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Neutron small-angle scattering from aqueous solutions of oxy- and deoxyhaemoglobin
J. Mol. Bid. (1969) 41,231-236
Neutron Small-angle Scattering from Aqueous Solutions of Oxy- and Deoxyhaemoglobin R. SCHNEIDER, A. MAYER Physik-Department der Technischen Hochschule, Miinchen, Germany
W. SCHMATZ, B. KAISER AND R. SCHERM Institut fiir Festktirper- und Neutronenphysik der Kernforschungsanluqe Jiilich, Germany (Received 15 November 1967, and in revised form 1 January 1969) The neutron small-angle scattering of human haemoglobin was measured. Oxygenated and deoxygenated haemoglobin in radius of gyration.
in aqueous solution were found to differ
1. Introduction While scattering of X-rays is due to the electron density distribution of the scattering medium, the scattering of neutrons is related to the nuclear density distribution. In general, electronic and nuclear density distributions are not identical, but in proteins observed at low resolution they would be expected to be similar. Comparative studies of X-ray and neutron scattering may give supplementary information about the structure of the scattering medium. In the experiments to be described, the neutron small-angle scattering from aqueous solutions of oxy- and deoxygenated human haemoglobin was measured and the results were compared with those obtained from X-ray small-angle scattering and X-ray diffraction analysis. 2. Theory Intensity and angular distribution of small-angle scattering give information on the shape and volume of the scattering particle. The theory of neutron small-angle scattering is analogous to that of X-ray scattering (Guinier & Fournet, 1955). The cross-section for scattering of a single particle (haemoglobin molecule) per solid angle is given by: d -=
=hb
dSZ
jflp(r) exp (iKr) d,r ’ I
C
where K is the scattering vector. Thus the scattering of neutrons is related to the difference of the densities of the scattering lengths of the particle phb (r) and of the surrounding medium pm: Ap = phb (r) - pm. The density of scattering length represents the scattering power per unit volume and is given by a sum taken over the coherent scattering lengths a, of the corresponding elements i multiplied by their space-dependent particle density N, (r) : 231
232
R.
p (r) = FIVi (r) a. The density
of scattering
SCHNEIUER
El’
dl,
length for light and heavy water (which are
the solvents of the haemoglobin solution) are ,o,,, -= -0.61 x l(Y” and $- 6.26 x IO’” cm/cm3, respectively. The density of scattering length phb of haemoglobin can be calculated in principle from the spatial distribution of the atoms within the haemoglobin molecule. For a first approximation, it is sufficient to assume a uniform distribution of the atoms within the volume. From the composition of haemoglobin (Braunitzer, Hilse, Rudloff & Hilschmann, 1964) its density of scattering length is calculated to be phb = 1.5 x 1Oro cm/cm3. given where
by the Fourier
By equation
transform
tI is the scattering
(1) the observable
of Ap (r) in reciprocal
space
parameter
2
is
K. IKI = 4 TTsin T,
and X is the neutron wavelength. In small-angle 27re scattering /Kl is approximately equal to -. As the molecular volume of the haemoA globin molecule (without hydration) a figure of lo5 A3 was taken (Cullis, Muirhead, Perutz, Rossmann & North, 1962). Equation (1) can be represented in a first approximation by a Gaussian function (Guinier & Fournet, 1955) :
!$ In equation
angle
= [JAp (r)d,r]’
(2) the radius of gyration
(exp
--?I
.
(2)
R, is defined by: (3)
To get equation (3), the origin of r-space is defined by the equation JrAp(r)d,r = 0 in analogy with the definition of the centre of mass. (For a homogeneous sphere, the radius of gyration is Ri = 315 Ri, where R, is the geometrical radius of the sphere.) The radius of gyration R, of a particle or changes in it can in principle be determined from the angular distribution of the scattering. The scattering in the forward direction can be taken as a measure for the volume of the scattering particle (equation (2)).
