`
`Solvent-Accessible Surfaces of
`Proteins and Nucleic Acids
`
`Michael L. Connolly
`
`reentrant surfaces and of Shrake and
`Rupley (12) for calculating solvent-ac(cid:173)
`cessible area, I developed a numerical
`computer algorithm for placing dots over
`the solvent-accessible molecular surface
`of a protein (13, 14). Belo\v, I briefly
`review the dot surface algorithm and
`present a new, analytical surface meth(cid:173)
`od.
`
`Dot Surfaces
`
`Computer graphics has made the re(cid:173)
`sults of x-ray crystallographic studies of
`proteins and nucleic acids more accessi(cid:173)
`ble to biochemists and molecular biolo(cid:173)
`gists. Traditionally. con1puter-generated
`images of n1olecular structures have con(cid:173)
`sisted of lines for the chemical bonds(/-
`3) or spheres (4-7) and ellipsoids (8) for
`the atoms. I present an alternative repre(cid:173)
`sentation, that of a smooth, continuous
`envelope in contact with the atoms that
`are accessible to solvent.
`Applications of this surface represen(cid:173)
`tation include enzymology, rational drug
`design, the elucidation of molecular dis(cid:173)
`eases such as sickle cell anemia, recogni(cid:173)
`tion of specific DNA base sequences by
`proteins and drugs, and the location of
`possible antigenic determinants on virus(cid:173)
`es.
`The historical basis for the smooth
`surface envelope method is the work of
`Richards (9) and colleagues on solvent(cid:173)
`accessible area. Their emphasis was on
`chemical calculations nteasuring quanti(cid:173)
`ties of hydrophobic and hydrophilic
`area, while the methods described below
`were developed primarily for the pur(cid:173)
`pose of visualizing n1olecular structure
`and
`interactions. Nevertheless, these
`new methods also permit the measure(cid:173)
`ment of area and volume in conjunction
`with the graphical display.
`
`Solvent-Accessible Arca
`
`Solvent-accessible area was originally
`defined and computed by Lee and Rich(cid:173)
`ards (10) as the area traced out by the
`center of a probe sphere representing a
`solvent molecule as it is rolled over the
`surface of the molecule of interest.
`These computational methods were in(cid:173)
`vented as a tool for attacking the protein
`
`19 AUGUST 1983
`
`folding problem (9). The problem is that
`of predicting
`the
`three-dimensional
`structure of a protein given only its pri(cid:173)
`mary sequence of amino acids.
`Simply measuring a quantity of area is
`insufficient for the study of many aspects
`of protein and nucleic acid function,
`such as substrate binding and catalysis,
`drug-nucleic acid interaction, and recog(cid:173)
`nition by the immune system. A method
`for visualizing solvent-accessible sur-
`
`The basic approach in this method is
`to place a probe sphere, representing a
`solvent molecule, tangent to the atoms of
`the protein at several thousand different
`positions. For each probe position that
`does not experience van der \Vaals over(cid:173)
`lap with the atoms of the protein, points
`lying on the inward-facing surface of the
`probe sphere become part of the pro(cid:173)
`tein's solvent-accessible surface. The
`probe may be placed tangent to (i) single
`
`Summary. A method Is presented for analytically calculating a smooth, three·
`dimensional contour about a molecule. The molecular surface envelope may be
`drawn on either color raster computer displays or real-time vector computer graphics
`systems. Molecular areas and volumes may be computed analytically from this
`surtace representation. Unlike most previous computer graphics representations of
`molecules, which lmllate wire models or space-filling plastic spheres, this surface
`shows only the atoms that are accessible to solvent. This analylical method extends
`the earlier dot surface numerical algorithm, which has been applied In enzymology,
`rational drug design, immunology, and understanding DNA base sequence recogni(cid:173)
`tion.
