SCIENTIFIC DATA VISUALIZATION AND DIGITAL IMAGE PROCESSING FOR STRUCTURAL BIOLOGY

Transcription

1 SCIENTIFIC DATA VISUALIZATION AND DIGITAL IMAGE PROCESSING FOR STRUCTURAL BIOLOGY A Thesis Submitted to the Faculty of Purdue University by Ioana Maria Boier Martin In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 1996

2 iv TABLE OF CONTENTS Page LIST OF TABLES vii LIST OF FIGURES viii ABSTRACT xi 1. INTRODUCTION Motivation and Goals Organization of the Thesis Research Contributions FUNDAMENTAL CONCEPTS IN STRUCTURAL BIOLOGY Crystals and Diffraction X-ray Crystallography Electron Microscopy Other Methods for Structure Determination COMBINING DATA VISUALIZATION WITH COMPUTATIONS Overview Survey of Software Packages for Structural Biology Tonitza aa Scientific Visualization Package for Structural Biology The Graphical User Interface Input/Output Computations Data Visualization Algorithms Computing Isosurfaces Arcball Rotations Software Engineering Design Issues Conclusion

3 v Page 4. IMAGE PROCESSING OF ELECTRON MICROGRAPHS Motivation Overview of Digital Image Processing Techniques Image Enhancement Image Segmentation Digital Image Processing of Electron Micrographs Automatic Particle Selection Related Work The Road to the Crosspoint Method The Crosspoint Method Preprocessing Particle identification Postprocessing Results Sensitivity of the Crosspoint Method EMMA aa Package for Image Processing of Electron Micrographs Motivation and General Structure Particle Extraction Image Processing Conclusion PARALLEL PROCESSING METHODS AND APPLICATIONS Introduction Adaptive Load Balancing Strategies Problem Definition Macromolecular Structure Computations Experimental Studies Parallel Algorithms for Objects with High Symmetry Problem Definition Structure Determination of Spherical Viruses Conclusion CONCLUSIONS AND FUTURE WORK Algorithms and Heuristics Software Packages Future Work

4 vi Page BIBLIOGRAPHY Appendix A: Data Sets Used in the Visualization Examples Appendix B: Electron Micrographs Used for Testing the Crosspoint Method.. 98 Appendix C: Data Formats Accepted in Tonitza and EMMA Appendix D: Using Tonitza for the Development of Cluster Labeling Algorithms 104 VITA LIST OF PUBLICATIONS

5 vii LIST OF TABLES Table Page LIST OF TABLES Table Page 3.1 Selected software packages used in molecular modeling Timing results for the Crosspoint Method Number of particles identified by the Crosspoint Method Sensitivity of the Crosspoint Method to changes in the particle radius in the case of the PHIX-B micrograph. True radius is approximately 25 pixels Approximate values of break points and slopes as the number N of work units varies (P = 20, t 0 = 2, α = 0.1) Approximate values of break points and slopes as the transfer latency t 0 varies (P = 20, N = 500, α = 0.1) Approximate values of break points and slopes as the dynamic load factor η varies (P = 20, t 0 = 2, α = 0.1) Execution time (in seconds) for single and double interpolation C.1 The MAP INTEGER*2 format C.2 The PURDUE INTEGER*2 format C.3 The PARTICLE format C.4 The SGI header format

6 viii LIST OF TABLES Table Page LIST OF FIGURES Figure Page 2.1 An icosahedron viewed along each of its symmetry axes Schematic representation of the diffraction process Portion of a diffraction pattern from an HRV14 crystal Fitting a structure in an electron density map Image formation in a lens (from [BAKE95]) A snapshot of the screen during a Tonitza session The colormap editor The material editor Data rotation window Average electron density as a function of the particle radius Correlation coefficient as a function of the magnification factor Correlation coefficient as a function of the particle radius Ross-River virus surface with antibody fragments attached. The surface of the antibodies was computed as a difference map between the complex form of the virus attached with antibodies and the native virus structure Electron density histogram for the Ross-River virus structure Equatorial contour map for the Ross-River virus structure Equatorial continuous scale map for the Ross-River virus structure

