- Email: [email protected]
Images of purple membrane at 2.8 Å resolution obtained by cryo-electron microscopy
J. Mol. Biol. (1988) 202, 585-591
Images of Purple Membrane at 24 A Resolution Obtained by Cryo-electron Microscopy J. M. Baldwin, R. Henderson MRC Laboratory of Molecular Biology Hills Road, Cambridge CB2 2&H, U.K.
E. Beckman and F. Zemlin Fritz Haber Institut der Max Plan& Gesellschaft Faradayweg 4-6, D-1000 Berlin 33, Germany (Received 19 November 1987, and in revised form 15 March 1988) Improvements in technique have produced electron micrographs of purple membrane that provide, after computer analysis, reproducibly measurable diffraction peaks extending to 2.8 A (1 A = O-1 nm). The improvements include better specimen preparation, a more stable cryo-electron microscope with better alignment and the addition of an image-processing step, which gives weights to local areas of the image according to the local strength of the periodic component of the image. These improvements have enabled the calculation of a directly phased projection map at 2.8 A resolution.
1. Introduction
It has been pointed out (Henderson & Glaeser, 1985) how poor most images of radiation-sensitive organic and biological materials are, and that increases in contrast enormous should be attainable. The work described here goes part of the way towards showing that this lost contrast can be recovered in practice. Further substantial improvements should eventually be attained.
We have previously determined the projection structure of two-dimensional crystals of bacteriorhodopsin (purple membrane) at 3.5 A resolution (1 A =O.l nm) and published the methods used to record, measure and evaluate the electron micrographs (Henderson et al., 1986). These methods included the use of cryo-electron microscopy for recording the images, and computer analysis to correct for distortions over large areas of the images. Our goal is to complete the analysis of the structure of purple membrane at near atomic resolution by continuing the analysis into three dimensions, with similar images of specimens tilted at various angles to the electron beam. We have obtained some preliminary results that suggest that the additional computational step needed to deal with the contrast transfer function for tilted specimens (Henderson & Baldwin, 1986) is working, but have not yet collected sufficient data for the full three-dimensional analysis to proceed. However, we have recently obtained images of untilted or slightly tilted specimens that have turned out to be consistently so much better than previous images (Henderson et al., 1986) that we felt the results should be reported. This paper presents a directly phased projection map at 2.8 8, a resolution that is now comparable with that of X-ray diffraction analysis of three-dimensional protein crystals, where initial phase determination is usually carried out by the method of isomorphous replacement. Phase determination by direct imaging of the native structure in the electron microscope should become very powerful as soon as the methods become quicker and easier. OOZZ-2836/SS/15058~7 $03.00/O
2. Methods The methods used are those described by Henderson et al. (1986), except for the following improvements. As before, the specimen consisted of large (10 pm in diameter), single membrane thick, crystals of bacteriorhodopsin applied to the thick (about 250 A) carbon support in a mixture of glucose and octylglucoside detergent (Baldwin & Henderson, 1984). On this occasion,
we were able to make grids that had a high proportion of crystals that were well separated and in which electron diffraction showed high resolution spots (3-O A at room
temperature, 2.5 a at liquid These desirable characteristics
nitrogen
temperature).
of the specimens are determined by the properties of the carbon films. Presumably the correct balance of the hydrophobicity to the hydrophilicity of the carbon films ensures that some membranes stick, but not so strongly that the degree of order is disrupted. The electron microscopy was improved. After several years of development, the Berlin liquid helium cryomicroscope (Suleika) is now very stable, with no drift. A more detailed description of this microscope, originally developed by Dr Dietrich (Siemens, Miinchen) has been given by Dietrich et al. (1977). The images were taken at higher magnifications than before (71,000x ), thus reducing problems from the relatively high ambient AC magnetic fields in the vicinity of the microscope. The
585
0 1988 Academic Press Limited
J. M. Baldwin
586
incident beam was particularly well aligned (see Results). It was almost exactly parallel to the axis of the objective lens, giving very symmetrical pairs of diffracted beams, which recombine with the direct beam to create each Fourier component of the image. Finally, the densitometry and image processing were improved. Images were measured by densitometry in 7.5 pm steps (smaller than before) over areas of up to 9600 x 7200 pixels, thus covering the entire area of the film. This required more disc space than was previously available. The step size was equivalent to 1 A on the specimen. Thus, at a resolution of 2.8 A, there was only a little extra noise from aliasing with resolutions beyond the edge of the Fourier transform box, a problem that is severe and results in a 50% reduction in signal to noise ratio when the image is sampled by the densitometry with a step size exactly at the required resolution limit. As before (Henderson et aZ., 1986) image distortions
c.t.f. 18 563: 2990,
3150,
30.0.
