystallization as a production process for proteins.

Judge, Russell A.↗

Protein crystals and their growth

Recent results on the associations between protein molecules in crystal lattices, crystal-solution surface energy, elastic properties, strength, and spontaneous crystal cracking are reviewed and discussed. In addition, some basic approaches to understanding the solubility of proteins are followed by an overview of crystal nucleation and growth. It is argued that variability of mixing in batch crystallization may be a source of the variation in the number of crystals ultimately appearing in the sample. The frequency at which new molecules join a crystal lattice is measured by the kinetic coefficient and is related to the observed crystal growth rate. Numerical criteria used to discriminate diffusion- and kinetic-limited growth are discussed on this basis. Finally, the creation of defects is discussed with an emphasis on the role of impurities and convection on macromolecular crystal perfection.

Review↗

Science Issues Associated with the Use of a Microfluidic Chip Designed Specifically for Protein Crystallization

The Iterative Biological Crystallization team in partnership with Caliper Technologies has produced a prototype microfluidic chip for batch crystallization that has been designed and tested. The chip is designed for the mixing and dispensing of up to five solutions with possible variation of the recipe being delivered to two growth wells. Developments that have led to the successful on-chip crystallization of a few model proteins have required investigative insight into many different areas, including fluid mixing dynamics, surface treatments, quantification and fidelity of reagent delivery. This presentation will encompass the ongoing studies and data accumulated toward these efforts.

Holmes, Anna M.↗

Feedback regulation of crystal growth by buffering monomer concentration

Abstract Crystallization is a ubiquitous means of self-assembly that can organize matter over length scales orders of magnitude larger than those of the monomer units. Yet crystallization is notoriously difficult to control because it is exquisitely sensitive to monomer concentration, which changes as monomers are depleted during growth. Living cells control crystallization using chemical reaction networks that offset depletion by synthesizing or activating monomers to regulate monomer concentration, stabilizing growth conditions even as depletion rates change, and thus reliably yielding desired products. Using DNA nanotubes as a model system, here we show that coupling a generic reversible bimolecular monomer buffering reaction to a crystallization process leads to reliable growth of large, uniformly sized crystals even when crystal growth rates change over time. Buffering could be applied broadly as a simple means to regulate and sustain batch crystallization and could facilitate the self-assembly of complex, hierarchical synthetic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