3. Experimental
Procedure
(a) Method The measurements were performed at the FRJ-2 (DID0 reactor at Jiilich). A Be-Bi filtered beam of neutrons with a mean wavelength of 4.7 f 0.3 A and a halfwidth of 1.0 A was used. The arrangement of the system is shown in Fig. 1. The filtered beam is guided by total reflection of neutrons to the scattering apparatus consisting of collimator, sample holder, scattering tube and detecting unit (Christ, Sohilling, Schmatz & Springer, 1965). In order to compensate for fluctuations of neutron flux a monitor was used. Guide tube and scattering apparatus were evacuated to 1 torr. The collimator slits had the dimensions 0.5 cm x 8 cm. The sample containers mounted on the sample holders were made of quartz glass. The thickness of the sample was 1.5 mm and 10 mm for solutions of haemoglobin in light water and heavy water, respectively. Oxygenated and deoxygenated haemoglobin solutions at 23°C mounted on movable sample holders were measured in turn (Fig. 1). The ligend state of the haemoglobin samples was changed periodically. The background scattering of the solvent water was determined and subtracted from the measured scattering curves of the haemoglobin solutions. As the background of heavy water is only 10% of that of light water (due to the smaller incoherent scattering cross-section of D,O),
NEUTRON
SMALL-ANGLE
FIQ. 1. Small-angle A, Reactor shield; B, Be-Bi filter; movable sample holder; H, scattering in the detecting plane in em.
233
SCATTERING
scattering apparatus (distances in cm). C, neutron guide; D, monitor; E, slits; F, collimator; G, tube; I, beam stop; K, movable BF3-counter; z, distance
the small-angle scattering of a heavy water solution of haemoglobin with greater accuracy. Therefore both light and heavy water solutions haemoglobin were investigated.
can be determined of oxy- and deoxy-
(b) Material Human haemoglobin solution has been prepared as described in the preceding paper (Conrad, Mayer, Thomas & Vogel, 1969) and was investigated by flow birefringence (Schneider, 1967). No birefringence within an accuracy of angle of less than 1’ could be molecules existed, observed. This means that, if dimeric aggregations of haemoglobin their concentration would be less than 0.5 vol. ye. The heavy water solution was prepared by haemolizing with D20. The resultant D,O/H,O ratio of the haemoglobin solution
obtained
by this procedure was approximately
20.
4. Results and Discussion A reasonable plot of the scattering curves is (according to equation (2) ) log du,,jdQ versus K2. This was done in Figure 2 for the most accurate measurements we obtained. The slope of the straight lines is proportional to Rg. It is apparent that the slopes
for deoxygenated haemoglobin are in all cases, i.e. for different concentrations and solvents (H,O and D,O), definitely steeper than those for oxygenated haemoglobin. The absolute values of the radii of gyration are not accurately determined, because the scattering
curves
have
to be corrected
for smearing
effects
and also careful
measurement of the neutron wavelength distribution is necessary. With the uncertainty of the wavelength distribution included, the radii of gyration of deoxy- and oxyhaemoglobin are 24.3 * 1.6 ,k and 23.8 f 1.6 A, respectively. Since the experimental conditions are the same in both measurements, the systematic error is eliminated in the formation of the difference between the radii of gyration of deoxygenated and oxygenated haemoglobin, which can be established with greater accuracy than the individual radii. This difference was found to be essentially the same within the limits of error for various solvents and concentrations of haemoglobin solution: R g (deoxu) - R, (oxy) = 0.54 + o-15 A. A difference in the radii of gyration would appear if different concentrations of rtggregates existed in the two ligand states. However, we have calculated that the
234
FICA 2. Intensity distribution of neutron small-angle scattering curves of light and heavy water solutions of human haemoglobin in deoxy- and oxygenated state (plot of log(l/l,) w-~2; z in cm. -@-a-, Oxyheemoglobin; -- O--O--, deoxyhaemoglobin. The circles are larger then the atatistioal error of measurement. Light-water solution of haemoglobin: a = 4%, b = 2% ; heavywater solution of hasmoglobin: A = 2.8%, B = 1.4%.