et al.
were determined by searching for correlation peaks between the whole filtered image and a reference patch normally taken from the centre of the image. The reference patch was a square area 400 A x400 A, containing approximately 50 unit cells and covering approximately 1/4OOth of the total area of the image. Smaller reference areas do not contain enough information to give a good signal to noise ratio on the correlation peaks, and larger areas do not allow the determination of the fine scale distortions. After reinterpolation of the image following the determination of image distortions (Henderson et al., 1986), a new step was added that was equivalent to multiplication of the image by a variable mask, giving higher weights to good areas and lower weights to bad areas. The weight distribution was derived from the correlation peak heights determined during the distortion correction procedure as follows. The image was divided
24.9.87
Figure 1. A plot of diffraction spots detected in the Fourier transform of one of the images (no. 18563). Only spots with a background corrected amplitude greater than the root-mean-square background level are plotted. The rings indicate the zero crossin s of the refined contrast transfer function. The midpoint of each edge of the box corresponds to a spacing of (l/2*75) A- !i resolution. In this case the defocus was 3070 A and the astigmatism 100 A.
Images of Purple Membrcme at 2-8 A Resolution into 6400 separate areas. In each area, the average peak height was determined, a global minimum threshold was chosen and subtracted from these average peak heights. The weight distribution was then obtained by scaling these values so that the mean weight was 1.0. In principle, the correlation peak heights can be determined in a second pass of distortion correction using only high resolution Fourier components in the calculation of the correlation map. This ensures the optimal weighting of the parts of the image with the best high resolution information. In practice it was found that the results obtained were essentially as good when the peak heights were determined from the lower resolution (up to 6.0 A) correlation maps. For the 2 images processed to 2.8 A, an additional slight improvement in the statistics was obtained by carrying out a further step of refinement of the 4 lattice parameters (a~, ay, bz, @). The mean amplitude at the predicted reciprocal lattice positions was maximized using only the high resolution data beyond 5.5 A. A significant improvement in the sharpness of the average high resolution spot was obtained. This small improve-
7
6
8
810
8
7
7
9
8
9
8
10
ment seems to demonstrate the existence of a slight expansion and rotation of the high resolution components of the image with respect to the low resolution components of the image by approximately 0*015%, as would be expected for a slightly divergent and spiral beam at the specimen (e.g. see Christenson & Eades, 1986). The phases from the 6 new micrographs were combined using a weighting scheme that takes account of the strength of the spots (Henderson et al., 1986). They were then compared with the completely independent set of phases published previously (Henderson et al., 1986). The mean phase difference between the 2 sets of data (i.e. 3” to 7 A, 17” from 7 to 5.5 A, and 42” from 55 to 3.5 A) was close to that expected from the error estimates. A final map to 2.8 A resolution was therefore calculated using the combined phase information from both the 6 higher quality images from this work and 11 from the previous work (Henderson et al., 1986). The amplitudes for the map were taken from unpublished electron diffraction data of T. A. Ceska, recorded at liquid nitrogen temperature using a cold stage. These data extended to 2.5 A, compared with the 3 A data used previously.
6
8
7
7
7
6
7
8
7
6
6
7
7
10
9
8
7
6
6
9
7
8
7
7
6
7
7
7
8
7
9
0
6
7
7
7
7
0
7
7
7
6
7
8
6
6
8
6
6
7
6
9
9
9v8
6
7
8
(a)
(b)
7
7
7
7
7
7
7
7
7
7
7
8
7
6
7
6
7
7
7
7
7
a
7
7
7
7
6
8
8
8
7
7
6
7
7
7
7
7
7
6
7
7
6
8
7
7
7
7
7
7
0
7
7
6
8
8
8
7
0
8
7
7
7
7
7
6
8
8
8
7
7
7
8 7
7
8
7
7
7
8
7
7
7
6
7
8
7
7
7
8
7
7
7
7
7
0
7
7
8
7
8
0
8
7
7
7
7
7
7
8
7
7
7
7
6
8
6
6
7
8
7
7
6
(c) Cd) Figure 2. A plot of the intensity distribution surrounding the predicted position of the spots in the Fourier transform of one of the images. Each box shows the average intensity of all spots in a given resolution band, scaled so that the mean perimeter intensity (at a distance of 11 sample points from the centre) is equal to 7.0. (a) 00 to 7.OA (105 spots); (b) 7.0 to 5.5 A (60 spots); (c) 55 to 3.5 A (255 spots); (d) 3.5 to 2.8 A (255 spots). It can be seen that the spots in the highest resolution band are above background by an amount that on average is nearly equal to the background level itself.