7 ix Figure Page 3.12 Stack of mask contours for a Coxackievirus B3 asymmetric unit Spherical sections viewed along two-, three-, and five-fold axes in the case of the Ross-River virus Shaded isosurface representations of Ross-River virus data: (a) boxed spike, (b) view along a three-fold axis overlaid with a lattice which shows the positions of the symmetry elements Ambiguous case in the Marching Cubes method: depending on the value at the centre of the top face of the cube, either (a) the hexagon, or (b) the two triangles belong to the surface polygonalization Naive implementation of the Marching Cubes algorithm Histogram of a low-dose digitized electron micrograph (the numbers on the left represent the indices of the gray levels present in the image) Pseudo-code for the histogram equalization algorithm Histogram of the same electron micrograph as in Figure 4.1 after equalization Spatial lowpass filter of size n n A basic highpass spatial filter Mask used for high-boost filtering The Sobel operator masks Mask used to compute the Laplacian Circle detection using the Hough transform Schematic representation of the 3D reconstruction process (from [DERO68]) (a) Portion of a micrograph containing the images of several virus particles, (b) the variation of the pixel intensity along the horizontal line shown in (a) The micrograph in Figure 4.11(a) after a Sobel transformation The steps of the Crosspoint Method: (a) original micrograph, (b) the micrograph after histogram equalization, (c) the micrograph after histogram equalization and averaging, (d) the final result of the Crosspoint Method

8 x Figure Page 4.14 Pseudo-code describing the marking phase of the Crosspoint Method Various situations in the clustering algorithms: (a) eight neighbors of the current pixel are considered in the stack algorithm, (b) four neighbors of the current pixel are considered in the coloring algorithm, (c) two separate clusters must be merged in the coloring algorithm Pseudo-code for the stack algorithm Pseudo-code for the coloring algorithm Disconnecting particles by thinning: (a) particle identification without thining, (b) particle identification with thinning The result of the Crosspoint Method applied to the PHIX-A micrograph The result of the Crosspoint Method applied to the PHIX-B micrograph The result of the Crosspoint Method applied to the BMV micrograph The result of the Crosspoint Method applied to the REO-18 micrograph The result of the Crosspoint Method applied to the T1LHC micrograph A snapshot of the screen during an EMMA session Plot of imbalance versus dispersion as η varies Plot of imbalance versus dispersion as N varies Generic model of the load imbalance function of the load dispersion Asymmetric unit and its border region The convergence rate of the single and double interpolation methods A parallel virtual environment for structural biology computations D.1 Using Tonitza to verify the correctness of a parallel labeling algorithm: (a) correct labeling of clusters, (b) incorrect labeling of clusters

9 xi ABSTRACT Martin, Ioana M. Boier Ph.D., Purdue University, August Scientific Data Visualization and Digital Image Processing for Structural Biology. Major Professor: Dan C. Marinescu. This thesis focuses on the design and development of algorithms and tools for interactive data visualization and digital image processing of large data sets produced in structural biology experiments. We describe various computational and visualization algorithms, which we have developed and implemented as part of the Tonitza package for interactive visualization and analysis of structural biology data. The computational algorithms include methods for fitting of data sets using correlation and scaling, various types of interpolation, and algorithms for generating statistical information. Several two- and three-dimensional representations of the data sets are described in detail. We present a number of image processing methods for extracting information from images, and we discuss their applications to electron microscopy. Such methods extend the scientist s ability to study images of biological structures. We describe the Crosspoint Method, a new technique we developed for automatic detection of the positions of virus particles in electron micrographs. We present the heuristics and the algorithms involved and compare the results obtained with those reported in the literature. We introduce EMMA, a new package for digital processing of micrograph images which includes the Crosspoint Method. As part of the research presented in this thesis, we also describe several parallel algorithms and load balancing schemes for structural biology applications. They helped improve our understanding of the complexity of the problems involved and of how the data is transformed from the moment it is collected until the moment it is displayed.

10 1 1. INTRODUCTION 1.1 Motivation and Goals The determination of the structure of biological macromolecules has traditionally required the most powerful computers available. Parallel and distributed computing has opened new possibilities in structural biology by allowing the analysis of larger and more complex problems, but interfacing with such computing systems has become more difficult. Complex problem solving environments with friendly user interfaces, which support data visualization, knowledge processing, and automatic data migration are necessary. The rate of data acquisition has also improved considerably because of more powerful synchrotrons and data collection devices such as CCD (Charge Coupled Device) detectors. Data rates of one frame every few seconds, with a frame consisting of up to pixels of 16 to 24 bits each will be quite common in a few years. Though most of the data processing can be done off line, the sheer volume of data collected in structural biology experiments requires efficient algorithms, data storage systems, and powerful computers. The research presented in this thesis is part of an interdisciplinary effort to apply high performance computing techniques to structural biology. Such techniques fall into three main categories: (a) the development of parallel algorithms and data management strategies for performing various tasks [CORN94], (b) the design of interactive tools for digital image processing, data visualization and analysis [BOIR96], and (c) the development of a parallel virtual environment that supports concurrent execution of parallel and sequential programs on computing platforms with various architectures [SIRB96]. The goals of this research are: (a) to develop a graphics environment which combines interactive visualization of large data sets with computational methods that allow for data analysis in terms of its structural significance, (b) to design a new algorithm for auto-