`
`faces is needed. For this purpose. an
`alternative
`solvent-accessible
`surface
`definition, proposed by Richards (9), is
`appropriate. Unlike the original surface
`of Lee and Richards (/0), this alternative
`molecular surface is not displaced from
`the van der \Vaals surface. Instead, it
`consists of the part of the van der \Vaals
`surface of the atoms that are accessible
`to the probe sphere (contact surface),
`connected by a network of concave and
`saddle~shaped surfaces (reentrant su,.
`face) that smooths over the crevices and
`pits bet\veen the atoms. This surface is
`the boundary of the volume from which a
`probe sphere is excluded if it is not to
`experience van der \Vaals overlap with
`the atoms.
`Improving on the algorithms of Greer
`and Bush(//) for calculating contact and
`
`atoms, creating a dot at the point of
`tangency, (ii) pairs of atoms, creating a
`concave arc of dots connecting the two
`points of tangency, and (iii) triples of
`atoms, creating a concave triangle of
`dots between the three points of tangen(cid:173)
`cy. For each surface point generated, the
`numerical algorithm produces not only
`its coordinates but also an approximate
`solvent~accessible area associated with
`the point and an outward-pointing unit
`vector perpendicular to the surface at
`that point. The pancreatic trypsin~tryp
`sin inhibitor complex (I 5) is shown in
`Fig. I, with a dot surface for the enzyme
`only.
`
`The author is a Helen Hay \Vhitney postdoctoral
`fellow in the Molecular Biology ~par1ment. Re·
`search Institute of Scripps Clinic, La Jolla, Ca!ifor·
`nia 92037.
`
`'"'
`Breckenridge Exhibit 1027
`Breckenridge v. Novartis AG
`
`
`
`This method has proved useful in
`enzymology (/6-20), immunology (21,
`22), virology (23), n1olecular pathology
`(24), and the study of protein-ligand (25)
`and protein-protein (26, 27) interactions.
`Despite the many applications of the
`dot surface numerical algorithm, it was
`necessary to invent an analytical surface
`algorithm in order to generate high-reso(cid:173)
`lution color raster display images and to
`compute more accurate molecular areas
`and volumes.
`
`Analytical ~tolecular Surface
`
`A continuous molecular surface con(cid:173)
`tour is defined as the union of pieces of
`spheres and tori joining smoothly at cir(cid:173)
`cular arcs. There are three kinds of
`pieces: concave spherical triangles, sad(cid:173)
`dle-shaped
`rectangles,
`and
`convex
`spherical regions (Fig. 2).
`The computer algorithm proceeds in
`three steps, one for each shape of sur(cid:173)
`face. First, a probe sphere is placed
`
`Fig. I. Stereo pair of the pancreatic trypsin-trypsin inhibitor complex, The enzyme is
`represented by a dot surface. The residues of the inhibitor in contact with the enzyme are
`represented by bonds. The part of the trypsin surface that is kept from contact with the solvent
`by the presence of the inhibitor is colored red.
`
`Fig. 2. Heme molecule drawn on a color raster graphics system. Green, convex surface; red,
`saddle surface; blue, concave surface. Surface pieces join at circular arcs.
`
`710
`
`tangent to every set of three neighboring
`atoms, and a concave triangle is generat(cid:173)
`ed whenever the probe sphere experi(cid:173)
`ences no collisions with any other atoms
`. of the molecule. Each concave triangle
`has three concave arcs as edges. Next,
`the saddle rectangles are formed by con(cid:173)
`necting adjacent concave arcs along the
`inner surfaces of tori (Fig. 3). The edges
`of each saddle rectangle consist of a pair
`of concave arcs and a pair of convex
`arcs. In the final step, the convex arcs on
`each atom are grouped to form-closed
`circuits, or cycles, and the boundary of
`each convex face is defined by zero, one,
`or nlore cycles. The equations defining
`the surface and the details of the comput(cid:173)
`er algorithm will be presented elsewhere
`(28).
`Since molecular areas and volumes are
`important physical chemical properties
`of molecules, efforts have been made to
`calculate them from x-ray coordinates.
