PHASE-DETERMINATION OF A DIFFRACTION PEAK OF A MYOGLOBIN SINGLE CRYSTAL BY NUCLEAR γ-RESONANCE SCATTERING

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PHASE-DETERMINATION OF A DIFFRACTION

PEAK OF A MYOGLOBIN SINGLE CRYSTAL BY

NUCLEAR γ-RESONANCE SCATTERING

F. Parak, R. Mössbauer, W. Hoppe, U. Thomanek, D. Bade

To cite this version:

F. Parak, R. Mössbauer, W. Hoppe, U. Thomanek, D. Bade. PHASE-DETERMINATION

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JOURNAL DE PHYSIQUE Colloque C6, suppliment au no. 12, Tome 37, Dicernbre 1976, page C6-703

PHASE-DETERMINATION OF A DIFFRACTION PEAK

OF

A

MYOGLOBIN

SPNGLE CRYSTAL BY NUCLEAR

yRESONANCE SCATTERING

F. PARAK, R. L. MOSSBAUER, W. HOPPE, U. F. THOMANEK and D. BADE Physik-Department Technische Universitat Munchen, D-8046 Garching, Germany

R6sumB. - Une expkrience de diffraction d'un monocristal de myoglobin est prksente. L'interference entre la diffusion Rayleigh et la diffusion resonante des rayons gamma sert a determiner la phase de la reflexion 603.

Abstract.

-

A diffraction experiment on a frozen single crystal of myoglobin is described. The phase of the 603 reflection is determined from the interference pattern of the Rayleigh and the nuclear y-resonance scattering.

1. Introduction.

-

The X-ray structure analysis of proteins by means of a Fourier synthesis requires an experimental determination of both the amplitudes and the phases of the scattered waves of a large number of Bragg reflections. The amplitudes follow immediately from the intensity measurements, while the phase determinations are much less trivial. The

Phase Problem of a protein structure determination

is usually solved by the multiple isomorphous repla- cement method developed by Perutz and Kendrew [I]. The principle of phase determination in proteins by a new method using the interference between Rayleigh scattering and y-resonance scattering was described previously [2]. Tests were performed on a small anorganic molecule [3]. In this communication we report first scattering experiments on a protein single crystal, i. e. measurements on the 603 reflection of sperm whale myoglobin.

2. Experimental details.

-

The experiment was performed on a single crystal of carbon monoxide liganded myoglobin (MbCO). The volume was less than 0.5 mm3. The crystal was grown from CO liganded, 57Fe enriched material, frozen immediately after the crystalisation [4] and continously kept in this state. About 80

%

of the iron content was 57Fe. The crystal was mounted on a goniometer head and oriented with the aid of a X-ray precession camera. The b*-axis of the monoclinic crystal coincided with the K-circle of the camera. The crystal was then brought to a vapor cryostat (80 K) mounted on a Siemens 3 circle diffractometer. The b*-axis was parallel to the @ 6' and 2 6'-axis of the diffractometer. First the correct orientation of the crystal was proved by a 812 &scan with MoK, radiation. Then the @-circle was adjusted for excitation of the

60%-reflection. Afterwards the X-ray tube was replaced by a 57Co-source.

A 200 mC source of 57CoRh-deposited on an area of 2 x 2.5 mm2 was u s e d r ~ t the time of the experiment the activity had decreased to less than 100 mC. Inclination of the source yielded an active area of 2.5 x 1 mm2 as seen by the crystal. The distance between the source and the crystal was 150 mm. A Si(Li) counter was used for data collection. Figure 1 shows the $12 $-scan of the 603-reflection of the MbCO crystal performed with y-radiation. The maximal counting rate was about 1 c/min the background about 0.1 cfmin. During the following experiments the angle 6' was adjusted to 2.760. Figure 2 shows the absorption spectrum of the MbCO crystal with the counter at position 2 8 = 0. The absorption spectrum was carefully measured before and after the scattering experiment. As shown in the next

Fig. 1.