J. M. Baldwin
588
et al.
Table 1
3. Results and Discussion
Correlation between image diffraction peak intensities and c.t.f. modified electron diffraction amplitudes
100 micrographs Examination of approximately of untilted purple membrane recorded in Berlin over the last one to two years with a variety of specimens showed that there were a few, all from a single session on the microscope using a single batch of carbon-coated grids, that gave slightly stronger diffraction spots in the optical diffractometer. For the (9,3) example, on the best micrographs, reflection at 5-O L% was just discernible in comparison to the (8,2) at 59 A, which was the highest resolution spot seen on previous pictures. When the six best of this new batch of pictures were subjected to computer analysis, it was found that all of the new images were better than all of the old ones by any of our numerical criteria for judging quality. The first four Figures and two Tables provide the evidence for this. Figure 1 shows a display of all spots detected at above background level from the Fourier transform of one image (no. 18563). Spots are detected at nearly all reciprocal lattice points out to 3.5 A resolution, and beyond this, more than double the number of spots are detected using our threshold criterion than would be obtained from an image area consisting of pure noise. The only spots missing out to 5 L% resolution (the 4th contrast transfer function (c.t.f.)t zero) are near c.t.f. zeros. Figure 2 shows the average intensity near the spots in resolution ranges. In comparison to the identical
Resolution (4 03-7.0 7a5.5 5.5-3.5 3.5-2.8
Correlation Coefficient of data
Number of comparisons
Correlation Coefficient for noise
0.99
105
-0.01
0.97 0.89 0.64
69 255 244
-0.12 0.04 -0.06
plot on the best previous image (Figure 4 of Henderson et al., 1986), the present image contrast is greater in terms of diffraction intensity by factors of 5 out to 7 8, 8 out to 5.5 L%and 15 out to 3.5 8. Previously, no detectable signal was found beyond 3.5 8, whereas now the average spot intensity is clearly above the noise, being approximately twice the background (Fig. 2(d)). That is, the average background-corrected spot intensity is equal to the background itself. Figure 3 shows a direct comparison of image amplitudes veraus resolution for the best image of this series, with the best images of Henderson et al. (1986) and Unwin & Henderson (1975). It is clear that the main reason for the greater number of detectable spots, for their greater strength and for their greater resolution is the slower fall-off in image contrast with resolution. This may be due to seve;al possible factors, which include the use of:
TAbbreviation used: c.t.f., contrast transfer function. 5
--v-v-+
-------3----------
,+=y$L$ XX
x
\c
0
1 4
% 5.0 il I
7.0 ii I I 8 Resolution
J(h2
t hk
I 12
t
3.5 % I
2.58 I
16
k2))
Figure 3. Demonstration of the fall-off in image amplitudes with resolution. The plot shows the ratio of the image amplitude (Image amp.) to the c.t.f. corrected electron diffraction pattern amplitude (E.D. amp). We have compared the best film in this study (no. 18563) with the best film from Henderson et al. (1986; no. 15096) as well as the best film from Unwin & Henderson (19’75; no. 2698). The main difference is the slower fall-off in image amplitude with resolution, giving more, stronger spots at all resolutions. Only spots with background corrected amplitudes greater than twice the root-mean-square background are plotted. + , Image 18563; 0, image 15606; x , image 2698. The broken line at the top of the Figure is an estimate of the theoretical level for a perfect image.
Images of Purple Membrane at 2.8 A Resolution
Table 2 Number of di@-action
peaks and electron
No. of spots
parameters for each image
optical
Defocus
Astigmatism
Image
to 3.5 A
(4
(4
18555
266 279 311 377 329 372
2450 1944 2707 2036 2450 3070
100 135 85 147 200 160
18556 18559 18560 18562 18563
Beam tilt (mr4 0.77 0.83 1.12 0.69 0.71 0.60
Note that the maximum number of spots that would be detected in an image with no noise is 429 for
purple membrane at this resolution. The 6 images are the best from a sequence of 9.
(1) well-preserved, large areas of crystal in the specimen, covering completely the area of the micrograph;
(2) carbon film that is thicker and therefore resists the specimen movement caused by radiation damage;
90
80
70
60
--I
______ I
-
-__.
3c
----I I___-.
I
0
0.02
0.04
006 Resolution
0.08
O-10
0.12
(i)-’
) Difference between mean phases from two Figure 4. Estimates of phase error in different resolution bands. (--halves of data, after dividing the data into two halves with roughly equal information content. (- - - -) Estimated phase error in final average of all measurements. In all these comparisons and estimates, the random number would be 90”.
