Macrobond Analysis of the Macro- and Micromorphology of Monoclinic

May 5, 2001 - The features of the advancing steps of the growing surface were related to the step ledge energies. The hydration enthalpy of dissolutio...
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Macrobond Analysis of the Macro- and Micromorphology of Monoclinic Lysozyme Crystal Hondoh,†,‡

Sazaki,*,‡

Hironori Gen Satoru Kazuo Nakajima,‡ and Yoshiki Matsuura†

Miyashita,‡,§

Stephen D.

Durbin,‡,⊥

CRYSTAL GROWTH & DESIGN 2001 VOL. 1, NO. 4 327-332

Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-087l, Japan, and Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Received February 11, 2001

ABSTRACT: Intermolecular contacts in crystals of monoclinic form hen egg-white lysozyme were analyzed using the macrobond approach. Both the macroscopic crystal morphology and the microscopic morphology observed by atomic force microscopy were explained well using macrobond energies. The features of the advancing steps of the growing surface were related to the step ledge energies. The hydration enthalpy of dissolution of the crystal was estimated using the macrobond energies and the dissolution enthalpy of the crystal obtained from solubility measurements, and showed good agreement with the reported values obtained from thermodynamic measurements. 1. Introduction Hen egg-white lysozyme is known to exhibit multiple polymorphism depending on the precipitant salts, pH, and temperature.1 The tetragonal form is the most extensively studied and characterized in terms of the crystal growth. Recently, the other forms have also been the subject of crystal growth studies.2-4 The morphologies of these polymorphous crystals are quite different from each other, reflecting the differences in the crystal packing of lysozyme molecules. Study of the intermolecular interactions in the crystal is particularly important for understanding the morphology of the crystal. In the case of low molecular weight compounds, the periodic bond chain (PBC) approach of Hartman and Perdok was successfully applied in predicting the morphology of the crystal.5-7 In the case of proteins, the PBC approach should also be able to predict the morphology on the basis of the relative strengths of the intermolecular interactions involved. Several studies were reported on the morphology of protein;8-12 however, evaluation of the absolute value of the interaction energy in protein crystals is still difficult, due to the complicated nature of the intermolecular interactions. Recently, for orthorhombic lysozyme, the correlation of morphology and intermolecular contacts has been reported.2 In that work, the method of macrobond analysis was used, that is, the intermolecular bond strengths were evaluated for each molecular contact (macrobond) in the crystal and discussed in relation to the morphology essentially by using the PBC approach. In the present study, we have applied the macrobond approach to monoclinic lysozyme crystals to explain the macroscopic morphology, and also the micromorphology * To whom correspondence should be addressed. Fax +81-22-2152011; E-mail [email protected]. † Osaka University. ‡ Tohoku University. § Present address: Department of Medicine, Toyama Medical and Pharmaceutical University, 2630 Sugitani, Toyama 930-0194, Japan. ⊥ Present address: RightNow Technologies, 77 Discovery Drive, P.O. Box 9300, Bozeman, MT 59718, USA.

of the steps on the growing crystal surface observed by atomic force microscopy (AFM). The sum of the macrobond energies has been compared to both the thermodynamically evaluated hydration energy and the observed dissolution enthalpy, showing good correlation among them. 2. Experimental Procedures 2.1. Crystallization. Six times recrystallized hen egg-white lysozyme (Seikagaku Kogyo Co. Ltd.) was used without further purification. The other chemicals used for preparing the solution were of reagent grade. The monoclinic lysozyme crystal was grown according to the method described before.13 The buffer solution was 50 mM sodium acetate (pH 4.5), and the precipitant was 40 mg/mL NaNO3 dissolved in the same buffer. Equal volumes of the lysozyme (40 mg/mL) and precipitant solutions were mixed on a glass plate using a sitting-drop vapor diffusion technique. The drop was kept at room temperature. Aggregated crystals (spherulites) appeared after 1 day. Single crystals were then prepared by the microseeding technique.14,15 The aggregated crystals were crushed using a Teflon ball (5.2 mm diameter) with simultaneous ultrasonication. A dilute suspension of the crushed crystals was transferred to the solution of 10 mg/mL lysozyme and 20 mg/mL NaNO3 in 50 mM acetate buffer (pH 4.5), and kept at 20 °C. Single crystals grew to a typical size of 0.7 mm in length along the b-axis in 1 day. These crystals were used for further studies. 2.2. Atomic Force Microscopy. The monoclinic lysozyme seed crystals for the AFM observations were grown on a glass cover slip as follows. According to the recipes described in the previous section, the supersaturated lysozyme solution was prepared and transferred into a small well made of a glass cover slip with a rubber O-ring. After the micro-seeding process, the crystals sedimented, grew, and fixed on the cover slip. Prior to the observation, the cover slip was attached to a steel support disk and rinsed in freshly prepared lysozyme solution containing 1.7 mg/mL lysozyme, 20 mg/mL sodium nitrate in 50 mM sodium acetate buffer at pH 4.5. Then the cover slip was mounted on the AFM stage equipped with a fluid cell, with no exposure of the crystals to the air. The microscope used for the observation was a Nanoscope III (Digital Instruments Inc.) equipped with a silicon nitride tip. All observations were carried out at room temperature (around 21 °C), and the micromorphology on the crystal surface was observed using tapping mode. The lysozyme solution of 1.7 mg/ mL was used for the AFM measurement. Since the tempera-