11 2 matic selection of virus particles from electron micrographs and a digital image processing package which is centered around the implementation of this algorithm, (c) to simulate the behavior of computationally intensive irregular problems for a given class of load balancing schemes, and (d) to study and compare the performance of two different algorithms for problems involving objects with a high degree of symmetry. 1.2 Organization of the Thesis This thesis focuses on applications of high-performance computing methods to structural biology. The emphasis is on computer graphics and digital image processing methods and their use for the determination of the structure of biological macromolecules. Sequential and parallel computational aspects are also considered. Chapter 2 gives a brief introduction to structural biology. Fundamental concepts related to structure determination, such as crystals, diffraction, image formation, etc., are defined. These concepts are essential for understanding the design of the algorithms and methods presented in later chapters. Chapter 3 is devoted to combining data visualization with computations to allow biologists to analyze, manipulate, display, and debug data. An interactive graphics system we developed for this purpose is described and compared with other existing molecular modeling software packages. Algorithms, computational methods, software engineering issues, and specific design problems are also discussed. Examples based on data sets representing virus structures recently under study are included. Chapter 4 is centered on the Crosspoint Method, a new algorithm for automatic selection of virus particles from electron micrographs. The method, results, and comparisons with existing automatic selection procedures are presented in detail. The method is discussed in the context of traditional digital image processing techniques, some of which are described. An interactive image processing package which includes the Crosspoint Method, traditional image processing transformations, and a mechanism for manual selection and extraction of individual particle images is also described. A glimpse at the computational challenges involved in generating the data sets used for structure determination is offered in Chapter 5. A simulation experiment, designed to

12 3 estimate the performance of hybrid load balancing schemes on distributed memory MIMD systems is presented. An application for which such schemes have proven useful is discussed. A comparison between two different techniques for performing computations related to highly symmetrical structures is also described. Chapter 6 summarizes the work presented in this thesis and describes some considerations for future research. 1.3 Research Contributions The most important contribution of the research described in this thesis is the Crosspoint Method for automatic detection of the positions of virus particles in electron micrographs (see section on page 55). This method combines traditional image processing techniques with heuristics and a new algorithm for the detection of particle centers. The complexity of the method is linear in the number of pixels in the image as opposed to the O( n logn ) complexity of the algorithms described in the literature [HEEL82], [FRAN84], [OLSO89], [THUM95]. The results obtained using this method are much better than those previously reported, both in terms of the running time and the quality of the solution. The Crosspoint Method is used to replace manual selection of particles and thus to improve the efficiency of the three-dimensional structure reconstruction process. The resolution of three-dimensional reconstructions can be increased by allowing a larger number of particle projections to be considered, but this is feasible only using an automated procedure for the identification of the positions of individual particles. The method is also very important for the control of the electron microscope. EMMA is a new image processing package built around the Crosspoint Method which allows the structural biologist to employ the automatic virus particle detection algorithm in an interactive, user-friendly environment. The package also provides capabilities for traditional processing of electron micrographs. A new correlation method for fitting data sets is outlined in section on page 24. This method is iterative and allows scaling of data sets obtained from separate computations relative to each other. It is particularly useful for analyzing the differences between two similar structures.

13 4 Tonitza is a graphics package for the visualization, analysis and manipulation of very large data sets specific to structural biology, developed as part of the work reported in this thesis. The integration of data manipulation and visualization offers distinct advantages (e.g., uniform graphical user interface, increased efficiency) over using separate packages for each of these tasks.

14 5 2. FUNDAMENTAL CONCEPTS IN STRUCTURAL BIOLOGY 2.1 Crystals and Diffraction Biomacromolecules often occur naturally or in vitro as organized structures composed of subunits arranged in a symmetrical way. Such structures are readily studied by diffraction methods. Some of the fundamental concepts concerning crystalline matter, symmetry relationships and diffraction theory are summarized in this chapter. A crystal is a regular arrangement of atoms, ions, or molecules, and is conceptually built up by the continuing translational repetition of some structural pattern [BAKE95]. This pattern, or unit cell, may contain one or more molecules or a complex assembly of molecules. In three dimensions, the unit cell is defined by three edge lengths a, b, c, and three interaxial angles, α, β, γ. The seven three-dimensional crystal systems (triclinic, monoclinic, orthorombic, tetragonal, trigonal, hexagonal, and cubic) arise from the seven basic space-filling shapes that unit cells can adopt. A lattice is a mathematical formalism that defines an infinite array of imaginary points: each point in the lattice is identical to every other point. That is, the view from each point of a lattice is identical to the view in the same direction from any other point (this condition is not obeyed by finite crystals). Three dimensional lattices are defined by three translations a, b, c, and three axes at angles α, β, γ to each other. Crystal lattices may be primitive, with one lattice point per unit cell, or centered, containing two or four points per unit cell. The crystal structure is built up by placing a motif at every lattice point. The motif may be asymmetric or symmetric. The symmetry of any crystal of a biological molecule can be described only by rotations and/or translations. This is because biological molecules such as proteins mainly consist of l-amino acids and hence, reflection and inversion symmetries are not allowed. Such structures are called enantiomorphic. The crystal structure, crystal lattice, and motif