590
J. 44. Baldwin et al.
(3) slightly
higher magnification; alignment of the microscope (see Table 2, beam tilt column); (5) a weighting scheme for inclusion of different areas of the image with different weights, at the final step of image processing. (4) good
The relative importance of the improvement due to the first four possible factors cannot be determined, since they all affect this batch of images. However, it is possible to compare the results with and without the weighting scheme. A factor of 1.5 improvement in mean intensity in the 5.5 to 3.5 A resolution band was obtained on application of the weighting scheme. We believe that the application of a weighting scheme in combining different image areas should produce a better result than schemes that use equal weights and apply a cut off to exclude bad areas (e.g. see Unzer et al., 1987). Our procedure excludes totally bad areas by giving them zero weight, but areas that are of weak contrast but still contain significant information are included at an appropriate weight. As further proof of the validity of the data
obtained for the highest resolution spots, we calculated the correlation coefficient between the image amplitude observed and the expected c.t.f. modified amplitude calculated from earlier electron diffraction data. Table 1 shows the correlation coefficient in resolution bands for the best image (no. 18563). It is clear that the high resolution signal (correlation 0.64) is still very significant. Control calculations, carried out by using the transform points from positions midway between the real diffraction spots, showed correlation coefficients around f0.05, as expected for noise with no relation to the electron diffraction intensities. In comparison to the best previous images, the present data are now nearly as good from 2-S to 3.5 A as they were between 3-5 and 5-5 A. As before, the raw image phases were corrected for c.t.f., beam tilt and phase origin and then compared with phases from all other images treated similarly. The data for the six new images are shown in Table 2 and a histogram of phase statistics for the entire merged dataset in resolution bands is given in Figure 4. Again the data are much better than before and show less than 30” phase error to
Figure 5. The 2.8 A projection structure. The phases were determined mainly from the data in this study and the amplitudes from electron diffraction at liquid nitrogen temperature (T. A. Ceska, unpublished results). Features in the region between protein molecules are believed to be ordered lipid. The density in the map is contoured at intervals of 4 0, starting at 2 cr, where c is the estimated root-mean-square error in the map.
Images of Purple Membrane at 2.8 d Regolution 3.3 A and less than 45” to 2.8 A. Note that only the two best of the six new images were processed to 24 A,. Thus, the 2.8 A phases have been determined, but the images remain far from perfect. For the best image shown in Figure 3, the contrast at 2.8 A is still less than 3% of that expected from electron diffraction. Considerable further improvements should therefore be possible. A map of the projected structure is shown in Figure 5. Features in the lipid regions that are probably lipid hydrocarbon chains viewed end-on can be seen but will require at least 20” tilted data before they can be interpreted in terms of detailed lipid hydrocarbon structure. In conclusion, a variety of technical improvements have been made that have helped the resolution of 2.8 A to be attained, but no individual identifiable factor is responsible for all of the improvement. Rather, improvements in several factors have combined to produce substantially better results. Most importantly, we have demonstrated in practice that 2.8 A images can be recorded and that phases can be recovered from them. Until now, the highest resolution images obtained from protein crystals have been at 3.5 8, from crotoxin (Jeng et al., 1984), which diffracts much more strongly than purple membrane, and from purple membrane (Henderson et al., 1986).
591
The present success should certainly raise the level of expectation about what is possible. We thank T. A. Ceska for the use of his electron diffraction amplitudes, which are not yet published. We are also grateful to J. Berriman, R. A. Crowther and N. Unwin for helpful discussion. References Baldwin, J. M. & Henderson, R. (1984). Ultramicroscopy, 14, 319-336. Christenson, K. K. & Eades, J. A. (1986). Ultramicroscopy, 19, 191-194. Dietrich, I., Fox, F., Knapek, E., Lefranc, G., Nachtrieb, K., Weyl, R. t Zerbst, H. (1977). Ultramicroscopy, 2, 241-249. Henderson, R. t Baldwin, J. M. (1986). 44th Annu. Proc. EMSA (Bailey, G. W., ed.), pp. 6-9, San Francisco Press Inc., San Francisco. Henderson, R. & Glaeser, R. M. (1985). Ultramicroscopy, 16, 139-150. Henderson, R., Baldwin, J. M., Downing, K. H., Lepault, J. & Zemlin, F. (1986). Ultramicroscopy, 19, 147-178. Jeng, T.-W., Chiu, W., Zemlin, F. & Zeitler, E. (1984). J. Mol. Biol. 175, 93-97. Unwin, P. N. T. & Henderson, R. (1975). J. Mol. Biol. 94, 425-440. Unzer, M., Trus, B. L. 6 Steven, A. C. (1987). Ultramicroscopy, 23, 3%51.