10.1021/cg015506n CCC: $20.00 © 2001 American Chemical Society Published on Web 05/05/2001

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ture in the fluid cell is usually several degrees higher than the room temperature, the supersaturation, σ ) ∆µ/kBT ) ln(C/Ce), was smaller than 0.31 at the measurement conditions, here ∆µ, kB, T, C, and Ce (1.25 mg/mL at 21 °C) are the difference in the chemical potential of lysozyme between crystal and solution, the Boltzmann constant, the absolute temperature, and initial and equilibrium concentrations of lysozyme, respectively. 2.3. Macrobond Analysis. The macrobond approach2 analyzes first the interatomic interactions between adjacent molecules in the crystal lattice. The program DISMAP (Y.M., unpublished) lists the atomic pairs whose distances are less than 4 Å in every contact site between symmetry-related molecules in the crystal. The van der Waals radii of ordinary atoms composing the protein molecule are in the range of 1.4 to 2.0 Å. The limiting distance value of 4 Å was chosen because no other atoms can come into the space between two atoms having that separation.2 A macrobond contact site is defined if at least one atom pair whose distance are less than 4 Å exists between neighboring molecules (and comprises all such pairs for the given molecules.) From the atomic interaction list in a macrobond, the types of interaction between the atom pairs are classified into four categories: hydrogen bond including ionic interaction, water-mediated hydrogen bond, water-water hydrogen bond, and van der Waals contacts representing all other interactions. For each independent macrobond, the numbers of each type of interactions are counted, and the macrobond energies are evaluated. Bond energies were approximated as 3.0, 1.5, 0.7, and 0.3 kcal/mol (12.6, 6.3, 2.9, and 1.3 kJ/mol) for the hydrogen bonds in normal atom pairs (including any ions in the solution), the water-mediated hydrogen bonds, the water-water hydrogen bonds, and the van der Waals interactions (all interactions besides the other three types), respectively. For the value of each bond energy, the approximation was discussed in the previous paper.2 Then the stereoscopic macrobond diagram (as in Figure 7 in ref 11) is drawn by computer graphics (program MACROB, Y.M., unpublished) representing a macrobond by a line with a unique color for each kind. The numbers of each macrobond crossing a certain crystallographic plane (h k l) is counted by eye with careful study of the diagram. The macrobond components for the (h k l) plane are listed, and the bonding energies across the (h k l) plane, Eacross, are calculated by summing the energies of the macrobonds crossing the plane. The value of Eacross corresponds to the energy to slice the (h k l) plane. The coordinates of the monoclinic lysozyme used in this analysis were taken from the Protein Data Bank (PDB id code, 5LYM).