15 6 are all restricted in the symmetries they can display, but biomacromolecular assemblies themselves are not restricted, in the sense that they may display additional internal, noncrystallographic symmetry (i.e., symmetry that is not contained within the allowed lattice symmetries). The symmetry of a three-dimensional structure is described by a space group. There are 230 ways to generate a regular pattern from a motif associated with a three-dimensional lattice, hence 230 space groups. Only 65 space groups are compatible with the enantiomorphic biological structures. The asymmetric unit is a part of a symmetric object from which the object can be generated by symmetry operations. The number of asymmetric units may be less than, equal, or greater than the number of molecules in the unit cell. If the number of asymmetric units is equal to or less than the number of molecules in the unit cell, then the molecule either contains no symmetry or it contains non-crystallographic symmetry. If the number of asymmetric units is greater than the number of molecules in the unit cell, then the molecules must occupy special positions and possess the appropriate symmetry elements of the space group. Of special interest for structure determination is the icosahedral symmetry, which generally denotes the symmetry of an icosahedron and/or that of a dodecahedron. This type of symmetry governs the arrangement of protein subunits within the shells of spherical viruses [BRAN91]. Figure 2.1 shows the symmetry properties of an icosahedron. There are three different types of rotations that bring it into self-coincidence. The symmetry elements corresponding to these rotations are twelve five-fold, twenty three-fold, and thirty two-fold axes of rotation. Figure 2.1 An icosahedron viewed along each of its symmetry axes

16 7 Diffraction methods including X-ray, neutron, electron, and optical diffraction provide a powerful way to study molecular structures. The ultimate goal is to understand the chemical properties of molecules by determining their atomic structures. Presently, only diffraction techniques such as X-ray and neutron diffraction are routinely capable of revealing the arrangement of atoms in molecular structures. Diffraction is the non-linear propagation of electromagnetic radiation and occurs when an object scatters the incident radiation. The rays scattered from different portions of the object interfere both constructively and destructively, producing a diffraction pattern which can be recorded. The recording can be made either on film (the classical method) or using an electronic detector which feeds the signals detected directly in a digitized form into a computer. Figure 2.2 is a schematic representation of the diffraction process. Figure 2.3 shows a portion of the diffraction pattern of an HRV14 crystal [STEL96]. The diffraction pattern consists of points, also called reflections. Each reflection arises from interference of rays scattered from all irradiated portions of the object. Structure determination by diffraction methods involves measuring or calculating structure factors at all points in the diffraction pattern. Each structure factor is a complex number, described by amplitude and phase. incident radiation crystal diffracted rays photographic film Figure 2.2 Schematic representation of the diffraction process

17 8 Figure 2.3 Portion of a diffraction pattern from an HRV14 crystal Amplitude is the strength of interference at a particular point and is proportional to the square root of the intensity in the recorded pattern. The phase is the relative time of arrival of the scattered radiation at a particular point (e.g., photographic film), and this information is lost when the diffraction pattern is recorded. Sir W. L. Bragg of Cambridge University described diffraction from crystals as arising from the reflection of radiation from imaginary parallel planes of electron density. Each set of planes is characterized by three Miller indices, (h, k, l), which are the reciprocals of the intercepts, in unit cell edge lengths, that the set of planes makes with the axes of the unit cell. The intensity of each (h, k, l) reflection is proportional to the electron density distribution in the (h, k, l) planes [BLUN76]. 2.2 X-ray Crystallography X-rays are short wavelength electromagnetic radiation, emitted when electrons jump from a higher to a lower energy state. In laboratories, X-rays are produced by high-voltage tubes in which a metal plate is bombarded with highly accelerated electrons and this causes X-rays of a specific wavelength to be emitted. More powerful X-ray beams are produced using synchrotron storage rings, where electrons travel close to the speed of light.