highest possible concentration of dimeric aggregations (Schneider, 1967) of O-5 volume O/Owould give a change of radius of gyration of only 0.18 A if it is assumed that no aggregation occurs in the oxygenated state and 0.5% in the deoxygenated state of haemoglobin. Furthermore, if aggregation influenced our results, then they would have had to be reversible in repeated oxygenation and deoxygenation processes, because the difference of the radii was observed whenever the ligand state of haemoglobin was changed. Within the limits of error, these results are in agreement with the X-ray small-angle scattering results for aqueous haemoglobin solutions reported in the preceding paper (see Table 1 of Conrad et al., 1969). According to equation (2), the scattering in the forward direction (K+O) is related
NEUTRON
SMALL-ANGLE TABLE
Radii
235
SCATTERING 1
R, (in rf) for human oxy- and deoxycyhaemuglobinas detemnined by neutron and X-ray smull-angle scattering ancl X-ray diffraction analysis
of gyration
Reference Neutron small-angle scattering X-ray small-angle scattering X-ray diffraction analysis (contour level at average density in protein crystal)
24.3h1.6
23.8*1.6
26.2f1.2
24*7&
24-3
24.0
1.1
0.54&0.16
This work
1.5*0.9
Conrad et al. (1969) J. M. Cox (personal communication)
to the volume of the scattering particle. The difference of scattering in the forward direction shown in Figure 2 suggests a volume change on oxygenation; however, it is presumably mainly due to concentration differences between our oxy- and deoxyhaemoglobin solutions. Taking this into account, we can state at the moment only that the process of oxygenation of haemoglobin in D,O solution is accompanied by a volume change of certainly less than 2%. For haemoglobin in H,O solution, the forward scattering is not so sensitive to volume changes. It has been shown in the preceding paper that no volume change is to be expected on the basis of the conformational change deduced from single-crystal X-ray analysis (Muirhead, Cox, Mazzarella & Per&z, 1967), and that the small-angle X-ray scattering data excluded changes in volume of more than 7%. We thank Professors N. Riehl and T. Springer for valuable discussions. This work was partly supported by a grant from Stiftung Volkswagenwerk which we gratefully acknowledge. REFERENCES Braunitzer, G., Hilse, K., Rudloff, V. & Hilschmann, N. (1964). Aduanc. Protein Chm. 19, 1. Christ, J., Schilling, W., Schmatz, W. & Springer, T. (1966). 2. angew. Phya. 18, 268. Conrad, H., Mayer, A., Thomas, H. P. & Vogel, H. (1969). J. Mol. Biol. 41, 225. Cullis, A. F., Muirhead, H., Perutz, M. F., Rossmann, M. G. & North, A. C. (1962). Proc. Roy. Sot. A,265, 161. Guinier, A. & Fournet, G. (1955). Snzall-angle Scattering of X-rays, New York: J. Wiley & Sons. Muirheed, H., Cox, J. M., Mozzarella, L. & Perutz, M. F. (1967). J. Mol. Biol. 28, 117. Schneider, R. (1967). Diplom-Arbeit, Physik-Department, Technische Hochschule, Miinchen.
Neutron Small-angle Scattering from Aqueous Solutions of Oxy- and Deoxyhaemoglobin R. SCHNEIDER, A. MAYER Physik-Department der Technischen Hochschule, Miinchen, Germany
W. SCHMATZ, B. KAISER AND R. SCHERM Institut fiir Festktirper- und Neutronenphysik der Kernforschungsanluqe Jiilich, Germany (Received 15 November 1967, and in revised form 1 January 1969) The neutron small-angle scattering of human haemoglobin was measured. Oxygenated and deoxygenated haemoglobin in radius of gyration.
in aqueous solution were found to differ
1. Introduction While scattering of X-rays is due to the electron density distribution of the scattering medium, the scattering of neutrons is related to the nuclear density distribution. In general, electronic and nuclear density distributions are not identical, but in proteins observed at low resolution they would be expected to be similar. Comparative studies of X-ray and neutron scattering may give supplementary information about the structure of the scattering medium. In the experiments to be described, the neutron small-angle scattering from aqueous solutions of oxy- and deoxygenated human haemoglobin was measured and the results were compared with those obtained from X-ray small-angle scattering and X-ray diffraction analysis. 2. Theory Intensity and angular distribution of small-angle scattering give information on the shape and volume of the scattering particle. The theory of neutron small-angle scattering is analogous to that of X-ray scattering (Guinier & Fournet, 1955). The cross-section for scattering of a single particle (haemoglobin molecule) per solid angle is given by: d -=
=hb
dSZ
jflp(r) exp (iKr) d,r ’ I
C
where K is the scattering vector. Thus the scattering of neutrons is related to the difference of the densities of the scattering lengths of the particle phb (r) and of the surrounding medium pm: Ap = phb (r) - pm. The density of scattering length represents the scattering power per unit volume and is given by a sum taken over the coherent scattering lengths a, of the corresponding elements i multiplied by their space-dependent particle density N, (r) : 231
232
R.