3. Results 3.1. Morphology. Figure 1 shows a photomicrograph of a monoclinic lysozyme crystal. The unit cell dimensions were identified as the same with those previously reported:16 space group P21; a ) 28.0, b ) 62.5, c ) 60.9 Å, and β ) 90.8°, with two molecules in the asymmetric unit. Miller indices of the crystal faces were determined by an optical device mounted on a four-circle diffractometer as described before.2 The indices of the developed faces are (1 0 1h ), (1 0 1), (0 0 1), and (0 1 0), as shown in Figure 2. The polarity of the crystal was determined by X-ray diffractometry. As seen in Figure 1, the shapes of the (0 1 0) faces appear differently on +b and -b sides. The (0 1 0) face of the -b side looks rounded while the +b side does not. This feature became more appreciable with increasing supersaturation, suggesting that kinetic roughening,17 which could eventually lead to a morphological instability, takes place on the -b face. One further pronounced feature was observed under high supersaturation. As shown in Figure 1 (the super-

Hondoh et al.

Figure 1. A photomicrograph of the monoclinic form lysozyme crystal, obtained with an initial lysozyme concentration of 20.0 mg/mL [σ ) ln(C/Ce) ) 2.91 at 20 °C], 20 mg/mL NaNO3 in 50 mM sodium acetate buffer (pH 4.5). The crystallization period was 4 days. Note the hollow region toward the +b end of the crystal.

Figure 2. Morphology of the monoclinic lysozyme crystal.

saturation σ ) 2.91), a hollow opening developed on the +b face. This hollow opening is considered to be brought about by higher supersaturation at the edge of the +b face than at the center of this face due to the Berg effect,18 resulting in enhanced growth rate at the edge. This feature shows that the growth rate of the +b face is much faster than that of the -b face, as proved from the anisotropic development of growth sectors in the crystal. 3.2. Surface Micromorphology Observed by AFM. Typical AFM images on the (1 0 1h ) face of the monoclinic crystals are shown in Figure 3. Figure 3a shows a spiral growth pattern. Similar spiral growth patterns were found on all five crystals observed by AFM. The region indicated by a black arrow in Figure 3a is a Frank-Read source,19,20 where adjacent right- and left-hand screw dislocations are merged, forming an enclosed hillock. An enlarged AFM image of this site, taken at a later time, is shown in Figure 3b. The height of a single step was measured as 2.5 nm, which corresponds to the interplanar spacing of (1 0 1 h ) plane, showing that the step height is that of one molecule. In the monoclinic lysozyme crystal, many screw dislocations that lie close to each other were observed, as shown in Figure 3c. A

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Figure 3. AFM images of the (1 0 1h ) face of the monoclinic lysozyme crystal, (a) showing spiral steps with elongated straight edges along , short straight along at the +b side, and round at the -b side. A black arrow in the figure shows Frank-Read source. (b) An enlarged image of this region. (c) A region showing many screw dislocations (white arrows).

high density of screw dislocations is a characteristic feature of the monoclinic crystal. In the case of tetragonal lysozyme, the number density of screw dislocations is much smaller than for the monoclinic crystal even when we observe the crystal under almost saturated conditions (on the order of one screw dislocation per crystal or less, depending on conditions21). The larger height of the single step of the tetragonal crystal [5.8 nm for the (1 1 0) face, two molecules high;22 3.4 nm for the (1 0 1) face, one molecule high23] gives the larger energy that is necessary to create a screw dislocation, since that energy is proportional to the square of the size of the Burgers vector.17 Then the larger step height might be one of the reasons that is responsible for the smaller density of the screw dislocation in the tetragonal crystal, although there still exist many factors that affect the creation of the screw dislocation, such as supersaturation and impurity incorporation. The shape of the spiral step also exhibits some

characteristic features. As shown in Figure 3a, the steps advancing to the [1 0 1] and [1h 0 1 h ] directions are smooth and long. The steps toward the [0 1 0] direction (on the +b side of the growth hill) exhibit straight edges, while the steps to the [0 1h 0] direction (on the -b side) show rough edges, which is due to the difference in the structure of the step ledges reflecting the polar structure of the crystal. This microscopic roughness of the steps to the [0 1h 0] direction might correspond to the macroscopic rounding of (0 1h 0) face (Figure 1), since such the roughness of the steps shows that stacking of the molecules to [0 1 h 0] direction tends to become rough also on the (0 1 h 0) face and such microscopically rough crystal surface could lead to a morphological instability. The density of the steps toward the [1 0 1] direction is higher (right-hand side of the figure) than that toward the [1 h01 h ] direction (left-hand side). The difference in the surface molecular structures in the two directions might