`The areas of the convex faces arc re(cid:173)
`ferred to in the literature as contact
`areas, and approximate numerical meth(cid:173)
`ods for their measurement have been
`developed {10, 29, 30). \Vith the surface
`defined in an analytical fashion, it is no\V
`possible to calculate these contact areas
`exactly. This is done by using the Gauss(cid:173)
`Bonnet theorem (3/) from differential
`geometry. This theorem is traditionally
`used to study the relation of surface
`topology to integrals of curvature, but
`since the curvature of a convex spherical
`face is constant, the integrals simplify
`and the contact area may be expressed
`as a function of the atomic radius and the
`geometry and topology of the boundary
`cycles. The area or a concave face is
`calculated in a similar fashion. The area
`of a saddle face may be calculated by
`using integral calculus, since it is part of
`a surface of revolution, the torus.
`r-.1-olecular volumes have been calcu(cid:173)
`lated from protein x-ray crystallographic
`coordinates, using a polyhedral defini(cid:173)
`tion of the protein surface, and these
`calculated volumes have been compared
`to experimentally measured partial spe(cid:173)
`cific volumes of proteins in solution (32).
`A smoothly curved definition of the pro(cid:173)
`tein surface, such as the analytically
`defined
`solvent-accessible
`surface,
`should help provide a ntore accurate
`measurement of molecular volume. The
`volume enclosed by the solvent-accessi(cid:173)
`ble surface may be calculated by parti(cid:173)
`tioning this volume into simpler shapes
`whose volumes may be easily calculated
`by solid geometry and integral calculus.
`Most of the molecular volume is con(cid:173)
`tained within an interior polyhedron
`whose vertices are the centers of the
`solvent-accessible atoms. Coating this
`
`SCIENCE, VOL. 22.1
`
`
`
`Fig. 3 Oeft). Trajectory of probe rolling over a molecular surface. The trajectory arcs (red) connect positions where the probe is simultaneously
`langent to three atoms. In a corresponding manner, saddle rectangles connect concave triangles. These reentrant surfaces (green) then define the
`boundaries of the convex surfaces (magenta).
`Fig. 4 (right). Yeast phenylalanyl transfer RNA anticodon (GAA). The contact surface of the
`three anticodon bases is shown. The contact areas in square angstroms are displayed next to the atom labels.
`
`polyhedron is a surface layer that is
`made up of one piece for each curved
`face of the analytical surface. This sur·
`face layer has an average thickness of
`about an atomic radius.
`As an example of an application of the
`area method, the contact areas of the
`atoms of the transfer RNA anticodon
`(33) have been computed and are shown
`in Fig. 4. The conjunction of both graphi·
`cal and area measurement methods
`makes it possible to see not only how
`much of an atom is accessible but also
`where the accessible regions are. For
`this anticodon and the DNA structures
`presented below, van der \Vaals radii
`with implicit hydrogens have·been taken
`from (30) and a probe \Vith a radius of 1.5
`A has been used.
`To illustrate the ability of the analyti(cid:173)
`cal method to measure small changes in
`area and volume, the room-temperature
`(34) and low-temperature (35} DNA do·
`decamer structures are con1pared. The
`molecular areas and volumes are 3631 A2
`and 6534 A' (290 K, 1.9-A resolution)
`and 3623 A' and 6514 A' (16 K. 2.7-A
`resolution). respectively, The low-tem(cid:173)
`perature structure is 0.3 percent smaller
`in volume. The room-temperature struc(cid:173)
`ture is shown in Fig. 5.