-

812 8 scan of the 603 reflection obtained with y-rad~a- tion. The error bars are &- 2/ JG, where N is the number

of counts.

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FIG. 2.

-

Absorption spectrum of MbCO single crystal. The crystal was oriented to obtain the 603 reflection. The fit parameters are linewidth

rexp

= 0.48 mmls, quadrupole splitting I!& = 0.36 mm/s, isomere shift S = 0.19 mm/s with respect t o the 57CoRh-source. The relative intensities of the two lines

_-

were 0.47 and 0.53.

section this spectrum provides some parameters which are necessary for the interpretation of the scattering experiment. The asymmetry of the intensities of the two lines of the quadrupole doublet due to the orientation of the crystal field gradient tensor relative to the incoming y-beam is clearly seen.

FIG. 3.

-

Scattering experiment on the 603 reflection of myoglobin. The solid curve represents a least square fit to the experimental data, the dashed curves represent theoretical calculations with phases differing by 90". For details see

text.

Figure 3 shows the result of the scattering experi- ment on the 603-reflection. The counter was set at the position 2 0 = 5.520. A 0-independent background counting rate of 146 counts has been subtracted. The total counting time was about 6 weeks.

3. Evaluation of the data.

-

A least square fit procedure was used to obtain the phase information from the experimental data presented in figure 3. The calculated counting rate R, used in this procedure is given by eq. (1)-(6).

2

; 1 2 1 + i p

rna,

2 n(E, Eaj) = - A

-

_faj

4 n 2 I Z - t l l + a

raj

2 W a j

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PHASE-DETERMINATION OF A DIFFRACTION PEAK OF A MYOGLOBIN SINGLE CRYSTAL C6-705

Conventional symbols have been used throughout (see i. e. 131). The unit cell of sperm whale myoglobin contains two molecules with one 57Fe nucleus each, which are specified by the index i (i = 1,2) [5]. The quadrupole splitting for each Fe nucleus is identical. The index j specifies the two lines ( j = 1,2). The indices a and s refer to absorber and source respec- tively.

I

Fo(hkl)

I

exp(icp(hk1)) gives for a particular reflection the Rayleigh scattering amplitude of the unit cell of a mosaic crystal. The aim of the present experiment is the determination of the phase cp(603). It was one of the two free parameters of the least square fit. For an unknown structure

I

F,(hkl)

I

may be determined by an X-ray scattering experiment which yields an intensity I(hk1) proportional to

(

Fo(hkl)

12.

In the present evaluation I~,(603)

I

was for simplicity calculated from the well known myoglobin structure [5]. n(E, Eaj) is the effective scattering amplitude of one iron nucleus with a resonance energy Eai. The phase ai which is determined by the relative positions of the two iron nuclei (i = 1, 2) in the unit cell, can be obtained for unknown structures by several methods [I]. For this paper it was taken for simplicity from the literature. The last factor of eq. (3) is a Debye Waller factor as discussed in [2, 3, 61.

The factor waj in eq. (4) takes into account the angular dependence of the two quadrupole transitions. The scattering amplitudes of the quadrupole lines with the resonance energies Eat and Ea2 depend on the orientation of the electric field gradient tensor with respect to the incoming beam and to the scattering angle. Measurements on deoxigenated sperm whale myoglobin crystals have shown, that the assumption of an axial symmetric field gradient is not neccessarily true [7]. Experiments for the determination of the electric field gradient tensor of MbCO are in progress [4], but final values do not yet exist. A rigorous treatment therefore was not possible. waj represents the percentage area of the line j in the absorption spectrum. Measurements yield w,, = 0.47 and

wa2 = 0.53. This treatment would be exact for a scattering angle 8 = 0 and is still a very good approxi- mation for 8 = 2.760.

No accurate determination of f a j for MbCO exists at present. The only data which are not very precise in the temperature region about 80 K were determined on metmyoglobin [6]. An interpolation showed that at 80 K f a values between 0.3 and 0.45 are reasonable. Good fits of the scattering experiment were obtained with fa, =fa, = 0.37. The line with

ra,

=

ra2

= 0.14 mm/s was used during the fit procedure. The factor p = 0.80 of eq. (4) gives the percentage of 57Fe enrichment of the sample.