Edited by R. Huber
Images of Purple Membrane at 24 A Resolution Obtained by Cryo-electron Microscopy J. M. Baldwin, R. Henderson MRC Laboratory of Molecular Biology Hills Road, Cambridge CB2 2&H, U.K.
E. Beckman and F. Zemlin Fritz Haber Institut der Max Plan& Gesellschaft Faradayweg 4-6, D-1000 Berlin 33, Germany (Received 19 November 1987, and in revised form 15 March 1988) Improvements in technique have produced electron micrographs of purple membrane that provide, after computer analysis, reproducibly measurable diffraction peaks extending to 2.8 A (1 A = O-1 nm). The improvements include better specimen preparation, a more stable cryo-electron microscope with better alignment and the addition of an image-processing step, which gives weights to local areas of the image according to the local strength of the periodic component of the image. These improvements have enabled the calculation of a directly phased projection map at 2.8 A resolution.
1. Introduction
It has been pointed out (Henderson & Glaeser, 1985) how poor most images of radiation-sensitive organic and biological materials are, and that increases in contrast enormous should be attainable. The work described here goes part of the way towards showing that this lost contrast can be recovered in practice. Further substantial improvements should eventually be attained.
We have previously determined the projection structure of two-dimensional crystals of bacteriorhodopsin (purple membrane) at 3.5 A resolution (1 A =O.l nm) and published the methods used to record, measure and evaluate the electron micrographs (Henderson et al., 1986). These methods included the use of cryo-electron microscopy for recording the images, and computer analysis to correct for distortions over large areas of the images. Our goal is to complete the analysis of the structure of purple membrane at near atomic resolution by continuing the analysis into three dimensions, with similar images of specimens tilted at various angles to the electron beam. We have obtained some preliminary results that suggest that the additional computational step needed to deal with the contrast transfer function for tilted specimens (Henderson & Baldwin, 1986) is working, but have not yet collected sufficient data for the full three-dimensional analysis to proceed. However, we have recently obtained images of untilted or slightly tilted specimens that have turned out to be consistently so much better than previous images (Henderson et al., 1986) that we felt the results should be reported. This paper presents a directly phased projection map at 2.8 8, a resolution that is now comparable with that of X-ray diffraction analysis of three-dimensional protein crystals, where initial phase determination is usually carried out by the method of isomorphous replacement. Phase determination by direct imaging of the native structure in the electron microscope should become very powerful as soon as the methods become quicker and easier. OOZZ-2836/SS/15058~7 $03.00/O
2. Methods The methods used are those described by Henderson et al. (1986), except for the following improvements. As before, the specimen consisted of large (10 pm in diameter), single membrane thick, crystals of bacteriorhodopsin applied to the thick (about 250 A) carbon support in a mixture of glucose and octylglucoside detergent (Baldwin & Henderson, 1984). On this occasion,
we were able to make grids that had a high proportion of crystals that were well separated and in which electron diffraction showed high resolution spots (3-O A at room
temperature, 2.5 a at liquid These desirable characteristics
nitrogen
temperature).
of the specimens are determined by the properties of the carbon films. Presumably the correct balance of the hydrophobicity to the hydrophilicity of the carbon films ensures that some membranes stick, but not so strongly that the degree of order is disrupted. The electron microscopy was improved. After several years of development, the Berlin liquid helium cryomicroscope (Suleika) is now very stable, with no drift. A more detailed description of this microscope, originally developed by Dr Dietrich (Siemens, Miinchen) has been given by Dietrich et al. (1977). The images were taken at higher magnifications than before (71,000x ), thus reducing problems from the relatively high ambient AC magnetic fields in the vicinity of the microscope. The
585
0 1988 Academic Press Limited
J. M. Baldwin
586
incident beam was particularly well aligned (see Results). It was almost exactly parallel to the axis of the objective lens, giving very symmetrical pairs of diffracted beams, which recombine with the direct beam to create each Fourier component of the image. Finally, the densitometry and image processing were improved. Images were measured by densitometry in 7.5 pm steps (smaller than before) over areas of up to 9600 x 7200 pixels, thus covering the entire area of the film. This required more disc space than was previously available. The step size was equivalent to 1 A on the specimen. Thus, at a resolution of 2.8 A, there was only a little extra noise from aliasing with resolutions beyond the edge of the Fourier transform box, a problem that is severe and results in a 50% reduction in signal to noise ratio when the image is sampled by the densitometry with a step size exactly at the required resolution limit. As before (Henderson et aZ., 1986) image distortions
c.t.f. 18 563: 2990,
3150,
30.0.
