Molecular Surfaces
5. Solvent Accessible Surfaces Michael L. Connolly
1259 El Camino Genuine, #184
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A significant advance inside the examine of protein surfaces was initiated
by Fred Richards' group at Yale University. His group incorporated: B.K. Lee, who
moved towards the University of Kansas and is now at the NIH, Tim Richmond,
who moved for the MRC, and that is now on the ETH in ZŸrich, and
Jonathan Greer, who moved to Columbia, and it is now at Abbott
Laboratories. Fred Richards has remained at Yale, during the Department of Molecular Biophysics and
Biochemistry and in the Center for Structural Biology.The motivation was the research of the protein-folding problem
(Anfinsen, 1973) and hydrophobicity (Tanford, 1980). The model of a
folded protein with the hydrophobic amino acid side chains during the
interior forming an oil drop (Kauzmann, 1959) implied that as the
protein folded the hydrophobic side chains were preferentially
buried away from the external solvent. In order to quantitate
hydrophobic burial (Chothia, 1974), B.K. Lee and Fred Richards
introduced the solvent-accessible surface (Lee and Richards, 1971).
The available surface is traced out by the probe sphere center as
it rolls over the protein. It is a kind of expanded van der Waals
surface. If you increase each atom's van der Waals radius by the
probe radius, you get so-called expandedatom radii. The
union of the expanded atoms is what Tim Richmond (1984) calls the
solvent-excluded volume. It is the region enclosed by the
accessible surface.Lee and Richards (1971) computed the available areas of each
atom in both the folded and extended state, and found that the
decrease in accessible area in going from the unfolded to the
folded state is greater for hydrophobic atoms than it is for
hydrophilic atoms.These ideas were further refined by (Richmond and Richards,
1978), when they introduced the contact surface. The contact
surface is the part of the van der Waals surface that can be
touched by a water-sized probe sphere.Soon afterwards, Richards introduced the reentrant surface,
which together with the contact surface form the "molecular
surface" (Richards, 1977). The molecular surface is the surface
traced by the inward-facing surface of the probe sphere. The
reentrant surface consists of the inward-facing part of the probe
sphere when it is in contact with more than one atom. While in the
diagram below the contact surface is in green and the reentrant
surface is in blue. In my own work, I use the term solvent-excluded volume to mean
the volume enclosed by the molecular surface. It is the volume that
the probe sphere is excluded from. During the diagram above the magenta
region at the left is the solvent-excluded volume. On the right the
van der Waals volume is in red and the interstitial volume is in
magenta. The solvent-excluded volume = the van der Waals volume +
the interstitial volume.The molecular surface was first computed by Jonathan Greer and
Bruce Bush (1978), after Greer moved from Yale to Columbia. (Bruce
Bush later moved to Merck in New Jersey). Greer and Bush (1978)
applied this method for the inter-subunit interface of hemoglobin,
where they were able to both visualize the protein surfaces
involved during the interface, and quantitate the amount of void volume
between the two surfaces. The diagram below illustrates their
molecular surface method. Probe spheres are rained down upon the
atoms from above, stopping just before a collision (van der Waals
overlap) would occur. A finer set of lines is used for the next
step. The lowest intersection point between each of these finer
lines and the bottom of the lowest sphere defines a point of the
molecular surface. In three dimensions this produces a grid. The
method works well for fairly flat surfaces, but cannot handle
irregular topographies with overhangs.Further diagrams of solvent-accessible surfaces can be found at
the University of
Leeds (Ligand Design Application), and the University of
York (An Introduction To Molecular Surfaces).The next advance in molecular surface computation occurred at
the University of California at San Francisco Computer Graphics
Laboratory. Robert Langridge had recently (1976) moved there from
Princeton, and with his NIH Research Resource grant had set up a
molecular modeling system consisting of a Digital PDP 1170
minicomputer running the UNIX operating system and an Evans &
Sutherland Picture System 2. His system manager Tom Ferrin had
translated the proprietary Evans and Sutherland graphics library
from assembly language into C (Ferrin and Langridge, 1980).