I,(E, v ) represents the intensity distribution of the incoming radiation. As described in the second section the 57CoRh-source had a large specific activity. Since it was usedabout one year after the preparation

the 57Fe content was rather large, thus producing a large line broading. Calibration experiments yielded

rs

= 0.32 mm/s at the time of the scattering experiment.

f,

was taken to be 0.75.

The function A(E) describes the absorption due to the 57Fe nuclei. n;(E, Eaj) is the imaginary part of n(E, Eaj) in eq. (4). t gives the number of the unit cells per cm2. A MbCO crystal has no uniform thickness. The path length of the y-beam therefore yields for each small volume element of the crystal a different t. Nevertheless the present evaluation uses as an approach an homogenous average thick- ness of 0.4 mm corresponding to t = 0.594 x 10'' since it is rather difficult to take the shape of the crystal correctly into account. The consequence of this assumption will be discussed in the next section.

The factor c in eq. (1) is beside the phase cp(603) the second free parameter of the least square fit procedure. It calibrates the absolute scattering intensity of the unit cell together with the source intensity normalized to unity to the actual observed counts of the reflection.

4. Discussion.

-

The solid line (Nr 1) of figure 3 shows the result of the least square fit.

A

value of cp(603) =

-

l o was obtained. From the structure of myoglobin one calculates the value q(603) = 0. The phase proved to be rather insensitive to even large variations in the nuclear resonance parameters such asf,,

rs,

fa,

ra

as well as the thickness t . This appears

to be a consequence of the large value of the dispersive contribution to the scattering amplitude.

The dashed lines in figure 3 were calculated with the phases cp = 1800 (curve 2), cp = 900 (curve 3) and cp = 2700 (curve 4) with all other parameters being kept constant like in curve 1.

Obviously there exists no agreement between these curves and the experimental data. We estimate that in spite of the poor statistic of the experiment the accuracy of the present phase determination is in any case better than

+

450. This is at any rate good enough for the purpose of a structure determination. Although the least square fit gives a good result, there remain some systematical deviations of the fitted curve 1 and the experimental values, giving rise to exaggerated asymmetries on either side of the resonance. This behaviour may result from the assumption of one uniform thickness (0.4 mm). Regions of the crystal in which the path length of the y-ray beam is shorter than the average thickness increase the dispersive part of the curve, while the absorption part which is mainly responsible for the behaviour in the center decreases. A better thickness correction is postponed to the future, since it will likely use a comparison of different reflections with similar indices (hkl).

It should be mentioned, that the present equipment - allows only the measurement of reflections with the

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indices (hOk). In this region all reflections have the fiir Forschung und Technologic. The source was phase 0 or 1800. An equipment modification is in provided by the Deutsche Forschungsgemeinschaft. progress which will eliminate this restriction. We gratefully acknowledge the assistence of B. Win-

This work was supported by the Bundesministerium tergerst concerning the crystal preparation.

References

[I] For a review see i. e. PHU.LIPS, D. C., in Advances in Structure [4] PARAK, F., THOMANEK, U. F., BADE, D., WINTERGERST, B.,

Research by Diffraction Methods. Ed. b y R. Brill to be published.

and R. Mason (Vieweg, Braunschweig) 1966, Vol. 2, [5] WATSON, H. C., The stereochemistry of the protein myo-

p. 75. globin. I n : Progress in Stereochemistry, IV. London.

[2] PARAK, F., MOSSBAUER, R. L., HOPPE, W., Ber. BUNSBNGES, Butterworths (1968).

Phys. Chem. 74 (1970) 1207-1216. [6] PARAK, F., FORMANEK, H., Acta cryst A 27 (1971) 573-578.

[3] PARAK, F., MOSSBAUER, R. L., BIEBL, U., FORMANEK, H., [71 EICHER, H., BADE, D., PARAK, F., J. Chem. Phys. 64 (1976)