`
`Computer Graphics
`
`The analytically defined surface, being
`continuous rather than discrete, is \Veil
`suited to raster display. The input to a
`raster graphics system consists of a two·
`dimensional array of picture elen1ents, or
`pixels, each of which has a color and
`shade value (36). In order to produce this
`
`19 AUGUST 1983
`
`pixel array from a three-dimensional
`curved surface, a hidden-surface elimi·
`nation algorithm is required (37). 'fhe
`analytical molecular surface representa·
`ticin is substantially different from previ(cid:173)
`ous curved surface representations, such
`as polygon mesh, parametric bicubic
`patches, and solid modeling (38, p. 506),
`so it was necessary to invent a hidden(cid:173)
`surface algorithm for it, which will be
`published elsewhere (39).
`The use of stereo, in conjuction with
`hidden-surface elimination and shading,
`gives a vivid demonstration of protein
`topography (Fig. 6). The copper atom is
`seen to lie in a deep pit at the active site
`of Cu,Zn superoxide dismutase (40).
`One is not restricted to using spheres
`to represent individual atoms. For large
`molecular complexes, it is useful to mod(cid:173)
`el a group of atoms with a single sphere.
`The 2.8-A structure of aspartate carbam·
`oyltransferase (41) has been modeled
`with each amino acid residue represent·
`ed by a sphere centered at the alpha
`carbon (Fig. 7).
`A method for smoothing the junctures
`between atoms by sun1ming Gaussian
`densities for each atom and drawing sur(cid:173)
`faces at various density contour levels
`was developed by Blinn (42). \Vhile the
`probe sphere method does a similar
`smoothing, its main effect is not the
`smoothing of crevices and pits, but rath(cid:173)
`er the complete removal of the van der
`\Vaals surface of interior atoms. This
`interior surface removal is important,
`because most of a protein's van der
`\Vaals surface is in the interior and not
`directly involved in molecular interac(cid:173)
`tions.
`Display of dot surfaces on a real-time
`
`color vector system is, in general, more
`useful than the raster surface representa(cid:173)
`tion because (i) the dot surfaces are
`transparent, Cnabling chemical bonds
`and atom labels to be seen, and (ii) the
`image may be rotated and sectioned in
`real tin1e. However, the raster system
`does have the advantage that it can show
`a larger region of surface at high resolu(cid:173)
`tion. This is because raster systems typi·
`cally display a quarter of a million pixels,
`while real-time vector systems can han(cid:173)
`dle only 10,000 to 20,000 vectors.
`In addition to the shaded-surface ras(cid:173)
`ter representation, an analytical surface
`has a real-time vector representation,
`where each face of the surface is repre(cid:173)
`sented by a set of concentric curved
`polygons (fig. 3). These polygons may
`be calculated in a straightfor\vard man(cid:173)
`ner for concave and saddle faces, but
`convex faces have less regular shapes.
`For convex faces, concentric cycles bor(cid:173)
`dering a shrinking contact area are gen(cid:173)
`erated by progressively incrementing the
`radii of neighboring atoms.
`An interactive display progran1 is re(cid:173)
`quired to manipulate molecular surfaces
`on a vector graphics systen1. For the
`Evans and Sutherland Multi Picture Sys·
`tern, this need is satisfied by the general(cid:173)
`purpose graphics program GRA~tPS
`(GRAphics for the Multi Picture Sys(cid:173)
`tem), developed by O'Donnell and Olson
`(43). GRAMPS may simultaneously dis(cid:173)
`play any combination of curved polygo(cid:173)
`nal surfaces, chemical bonds, atom la·
`be!s, dot surfaces, and arbitrary geomet(cid:173)
`ric figures, such as an icosahedron repre(cid:173)
`senting a virus capsid (44}. The various
`graphical objects are organized into a
`hierarchical tree structure and each ob-
`
`711
`
`
`
`.S. DNA dodecamer with sequence:
`Fig.
`CGCGAATfCGCG. The part of the van der
`Waals surface of each atom that is accessible
`to solvent is colored by atom type (red, oxy(cid:173)
`gen; green, carbon; blue, nitrogen). Reentrant
`surface (white) smooths out the crevices and
`pits between the atoms.
`
`ject may be independently transformed
`and colored in real tin1e.
