Capillarity effects on crystallization kinetics: insulin

The elementary reactions for incorporation into crystals

The growth rates of crystals are largely dictated by the chemical reaction between solute and kinks, in which a solute molecule severs its bonds with the solvent and establishes new bonds with the kink. Details on this sequence of bond breaking and rebuilding remain poorly understood. To elucidate the reaction at the kinks we employ four solvents with distinct functionalities as reporters on the microscopic structures and their dynamics along the pathway into a kink. We combine time-resolved in situ atomic force microscopy and x-ray and optical methods with molecular dynamics simulations. We demonstrate that in all four solvents the solute, etioporphyrin I, molecules reach the steps directly from the solution; this finding identifies the measured rate constant for step growth as the rate constant of the reaction between a solute molecule and a kink. We show that the binding of a solute molecule to a kink divides into two elementary reactions. First, the incoming solute molecule sheds a fraction of its solvent shell and attaches to molecules from the kink by bonds distinct from those in its fully incorporated state. In the second step, the solute breaks these initial bonds and relocates to the kink. The strength of the preliminary bonds with the kink determines the free energy barrier for incorporation into a kink. The presence of an intermediate state, whose stability is controlled by solvents and additives, may illuminate how minor solution components guide the construction of elaborate crystal architectures in nature and the search for solution compositions that suppress undesirable or accelerate favored crystallization in industry.

Unraveling the Impact of pH on the Crystallization of Pharmaceutical Proteins: A Case Study of Human Insulin

One of the most crucial parameters in protein crystallization is pH, as it governs the protein's electrostatic interactions. However, the fundamental role of pH on crystallization still remains unknown. Here, we systematically investigated the crystallization of human insulin (isoelectric point 5.3) at various pHs between 6.0 and 6.7 at different supersaturation ratios, up to 20.9. Our results demonstrate that the pH has an opposing effect on solubility and nucleation rate as a shift in pH toward a more basic milieu increases the solubility by 5-fold while the onset of nucleation was accelerated by a maximum of 8.6-fold. To shed light on this opposing effect, we evaluated the protein-protein interactions as a function of pH by measuring the second virial coefficient and hydrodynamic radius and showed that a change in pH of less than one unit has no significant impact on the protein-protein interactions. As it is widely understood that the increase in protein solubility as a function of pH is due to the increase in the repulsive electrostatic interactions, we have demonstrated that the increase in insulin solubility and decrease in the onset of nucleation are independent of the protein-protein interactions. We hypothesize that it is the electrostatic interactions between both ions and solvent molecules and the protein residues that are governing the crystallization of human insulin. The findings of this study will be of crucial importance for the design of novel crystallization pathways.

What roles do alkali metal ions play in the pathological crystallization of uric acid?

Na+ and K+ regulate the crystal growth of uric acid dihydrate by kink blocking and rough growth mechanisms.

Price of disorder in the lac repressor hinge helix

The Lac system of genes has been pivotal in understanding gene regulation. When the lac repressor protein binds to the correct DNA sequence, the hinge region of the protein goes through a disorder to order transition. The structure of this region of the protein is well understood when it is in this bound conformation, but less so when it is not. Structural studies show that this region is flexible. Our simulations show this region is extremely flexible in solution; however, a high concentration of salt can help kinetically trap the hinge helix. Thermodynamically, disorder is more favorable without the DNA present.

Influences of Crystal Anisotropy in Pharmaceutical Process Development

Crystalline materials are of crucial importance to the pharmaceutical industry, as a large number of APIs are formulated in crystalline form, occasionally in the presence of crystalline excipients. Owing to their multifaceted character, crystals were found to have strongly anisotropic properties. In fact, anisotropic properties were found to be quite important for a number of processes including milling, granulation and tableting. An understanding of crystal anisotropy and an ability to control and predict crystal anisotropy are mostly subjects of interest for researchers. A number of studies dealing with the aforementioned phenomena are grounded on over-simplistic assumptions, neglecting key attributes of crystalline materials, most importantly the anisotropic nature of a number of their properties. Moreover, concepts such as the influence of interfacial phenomena in the behaviour of crystalline materials during their growth and in vivo, are still poorly understood. The review aims to address concepts from a molecular perspective, focusing on crystal growth and dissolution. It begins with a brief outline of fundamental concepts of intermolecular and interfacial phenomena. The second part discusses their relevance to the field of pharmaceutical crystal growth and dissolution. Particular emphasis is given to works dealing with mechanistic understandings of the influence of solvents and additives on crystal habit. Furthermore, comments and perspectives, highlighting future directions for the implementation of fundamental concepts of interfacial phenomena in the rational understanding of crystal growth and dissolution processes, have been provided.