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Hondoh et al. Table 1. Direct Hydrogen Bonds between Amino Acid Residue Atoms in the Intermolecular Contacts (1) Macrobond A0B1 molecule at (x, y, z)

molecule at (x-1, y, z-1)

distance (Å)

Ser 81 OG

ASN 113 O

2.85

(2) Macrobond A0A2 molecule at (x, y, z)

molecule at (x-1, y, z)

distance (Å)

GLY 16 O GLY 16 O ASN 77 ND2 LYS 97 NZ

ARG 114 NH1 ARG 114 NH2 ARG 45 NH1 THR 47 OG1

2.72 3.42 3.47 3.02

(3) Macrobond A0B2

Figure 4. Macrobond diagram in the unit cell of the monoclinic lysozyme crystal. Cross points of the macrobonds represent the center of mass of lysozyme molecules. Four molecules exist in the unit cell, and an asymmetric unit contains molecules A and B. Eleven different types of the macrobonds present in the crystal.

cause this difference in the step density, although its mechanism is not clear yet. 3.3. Macrobond Analysis. In the present monoclinic crystal, the unit cell contains four molecules, with two molecules in the asymmetric unit. The macrobonds must be defined separately for the two asymmetric molecules A and B. The analysis showed that a total of 11 independent macrobonds exist in the monoclinic crystal (Figure 4), in contrast to three in the orthorhombic crystal.2 The hydrogen bonds involved in macrobonds are listed in Table 1. An intermolecular hydrogen bond is recognized when potential hydrogen bond pair atoms are closer than roughly 3.5 Å. The values of the macrobond energies are listed in Table 2. From the macrobond diagram (Figure 4), the macrobond components and the slicing energy of the (h k l) plane in vacuo Eacross(h k l) were evaluated as shown in Table 3. The values for {1 0 1h } and {1 0 1} are smaller than the others. This is consistent with the observed morphology, where these faces are highly developed. This result indicates that the macrobond analysis is a useful technique for rough prediction of developed faces of protein crystals. The less developed {0 0 1} face also has a small value. However, the {0 1 0} face that develops at the tops of the rod crystal has the highest Eacross of any face. The value for the {0 1 1} face is smaller than that of the {0 1 0} face; thus the {0 1 1} face might be thought more likely to develop at the tops of the rod. This is not consistent with the observation. In the case of the {0 1 0} face, the growth kinetics would play an important role for the development. Although data are not shown here, after a growth period of 1 year, truncated faces that apparently look like the {0 1 1} face appeared on the edges of the {1 0 1 h } faces. Eacross(h k l) is the energy to slice the plane (h k l), and not the surface energy. The different behavior of {0 1 0} faces of the +b and -b sides of the crystal should be attributed to the difference in the surface structures of those faces, due to the polar nature of the crystal structure with respect to the unique monoclinic b-axis.

molecule at (x, y, z)

molecule at (x-1, y, z)

distance (Å)

GLY 22 N SER 24 OG GLN 121 OE1

NO3 512 O1 GLN 41 NE2 THR 47 OG1

3.51 2.98 3.02

(4) Macrobond B0B2 molecule at (x, y, z)

molecule at (x-1, y, z)

distance (Å)

ASP 18 O ASN 19 O ARG 21 N

ARG 114 NH2 ARG 114 NH1 NO3 515 O1

3.33 3.48 3.25

(5) Macrobond A0A3 molecule at (x, y, z)

molecule at (x, y-0.5, z+1)

distance (Å)

ARG 73 NH2 ASP 101 O ASP 101 O ASP 101 OD1 ASP 101 OD1 ASP 101 OD2 ASP 101 OD2 GLY 102 O ASN 103 OD1 ASN 103 OD1 ASN 103 OD1 ASN 103 ND2 ASN 103 ND2 ASN 106 O

ARG 125 NH1 ARG 5 NE ARG 5 NH2 ARG 125 NE ARG 125 NH2 ARG 5 NH2 ARG 125 NE ARG 5 N ARG 5 N CYS 6 N CYS 6 SG ARG 5 NH2 CYS 6 SG ARG 128 NH2