`A primary value of the graphical dis(cid:173)
`play of solvent-accessible surfaces is
`that it provides immediately comprehen·
`sible information about steric comple·
`mentarity. This is illustrated by the work
`of Blaney et al. (45), who used real-time
`color dot surface graphics to study the fit
`of the thyroid hormone thyroxin into the
`binding site of a blood transport protein,
`prealbumin. They noticed an empty
`pocket adjacent to one of the phenyl
`rings of thyroxin. Computer graphics
`modeling shO\ved that naphthyl analogs
`of thyroxin would fit into the binding site
`and the larger naphthyl ring would fill
`this pocket. \Vhen a \Vide variety of
`thyroid hormone analogs \Vere tested,
`
`those with a naphthyl ring filling this
`pocket were found to bind better than
`those which left the pocket empty.
`Another use of this surface representa(cid:173)
`tion has been to paint chemical informa(cid:173)
`tion onto it. \Veiner et al. (46) did this by
`coloring the surface dots of proteins and
`nucleic acids according to electrostatic
`potential. [nterfacing surfaces in protein·
`protein, protein-ligand, and drug-nucleic
`acid interactions were seen to have not
`only topographic but also electrostatic
`complementarity. The electrostatic sur(cid:173)
`face potential of DNA was seen to be
`strongly
`sequence-dependent.
`This
`method has also been used to study the
`binding of the negatively charged super(cid:173)
`oxide radical to the enzyme superoxide
`dismutasc (47). In the electrostatic meth(cid:173)
`od, the potential is evaluated at the cen(cid:173)
`ter of each probe sphere position that
`generates a surface point. That is, in
`addition to being a canvas for displaying
`chemical information, the surface can
`play a fundan1ental role in calculating
`that information.
`
`Conclusions
`
`The principal use of computer graph(cid:173)
`ics by macromolecular x-ray crystallog(cid:173)
`raphers has been in fitting the model to
`the electron density and in refining the
`structure {1-3). The methods described
`above will help crystallographers in the
`succeeding step of
`interpreting
`the
`solved structure. Scientists in related
`disciplines will also benefit, since the
`structures of n1ore than 100 proteins,
`nucleic acids, and virus capsids have
`been deposited for general distribution at
`the Protein Data Bank at Brookhaven
`National Laboratory (48).
`\Vhile the display of solvent-accessible
`surfaces on real·tin1e vector graphics
`systen1s is preferred for interactively ex(cid:173)
`ploring a macromolecular structure, the
`color raster display of solvent-accessible
`surfaces made possible by the analytical
`algorithm is better able to comn1unicate
`structural discoveries because of its
`higher resolution and greater visual real(cid:173)
`ism.
`In time, the raster solvent-accessible
`surface display will acquire more of the
`capabilities of the vector display. For
`example, raster graphics methods for
`displaying transparent surfaces exist (49)
`and can be adapted to this systen1. Also,
`it should be possible to section away the
`front surface of a protein to display inte(cid:173)
`rior pockets and cavities, since the hid(cid:173)
`den-surface algorithm (39) uses a depth
`buffer (38, pp. 560-561), where
`the
`height of each pixel is stored.
`
`SCIENCE, VOL. 221
`
`Fig. 6. Stereo pair ofCu,Zn supcroxide dismutase. Same color-coding as in Fig. 5, but with the
`contact and reentrant surfaces of sulfur and copper colored yellow and copper. The copper
`atom is part of the active site and interacts with the superoxide radical. Hydrogen atoms are
`given the color of the heavy atom they are bonded to. Self-intersecting surfaces create point and
`edge cusps and other artifacts in deep grooves.
`
`Fig. 7. Stereo pair of aspartate carbamoyltransferase. The top catalytic trimer is colored green,
`light green, and cyan. The bottom catalytic trimer is colored red, pink, and magenta. The
`regulatorl_' dimers are colored yellow and white. Each amino acid residue is represented by one
`sphere 3 A in radius positioned at the alpha carbon, and a probe sphere 3 A in radius was used to
`calculate the surface of each subunit.