Illuminating protein crystal growth using fluorophore-labelled proteins

Incorporation of trace amounts of fluorophore-labelled proteins is used to study several optical properties and the growth history of protein crystals.

Investigation of mechanical properties of insulin crystals by atomic force microscopy

Mechanical properties of protein crystals and aggregates depend on the conformational and structural properties of individual protein molecules as well as on the packing density and structure within solid materials. An atomic force microscopy (AFM)-based approach is developed to measure the elastic modulus of small protein crystals by nanoindentation and is applied to measure the elasticity of insulin crystals. The top face of the crystals deposited on mica substrates is identified as the (001) face. Insulin crystals exhibit a nearly elastic response during the compression cycle. The elastic modulus measured on the top face has asymmetric distribution with a significant width. This width is related to the uncertainty in the deflection sensitivity. A model that takes into account the distribution of the sensitivity values is used to correct the elastic modulus. Measurements performed in aqueous buffer on several crystals at different locations with three different AFM probes give a mean elastic modulus of 164 +/- 10 MPa. This value is close to the static elastic moduli of other protein crystals measured by different techniques that are usually measured in the range from 100 MPa to 1 GPa. The measured modulus of insulin crystals falls between the elastic modulus values of insulin amyloid fibrils measured previously at two orthogonal directions (a modulus of 14 MPa was measured by compressing the fibril in the direction perpendicular to the fibril axis, and a modulus of 3.3 GPa was measured in the direction along the fibril axis). This comparison indicates the heterogeneous structure of fibrils in the direction perpendicular to the fibril axis, with a packing density of the amyloid fibril core that is higher than the average packing density in insulin crystals. The mechanical wear of insulin crystals is detected during AFM measurements. In nanoindentation experiments on insulin crystal, the compressive load by the AFM tip ( approximately 1 nN, corresponding to a pressure of around 5 MPa) occasionally removes protein molecules from the top or the second top layer of insulin crystal in a sequential manner. The molecular model of this surface damage is proposed. In addition, the removal of the multiple layers of molecules is observed during the AC-mode imaging in aqueous buffer. The number of removed layers depends on the scan size.

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-microm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol(-1) K(-1), very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.

Sickle-cell haemoglobin polymerization: is it the primary pathogenic event of sickle-cell anaemia?

Sickle cell anaemia is associated with a mutant haemoglobin, HbS, which forms polymers in the red blood cells of patients. The primary role of the HbS polymerization for the pathophysiology has been questioned: observations in patients and model organisms contradict deterministic scenarios of sickling crises triggered by polymerization. However, results with knock-out sickle-cell mice, which were cured by delaying HbS polymerization, reconfirm polymerization's primary role. To reconcile the contradictory observations, this article reviews recent findings on two steps in polymerization: homogeneous nucleation of fibres, and their growth. The fibre growth is faster by far than for any other protein ordered structure. This is due to a negligible free-energy barrier for incorporation into a fibre, determined by an entropy gain, stemming from the release of water molecules structured around HbS. The kinetics of fibre nucleation have shown that the formation of the polymer nucleus is preceded by a metastable droplet of a dense liquid. The properties of the dense liquid are sensitive functions of solution composition, including components in micro- and nanomolar amounts. This mechanism allows low-concentration solution components to strongly affect the nucleation kinetics, accounting for the high variability of the disease. These insights can potentially be utilized for control of HbS polymerization and treatment of the disease.

Three frontiers in the thermodynamics of protein solutions

Three examples illustrate the versatility and usefulness of biothermodynamics. The first example concerns calculation of a phase diagram for aqueous lysozyme with a new potential of mean force that takes the Hofmeister effect into account; such calculations may be useful for design of a separation process where addition of a salt to an aqueous protein mixture precipitates a target protein. The second example concerns thermodynamic studies to elucidate the effect of an organic cosolvent on the mechanism of crystallizing aqueous insulin. The final example concerns a thermodynamic contribution to mitigating the AIDS epidemic; it indicates how isothermal-titration-calorimetry studies are helpful for choosing an optimum inhibitor that is effective not only for the wild-type HIV protease but also for at least some of its mutants.

