Qualitative evaluation of the molecular-level parameters that govern crystallization
We used the atomic force microscope in-situ, during the crystallization of apoferritin to visualize and quantify at the molecular-level the processes responsible for crystal growth. To evaluate the governing thermodynamic parameters, we imaged the configuration of the incorporation sites, "kinks", on the surface of a growing crystal. We showed that the kinks are due to thermal fluctuations of the molecules at the crystal-solution interface. This allowed evaluation of the free energy of the intermolecular bond f = 3.0 kBT = 7.3 kJ/mol. The crystallization free energy, extracted from the protein solubility, is – 42 kJ/mol. Published determinations of the second virial coefficient and the protein solubility between 0 and 40 oC revealed that the enthalpy of crystallization is close to zero. Analyses based on these three values suggest that the main component in the crystallization driving force is the entropy gain of the waters bound to the protein molecules in solution and released upon crystallization. Furthermore, monitoring the incorporation of individual molecules in to the kinks, we determined the characteristic frequency of attachment of individual molecules at one set of conditions. This allows a correlation between the mesoscopic kinetic coefficient for growth and the molecular-level thermodynamic and kinetic parameters determined here. We found that step growth velocity, scaled by the molecular size, equals the product of the kink density and attachment frequency, i.e., the latter pair are the molecular-level parameters for self-assembly of the molecules into crystals.
S.-T. Yau, B.R. Thomas and P.G. Vekilov, Molecular mechanisms of crystallization and defect formation. Phys. Rev. Lett. 85 (2000) 353-356 [Abstract, PDF]
S.-T. Yau, D.N. Petsev, B.R. Thomas, and P.G. Vekilov, Molecular-level thermodynamic and kinetic parameters for the self-assembly of apoferritin molecules into crystals. J. Mol. Biol 303 (2000) 667-678.
Visualization of the structure of the critical nucleus for a first order phase transition
The structure of the nucleus largely determines the thermodynamics and kinetics of first-order phase transitions. A compact three-dimensional arrangement of the molecules in the nucleus has often been assumed. Recent molecular dynamics simulations predict a compact nucleus structure for atoms or molecules with a spherical interaction field, while strongly anisotropic, dipolar molecules may bear nuclei consisting of a single chain of molecules. Using atomic force microscopy (AFM) in situ during the crystallisation of the protein apoferritin, we image for the first time the arrangement of the molecules in near-critical clusters, larger or smaller than the crystal nucleus, that are representative of its structure. In the supersaturation Dm/kBT range of 1.1–1.6, the nuclei contain 50–20 molecules. Within the nuclei, the molecules are arranged as in a large crystal. Contrary to the general belief, the nuclei are not compact molecular assemblies, but are planar arrays of about 5-10 rods of 5-7 molecules set in one or two monomolecular layers. Similarly unexpected nuclei structures might be common, especially for anisotropic molecules. Hence, the nucleus structure should be considered as a variable by advanced theoretical treatments.
S.-T. Yau and P.G. Vekilov, Quasi-planar nuclus structure in apoferritin crystallization, Nature 406 (2000) 494-497 [First Paragraph, PDF, N&V]
Rationale for the control of the nucleation of protein crystals
The capability to enhance or suppress the nucleation of protein crystals opens opportunities in various fundamental and applied areas, including protein crystallography, production of protein crystalline pharmaceuticals, protein separation, and treatment of protein condensation diseases. We showed that the rate of homogeneous nucleation of lysozyme crystals passes through a maximum in the vicinity of the liquid-liquid phase boundary hidden below the liquidus (solubility) line in the phase diagram of the protein solution. We found that glycerol and polyethylene glycol (PEG) (that do not specifically bind to proteins) shift this phase boundary and significantly suppress or enhance the crystal nucleation rates, although no simple correlation exists between the action of PEG on the phase diagram and the nucleation kinetics. The control mechanism does not require changes in the protein concentration, acidity and ionicity of the solution. The effects of the two additives on the phase diagram strongly depend on their concentration and this provides opportunities for further tuning of nucleation rates.