18 9 The first prerequisite for solving a three-dimensional structure of a protein by X-ray crystallography is a well-ordered crystal that strongly diffracts X-rays. Crystallization is often quite difficult to achieve for large macromolecules, and crystal growth can be slow [BRAN91]. For a typical protein crystal of a small macromolecule such as myoglobin, each of the about 20,000 diffracted beams measured contains scattered X-rays from each of the 1500 or so atoms in the molecule. To extract information about individual atoms from such a system requires a considerable computational effort. A major concern of structure determination using X-ray crystallography is retrieving the phase information lost upon recording of the diffraction pattern. The phases could be obtained if it were possible to focus the scattered rays with a lens to form an image. Unfortunately, such lenses do not exist, and some other method must be used. For small molecules (several thousands of atoms), the phase problem has been solved by Nobel Prize winners J. Karle and H. Hauptman [HAUP53] who developed the so-called direct methods. For large proteins however (millions of atoms), the problem remains and several techniques, such as the Multiple Isomorphous Replacement and the Molecular Replacement have been devised [BRAN91]. The Molecular Replacement method (MR) [ROSS72] utilizes the identity of structure in different parts of the crystallographic asymmetric unit, caused by the repetition of the same subunit structure in the formation of the whole molecule. It may also use the relationship between different crystal forms of the same or similar molecules. The method consists of solving three main problems. (a) The rotation problem: systematic inspection of the Patterson map (this is a map of vectors connecting the heavy atoms [BRAN91]) allows determination of the relative orientation of independent molecules (or subunits of molecules) within one crystal lattice or between different crystal forms. Rotation matrices, C, are computed in this stage. (b) The translation problem: the translation of subunits must be determined with respect to the designated crystallographic symmetry elements. This may also be done by inspection of the Patterson function. A translation vector, d, is computed in this stage. Using the rotation matrices determined in the previous stage, the

19 10 exact relationship between a point x in a standard molecule (or subunit) and the corresponding point x', in a different subunit, can be expressed as x' = C x + d. (c) The phase problem: determine the phases corresponding to the recorded amplitudes. Two types of symmetry are considered at this stage: the crystallographic symmetry, independent of the molecules under study, and the non-crystallographic symmetry, occurring within a molecule itself. In order to determine the phases which will allow determination of the molecular structure, a number of equations are set up. These represent the condition that for the set of observed structure factor amplitudes the electron density distribution within the volume of the unit-cell is identical within all subunits related by both crystallographic and non-crystallographic symmetry and that it is zero, or constant outside these volumes. The iterative computation required for solving these equations is currently being carried out on parallel machines, in a process known as phase refinement and extension. The amplitudes of the structure factors are obtained by processing the diffraction data and are used to determine the non-crystallographic symmetry. An initial, low resolution model for the phases (and hence for the molecular structure) is obtained by one of a series of methods. For example, a virus may be assumed to be a hollow shell or the model of a related virus may be used. In the first iteration, the phases derived from the model are combined with the corresponding observed structure factor amplitudes. In subsequent iterations, calculated structure factor amplitudes are replaced by observed ones. In the next step, the model is expanded from one asymmetric unit to the whole unit cell. An electron density map is computed by Fourier synthesis. The electron density values are then averaged among all the structurally identical non-crystallographic units. As a result, a new and more accurate map is obtained. Using this map and an inverse Fourier transform, a set of calculated structure factors (phases and amplitudes) is produced (also at this point, the resolution can be extended). These phases, better than the original ones, are combined with the observed amplitudes replacing the previous, less exact phase set and the entire cycle is repeated. After a number of cycles the phases usually converge. The measure of convergence is evaluated by a correlation coefficient which relates the observed structure factors (determined experimentally) and the calculated ones.

20 11 Figure 2.4 Fitting a structure in an electron density map The electron density map has to be interpreted as a polypeptide chain with a particular amino acid sequence. Several limitations of the data may complicate the interpretation of this map. The map itself may contain approximation errors in the phases. The resolution of the data is also a factor that affects the quality of the map and is, in turn, affected by the quality of the crystal. From a map at low resolution (10 A or larger) one can obtain only the shape of the molecule. At medium resolution (between 4 A and 6 A ) it is possible to distinguish some secondary structural features (e.g., α-helices, β-sheets), and at higher resolution the path of the polypeptide chain can be traced and a known amino acid sequence can be fit into the map. Very high resolution (1 ) is required to observe atoms as discrete spheres of density. However, few structures have been determined to such high resolution. Figure 2.4 shows a two-dimensional example of how a known model can be fitted into an electron density contour map, by placing the atoms of the known structure at peaks of electron density. Mask maps are sometimes used in conjunction with electron density maps to distinguish between different particles. Computer graphics is currently extensively used for both chain tracing and model building, to present the data and to manipulate the models. A 2 A

21 Electron Microscopy In the case of electron microscopy, structure can be directly visualized because the electrons can be focused with lenses to form images. In the absence of noise, an image is considered to contain structural information (amplitudes and phases of the structure factors) in directly interpretable form. According to Abbe s theory, image formation is a twostage, double-diffraction process. That is, an image is the diffraction pattern of the diffraction pattern of an object (see Figure 2.5 ). incident radiation object lens diffraction plane image plane Figure 2.5 Image formation in a lens (from [BAKE95]) With an ideal lens system, an image depicts every detail present in the object. In the first stage a parallel beam of rays incident on the object is scattered and the interference pattern (Fraunhofer diffraction pattern) is brought to focus at the back focal plane of the lens. This stage is also referred to as the forward Fourier transformation. The intensity distribution of the recorded diffraction pattern of an object is proportional to the square of the Fourier transform of that object. The second stage of image formation occurs when the scattered radiation passes beyond the back focal plane of the lens and interferes (recombines) to form an image. This is the inverse Fourier transformation stage. Note that the image cannot exactly represent the object, because some scattered rays never enter the lens and cannot be focused at the image plane. Image processing of electron micrographs provides an objective way to extract reliable structural information from noisy images. Noise appears in all micrographs to various