`
`712
`
`
`
`these graphical methods
`Although
`were developed to study the protein sur(cid:173)
`face, they should also be useful in visual(cid:173)
`izing the packing of alpha helices and
`beta sheets in the protein interior, simply
`by giving these structural elements indi(cid:173)
`vidual surface contours. This \Viii bring
`solvent-accessibility studies back full(cid:173)
`circle to their original scientific problem,
`the understanding of the folding of the
`polypeptide chain to form protein ter(cid:173)
`tiary structure.
`
`Rcrcrtn«s and Nottt
`I. R. Diamond. in Compu1111iomi/Crystallography,
`D. Sayre, Ed. (Ox.ford Univ. Press, Oxford,
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`tnlng, B. Gilchrist, Ed. (North-Holland. Am(cid:173)
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`14. - - • QCPE Bull. I (1981), p. 15. The dot
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`
`Ground Water Contamination
`in the United States
`
`Veronica I. Pye and Ruth Patrick
`
`lation of water between the oceans, at(cid:173)
`mosphere, and land. It constitutes ap(cid:173)
`proximately 4 percent of the water in the
`hydrologic cycle, second only to the
`oceans and seas, \Vhich account for
`about 94 percent (5). The volume of
`ground water in storage exceeds the vol(cid:173)
`ume of fresh surface water in lakes,
`streams, and rivers. Approximately 30
`percent of the streamflow of the United
`States
`is supplied by ground water
`emerging as natural springs or other
`seepage areas (2), Ground water forms
`most, if not all, of the Jo\v water flow of
`streams during dry periods. The interre(cid:173)
`lation bel\veen surface water and ground
`water is further indicated by the fact
`that, under certain conditions, surface
`water may recharge ground water aqui(cid:173)
`fers.
`Aquifers may be composed of perme(cid:173)
`able or porous geological material, either
`unconsolidated sand and gravel or con(cid:173)
`solidated material such as carbonate
`
`nation has occurred for centuries, in(cid:173)
`creased
`industrialization, population
`density, and agricultural activities have
`greatly exacerbated the problem in some
`areas. As our dependence on ground
`water increases, its quality becomes an
`ever more important issue.
`Ground water is not only important to
`man, it is also an integral part of the
`hydrologic cycle of the earth-the circu-
`
`Ground water that is used by humans
`consists of subsurface water which oc(cid:173)
`curs in fully saturated soils and geologi·
`cal formations. Nearly half the popula(cid:173)
`tion of the United States use ground
`water from wells or springs as their pri(cid:173)
`mary source of drinking water(/, 2); 36
`percent of the municipal public drinking
`water supply comes from ground water
`(});and 75 percent of major U.S. cities
`depend on ground water for most of their
`supply (J). Total fresh ground water
`withdrawals in 1980 were estimated as
`88.5 billion gallons per day, of which 65
`percent were used for irrigated agricul(cid:173)
`ture (4). Although ground water contami-
`
`19 AUGUST 1983
`
`Veronica I. Pye is Research Director of the Environmental Assessment Council, Academy or Na!ural
`Sciences, Philadelphia. Pennsylvania 19103. Rulh Patrick is Chairman of the Environmental Assessment
`Council, is Senior Curator of Limnology and occupies the Francis Boyer Research Chair at the Academy of
`Natural Sciences, Philadelphia, and is Adjunct Professor al the University of Pennsylvania. The report on
`ground water on which this article is based was pn:pared by the Environmenlal Assessment Council. Council
`members were Robert G. Dunlof., Caryl Haskins, Richard E. Heckert, Lane Kirkland, George Lamb,
`Charles F. Luce, Ruth Patrick, Gen Paulson, William Rei!ty, Laurance S. Rockefeller, Abel \Volman, and
`George With.
`
`713