Nishinaga Handbook of Crystal Growth

Fundamentals
2. Auflage 2014
ISBN: 978-0-444-59376-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 1A-1B, 1214 Seiten

Reihe: Handbook of Crystal Growth

Volume IAHandbook of Crystal Growth, 2nd Edition (Fundamentals: Thermodynamics and Kinetics) Volume IA addresses the present status of crystal growth science, and provides scientific tools for the following volumes: Volume II (Bulk Crystal Growth) and III (Thin Film Growth and Epitaxy). Volume IA highlights thermodynamics and kinetics. After historical introduction of the crystal growth, phase equilibria, defect thermodynamics, stoichiometry, and shape of crystal and structure of melt are described. Then, the most fundamental and basic aspects of crystal growth are presented, along with the theories of nucleation and growth kinetics. In addition, the simulations of crystal growth by Monte Carlo, ab initio-based approach and colloidal assembly are thoroughly investigated. Volume IBHandbook of Crystal Growth, 2nd Edition (Fundamentals: Transport and Stability) Volume IB discusses pattern formation, a typical problem in crystal growth. In addition, an introduction to morphological stability is given and the phase-field model is explained with comparison to experiments. The field of nanocrystal growth is rapidly expanding and here the growth from vapor is presented as an example. For the advancement of life science, the crystal growth of protein and other biological molecules is indispensable and biological crystallization in nature gives many hints for their crystal growth. Another subject discussed is pharmaceutical crystal growth. To understand the crystal growth, in situ observation is extremely powerful. The observation techniques are demonstrated. Volume IA - Explores phase equilibria, defect thermodynamics of Si, stoichiometry of oxides and atomistic structure of melt and alloys - Explains basic ideas to understand crystal growth, equilibrium shape of crystal, rough-smooth transition of step and surface, nucleation and growth mechanisms - Focuses on simulation of crystal growth by classical Monte Carlo, ab-initio based quantum mechanical approach, kinetic Monte Carlo and phase field model. Controlled colloidal assembly is presented as an experimental model for crystal growth. Volume IIB - Describes morphological stability theory and phase-field model and comparison to experiments of dendritic growth - Presents nanocrystal growth in vapor as well as protein crystal growth and biological crystallization - Interprets mass production of pharmaceutical crystals to be understood as ordinary crystal growth and explains crystallization of chiral molecules - Demonstrates in situ observation of crystal growth in vapor, solution and melt on the ground and in space

Autoren/Hrsg.

Nishinaga, Tatau

Leseproben

19.3. The Thermodynamics of Protein Crystallization

19.2.1. Definitions

In correspondence to the typical physiological, laboratory, and industrial conditions, protein phase transitions are typically considered under constant temperature and pressure. With such constraints, the transfer of protein molecules from solution to the crystal is driven by the change of Gibbs free energy [35]. The change in Gibbs free energy of crystallization ?Gocryst at constant temperature T is the sum of the contributions of the enthalpy ?Hocryst and entropy ?Socryst: ?Gocryst = ?Hocryst – T?Socryst. The associated crystallization equilibrium constant,

cryst=exp(-?Gcrysto/RT),Kcryst=Ce-1,

(19.1)

in which e-1 is the protein solubility with respect to the studied crystalline form, R is the universal gas constant, and T is the absolute temperature.

19.2.2. Molecular Processes Underlying the Thermodynamics of Protein Crystallization

In the last few years, chemists and physicists working in the area of protein solutions realized that the molecular-level processes in protein solutions operate on two distinct microscopic length scales: a finer scale, determined by the size of water and other solvent molecules, and a coarser one, corresponding to the size of the significantly larger protein molecules [16,36,37]. Whereas some features of the mechanisms of protein crystallization can be reasonably well understood on the coarser length scale of the protein molecules, understanding of principles that govern molecular recognition and the thermodynamic driving forces leading to or preventing crystallization requires consideration of the finer length scale of the solvent [38,39]. Various techniques have shown that a several ångstrom thick solvent layer exists around protein molecules [40–44]. Within this biological layer [44,45], the water molecules are in either of two states, between which a dynamic equilibrium exists: directly attached to the protein surface, and free, Figure 19.5. Another equilibrium exists between the biological layer and the bulk solution water [44]. This layer affects enzyme-substrate and deoxyribonucleicacid (DNA)-drug binding [46,47], and is natural to expect a similar effect on the protein–protein interactions involved in protein crystallization.

FIGURE 19.5 Schematic of exchange of waters within a biological layer and between this layer and solution bulk. Hydrogen bonds are shown as dashed lines. There are also free water molecules that are not directly hydrogen bonded to the protein. Solid curved arrows indicate the dynamical exchange between free and bound water. Free water molecules diffuse into the layer from the bulk, and this represents a feedback mechanism of layer hydration. zL, width of hydration layer, kbf and kfb, kinetic constants of exchange between the free water and bound water molecules in the hydration layer. With permission from Ref. [44].