O. Galkin and P.G. Vekilov, Control of protein crystal nucleation around the metastable liquid-liquid phase boundary, Proc. Natl. Acad. Sci. USA 97 (2000) 6277-6281 [Abstract, PDF]
Novel technique for determination of the rates of homogeneous nucleation of protein crystals
We developed a novel method for direct determinations of the steady-state rates of homogeneous nucleation. The method is applicable to studies of crystallization, aggregation, and similar first-order phase transitions in solutions of proteins or other soluble slow-growing materials with temperature-dependent solubility. Temperature T control of the solution supersaturation allows fast supersaturation changes from a level inductive of nucleation to a level where no nucleation occurs, but existing crystals grow to detectable dimensions. In this way, nucleation takes place only at the first T setting at a constant supersaturation before solution depletion due to crystal growth becomes significant. We use inert oil to cover nucleating solutions and suppress nucleation on the solution-air interface. To obtain reproducible statistical characteristics of the intrinsically random nucleation process, a large number of simultaneous trials take place under identical conditions.
O. Galkin and P.G. Vekilov, Direct determination of the nucleation rates of protein crystals. J. Phys. Chem. 103 (1999) 10965-10971.
O. Galkin and P.G. Vekilov, Are nucleation kinetics of protein crystals similar to those of liquid droplets? J. Am. Chem. Soc. 122 (2000) 156-163 [Abstract, PDF]
Experimental evidence for the action of a novel hydration force between protein molecules in solution
We studied the molecular interactions in solutions of the protein apoferritin by static and dynamic light scattering. When plotted against the electrolyte concentration, the second osmotic virial coefficient exhibits a minimum. The ascending branch of this dependence is a manifestation of a surprisingly strong repulsion between the molecules at electrolyte concentrations about and above 0.2 M, where electrostatic interactions are suppressed. We argue that the repulsion is due to the water structuring, enhanced by the accumulation of hydrophilic counterions around the apoferritin molecules, giving rise to so-called hydration forces.
D.N. Petsev and P.G. Vekilov, Evidence for non-DLVO hydration interactions in solutions of the protein apoferritin. Phys. Rev. Lett. 84 (2000) 1339-1342 [Abstract, PDF]
D.N. Petsev, B.R. Thomas, S.-T. Yau and P.G. Vekilov, Interactions and aggregation of apoferritin molecules in solution: Effects of added electrolyte. Biophysical J. 78 (2000) 2060-2069.
Rationale for the advantages and disadvantages of microgravity growth for the perfection of protein crystal
Protein crystals, grown under reduced gravity conditions, are either superior or inferior in their structural perfection than their Earth-grown counterparts. A reduction of the crystals’ quality due to low-gravity effects on the growth processes cannot be understood from existing models. We put forth a rationale which predicts either advantages or disadvantages of microgravity growth. This rationale is based on the changes in the effective supply rate in microgravity and their effects on the intrinsic growth rate fluctuations that arise from the coupling of bulk transport to nonlinear interfacial kinetics and cause severe inhomogeneities. Depending on the specific diffusivity and kinetic coefficient of a protein and the impurities in the solution, either transport enhancement through forced flow or transport reduction under reduced gravity can result in a reduction of the step bunching and, thus, growth with higher structural perfection. Investigating this mechanism of microgravity effects, we first demonstrate a one-to-one correspondence between these fluctuations that are due to the bunching of growth steps, and the formation of defects in the crystals. We have confirmed the forced flow aspects of this rationale in ground-based experiments with lysozyme utilizing flowing solutions with varying, well-characterized impurity contents.