et al.
were determined by searching for correlation peaks between the whole filtered image and a reference patch normally taken from the centre of the image. The reference patch was a square area 400 A x400 A, containing approximately 50 unit cells and covering approximately 1/4OOth of the total area of the image. Smaller reference areas do not contain enough information to give a good signal to noise ratio on the correlation peaks, and larger areas do not allow the determination of the fine scale distortions. After reinterpolation of the image following the determination of image distortions (Henderson et al., 1986), a new step was added that was equivalent to multiplication of the image by a variable mask, giving higher weights to good areas and lower weights to bad areas. The weight distribution was derived from the correlation peak heights determined during the distortion correction procedure as follows. The image was divided
24.9.87
Figure 1. A plot of diffraction spots detected in the Fourier transform of one of the images (no. 18563). Only spots with a background corrected amplitude greater than the root-mean-square background level are plotted. The rings indicate the zero crossin s of the refined contrast transfer function. The midpoint of each edge of the box corresponds to a spacing of (l/2*75) A- !i resolution. In this case the defocus was 3070 A and the astigmatism 100 A.
Images of Purple Membrcme at 2-8 A Resolution into 6400 separate areas. In each area, the average peak height was determined, a global minimum threshold was chosen and subtracted from these average peak heights. The weight distribution was then obtained by scaling these values so that the mean weight was 1.0. In principle, the correlation peak heights can be determined in a second pass of distortion correction using only high resolution Fourier components in the calculation of the correlation map. This ensures the optimal weighting of the parts of the image with the best high resolution information. In practice it was found that the results obtained were essentially as good when the peak heights were determined from the lower resolution (up to 6.0 A) correlation maps. For the 2 images processed to 2.8 A, an additional slight improvement in the statistics was obtained by carrying out a further step of refinement of the 4 lattice parameters (a~, ay, bz, @). The mean amplitude at the predicted reciprocal lattice positions was maximized using only the high resolution data beyond 5.5 A. A significant improvement in the sharpness of the average high resolution spot was obtained. This small improve-
7
6
8
810
8
7
7
9
8
9
8
10
ment seems to demonstrate the existence of a slight expansion and rotation of the high resolution components of the image with respect to the low resolution components of the image by approximately 0*015%, as would be expected for a slightly divergent and spiral beam at the specimen (e.g. see Christenson & Eades, 1986). The phases from the 6 new micrographs were combined using a weighting scheme that takes account of the strength of the spots (Henderson et al., 1986). They were then compared with the completely independent set of phases published previously (Henderson et al., 1986). The mean phase difference between the 2 sets of data (i.e. 3” to 7 A, 17” from 7 to 5.5 A, and 42” from 55 to 3.5 A) was close to that expected from the error estimates. A final map to 2.8 A resolution was therefore calculated using the combined phase information from both the 6 higher quality images from this work and 11 from the previous work (Henderson et al., 1986). The amplitudes for the map were taken from unpublished electron diffraction data of T. A. Ceska, recorded at liquid nitrogen temperature using a cold stage. These data extended to 2.5 A, compared with the 3 A data used previously.
6
8
7
7
7
6
7
8
7
6
6
7
7
10
9
8
7
6
6
9
7
8
7
7
6
7
7
7
8
7
9
0
6
7
7
7
7
0
7
7
7
6
7
8
6
6
8
6
6
7
6
9
9
9v8
6
7
8
(a)
(b)
7
7
7
7
7
7
7
7
7
7
7
8
7
6
7
6
7
7
7
7
7
a
7
7
7
7
6
8
8
8
7
7
6
7
7
7
7
7
7
6
7
7
6
8
7
7
7
7
7
7
0
7
7
6
8
8
8
7
0
8
7
7
7
7
7
6
8
8
8
7
7
7
8 7
7
8
7
7
7
8
7
7
7
6
7
8
7
7
7
8
7
7
7
7
7
0
7
7
8
7
8
0
8
7
7
7
7
7
7
8
7
7
7
7
6
8
6
6
7
8
7
7
6
(c) Cd) Figure 2. A plot of the intensity distribution surrounding the predicted position of the spots in the Fourier transform of one of the images. Each box shows the average intensity of all spots in a given resolution band, scaled so that the mean perimeter intensity (at a distance of 11 sample points from the centre) is equal to 7.0. (a) 00 to 7.OA (105 spots); (b) 7.0 to 5.5 A (60 spots); (c) 55 to 3.5 A (255 spots); (d) 3.5 to 2.8 A (255 spots). It can be seen that the spots in the highest resolution band are above background by an amount that on average is nearly equal to the background level itself.
J. M. Baldwin
588
et al.