p (r) = FIVi (r) a. The density
of scattering
SCHNEIUER
El’
dl,
length for light and heavy water (which are
the solvents of the haemoglobin solution) are ,o,,, -= -0.61 x l(Y” and $- 6.26 x IO’” cm/cm3, respectively. The density of scattering length phb of haemoglobin can be calculated in principle from the spatial distribution of the atoms within the haemoglobin molecule. For a first approximation, it is sufficient to assume a uniform distribution of the atoms within the volume. From the composition of haemoglobin (Braunitzer, Hilse, Rudloff & Hilschmann, 1964) its density of scattering length is calculated to be phb = 1.5 x 1Oro cm/cm3. given where
by the Fourier
By equation
transform
tI is the scattering
(1) the observable
of Ap (r) in reciprocal
space
parameter
2
is
K. IKI = 4 TTsin T,
and X is the neutron wavelength. In small-angle 27re scattering /Kl is approximately equal to -. As the molecular volume of the haemoA globin molecule (without hydration) a figure of lo5 A3 was taken (Cullis, Muirhead, Perutz, Rossmann & North, 1962). Equation (1) can be represented in a first approximation by a Gaussian function (Guinier & Fournet, 1955) :
!$ In equation
angle
= [JAp (r)d,r]’
(2) the radius of gyration
(exp
--?I
.
(2)
R, is defined by: (3)
To get equation (3), the origin of r-space is defined by the equation JrAp(r)d,r = 0 in analogy with the definition of the centre of mass. (For a homogeneous sphere, the radius of gyration is Ri = 315 Ri, where R, is the geometrical radius of the sphere.) The radius of gyration R, of a particle or changes in it can in principle be determined from the angular distribution of the scattering. The scattering in the forward direction can be taken as a measure for the volume of the scattering particle (equation (2)).
3. Experimental
Procedure
(a) Method The measurements were performed at the FRJ-2 (DID0 reactor at Jiilich). A Be-Bi filtered beam of neutrons with a mean wavelength of 4.7 f 0.3 A and a halfwidth of 1.0 A was used. The arrangement of the system is shown in Fig. 1. The filtered beam is guided by total reflection of neutrons to the scattering apparatus consisting of collimator, sample holder, scattering tube and detecting unit (Christ, Sohilling, Schmatz & Springer, 1965). In order to compensate for fluctuations of neutron flux a monitor was used. Guide tube and scattering apparatus were evacuated to 1 torr. The collimator slits had the dimensions 0.5 cm x 8 cm. The sample containers mounted on the sample holders were made of quartz glass. The thickness of the sample was 1.5 mm and 10 mm for solutions of haemoglobin in light water and heavy water, respectively. Oxygenated and deoxygenated haemoglobin solutions at 23°C mounted on movable sample holders were measured in turn (Fig. 1). The ligend state of the haemoglobin samples was changed periodically. The background scattering of the solvent water was determined and subtracted from the measured scattering curves of the haemoglobin solutions. As the background of heavy water is only 10% of that of light water (due to the smaller incoherent scattering cross-section of D,O),
NEUTRON
SMALL-ANGLE
FIQ. 1. Small-angle A, Reactor shield; B, Be-Bi filter; movable sample holder; H, scattering in the detecting plane in em.
233
SCATTERING
scattering apparatus (distances in cm). C, neutron guide; D, monitor; E, slits; F, collimator; G, tube; I, beam stop; K, movable BF3-counter; z, distance
the small-angle scattering of a heavy water solution of haemoglobin with greater accuracy. Therefore both light and heavy water solutions haemoglobin were investigated.
can be determined of oxy- and deoxy-
(b) Material Human haemoglobin solution has been prepared as described in the preceding paper (Conrad, Mayer, Thomas & Vogel, 1969) and was investigated by flow birefringence (Schneider, 1967). No birefringence within an accuracy of angle of less than 1’ could be molecules existed, observed. This means that, if dimeric aggregations of haemoglobin their concentration would be less than 0.5 vol. ye. The heavy water solution was prepared by haemolizing with D20. The resultant D,O/H,O ratio of the haemoglobin solution
obtained
by this procedure was approximately
20.