Role of molecular charge and hydrophilicity in regulating the kinetics of crystal growth

The composition of biologic molecules isolated from biominerals suggests that control of mineral growth is linked to biochemical features. Here, we define a systematic relationship between the ability of biomolecules in solution to promote the growth of calcite (CaCO3) and their net negative molecular charge and hydrophilicity. The degree of enhancement depends on peptide composition, but not on peptide sequence. Data analysis shows that this rate enhancement arises from an increase in the kinetic coefficient. We interpret the mechanism of growth enhancement to be a catalytic process whereby biomolecules reduce the magnitude of the diffusive barrier, Ek, by perturbations that displace water molecules. The result is a decrease in the energy barrier for attachment of solutes to the solid phase. This previously unrecognized relationship also rationalizes recently reported data showing acceleration of calcite growth rates over rates measured in the pure system by nanomolar levels of abalone nacre proteins. These findings show that the growth-modifying properties of small model peptides may be scaled up to analyze mineralization processes that are mediated by more complex proteins. We suggest that enhancement of calcite growth may now be estimated a priori from the composition of peptide sequences and the calculated values of hydrophilicity and net molecular charge. This insight may contribute to an improved understanding of diverse systems of biomineralization and design of new synthetic growth modulators.

Insulin particle formation in supersaturated aqueous solutions of poly(ethylene glycol)

Protein microspheres are of particular utility in the field of drug delivery. A novel, completely aqueous, process of microsphere fabrication has been devised based on controlled phase separation of protein from water-soluble polymers such as polyethylene glycols. The fabrication process results in the formation of spherical microparticles with narrow particle size distributions. Cooling of preheated human insulin-poly(ethylene glycol)-water solutions results in the facile formation of insulin particles. To map out the supersaturation conditions conducive to particle nucleation and growth, we determined the temperature- and concentration-dependent boundaries of an equilibrium liquid-solid phase separation. The kinetics of formation of microspheres were followed by dynamic and continuous-angle static light scattering techniques. The presence of PEG at a pH that was close to the protein's isoelectric point resulted in rapid nucleation and growth. The time elapsed from the moment of creation of a supersaturated solution and the detection of a solid phase in the system (the induction period, t(ind)) ranged from tens to several hundreds of seconds. The dependence of t(ind) on supersaturation could be described within the framework of classical nucleation theory, with the time needed for the formation of a critical nucleus (size <10 nm) being much longer than the time of the onset of particle growth. The growth was limited by cluster diffusion kinetics. The interfacial energies of the insulin particles were determined to be 3.2-3.4 and 2.2 mJ/m(2) at equilibrium temperatures of 25 and 37 degrees C, respectively. The insulin particles formed as a result of the process were monodisperse and uniformly spherical, in clear distinction to previously reported processes of microcrystalline insulin particle formation.

A fast response mechanism for insulin storage in crystals may involve kink generation by association of 2D clusters

Crystals that are likely rhombohedral of Zn-insulin hexamers form in the islets of Langerhans in the pancreases of many mammals. The suggested functions of crystal formation is to protect the insulin from proteases and increase the degree of conversion of soluble proinsulin. To accomplish these ends, crystal growth should be fast and adaptable to rate fluctuations in the conversion reaction. Zn-insulin crystals grow layer by layer. Each layer spreads by the attachment of molecules to kinks located at the layers' edges, also called steps. The kinks are thought to be generated either by thermal fluctuations, as postulated by Gibbs, or by 1D nucleation of new crystalline rows. The kink density determines the rate at which steps advance, and these two kink-generation mechanisms lead to weak near-linear responses of the growth rate to concentration variations. We demonstrate for the crystallization of Zn-insulin a mechanism of kink generation whereby 2D clusters of several insulin molecules preformed on the terraces between steps associate to the steps. This mechanism results in several-fold-higher kink density, a faster rate of crystallization, and a high sensitivity of the kinetics to small increases of the solute concentration. If the found mechanism operates during insulin crystallization in vivo, it could be a part of the biological regulation of insulin production and function. For other crystallizing materials in biological and nonbiological systems, this mechanism provides an understanding of the often seen nonlinear acceleration of the kinetics.