22 13 extents and can arise from a variety of sources, such as the specimen itself, specimen support film, microscope, and photography. The goal of structure determination by means of electron microscopy is to produce three-dimensional electron density maps based on information obtained from projected specimen images. The theoretical foundation for this three-dimensional reconstruction process is given by the Projection Theorem which states that the Fourier transform of the projected structure of a three-dimensional object is equivalent to a two-dimensional central section of the three-dimensional Fourier transform of the object, normal to the direction of projection [CROW70]. Indeed, the Fourier transform of the function ρ( xyz,, ) is: The central section Z = 0 of the transform is given by: dxdydz. FXY0 (,, ) = σ( xy, ) e dxdy, with σ( x, y) = ρ( xyz,, ) dz. This approach is similar to conventional X-ray crystallography, except that in this case the phases can be computed from the image. The different views may be collected either from a single particle by using a tilting stage in the microscope, or from a number of particles in different but identifiable orientations. In general, it is desirable to combine data from different particles, so that imperfections can be averaged out [CRRA71]. Methods for digital image processing of electron micrographs are presented in detail in section 4.3 on page 50. FXYZ (,, ) = ρ( xyz,, ) e 2 π i ( xx + yy ) 2 π i ( xx + yy + zz ) 2.4 Other Methods for Structure Determination X-ray crystallography and electron microscopy are only two of a number of methods developed to investigate molecular structures. Diffraction is only one of the many phenomena that can be exploited to gather information about the arrangement of atoms within molecules. For example, certain atomic nuclei have a magnetic moment or spin. The chemical environment of such nuclei can be probed by Nuclear Magnetic Resonance (NMR). This technique can be exploited to give information on the distances between atoms in a molecule. These distances can then be used to derive a three-dimensional

23 14 model of the molecule. NMR and X-ray crystallography are in many respects complementary. X-ray crystallography deals with the structure of proteins in crystalline state, whereas NMR determines the structure in solution. X-ray crystallography is more suitable for characterization of protein surfaces and the water structure around the protein, whereas NMR is more suitable for investigation of dynamic processes such as those during folding. X-ray crystallography remains the only method available to determine the structure of large protein molecules, whereas NMR is the method of choice for small protein molecules that might be difficult to crystallize [BRAN91]. Structural studies are often insufficient to infer the function of a protein from its structure. It is then necessary to combine biochemical studies with structural information. The specific role of each amino acid residue for the function of the protein can be tested by making specific mutations of that residue and examining the properties of the new protein. By combining such functional studies in solution, DNA techniques, and three-dimensional structure determination, scientists are trying to gain insights into the way molecules work.

24 15 3. COMBINING DATA VISUALIZATION WITH COMPUTATIONS 3.1 Overview Graphics packages for data exploration like IRIS Explorer [EXPL91] and AVS (Application Visualization System) [AVSP89] offer distinct advantages to scientists and engineers in need of data visualization tools. Yet, when data visualization and very specific computations are tightly coupled together, the use of generic graphics packages looses some of its appeal. For example, to display simultaneously two three-dimensional reconstructions of a spherical virus may require resizing one of the data sets relative to the other so that the two are brought to the same scale [BAKE95]. Finding the optimal magnification factor to be used for resizing is based on computing the correlation of the two data sets. The correlation procedure is iterative and consists of defining the correlation regions (one is not interested in correlating densities within the nucleic acid core) and the magnification range, determining an optimal magnification factor that maximizes the correlation coefficient, refining it, and scaling one map relative to the other. For such a sequence of computation and visualization steps, the integration of data transformations and data visualization into a specialized tool provides distinct advantages: there is a uniform graphical user interface, the efficiency is increased because data manipulation is done in main memory and the need for I/O operations is minimized. Considerations like the ones described above provided the motivation for Tonitza, an interactive package for visualization, analysis, and data manipulation. It is aimed at the field of structural biology, but it can be used to explore any scalar field data (see Appendix D). It allows processing and display of multivariate gridded data in a variety of representations and it is available on graphics workstations running OpenGL [OPGL93].