2.61 3.29 3.14 3.45 3.06 3.02 2.50 3.49 3.46 2.74 3.36 3.27 3.28 3.27

(6) Macrobond B0B3 molecule at (x, y, z) ARG 61 NH1 ARG 73 NE ARG 73 NH2 ASP 101 O ASP 101 OD1 ASP 101 OD2 ASN 103 ND2 ALA 107 O ARG 112 NH1 ARG 112 NH2

molecule at (x+1, y-0.5, z+2) ASP 119 OD1 ASP 119 OD2 ASP 119 OD2 ARG 5 NH2 ARG 125 NH2 ARG 5 NE GLY 126 O ARG 128 NE ARG 128 O ARG 128 O

distance (Å) 3.01 3.27 3.26 2.94 3.03 2.96 2.95 3.41 2.95 2.68

(7) Macrobond B0A3 molecule at (x, y, z) ARG 73 NH2

molecule at (x, y-0.5, z+1) ASP 87 OD1

distance (Å) 2.75

(8) Macrobond A0B4 molecule at (x, y, z) ARG 68 NH2 ARG 68 NH2

molecule at (x, y, z-1) ARG 21 O GLY 22 O

distance (Å) 3.25 3.13

(9) Macrobond A0B0 molecule A at (x, y, z)

molecule B at (x, y, z)

distance (Å)

LYS 116 NZ ASP 119 N

ASN 77 OD1 ASP 87 OD2

3.49 2.99

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Table 2. Macrobond Energy macrobond

A0B1

A0A2

B0B2

A0B2

A0A3

B0B3

B0A3

A0B4

A0B5

B0A5

A0B0

total number of atom-atom pairs direct H-bonds water-mediated H-bonds van der Waals interactions macrobond energy (kJ/mol)

40 1 5 34 86.6

40 4 3 33 110

20 3 2 15 69.0

34 3 5 26 102

89 14 5 70 296

104 10 6 88 274

14 1 3 11 45.2

19 2 0 17 46.4

16 0 2 14 30.2

13 0 4 9 36.4

27 2 1 24 61.6

Table 3. Macrobond Components Vacross and Slicing Energy of the {h k l} Plane Eacross in Vacuo {h k l}

Vacross

Eacross (× 10-2 J/m2)

{1 0 1 h} {1 0 1} {1 0 0} {0 0 1} {1 1 0} {0 1 1} {0 1 0}

2A0A2+2A0B2+2B0B2+2A0B4+2A0B5+2B0A5 2A0B1+2A0A2+2B0B2+2B0A3+2A0B0 A0B1+2A0A2+2B0B2+A0B2+B0A3+A0B4+A0B5+B0A5+A0B0 A0B1+A0B2+B0A3+A0B4+A0B5+B0A5+A0B0 2A0A2+2B0B2+A0A3+B0B3+B0A3+2A0B4+A0B5+B0A5+2A0B0 A0B1+A0B2+A0A3+B0B3+A0B4+2A0B5+A0B0 B0B2+A0A3+B0B3+A0B4+A0B5

1.57 1.60 1.75 1.78 2.63 3.03 3.64

Figure 5. Schematic illustration of the possible step directions that are expected to develop on the (1 0 1h ) face of the monoclinic lysozyme crystal. Step advancing directions (a) normal (), (b) parallel (), and (c) oblique () to the b-axis. No other slant step direction is considered because of their large ledge energy. Shaded and white molecules in the figure represent the lysozyme molecules A and B in the asymmetric unit, respectively.

The features of the steps on the (1 0 1 h ) face observed by AFM can also be interpreted in terms of the macrobond energies. The packing of the molecules on the (1 0 1 h ) face, and the step directions corresponding to low slicing energy of the step ledge are depicted in Figure 5. As shown in the figure, three step directions exist that are plausible. These are the step advancing directions normal (), parallel (), and oblique () to the b-axis: respective step directions (a), (b), and (c) in Figure 5. The calculated step ledge slicing energies were 1.0, 3.0, and 4.2 × 10-2 J/m2, respectively. No other slant step direction was considered because their rough step shape would imply a large ledge energy. As shown in Figure 3, the steps that actually appeared on the (1 0 1 h ) face advanced normal and parallel to the b-axis, which is consistent with the calculated energy values. Furthermore, the steps advancing normal to the b-axis were longer than those advancing parallel (Figure 3a), consistent with the former having the lower calculated ledge slicing energy. Macrobond analysis gives us the enthalpy change, ∆Hmacro, to take the all lysozyme molecules out of the

