Visualization of Molecular Structure: the State of the Art
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Eurographics Conference on Visualization (EuroVis) (2015) STAR – State of The Art Report R. Borgo, F. Ganovelli, and I. Viola (Editors) Visualization of Molecular Structure: The State of the Art B. Kozlíkováy1, M. Kroney2, N. Lindow3, M. Falk4, M. Baaden5, D. Baum3, I. Viola6;7, J. Parulek7, and H.-C. Hege3 1Masaryk University, Czech Republic 2Visualization Research Center, University of Stuttgart, Germany 3Zuse Institute Berlin, Germany 4Immersive Visualization Group, Linköping University, Sweden 5Laboratoire de Biochimie Théorique, UPR 9080 CNRS, France 6Institute of Computer Graphics and Algorithms, Vienna University of Technology, Austria 7Department of Informatics, University of Bergen, Norway Abstract Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large, and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualization techniques for molecular structures, strategies for efficient display in terms of image quality and frame rate, then it covers different aspects of level of detail and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The report concludes with an outlook on promising and important research topics to enable further success in advancing the knowledge about interaction of molecular structures. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations 1. Introduction of an atomic orbital depends on the energy, angular mo- mentum and magnetic moment of its (up to two) electrons. Molecular visualization is one of the oldest branches of data In a simplified model, atomic orbitals are arranged in lay- visualization, with deep roots in the pre-computer era. Be- ered shells and sub-shells. The outer electrons of two atoms fore sketching the developments that led to modern molecu- can interact and form molecular orbitals, potentially creat- lar visualization, let us characterize the objects of interest. ing a chemical bond between the atoms. Thereby molecules All ordinary matters consist of atoms and molecules, emerge, i.e., sets of atoms that are held together by chemi- which in turn embody protons, neutrons and electrons. The cal bonds. A molecule thus is a structure composed of tiny protons and neutrons are bound together by nuclear forces nuclei (defining the atom positions) and their core electrons (residual effects of the strong force), forming the nuclei of (inner electron shells); these are held together by an outer the atoms. The tiny and positively charged nuclei attract neg- electronic shell (valence shell) that is composed of differ- atively charged electrons. Due to quantum mechanical ef- ent molecular orbitals. Molecules are the smallest units of fects, electrons and nuclei do not collide. Instead the elec- a compound, i.e., of a pure chemical substance. The huge trons surround the nuclei in defined distances, comprising diversity of the material world, both inorganic and organic, stable and electrically neutral atoms. Atoms are the smallest originates from the large numbers of possibilities to combine units of a chemical element. different types of atoms to molecules and of spatial arrange- ments in which these can be grouped to form condensed mat- According to quantum mechanics, the electrons in an ter. atom are organized in orbitals, i.e., regions of space, in which electrons stay with high probability. The shape and location The primary purpose of molecular visualization is to sup- port our understanding of this rich, complex world, by mak- ing molecular structures, their properties and their interac- y These authors contributed equally tions apprehensible and intelligible. In addition it aims at c The Eurographics Association 2015. Kozlíková, Krone et al. / Visualization of Molecular Structure supporting the ‘rational’ design of new molecules, such as the mathematical side a hierarchy of approximations is em- chemically and pharmaceutically active compounds, or cus- ployed: as long as no measurement process is involved and tomized substances possessing specific chemical, optical, quantum electrodynamical as well as relativistic (i.e., high- electrical, or mechanical properties, or even of molecular energy) effects are negligible, phenomena are described to machines implementing certain functions. The first question great precision by the time-dependent Schrödinger equa- is, how to visualize atoms and molecules? Since these are tion [Sch26]. This equation, describing the evolution of the physical objects in space and time, the answer seems obvi- Y function in time and in configuration space (i.e., 3N di- ous: “depict their spatial extension, their shape”. However, mensional space for N particles), can be solved numerically this principle cannot be fully maintained – as can be best un- only for low N or few quantum mechanical degrees of free- derstood from the history of the development of atom and dom (dof). Therefore, one has to rely on approximations: molecule physics, which was accompanied by various types either mixed quantum-classical models or even purely clas- of visual representations. sical models. The latter ones are good descriptions when no covalent bonds are formed or broken and when the behavior Forerunners of today’s visual representations are hand- of the molecular system considered does not depend sen- drawn depictions and physical models. Pictorial represen- sitively on fine-tuned energy values. In molecular biology, tations have been used, e.g., by Kepler (1611) [Kep11] and where systems with large particle number N have to be con- Huygens (1690) [Huy90], centuries before 1808, when Dal- sidered, one is trying to get by with as little as possible quan- ton published the modern, but still pre-quantum formula- tum dof. The majority of systems is treated classically; this tion of atomic theory [Dal10]. In these three groundbreak- means, no molecular orbitals are computed and the atoms are ing works, atomic arrangements were illustrated, display- considered as classical particles that move under the influ- ing atoms simply as spheres. Van der Waals, when deriving ence of (suitably parametrized) multi-body forces that mimic the equation of state for gases and lipids (1873) [Waa73], quantum effects. Due to the strong repulsion between neutral saw the necessity of taking into account the volumes of atoms and molecules (in the Lennard-Jones potential often molecules as well as attracting intermolecular forces; he modeled by a r−12 term, where r is the distance), atoms can computed from experimental data the volume “occupied” by be considered approximately as ‘hard’ spheres; this means, an individual atom or molecule. From now on, atomic radii they are fully characterized by their mass, their radius and for several chemical elements were approximately known the forces they exert on other atoms. and used in depictions. Also physical models of molecules have been used for visualization purposes. They allowed to On the visualization side, therefore one is operating correlate mechanical, optical, electrical, magnetic, and ther- mainly on three levels: (i) visualization of quantum phys- mal properties with the atomic structure. Dynamic models ical data, (ii) visualization of quantum chemical data, and have been built too, allowing to reproduce atomic and molec- (iii) visualization of classical molecular trajectories. ular movements and interactions. For a survey with many On level (i) the data are the complex wave function Y, references covering the period 1880–1960 see [Smi60]. typically sampled on a (potentially sparse) grid, plus real With the emergence of increasingly elaborate atomic expectation values of physical variables. Since Y is a com- models by Thompson (1904), Rutherford (1911), Bohr plex function, often living on a higher-dimensional space, (1913), and Sommerfeld (1916), more detailed visualiza- and sometimes with more than one component (express- tions became necessary—culminating in detailed depictions ing quantum mechanical spin), this is quite challenging. of complex atoms in the popular book of Kramers and Holst Up to now only limited work is available; examples are [KH23], showing the elliptic orbits of the electrons in the [Tha00, Tha05, BD12]. On level (ii) the data represent ex- Bohr-Sommerfeld model. Afterwards, it became clear that pectation values of physical variables, like, e.g., electron and atoms and molecules are of truly quantum nature. Quantum nuclear densities or fluxes. They describe, e.g., equilibrium physics, however, seems to be intrinsically non-visualizable. geometries and reaction energetics. For an elementary, very One of several reasons is that no (mental) image exists accessible introduction to quantum chemistry and classical that simultaneously represents the corpuscular and wave-like MD, see, e.g., [Heh03]. On the visualization side typically character of particles. According to Heisenberg’s uncertainty depiction of sampled fields, often of multiple fields, is re- relation, an electron cannot be considered to have