Table 1
3. Results and Discussion
Correlation between image diffraction peak intensities and c.t.f. modified electron diffraction amplitudes
100 micrographs Examination of approximately of untilted purple membrane recorded in Berlin over the last one to two years with a variety of specimens showed that there were a few, all from a single session on the microscope using a single batch of carbon-coated grids, that gave slightly stronger diffraction spots in the optical diffractometer. For the (9,3) example, on the best micrographs, reflection at 5-O L% was just discernible in comparison to the (8,2) at 59 A, which was the highest resolution spot seen on previous pictures. When the six best of this new batch of pictures were subjected to computer analysis, it was found that all of the new images were better than all of the old ones by any of our numerical criteria for judging quality. The first four Figures and two Tables provide the evidence for this. Figure 1 shows a display of all spots detected at above background level from the Fourier transform of one image (no. 18563). Spots are detected at nearly all reciprocal lattice points out to 3.5 A resolution, and beyond this, more than double the number of spots are detected using our threshold criterion than would be obtained from an image area consisting of pure noise. The only spots missing out to 5 L% resolution (the 4th contrast transfer function (c.t.f.)t zero) are near c.t.f. zeros. Figure 2 shows the average intensity near the spots in resolution ranges. In comparison to the identical
Resolution (4 03-7.0 7a5.5 5.5-3.5 3.5-2.8
Correlation Coefficient of data
Number of comparisons
Correlation Coefficient for noise
0.99
105
-0.01
0.97 0.89 0.64
69 255 244
-0.12 0.04 -0.06
plot on the best previous image (Figure 4 of Henderson et al., 1986), the present image contrast is greater in terms of diffraction intensity by factors of 5 out to 7 8, 8 out to 5.5 L%and 15 out to 3.5 8. Previously, no detectable signal was found beyond 3.5 8, whereas now the average spot intensity is clearly above the noise, being approximately twice the background (Fig. 2(d)). That is, the average background-corrected spot intensity is equal to the background itself. Figure 3 shows a direct comparison of image amplitudes veraus resolution for the best image of this series, with the best images of Henderson et al. (1986) and Unwin & Henderson (1975). It is clear that the main reason for the greater number of detectable spots, for their greater strength and for their greater resolution is the slower fall-off in image contrast with resolution. This may be due to seve;al possible factors, which include the use of:
TAbbreviation used: c.t.f., contrast transfer function. 5
--v-v-+
-------3----------
,+=y$L$ XX
x
\c
0
1 4
% 5.0 il I
7.0 ii I I 8 Resolution
J(h2
t hk
I 12
t
3.5 % I
2.58 I
16
k2))
Figure 3. Demonstration of the fall-off in image amplitudes with resolution. The plot shows the ratio of the image amplitude (Image amp.) to the c.t.f. corrected electron diffraction pattern amplitude (E.D. amp). We have compared the best film in this study (no. 18563) with the best film from Henderson et al. (1986; no. 15096) as well as the best film from Unwin & Henderson (19’75; no. 2698). The main difference is the slower fall-off in image amplitude with resolution, giving more, stronger spots at all resolutions. Only spots with background corrected amplitudes greater than twice the root-mean-square background are plotted. + , Image 18563; 0, image 15606; x , image 2698. The broken line at the top of the Figure is an estimate of the theoretical level for a perfect image.
Images of Purple Membrane at 2.8 A Resolution
Table 2 Number of di@-action
peaks and electron
No. of spots
parameters for each image
optical
Defocus
Astigmatism
Image
to 3.5 A
(4
(4
18555
266 279 311 377 329 372
2450 1944 2707 2036 2450 3070
100 135 85 147 200 160
18556 18559 18560 18562 18563
Beam tilt (mr4 0.77 0.83 1.12 0.69 0.71 0.60
Note that the maximum number of spots that would be detected in an image with no noise is 429 for
purple membrane at this resolution. The 6 images are the best from a sequence of 9.
(1) well-preserved, large areas of crystal in the specimen, covering completely the area of the micrograph;
(2) carbon film that is thicker and therefore resists the specimen movement caused by radiation damage;
90
80
70
60
--I
______ I
-
-__.
3c
----I I___-.
I
0
0.02
0.04
006 Resolution
0.08
O-10
0.12
(i)-’
) Difference between mean phases from two Figure 4. Estimates of phase error in different resolution bands. (--halves of data, after dividing the data into two halves with roughly equal information content. (- - - -) Estimated phase error in final average of all measurements. In all these comparisons and estimates, the random number would be 90”.
