# Orientation determination by wavelets matching for 3D reconstruction of very noisy electron microscopic virus images

- Ali Samir Saad
^{1}Email author

**5**:5

https://doi.org/10.1186/1472-6807-5-5

© Saad; licensee BioMed Central Ltd. 2005

**Received: **19 August 2004

**Accepted: **02 March 2005

**Published: **02 March 2005

## Abstract

### Background

In order to perform a 3D reconstruction of electron microscopic images of viruses, it is necessary to determine the orientation (Euler angels) of the 2D projections of the virus. The projections containing high resolution information are usually very noisy. This paper proposes a new method, based on weighted-projection matching in wavelet space for virus orientation determination. In order to speed the retrieval of the best match between projections from a model and real virus particle, a hierarchical correlation matching method is also proposed.

### Results

A data set of 600 HSV-1 capsid particle images in different orientations was used to test the proposed method. An initial model of about 40 Å resolutions was used to generate projections of an HSV-1 capsid. Results show that a significant improvement, in terms of accuracy and speed, is obtained for the initial orientation estimates of noisy herpes virus images. For the bacteriophage (P22), the proposed method gave the correct reconstruction compared to the model, while the classical method failed to resolve the correct orientations of the smooth spherical P22 viruses.

### Conclusion

This paper introduces a new method for orientation determination of low contrast images and highly noisy virus particles. This method is based on weighted projection matching in wavelet space, which increases the accuracy of the orientations. A hierarchical implementation of this method increases the speed of orientation determination. The estimated number of particles needed for a higher resolution reconstruction increased exponentially. For a 6 Å resolution reconstruction of the HSV virus, 50,000 particles are necessary. The results show that the proposed method reduces the amount of data needed in a reconstruction by at least 50 %. This may result in savings 2 to 3 man-years invested in acquiring images from the microscope and data processing. Furthermore, the proposed method is able to determine orientations for some difficult particles like P22 with accuracy and consistency. Recently a low PH sindbis capsid was determined with the proposed method, where other methods based on the common line fail.

## Background

Three-dimensional (3D) reconstruction of virus particles like SARS (Severe Acute Respiratory Syndrome) and HSV (Herpes Simplex Virus) using electron microscopy yields crucial information for understanding the assembly and infectivity mechanism. The structural determination begins with acquisition of projection images in an electron-microscope. A major part of data processing is aimed at determining the direction of projection for each particle image (2D projection of virus) so that a 3D reconstruction can be computed. The first step in a virus reconstruction is the detection and selection of the individual particle images from a large area of an electron micrograph.

One approach is to take two consecutive pictures of the same particles one close-to-focus (Fig. 1-a) and another farther from focus with a higher contrast (Fig. 1-c) from which the initial orientations are easily determined [4, 5]. The initial orientations are then assigned to the corresponding particles in the close-to-focus images for structural refinement (henceforth, called focal pair method). In a high resolution structure determination, one would require over 6000 particles of data for 8.5 Å resolutions [6]. If a focal pair is required, one would need over 12,000 particles and hence it is a labor-intensive process of data recording, digitization and archiving. In this paper, we propose a method for determining the initial orientations of the particles from low contrast (close-to-focus) images without necessity for a second set of highly defocused images. In this technique, we use the wavelet transformation in a multi-resolution analysis [7, 8] to enhance the contrast of the image and the hierarchical weighted projection matching to accelerate the processing. The wavelet-transformed images have the same size as the original images. Wavelet decomposition separates the low-resolution information, called "approximation", from the high resolution information, called "details". This method computationally generates an image equivalent to the far-from-focus picture taken by the microscope and separates images containing details and noise. The technique proposed here is a model-based approach in wavelet space, which we call Hierarchical Wavelet Projection Matching (HWPM).

## Results

A data set of 600 HSV-1 capsid particle images in different orientations was used to test the HWPM method. The defocus range of herpes particles was chosen to be close to focus between 1.7 μm and 0.4 μm. An initial model of about a 40 Å resolution [4] was used to generate projections uniformly covering the asymmetric triangle of the icosahedrally symmetric HSV-1 capsid particle [4, 5]. A grid sampling of 0.5° in each direction of the asymmetric triangle of icosahedral particles was used. The number of projections obtained with this grid was relatively high (2616 projections). First, the 2616 projections were grouped into 200 classes, each class containing about 13 projections.

A match of the particle into the best 3 of the 200 classes was obtained using the wavelet correlation coefficient (wccf) criterion. Next, the particle was compared to the 39 projections of the best three classes, and the correct orientation was that of the projection giving the highest wccf. The hierarchical implementation wavelet projection matching reduced the time at least by a factor of 10 compared with the classical projection matching method. In the example of 600 particles, by using HWPM it took approximately 3 hours to determine the orientations, instead the 33 hours it took with the classical matching algorithm. Both algorithms were running on the SGI Origin-2000 supercomputer using 10 processors.