Figure 6. Enthalpy diagram in the dissolution process of a protein crystal. ∆Hmacro represents the enthalpy change to transfer the molecule from crystal to vacuo and is calculated from the sum of the macrobond energies. ∆Hdis represents the enthalpy of dissolution to transfer molecules from crystal to solution, which is derived from the van’t Hoff plot. The contribution of the enthalpy of hydration of the molecule ∆Hhyd can be calculated as ∆Hmacro - ∆Hdis.

crystal in vacuo. ∆Hmacro was estimated to be 1158 kJ/ mol from the sum of the macrobond energies for a molecule. If the dissolution enthalpy of the crystal is known, we can estimate the hydration energy of the molecule, as schematically illustrated in Figure 6. The dissolution enthalpy of the crystal can be calculated from the van’t Hoff plot using the solubility data shown in Figure 7. These data were measured using the interferometric technique. The details of the solubility measurement were reported in the previous paper.24 As shown in Figure 7, the solubility data were well fitted by the van’t Hoff equation:

(

Ce ) exp -

)

∆Hdis 1 ∆Sdis ‚ R T R

(1)

Here, Ce, R, ∆Hdis, and ∆Sdis are the solubility (in mole fraction), the gas constant, the dissolution enthalpy and entropy, respectively. From the fitting curve, ∆Hdis and T∆Sdis of the monoclinic crystal at T ) 300 K were calculated as 102 ( 13 and 70 ( 12 kJ/mol, respectively. Then, the hydration enthalpy for the contact area on the lysozyme molecule can be estimated to be 1056 kJ/ mol. An accessible surface area25 of the lysozyme molecule and the contact area in the monoclinic lysozyme

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Hondoh et al.

Acknowledgment. The authors thank Prof. H. Komatsu for useful discussions. Thanks are also due to the partial support by Grants-in-Aid of Scientific Research Nos. 10555001 and 12750006 (G.S.) and No. 11305001 (K.N.) of the Japanese Ministry of Education, Science and Culture, and to partial supports by funds from REIMEI Research Resources of Japan Atomic Energy Research Institute. This study was carried out as a part of “Ground Research Announcement for Space Utilization” promoted by NASDA and Japan Space Forum. Supporting Information Available: Photomicrograph of the monoclinic form lysozyme crystal and a van’t Hoff plot of the solubility curve of the monoclinic lysozyme crystals shown in Figure 7. This material is available free of charge via the Internet at http://pubs.acs.org. Figure 7. Solubility curve of the monoclinic lysozyme crystals. The solubility of the crystal was measured using the interferometric technique.24 Solid curve in the figure is obtained from the exponential fit to the van’t Hoff plot. Solution of 20 mg/mL NaNO3, in 50 mM sodium acetate buffer (pH 4.5).

crystal were estimated to be 6.48 × 10-17 and 3.02 × 10-17 m2 (46.6%), respectively. Then the hydration enthalpy for the total accessible surface area of the lysozyme molecule can be roughly estimated as 2300 kJ/ mol assuming that the hydration enthalpy in the contact area is almost the same as that in the remaining area. This rough estimation of the hydration enthalpy shows quite good agreement with the enthalpy value estimated by summing up the experimentally determined hydration enthalpies of each functional groups,26 which gave a value of 1970 kJ/mol for a lysozyme molecule, supporting the validity of the macrobond approach for quantitative analysis. 4. Conclusions The intermolecular contacts in the monoclinic hen egg-white lysozyme crystal have been analyzed successfully using the macrobond approach. The macromorphology in terms of observed developed faces of the crystal could be understood from the anisotropic macrobond energies. The micro-morphology (step patterns) observed by AFM was interpreted within the same approach. The method of macrobond analysis, like the PBC approach that has been successful for the interpretation of the habit of small molecule crystals, was shown to be applicable to protein crystals. In protein crystals, the macrobond energy is significantly affected by the presence of ordered water molecules. We measured the solubility of the monoclinic crystals and showed that the macrobond energy that corresponds to the intermolecular bond energy in the crystal in vacuo can be considered as the sum of the dissolution enthalpy obtained from the solubilities and the thermodynamically estimated value of hydration enthalpy of protein molecules.

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