Although the existence of this layer is necessary for the protein's conformational stability [48], it may interfere thermodynamically with protein function (DNA or substrate binding, or other) and assembly. This potential conflict is resolved by the fact that in contrast to the classically envisioned iceberg structure [48], the solvent layer is not rigid, and the water molecules are constantly exchanged between the different states [44,45]. Below, we show that the enthalpy and entropy contributions from the biological solvent layer largely determine the thermodynamics of crystallization.

A number of recent molecular dynamics (MD) studies of model mesoscopic solutes: colloid particles, graphene sheets, protein molecules, etc., were aimed at quantification of the intermolecular interaction potentials on the length scales of a water molecule [40–44,49–57]. As expected, these studies demonstrate in these potentials a primary attractive minimum, mostly due to the van der Waals interactions. The MD results also indicate that in addition to this minimum, there exist relatively shallow secondary and tertiary minimums, Figure 19.6. These extra minimums correspond to one and two water layers between the solutes. Three key observations are in order: (1) The extra minimums have depth of several units of the thermal energy kBT. (2) They are present independent of whether the solutes are hydrophilic or hydrophobic, and whether the bare solutes attract or repel [52–54,56–58]. (3) The secondary and tertiary minimums are at distances significantly greater than the typical binding distances between small molecules.

Several analyses of protein crystallization thermodynamics have shown that the standard free energy change for crystallization ?Gocryst is only moderately negative; this makes the crystallization process sensitive to even the slightest changes in the experimental conditions. Intuitively, it appears that crystallization is prohibitively disfavored by a massive negative change in entropy as three-dimensional (3D) order is imposed on the molecules in the crystal lattice. Indeed, this entropy cost consists of the loss of six translational and rotational degrees of freedom per protein molecule, and is only fractionally compensated by the newly created vibrational degrees of freedom [59,60]. Theoretical models suggest that the balance should yield an average entropy loss of about -100 J mol-1 K-1 [59,61] although it may be as high as -280 J mol-1 K-1, as predicted for insulin [60]. This negative entropy contributes to a positive ?Gocryst and, unless it is compensated, no crystallization will occur. The compensation may come from a negative ?Hocryst or from the entropy of accompanying processes.

FIGURE 19.6 The potential of mean force for interaction in water between two graphene sheets, each consisting of 60 carbon atoms, which imitate the interactions between the hydrophobic amino acid groups on the surface of protein molecules. Separation is measured from the centers of the C-atoms. vdW indicates the deepest minimum due to van der Waals attraction between bare C atoms, the other two minimums, and all three local maximums are due to water structured at the surfaces of the graphene sheets. With permission from Ref. [53].

In those few cases where accurate measurements were made, the crystallization enthalpy ?Hocryst varied within a broad range, from -70 kJ mol-1 for lysozyme [62], through ~0 kJ mol-1 for ferritin, apoferritin, and lumazine synthase [63–65], to 155 kJ mol-1 for hemoglobin C [66,67]. Thus, enthalpy effects are unlikely to rationalize crystallization in a general sense, and in many cases are also unfavorable.

To understand entropy effects, we consider the two distinct microscopic length scales significant for protein solutions. Experimental studies of crystallization of such proteins as apoferritin, ferritin, hemoglobin C, lysozyme, insulin and lumazine synthase allowed estimates of the enthalpy, entropy, and the standard free energy change for crystallization as functions of the temperature and of the composition of the respective solutions [63,66–68]. These thermodynamic determinations indicate that upon incorporation into a crystal lattice, some of the structured water/solvent molecules, bound to the protein molecule in solution, are released or, conversely, additional water/solvent molecules may be trapped, as schematically depicted in Figure 19.7. Both phenomena would have a significant entropy effect: the analogous transfer of water from clathrate, crystal hydrate, or other ice-like structures leads to an entropy gain of ~22 J mol-1 K-1 [61,69] Considering the complexity and importance of the entropy effects, the solvent and protein entropy changes during crystallization have been distinguished:

Gcrysto=?Hcrysto-T(?Sproteino+?Ssolvento).

(19.2)

FIGURE 19.7 A schematic illustration of ?Ssolvent > 0. The protein molecules in solution and its incorporation site are coated with water molecules, which are released upon attachment of the protein molecules to the crystal. If, alternatively, additional water molecules are trapped upon attachment of a protein molecule, ?Ssolvent < 0 would ensue.

A more negative ?Gocryst is favored by a positive sum (?Soprotein + ?Sosolvent). In some cases it has been...