590
J. 44. Baldwin et al.
(3) slightly
higher magnification; alignment of the microscope (see Table 2, beam tilt column); (5) a weighting scheme for inclusion of different areas of the image with different weights, at the final step of image processing. (4) good
The relative importance of the improvement due to the first four possible factors cannot be determined, since they all affect this batch of images. However, it is possible to compare the results with and without the weighting scheme. A factor of 1.5 improvement in mean intensity in the 5.5 to 3.5 A resolution band was obtained on application of the weighting scheme. We believe that the application of a weighting scheme in combining different image areas should produce a better result than schemes that use equal weights and apply a cut off to exclude bad areas (e.g. see Unzer et al., 1987). Our procedure excludes totally bad areas by giving them zero weight, but areas that are of weak contrast but still contain significant information are included at an appropriate weight. As further proof of the validity of the data
obtained for the highest resolution spots, we calculated the correlation coefficient between the image amplitude observed and the expected c.t.f. modified amplitude calculated from earlier electron diffraction data. Table 1 shows the correlation coefficient in resolution bands for the best image (no. 18563). It is clear that the high resolution signal (correlation 0.64) is still very significant. Control calculations, carried out by using the transform points from positions midway between the real diffraction spots, showed correlation coefficients around f0.05, as expected for noise with no relation to the electron diffraction intensities. In comparison to the best previous images, the present data are now nearly as good from 2-S to 3.5 A as they were between 3-5 and 5-5 A. As before, the raw image phases were corrected for c.t.f., beam tilt and phase origin and then compared with phases from all other images treated similarly. The data for the six new images are shown in Table 2 and a histogram of phase statistics for the entire merged dataset in resolution bands is given in Figure 4. Again the data are much better than before and show less than 30” phase error to
Figure 5. The 2.8 A projection structure. The phases were determined mainly from the data in this study and the amplitudes from electron diffraction at liquid nitrogen temperature (T. A. Ceska, unpublished results). Features in the region between protein molecules are believed to be ordered lipid. The density in the map is contoured at intervals of 4 0, starting at 2 cr, where c is the estimated root-mean-square error in the map.
Images of Purple Membrane at 2.8 d Regolution 3.3 A and less than 45” to 2.8 A. Note that only the two best of the six new images were processed to 24 A,. Thus, the 2.8 A phases have been determined, but the images remain far from perfect. For the best image shown in Figure 3, the contrast at 2.8 A is still less than 3% of that expected from electron diffraction. Considerable further improvements should therefore be possible. A map of the projected structure is shown in Figure 5. Features in the lipid regions that are probably lipid hydrocarbon chains viewed end-on can be seen but will require at least 20” tilted data before they can be interpreted in terms of detailed lipid hydrocarbon structure. In conclusion, a variety of technical improvements have been made that have helped the resolution of 2.8 A to be attained, but no individual identifiable factor is responsible for all of the improvement. Rather, improvements in several factors have combined to produce substantially better results. Most importantly, we have demonstrated in practice that 2.8 A images can be recorded and that phases can be recovered from them. Until now, the highest resolution images obtained from protein crystals have been at 3.5 8, from crotoxin (Jeng et al., 1984), which diffracts much more strongly than purple membrane, and from purple membrane (Henderson et al., 1986).
591
The present success should certainly raise the level of expectation about what is possible. We thank T. A. Ceska for the use of his electron diffraction amplitudes, which are not yet published. We are also grateful to J. Berriman, R. A. Crowther and N. Unwin for helpful discussion. References Baldwin, J. M. & Henderson, R. (1984). Ultramicroscopy, 14, 319-336. Christenson, K. K. & Eades, J. A. (1986). Ultramicroscopy, 19, 191-194. Dietrich, I., Fox, F., Knapek, E., Lefranc, G., Nachtrieb, K., Weyl, R. t Zerbst, H. (1977). Ultramicroscopy, 2, 241-249. Henderson, R. t Baldwin, J. M. (1986). 44th Annu. Proc. EMSA (Bailey, G. W., ed.), pp. 6-9, San Francisco Press Inc., San Francisco. Henderson, R. & Glaeser, R. M. (1985). Ultramicroscopy, 16, 139-150. Henderson, R., Baldwin, J. M., Downing, K. H., Lepault, J. & Zemlin, F. (1986). Ultramicroscopy, 19, 147-178. Jeng, T.-W., Chiu, W., Zemlin, F. & Zeitler, E. (1984). J. Mol. Biol. 175, 93-97. Unwin, P. N. T. & Henderson, R. (1975). J. Mol. Biol. 94, 425-440. Unzer, M., Trus, B. L. 6 Steven, A. C. (1987). Ultramicroscopy, 23, 3%51.
Edited by R. Huber