P.G. Vekilov and J.I.D. Alexander, Dynamics of layer growth in protein crystallization, Chem. Rev. 100 (2000), 2061-2089 [Table of Contents, PDF]
These results were the basis for the first rationale for system dependent effects of changes in the transport conditions (forced flow for faster transport, or elimination of buoyancy driven convection through growth in space) on the protein crystal perfection.
* Number according to list of publications
* Number according to list of publications
Research Plans
Effects of convective transport of solute and impurities on defect-causing kinetics instabilities in protein crystallization
Our previous NASA-supported research has revealed that protein crystallization occurs with intrinsic growth rate fluctuations that arise from the coupling of bulk transport to nonlinear interfacial kinetics. In the layer growth mode found for the faceted proteins crystals, these fluctuations occur through the dynamic formation of bunches of steps (the edges of unfinished, just forming layers on the crystal surface). We established a one-to-one correspondence between these fluctuations and the step bunches and the formation of defects in the crystals. In addition, based on numerical simulations, we have developed a criterion for the improvement of crystal quality through imposed changes in the transport conditions in the solution. We have confirmed the forced flow aspects of this rationale in ground-based experiments with lysozyme utilizing flowing solutions with varying, well characterized impurity contents. The microgravity aspects of our rationale, though supported by the numerical modeling and scaling analysis of the space results of other investigators, require scrutinization through specifically designed flight experiments.
In these flight experiments we will use proteins, chosen for their different combinations of diffusivities and kinetic coefficients. The proteins will be crystallized in six individually temperature-controlled cells, from pure as well as specifically heterogeneity-doped solutions. We will monitor the response of kinetics fluctuations to variations in the convective bulk transport conditions on Earth. This, together with numerical simulations of dependence of the kinetics instabilities on the diffusive-convective transport of solute and impurities, will allow us to optimize the scientific yield of the flight experiments. For the kinetics monitoring of crystal surfaces in space, we will design an automatic phase-shifting interferometer for in-situ surface characterization that can be operated from the ground. Based on the insight gained from the space experiments in comparison with the controls on Earth, we will chose specific growth conditions that are expected to result in a minimization or enhancement of crystal defect formation on Earth. Crystals grown under these conditions will be evaluated for their X-ray diffraction resolution. This will result in a closure of our rationale on the role of transport in crystal perfection.
Funded by NASA
Crystallization tools for structural genomics
Although many of the Structural Genomics target proteins will readily form microcrystals, the production of crystals of size and perfection sufficient for biologically and medically meaningful structure analyses may be problematic. In some cases, examples of the unique protein folds that may be present in the uncrystallizable proteins may come from NMR studies. Still, there will be a significant number of target proteins crucial for medical and biological applications that will not allow high-resolution structure determinations within the timeframe of a high-throughput project. Hence, the objective of the proposed research is to develop tools that accelerate the optimization of the crystallization conditions leading from microcrystals to crystals of size and perfection sufficient for the desired resolution of diffraction.
Funding by NIH applied for. A proposal to NASA with similar objectives is currently being prepared
Novel approach to the control of polymerization of sickle hemoglobin
The primary pathogenic event of sickle cell anemia has been identified as the polymerization of deoxy sickle cell hemoglobin (Hb S). In the absence of a gene correction for the disease, means to control the process of hemoglobin S polymerization are sought. It has been shown that polymerization is triggered by homogeneous nucleation of deoxy Hb S polymers. Furthermore, recent experiments carried out in our Laboratory, in agreement with theory, suggest a control mechanism for the rate of nucleation of ordered solid phases of proteins (e.g., Hb S polymers). For this, the liquid-liquid (L-L) phase boundary typical for many proteins is shifted by adding inert organic molecules. For deoxy Hb S, the spinodal of the L-L separation is at about 30 oC at physiological Hb S concentrations. The molar concentration of the additive can be significantly lower than the concentration of the hemoglobin. The overall objective of the research proposed here is to test the applicability of this control mechanism to the polymerization of deoxy Hb S.
Funding by NIH applied for.