25 Survey of Software Packages for Structural Biology A variety of generic as well as specialized software packages for molecular modeling are available today. Generic visualization packages like AVS [AVSP89] and IRIS Explorer [EXPL91] are suitable for physical sciences and engineering and can be used for molecular modeling. Such packages have a modular design and application specific software can be generated by combining different modules into flow networks. Flow networks are then executed as scripts. According to [NIHG96], specialized software packages used for molecular modeling can be classified into several categories, based on their functionality (see also Table 3.1). (a) Structure database manipulation packages are designed to either search and access the major chemical structure databases (the Brookhaven Protein Databank, the Cambridge Structural Database, the Drug Information System 3D Database) or create, maintain and search local chemical structure databases. PDBtool, for example, is a Protein Data Bank browser that allows querying and verification of macromolecular structure data. It includes a three-dimensional viewer and renderer and a variety of graphical and textual structure verification tools. It runs on SGI and SUN platforms. (b) Model building packages allow the user to fit structures into electron density maps and/or compute and display all the molecular graphs that correspond to a given chemical formula, prescribed and forbidden substructures, optional conditions (intervals for possible ring sizes, hybridization of carbon atoms), stereo isomers, etc. An example is O, a general purpose macromolecular modeling environment. The program supports model building and display of macromolecules. Due to specific features such as building and rebuilding of models into electron density, O is mainly aimed at the field of protein crystallography. The program is built on top of a versatile database system which contains the entire molecular data in a predefined structure. It is available on ESV, SGI, and HP platforms. Another example is XtalView, a complete package for solving macromolecular crystal structures by isomorphous replacement, including building the molecular model. It runs on Sun, DEC, SGI, IBM, and PC computers and takes full advantage of the modern workstation environment. (c) Structure drawing/visualization packages have revolutionized the publication and presentation of chemistry information. In addition, they can be used to visualize and manipu-

26 17 late structures in various representations and/or to input structures to some molecular modeling programs. RasMol, for example, is a program for the visualization of proteins, nucleic acids and small molecules, aimed at displaying, teaching, and generation of publication quality images. The program runs on X-compatible Unix computers, Macintosh, PowerMac, and PCs running Microsoft Windows. Another example for this category is VMD, designed for the visualization of biological systems such as proteins, nucleic acids, and lipid bilayer assemblies. It provides a wide variety of methods for rendering and coloring a molecule: simple points and lines, CPK spheres and cylinders, licorice bonds, backbone tubes and ribbons, etc. It runs on SGI workstations. Functionality Name Source Structure database manipulation Model building Structure drawing / visualization Iditis PROTEP PDBtool ChemDBS-3D O XtalView MOLGEN+ CONCORD Cobra RasMol ChemDraw ISIS Draw Raster3D VMD Kekule Oxford Molecular Tripos Associates San Diego Supercomputing Center Chemical Design, Inc. Aarhus University Scripps Institute University of Bayreuth Tripos Associates Oxford Molecular University of Edinburgh Cambridge Scientific Molecular Design, Ltd. University of Washington University of Illinois, Urbana PSI International Table 3.1 Selected software packages used in molecular modeling

27 18 Functionality Name Source Molecular mechanics Molecular dynamics Distance geometry Quantum chemistry NMR-based structure determination CHARMm Discover Polaris MacroModel QUANTA/ CHARMm SYBYL Cobra Insight II DGEOM X-PLOR SYBYL GAMESS HONDO UniChem NMRchitect X-PLOR DGEOM Molecular Simulations, Inc. Biosym Technologies Molecular Simulations, Inc. Columbia University Columbia University Tripos Associates Oxford Molecular Biosym Technologies Dupont Molecular Simulations, Inc. Tripos Associates Iowa State University IBM Corporation Cray Research Biosym Technologies Molecular Simulations, Inc. Dupont Table 3.1 Selected software packages used in molecular modeling (d) Molecular mechanics packages include features such as energy minimization (used to optimize initial geometries or to repair poor geometries), template forcing (i.e., evaluating whether a molecule can adopt a template conformation consistent with a given model), and torsion forcing (to obtain Ramachandran-type contour plots for proteins). (e) Molecular dynamics packages attempt to solve Newton s equation of motion: 2 x i m i t 2 = xi E total (where i runs through all free atoms and the gradient xi E total is

