Sound velocity and dynamic elastic constants of lysozyme single crystals
Introduction
The measurement of sound velocity in protein crystals is one of most suitable methods to examine elastic constants related to the inter-molecular force between proteins. The sound velocity measurement for only two protein crystals, i.e., ribonuclease-A and human haemoglobin, has been carried out using a laser-generated ultrasound so far [1]. The average value of those sound velocities was 1791 m/s.
As for the elastic constants, a Young modulus of the cross-linked crystalline lysozyme has been measured by a static method and estimated to be 0.2 GPa in wet condition [2], [3]. However, the used crystals were cross-linked by glutaraldehyde and the crystal sizes were an order of sub-millimeters. Thus, it is required to estimate elastic constants in intrinsic bulk crystals by measuring the sound velocity.
Recently, we have developed the crystal growth method to obtain protein crystals with millimeter sizes [4]. In addition, the high quality was identified by X-ray topography [5]. This success in obtaining large crystals with high quality has led to the measurement of sound velocity in intrinsic protein crystals. In this Letter, we present the measurement of the sound velocity of lysozyme single crystals in solution by an ultrasonic pulse-echo method. The sound velocity is obtained to be 1817 m/s. The dynamic Young modulus is estimated to be 2.70 GPa. The temperature and pH dependences are also presented.
Section snippets
Preparation of samples
Lysozyme crystals were grown by the so-called solubility gradient method [6] in the below procedure. Hen egg-white lysozyme (six times crystallized, Seikagaku Kogyo, Japan) was dissolved into the distilled water and 5% lysozyme solution was made. The lysozyme solution was adjusted to pH 4.0 by dropping HCl. A precipitant NiCl2 was put on the bottom in the test tube held vertically, to which the lysozyme solution was slowly added. The test tube was kept at 23°C in a clean room. The NiCl2
Sound velocity
The typical waveform of the reflective ultrasonic wave, measured using a transducer at frequency of 10 MHz, is presented in Fig. 1. The first reflective wave shows the reflective echo from the top of the crystal surface and the second wave comes from the bottom of the crystal. Therefore, the traveling time Δt spent passing through the crystals can be estimated as the peak-to-peak time difference. The traveling time was measured on several 10s of crystals with different thickness W over ∼2 mm to
Acknowledgements
We thank Prof. A. Kidera of Kyoto University for his critical comments on the experimental results. We also thank Riyon Co. and Sonix K.K. for their supports on the experimental equipments and Ms. Y. Shirai and Ms. Y. Ariyoshi for their help for the ultrasonic measurements.
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