Stable equidistant step trains during crystallization of 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.

Precrystallization solute assemblies and crystal symmetry

Solution crystallization is a part of the synthesis of materials ranging from geological and biological minerals to pharmaceuticals, fine chemicals, and advanced electronic components. Attempts to predict the structure, growth rates and properties of emerging crystals have been frustrated, in part, by the poor understanding of the correlations between the oligomeric state of the solute, the growth unit, and the crystal symmetry. To explore how a solute monomer or oligomer is selected as the unit that incorporates into kinks and how crystal symmetry impacts this selection, we combine scanning probe microscopy, optical spectroscopy, and all-atom molecular simulations using as examples two organic materials, olanzapine (OZPN) and etioporphyrin I (EtpI). The dominance of dimeric structures in OZPN crystals has spurred speculation that the dimers preform in the solution, where they capture the majority of the solute, and then assemble into crystals. By contrast, EtpI in crystals aligns in parallel stacks of flat EtpI monomers unrelated by point symmetry. Raman and absorption spectroscopies show that solute monomers are the majority solute species in solutions of both compounds. Surprisingly, the kinetics of incorporation of OZPN into kinks is bimolecular, indicating that the growth unit is a solute dimer, a minority solution component. The disconnection between the dominant solute species, the growth unit, and the crystal symmetry is even stronger with EtpI, for which the (010) face grows by incorporating monomers, whereas the growth unit of the (001) face is a dimer. Collectively, the crystallization kinetics results with OZPN and EtpI establish that the structures of the dominant solute species and of the incorporating solute complex do not correlate with the symmetry of the crystal lattice. In a broader context, these findings illuminate the immense complexity of crystallization scenarios that need to be explored on the road to the understanding and control of crystallization.

The Ambiguous Functions of the Precursors That Enable Nonclassical Modes of Olanzapine Nucleation and Growth

One of the most consequential assumptions of the classical theories of crystal nucleation and growth is the Szilard postulate, which states that molecules from a supersaturated phase join a nucleus or a growing crystal individually. In the last 20 years, observations in complex biological, geological, and engineered environments have brought to light violations of the Szilard rule, whereby molecules assemble into ordered or disordered precursors that then host and promote nucleation or contribute to fast crystal growth. Nonclassical crystallization has risen to a default mode presumed to operate in the majority of the inspected crystallizing systems. In some cases, the existence of precursors in the growth media is admitted as proof for their role in nucleation and growth. With the example of olanzapine, a marketed drug for schizophrenia and bipolar disorder, we demonstrate that molecular assemblies in the solution selectively participate in crystal nucleation and growth. In aqueous and organic solutions, olanzapine assembles into both mesoscopic solute-rich clusters and dimers. The clusters facilitate nucleation of crystals and crystal form transformations. During growth, however, the clusters land on the crystal surface and transform into defects, but do not support step growth. The dimers are present at low concentrations in the supersaturated solution, yet the crystals grow by the association of dimers, and not of the majority monomers. The observations with olanzapine emphasize that detailed studies of the crystal and solution structures and the dynamics of molecular association may empower classical and nonclassical models that advance the understanding of natural crystallization, and support the design and manufacture of promising functional materials.

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.

Universal laws in the force-induced unraveling of biological bonds

Universal laws in the force-induced unbinding of receptor-ligand complexes are established for a general functional dependence of the dissociation rate constant on the applied force and are detailed with the two-pathway model that describes the recently discovered biological catch bond. The relationships link the data obtained with constant and time-dependent forces in different regimes, provide common representation for the previously unrelated data sets, and, thereby, greatly facilitate analysis and interpretation of experiments. The universal laws are demonstrated with the monomeric and dimeric catch-slip bonds between P-selectins and P-selectin glycoprotein ligands-1, and the slip bond between E-selectin and sialyl Lewis;{x} antigen.

Mass transfer limitations at crystallizing interfaces in an atomic force microscopy fluid cell: a finite element analysis

Although atomic force microscopy (AFM) has emerged as the preeminent experimental tool for real-time in situ measurements of crystal growth processes in solution, relatively little is known about the mass transfer limitations that may impact these measurements. We present a continuum analysis of flow and mass transfer in an atomic force microscope fluid cell during crystal growth, using data acquired from calcium oxalate monohydrate (COM) crystal growth measurements as a comparison. Steady-state flows and solute concentration fields are computed using a three-dimensional, finite element method implemented on a parallel supercomputer. Steady-state flow results are compared with flow visualization experiments to validate the model. Computations of the flow field demonstrate how nonlinear momentum transport alters the spatial structure of the flow with increasing flow volume, altering mass transport conditions near the AFM cantilever and tip. The simulations demonstrate that the combination of solute depletion from crystal growth and mass transfer resistance lowers the solute concentration in the region between the tip and the crystal compared with the solute concentration at the inlet of the AFM cell. For example, using experimentally measured growth rates for COM, the solute concentration in this region is 3.1% lower than the inlet value because the solute consumed by crystal growth beneath the AFM tip cannot be replenished fully due to mass transport limitations. The simulations also reveal that increasing the flow rate through the cell does not affect this difference significantly because of the inherent shielding by the AFM tip in proximity with the crystal surface. Models such as the one presented here, used in conjunction with AFM measurements, promise more precise interpretations of measurement data.

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.

Capillarity effects on crystallization kinetics: insulin

During layerwise growth of crystals, capillarity governs the generation of new crystal layers. Theory predicts that the line tension of the layer edge determines, via the characteristic two-dimensional capillary length L(c), the rates of generation and initial growth of the new layers. To test the correlation between L(c) and the rate of layer generation, we used in situ Tapping Mode Atomic Force Microscopy (TM-AFM) to study the generation and spreading of layers during crystallization of rhombohedral, R3, porcine insulin. We show that crystallization of this insulin form is uniquely suitable for such an investigation due to the linear kinetics of step growth it exhibits. This linear kinetics reflects the abundance of the incorporation sites along the rough steps, the lack of long-range step-step interactions, and the transport control of the growth kinetics. The kinetic coefficients are 7 x 10(-)(3) and 4 x 10(-)(2) cm s(-)(1), respectively, in the absence and presence of the cosolvent acetone-somewhat high for proteins and comparable to values for inorganic systems. We show that (i). the relevant capillary length, the size of a critical quadrangular 2D nucleus L(c), is the main scaling factor for the density of growth steps, while (ii). all steps longer than L(c) grow with a rate determined only by the supersaturation and independent of their length. We explain the divergence of (ii). from theoretical predictions with the high supersaturations typical of the growth of this protein system.