Elastic constants in orthorhombic hen egg-white lysozyme crystals

The ultrasonic sound velocities of cross-linked orthorhombic hen egg-white lysozyme (HEWL) crystals, including a large amount of water in the crystal, were measured using an ultrasonic pulse-echo method. As a result, seven elastic constants of orthorhombic crystals were observed to be $C_{11}$ = 5.24 GPa, $C_{22}$ = 4.87 GPa, $C_{12}$ = 4.02 GPa, $C_{33}$ = 5.23 GPa, $C_{44}$ = 0.30 GPa, $C_{55}$ = 0.40 GPa, and $C_{66}$ = 0.43 GPa, respectively. However, $C_{13}$ and $C_{23}$ could not be observed because the suitable crystal planes could not be cut from bulk crystals. We conclude that the observed elastic constants of the cross-linked crystals are coincident with those of the intrinsic crystals without cross-linking. Moreover, the characteristics of the elastic constants in orthorhombic HEWL crystals are due to the fact that the shear elastic constants, $C_{44}$, $C_{55}$, and $C_{66}$, are softer than in tetragonal crystals. That is, the shear components, $C_{44}$, $C_{55}$, and $C_{66}$, are one half of those of the tetragonal crystals.

Figure 1

Typical optical micrograph of the orthorhombic HEWL crystal (left) and a schematic figure of orthorhombic HEWL crystals (right). Growth habit planes and polarization directions of the transverse ultrasonic waves are illustrated in the figure.

Figure 2

The relationship between traveling distance and traveling time for the reflected transverse ultrasonic wave ${\upsilon }_3$, perpendicular to the (110) direction of cross-linked orthorhombic HEWL crystals. The wave is polarized along the [$1\overline{1}0$] direction.