4. Results and Discussion A reasonable plot of the scattering curves is (according to equation (2) ) log du,,jdQ versus K2. This was done in Figure 2 for the most accurate measurements we obtained. The slope of the straight lines is proportional to Rg. It is apparent that the slopes
for deoxygenated haemoglobin are in all cases, i.e. for different concentrations and solvents (H,O and D,O), definitely steeper than those for oxygenated haemoglobin. The absolute values of the radii of gyration are not accurately determined, because the scattering
curves
have
to be corrected
for smearing
effects
and also careful
measurement of the neutron wavelength distribution is necessary. With the uncertainty of the wavelength distribution included, the radii of gyration of deoxy- and oxyhaemoglobin are 24.3 * 1.6 ,k and 23.8 f 1.6 A, respectively. Since the experimental conditions are the same in both measurements, the systematic error is eliminated in the formation of the difference between the radii of gyration of deoxygenated and oxygenated haemoglobin, which can be established with greater accuracy than the individual radii. This difference was found to be essentially the same within the limits of error for various solvents and concentrations of haemoglobin solution: R g (deoxu) - R, (oxy) = 0.54 + o-15 A. A difference in the radii of gyration would appear if different concentrations of rtggregates existed in the two ligand states. However, we have calculated that the
234
FICA 2. Intensity distribution of neutron small-angle scattering curves of light and heavy water solutions of human haemoglobin in deoxy- and oxygenated state (plot of log(l/l,) w-~2; z in cm. -@-a-, Oxyheemoglobin; -- O--O--, deoxyhaemoglobin. The circles are larger then the atatistioal error of measurement. Light-water solution of haemoglobin: a = 4%, b = 2% ; heavywater solution of hasmoglobin: A = 2.8%, B = 1.4%.
highest possible concentration of dimeric aggregations (Schneider, 1967) of O-5 volume O/Owould give a change of radius of gyration of only 0.18 A if it is assumed that no aggregation occurs in the oxygenated state and 0.5% in the deoxygenated state of haemoglobin. Furthermore, if aggregation influenced our results, then they would have had to be reversible in repeated oxygenation and deoxygenation processes, because the difference of the radii was observed whenever the ligand state of haemoglobin was changed. Within the limits of error, these results are in agreement with the X-ray small-angle scattering results for aqueous haemoglobin solutions reported in the preceding paper (see Table 1 of Conrad et al., 1969). According to equation (2), the scattering in the forward direction (K+O) is related
NEUTRON
SMALL-ANGLE TABLE
Radii
235
SCATTERING 1
R, (in rf) for human oxy- and deoxycyhaemuglobinas detemnined by neutron and X-ray smull-angle scattering ancl X-ray diffraction analysis
of gyration
Reference Neutron small-angle scattering X-ray small-angle scattering X-ray diffraction analysis (contour level at average density in protein crystal)
24.3h1.6
23.8*1.6
26.2f1.2
24*7&
24-3
24.0
1.1
0.54&0.16
This work
1.5*0.9
Conrad et al. (1969) J. M. Cox (personal communication)
to the volume of the scattering particle. The difference of scattering in the forward direction shown in Figure 2 suggests a volume change on oxygenation; however, it is presumably mainly due to concentration differences between our oxy- and deoxyhaemoglobin solutions. Taking this into account, we can state at the moment only that the process of oxygenation of haemoglobin in D,O solution is accompanied by a volume change of certainly less than 2%. For haemoglobin in H,O solution, the forward scattering is not so sensitive to volume changes. It has been shown in the preceding paper that no volume change is to be expected on the basis of the conformational change deduced from single-crystal X-ray analysis (Muirhead, Cox, Mazzarella & Per&z, 1967), and that the small-angle X-ray scattering data excluded changes in volume of more than 7%. We thank Professors N. Riehl and T. Springer for valuable discussions. This work was partly supported by a grant from Stiftung Volkswagenwerk which we gratefully acknowledge. REFERENCES Braunitzer, G., Hilse, K., Rudloff, V. & Hilschmann, N. (1964). Aduanc. Protein Chm. 19, 1. Christ, J., Schilling, W., Schmatz, W. & Springer, T. (1966). 2. angew. Phya. 18, 268. Conrad, H., Mayer, A., Thomas, H. P. & Vogel, H. (1969). J. Mol. Biol. 41, 225. Cullis, A. F., Muirhead, H., Perutz, M. F., Rossmann, M. G. & North, A. C. (1962). Proc. Roy. Sot. A,265, 161. Guinier, A. & Fournet, G. (1955). Snzall-angle Scattering of X-rays, New York: J. Wiley & Sons. Muirheed, H., Cox, J. M., Mozzarella, L. & Perutz, M. F. (1967). J. Mol. Biol. 28, 117. Schneider, R. (1967). Diplom-Arbeit, Physik-Department, Technische Hochschule, Miinchen.