28 19 derived from the energy function), produce molecular dynamics simulations, store them in trajectory files, etc. (f) Conformational searching packages include algorithms for efficient searching of conformational space defined in terms of torsion angles and multimolecular translations/rotations, some of which pertain well to parallelization. (g) Distance geometry packages facilitate molecular structure determination using metric matrix distance geometry. (h) Quantum chemistry packages include various applications of density functional theory. (i) NMR-based structure determination packages allow determination and refinement of structures based on interproton distance estimates, coupling constants measurements, and other information, such as known hydrogen-bonding patterns. These are just a few examples of molecular modeling packages. There are many others not listed in this survey which focuses only on programs widely used by the structural biology community. 3.3 Tonitza A Scientific Visualization Package for Structural Biology We have developed Tonitza, a package which consists of a graphical user interface (GUI), input/output, visualization, and computation modules. This section describes the overall structure of these modules. All figures are based on data sets representing Ross- River or Coxackie B3 virus structures [CHEN95], [MUCK95] (see Appendix A) The Graphical User Interface The user interface is based on X-Windows and Motif [YOUN90]. The main style is that of a direct-manipulation user interface [FOLE90] in which the objects and attributes that can be operated on are represented visually and operations are invoked by actions performed on the visual representations, typically by using the mouse. However, this interaction style is not sufficient by itself and other interface styles, such as menus, are also included. Figure 3.1 shows a snapshot of the screen during a Tonitza session and illustrates the style of the user interface.

29 20 Once an object has been displayed in the main window, it can be manipulated in various ways using the mouse or the dials. Figure 3.1 A snapshot of the screen during a Tonitza session

30 21 Depending on the representation, objects may be rotated, translated, scaled, and/or clipped with a plane. A special algorithm, based on quaternion algebra was used to implement rotation of objects around an arbitrary axis using the mouse and will be discussed in section on page 36. Objects may be customized using colormap and material editors. A colormap editor allows the user to specify the mapping of data values to colors to create a so-called colormap. Such maps are used for continuous scale representations. The design of the colormap editor is based on Icol [ICOL92]. The visualization session usually starts with a gray scale colormap, with colors varying linearly from black (corresponding to the lowest data value) to white (for the highest data value). A colormap saved from a previous session may also be used as an initial colormap for the current session. The editor allows the user to create linearly interpolated colormaps between key points in the Red-Green- Blue (RGB) color space. It consists of a menu, a graph area, a color cell area, and a set of slider bars (see Figure 3.2). The menu has options for saving the current colormap in a file and for restoring a previous mapping. The graph area consists of two parts: the lower half contains the colors currently stored in the colormap in the form of vertical rectangles (the overall appearance is that of a smoothly varying color scale); the upper half contains a graph depicting the red, green, and blue color components for each of the colors in the colormap. The color cell area consists of cells, one for each color in the graph area. Tonitza tries to allocate the largest number of colors available. It first tries to allocate 256 colors. If it cannot, then it tries to allocate 128, and so on. Each color cell is selectable with the mouse and, when selected, it defines a key point or knot. Key points are displayed in the graph area as black vertical lines. The slider bars (one for each of the R, G, and B components) allow the color corresponding to the current key point to be modified. This change is reflected in both the graph and color cell areas. The R, G, B components are no longer linearly varying between two colors, but they are piecewise linearly varying between consecutive key points. Figure 3.2 shows a snapshot of the colormap editor. The material editor may be used in conjunction with surface representations to modify the material properties of the current object, whether it is displayed in a wireframe or shaded representation. For wireframe objects, only the color can be altered. Shaded objects can be displayed as being made of a particular material by defining a light source

31 22 and adjusting the primary reflections of light from the object surface [WATT93]. All shading and lighting calculations are done via OpenGL library calls [OPGL93] which implement the Phong reflection model [WATT93]. In this model the intensity associated with a vertex in the polygonal representation of an object has three components. (a) The ambient term is the ambient color of the light scaled by the ambient material property. The ambient material property affects the overall color of the object. It is independent of the position of the viewpoint and it is most noticeable where an object receives no direct illumination. (b) The diffuse term has a more complex expression, depending on the angle at which light impinges on the surface. The diffuse reflectance of the material plays the most important role in determining what the human eye perceives the color of the object to be. It is affected by the color of the incident diffuse light and the angle of the incident light relative to the normal direction. The position of the viewpoint does not affect the diffuse reflectance of the material at all. (c) The specular term combines the specular color of the light, the specular property of the material, the shininess of the material (also known as specular exponent), and the angle between the direction of the light and the direction of the viewer. The specular reflection from objects produces highlights. The higher the shininess of the object, the smaller and brighter the highlight is. The material editor allows the user to define the ambient, diffuse, and specular material properties of an object, to specify its shininess and its opacity. Figure 3.3 shows the material editor. In addition to the interface components necessary for material specification, it contains a small drawing area in which an ellipsoid made of the current material is displayed. This helps the user to get an idea of what material a particular choice of parameters yields, before this material is applied to any of the objects displayed Input/Output In Tonitza, the input/output (I/O) module is responsible for: reading/writing data files from/to the disc, automatic file format recognition, conversion between formats, and handling I/O errors. The program accepts as input gridded data produced by scientific and engineering software. It provides support for a variety of data formats used in X-ray crystallography and electron microscopy (see Appendix C). In addition, it accepts as input