At this point, each particle had been assigned the orientation of the closest projection. A quality factor was assigned to each orientation, which was the wavelet correlation coefficient. Particles having high wccf coefficients were selected for reconstruction of a first 3D model of the virus.

Refinement of initial orientations obtained by HWPM was realized by the same iterative refinement process used in focal pair method [5]. This refinement process uses both local and global refinement. Local-refinement refines orientations against a set of projections from the 3D density map. In global refinement, all the raw particle orientations are refined against each other, without using projections from the 3D model. A potential merit of global refinement is the absence of possible bias arising from the 3D model.

HWPM was tested on a P22 empty shell capsid which was circular and whose shell is very thin (~40 Angstrom). Twenty micrographs of the P22 empty shell capsid with defocus range [0.5 to 2 μm] were used for testing purpose. The total number of particles is 1340, each image has a size of 300 × 300 pixels, and the dimension of each pixel is 2.8 Å.

Concerning the initial orientations determinations using HWPM method, an initial model of around 20 Å resolutions was used to generate projections which uniformly covered the asymmetric triangle of the icosahedrally symmetric model. A grid sampling of 2° in each direction of the asymmetric triangle of icosahedral symmetry was used to obtain an initial orientation, targeting a structure of 30 Å. The number of projections obtained with this grid was about 200 projections. A match of the particle with the projections was obtained by using the wccf criterion. The correct orientation was selected as the one of the projection giving the highest wccf. The better half of the orientations projections (650) according to wccf criterion was chosen for final reconstruction.

The initial orientations for the same set of data were determined using the Improved Common Line (ICL) method, with the same input parameters for the software described in [2]. ICL use one single micrograph and does not use focal pair technique. The best half of the particles orientations (650) was chosen, according to the phase residual criterion, in the 3D reconstruction of the P22.

## Discussion

During the last thirty years the common lines methods were a great method to resolve icoshedral particles up to 7–8 Å [6]. Recently, a method using polar transformation and projection matching were used for the purpose of orientation determination [3], but this last method is not suitable for the high resolution of large virus because the resulting transformed images, could be double the size of the original image. The proposed method combines the projection matching of wavelet denoising for an initial determination of particle orientation, with the common lines method for refinement to a higher resolution. It is clear that HWPM method works only if the initial low resolution model of the particle is already known. This method is very interesting if we need to add more particles to an existing intermediate resolution reconstruction in order to increase the resolution. Particles having high resolution information are very noisy [9, 14]. The best that we can get using the ICL method is less than 40 % of good orientations, for defocus values between 1.9 μm and 1.2 μm, for the P22 capsid [2]. Usually, very high resolutions use defocus values which go much lower than 1.2 μm as in the HSV data, or the current P22 data which goes to 0.5 μm. The 40% rate of correct orientations would certainly become smaller if we used data at closer defocus. The study accomplished on high resolution for HSV reconstruction showed that using a close-to-focus single micrograph with CL method was not effective, because a small number of orientations were found to be correct [9], for this reason a focal pair method was used for 8.5 Å structure[9].

At high resolution reconstructions, the number of particles needed increases drastically, and the data with a signal-to-noise ratio valid up to the targeted resolution, tend to be very noisy. For an 8.5 Å structure of HSV-1 it took about 6000 particles for a final reconstruction. For a 6.5 Å structure resolution, the estimated value was about 50,000 particles using the same electron microscope [14].

To further increase the resolution of the HSV virus to 6.5 Å or higher (4 Å), the focal pair method would be impracticable. The focal pair method, for intermediate resolution up to (8 Å) for big viruses like HSV, works well for orientations determinations. The number of particles selected for the final reconstruction about 40% of the original number of particles (taking into account the far-focus and close-focus micrographs). It is necessary to emphasize that results from both methods are very similar in terms of visual resemblance. But, there are two advantages of HWPM over the focal pair method. First, focal pair method uses as much as double the data used for the HWPM. Second, the quality of the density maps shows that HWPM gives a better resolution for the same number of particles (figure 6). This proves a better accuracy of orientations determinations obtained by the HWPM.

One of the more obvious advantages of the HWPM for orientation accuracy appears in two examples of real reconstructions. The first is for the P22 capsid, the ICL method does not give a good initial orientation, and the refinement of the orientations does not help to converge toward the right orientations. The probable reasons why the ICL method did not work properly for the P22 capsid are: first the P22 capsid has a smooth surface (the thickness of the shell is about 40 Å); second most of the data are very close-to-focus with defocus range of 0.5 μm to 1.3 μm. The data was noisy and had a very low contrast. The ICL method was able to give 40% of good orientations for the defocus range between 1.9 and 1.2 μm, here the data was closer to focus, which reduced the percentage of good orientations to less then 22%.