Nucleation of ordered solid phases of proteins via a disordered high-density state: Phenomenological approach

Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.

Crystallization of Transmembrane Proteins in cubo: Mechanisms of Crystal Growth and Defect Formation

Crystallization of membrane proteins is a major stumbling block en route to elucidating their structure and understanding their function. The novel concept of membrane protein crystallization from lipidic cubic phases, "in cubo", has yielded well-ordered crystals and high-resolution structures of several membrane proteins, yet progress has been slow due to the lack of understanding of the molecular mechanisms of protein transport, crystal nucleation, growth, and defect formation in cubo. Here, we examine at molecular and mesoscopic resolution with atomic force microscopy the morphology of in cubo grown bacteriorhodopsin crystals in inert buffers and during etching by detergent. The results reveal that crystal nucleation occurs following local rearrangement of the highly curved lipidic cubic phase into a lamellar structure, which is akin to that of the native membrane. Crystals grow within the bulk cubic phase surrounded by such lamellar structures, whereby transport towards a growing crystalline layer is constrained to within an individual lamella. This mechanism leads to lack of dislocations, generation of new crystalline layers at numerous locations, and to voids and block boundaries. The characteristic macroscopic lengthscale of these defects suggests that the crystals grow by attachment of single molecules to the nuclei. These insights into the mechanisms of nucleation, growth and transport in cubo provide guidance en route to a rational design of membrane protein crystallization, and promise to further advance the field.

Crystallization mechanisms of hemoglobin C in the R state

Crystallization of the mutated hemoglobin, HbC, which occurs inside red blood cells of patients expressing betaC-globin and exhibiting the homozygous CC and the heterozygous SC (in which two mutant beta-globins, S and C, are expressed) diseases, is a convenient model for processes underlying numerous condensation diseases. As a first step, we investigated the molecular-level mechanisms of crystallization of this protein from high-concentration phosphate buffer in its stable carbomonoxy form using high-resolution atomic force microscopy. We found that in conditions of equilibrium with the solution, the crystals' surface reconstructs into four-molecule-wide strands along the crystallographic a (or b) axis. However, the crystals do not grow by the alignment of such preformed strands. We found that the crystals grow by the attachment of single molecules to suitable sites on the surface. These sites are located along the edges of new layers generated by two-dimensional nucleation or by screw dislocations. During growth, the steps propagate with random velocities, with the mean being an increasing function of the crystallization driving force. These results show that the crystallization mechanisms of HbC are similar to those found for other proteins. Therefore, strategies developed to control protein crystallization in vitro may be applicable to pathology-related crystallization systems.

Thermodynamics of the hydrophobicity in crystallization of insulin

For insight into the solvent structure around protein molecules and its role in phase transformations, we investigate the thermodynamics of crystallization of the rhombohedral form of porcine insulin crystals. We determine the temperature dependence of the solubility at varying concentration of the co-solvent acetone, Cac=0%, 5%, 10%, 15%, and 20%, and find that, as a rule, the solubility of insulin increases as temperature increases. The enthalpy of crystallization, undergoes a stepwise shift from approximately -20 kJ mol(-1) at Cac=0%, 5%, and 10% to approximately -55 kJ mol(-1) at Cac=15% and 20%. The entropy change upon crystallization is approximately 35 J mol(-1) K(-1) for the first three acetone concentrations, and drops to approximately -110 J mol(-1) K(-1) at Cac=15% and 20%. DeltaS degrees cryst>0 indicates release of solvent, mostly water, molecules structured around the hydrophobic patches on the insulin molecules' surface in the solution. As Cac increases to 15% and above, unstructured acetone molecules apparently displace the waters and their contribution to DeltaS degrees cryst is minimal. This shifts DeltaS degrees cryst to a negative value close to the value expected for tying up of one insulin molecule from the solution. The accompanying increase in DeltaH degrees cryst suggests that the water structured around the hydrophobic surface moieties has a minimal enthalpy effect, likely due to the small size of these moieties. These findings provide values of the parameters needed to better control insulin crystallization, elucidate the role of organic additives in the crystallization of proteins, and help us to understand the thermodynamics of the hydrophobicity of protein molecules and other large molecules.