The application of the HWPM to the P22 empty shell capsid gave the expected structure (Fig. 7). The wavelet denoising in the HWPM not only helped in reducing the noise and enhancing the contrast of the particles, but also used the entire information from the image (instead of using several lines) which is enhanced accuracy for highly noisy particles.

Another example of real data reconstruction is the VP5-VP19C recombinant. After long investigation using CL and ICL algorithms, the classical projection matching scheme was also tested in order to determine the orientations, but unfortunately all those methods failed. The wavelet filtering and matching was used during the classification step of the recombinant particle VP5-VP19C [15, 16], which significantly improved the quality of the class averages [16–18] and enabled the determination of the structure of that particle. A study [16] shows the superiority of the wavelet projection matching over the Gaussian filtered projection matching.

The third examples for low PH sindbis: Three years of investigation using CL and ICL methods failed to obtain the correct density map of the low PH sindbis capsid which is subject to conformational changes and an alteration of the symmetry. Recently the proposed method (HWPM) was tested on low PH sindbis and the correct structure was finally observed and analyzed [19].

Wavelet multi-resolution analysis and processing improves particle detections [8], classification [15, 16], and orientation determination on a variety of electron microscopy images which are highly noisy and have an extremely low contrast. This prove that wavelet techniques are adequate in the 3 main steps of 3D virus reconstruction and in the classification step of single particle reconstruction [16, 17].

## Conclusion

This paper describes the development and implementation of a new method for orientation determination for low contrast images of virus particles. This method is based on wavelet filtering, which enhances the contrast of the particles and reduces the noise, and on weighted projection matching in wavelet space. A hierarchical implementation of this method increases the speed of orientation determination. Results show that, HWPM have been able to determine accurately more than 85% of the orientations of low-contrast particles. Compared to the focal pair method (for orientation determination from low contrast data) the HWPM reduced the amount of data required in a reconstruction by at least 50 %. In addition the accuracy of the orientations obtained by the proposed method is higher than those obtained by focal pair method [9]. This improved accuracy is shown clearly by the resolution assessment in Fig. 6. The estimated number of particles needed for a 6.5 Å reconstruction of the HSV-1 capsid was about 50,000 [14]. By using the HWPM method, only half as much data was necessary. The proposed method could save 2 to 3 man-years invested in acquiring images from the microscope and data processing. Another advantage of this method is the ability to give accurate orientations for some particles having conformational changes or alteration of symmetry as seen for VP5-VP19C recombinant and recently with the low PH sindbis capsid.

## Methods

### Choice of wavelet Base

The choice of wavelet filter bases depends on the signal. Signals coming from different sources have different characteristics. For audio, speech, image and video signals the best choices of wavelet bases are known. The best choice for electron microscopic images is not clear. The problem is to represent typical signals with a small number of convenient computable functions.

An investigation to choose the best wavelet bases for electron microscopic images was performed here. During this study, simulated and real electron microscopy images were used. The majority of the wavelets basis existing in Matlab-5 software [20–24] was tested. The criterion used to determine the best wavelet base was the one which optimizes the signal to noise ratio in a broad spectrum of spatial frequencies. The bi-orthogonal wavelets basis [25–27] especially the 3.5 basis in Matlab-5 yielded the best average signal to noise ratio in the range of the spatial frequency (1/100 - 1/8 Å^{-1}) relevant to data analysis.

### Wavelet Projection Matching (WPM) Principle

The approximation component is obtained after applying a bi-orthogonal low-pass wavelet filter in each direction (horizontal and vertical) followed by a sub-sampling of each image by a factor of 2 for each dimension. The details are obtained with the application of a low-pass filter in one direction and a high-pass filter in the other, or a high-pass filter in both directions. The noise is mainly present in the detail components. A higher level of decomposition is obtained by repeating the same filtering operations on the approximation. The wavelet correlation coefficient between two wavelet-transformed images, for a given level, is :

Where W_{1} to Wp are weights given for each components of the wavelet correlation, p is the number of components of wavelet decomposition. A_{1}, A_{2} are the approximations. ⊗ denote the correlation between two components images. D_{1i}, D_{2i} are the details (Fig. 2). This implementation starts first by a wavelet filtering which is performed by thresholding [21, 28, 29] of the details components in order to reduce the noise effects in the correlation matching. Higher weight is given to the approximation component to further reduce the noise effect in the decision. The weights given in this implementation are 0.75 for the approximation and 0.25 for the details.

### Orientation determination with Hierarchical WPM (HWPM)

## Declarations

### Acknowledgements

I thank Wah Chiu for helpful and interesting discussions. Frazer Rixon, Joanita Jakana, Zhang Zhixian for providing the HSV-1 and P22 capsid data and Kelechi Ogbueh for the English revision of the manuscript. This work was supported by the National Institutes of Health (P41RR002250, R01AI38469) and Human Frontier Science Program.

## Authors’ Affiliations

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