Historically, there had been a close relationship between the Evans
and Sutherland graphics systems and the Digital (DEC)
minicomputers. The Digital operating systems run on the
minicomputers in these combos were not as conducive to rapid
software system development as the platform-independent UNIX operating
system developed by AT&T. Also, with the Fortran-callable
E&S routines replaced by C routines, it was possible to develop
interactive graphics program within the superior C language. From
Princeton, Robert Langridge brought with him a graphics programmer,
Martin Pensak, and Martin was joined by a local student, Conrad
Huang, and also a former graphics programmer from the Yale group,
Oliver Jones. Pensak and Huang wrote a molecular modeling program
in C called MMS (Molecular Modelling System). This work was
initiated in conjunction with Steve Dempsey and Joe Kraut of the
U.C.S.D. Chemistry Department, but the two groups soon went their
separate ways, with the San Diego group concentrating on
crystallographic applications, and the Langridge group, which was
located while in the School of Pharmacy, concentrating on structure-based
drug design. The MMS program was renamed MIDS in order to avoid a
name conflict with the MMS-X system of Washington University in St.
Louis. It was redesigned by Tom Ferrin , recoded by Conrad
Huang and renamed MIDAS during the early eighties (Huang, Jarvis,
Ferrin and Langridge, 1982; Ferrin and Langridge, 1986; Ferrin,
1987; Ferrin, Huang, Jarvis and Langridge, 1988). The most recent
release is called MidasPlus.In 1978 Ollie Jones coded the Greer & Bush (1978)
molecular-surface-net algorithm and showed the output to me (Mike
Connolly) using his general purpose display program BILD (from the
German for picture). The next year, Ollie Jones moved to Chicago to
do cartographic work, and I lost interest in molecular surfaces
until they were again brought to my attention by Howard Schachman,
in his Biochemistry 206 (Physical Chemistry of Proteins) course at
U.C. Berkeley in the fall of 1979. Schachman handed out photocopies
of the surface diagrams in Fred Richards 1977 article. At that time
I was a graduate student of Irwin D. (Tack) Kuntz, working on the
protein-protein docking problem. I was trying to dock proteins
together based upon complementary surface curvature and needed a
good protein surface representation. I tried to apply the
surface-net algorithm, but ran into two limitations of the method:
(a) it gave a surface for only one side of the protein, and (b) it
did not represent the surface under overhangs. I tried turning
Ollie's program into a subroutine that would generate many small
nets over the protein surface, but could not think of a good way to
glue the nets together to form a continuous surface. I kept
increasing the number of nets, and decreasing their size, until
eventually I was dropping nets for each atom of the molecule, from
the six (±x, ±y, ±z) coordinate-axis
directions.At that point (early December, 1979) it occurred me to simply
place the probe tangent to each atom of the protein at six
positions: ±x, ±y, ±z, recording a contact
point if there were no collisions. Then it occurred to me to place
the probe tangent at more positions (independently discovering the
Shrake and Rupley (1973) algorithm), and then tangent to two and
three atoms simultaneously, in accordance with the definition of
reentrant surface (Richards, 1977). When the probe sphere is
tangent to three atoms, the inward-facing triangle defined by the
three points of contact defines a concave patch of reentrant
surface. When the probe sphere rolls around a pair of adjacent
atoms, the inward-facing arc connecting the two points of contact
traces out a saddle-shaped toroidal patch of reentrant surface. The
concave and toroidal patches are represented by points. This method
solves the overhang problem,
Microsoft Office Professional 2007, but there is still no information on
connecting the small surface patches together. There is only a set
of discrete surface points in three-dimensional space. A surface
normal vector, pointing towards the probe center, was added to each
point, for docking purposes. An area, in square angstroms, was
added to each point. These areas were not accurate, and were
sensitive to the spacing between the points. The next step, taken
in late December, 1979, was to deal with self-intersections inside the
surface by removing surface points of one probe sphere that lay
inside an opposing sphere.The MS program was written in RATFOR (Rational Fortran), a language developed at Bell Labs in
the UNIX group (Kernigan & Plauger, 1976). The MS program wrote
out an ascii file of dots that
could be read by Ollie Jone's BILD program and displayed on the
Evans and Sutherland (E&S) Picture System 2. In 1980 the
U.C.S.F. acquired the new color calligraphic monitor recently
developed by E&S. The MMSMIDS and BILD programs were modified
to handle color , and it became possible to show interfacing
molecules in different colors (Langridge, Ferrin, Kuntz and
Connolly, 1981). One of the advantages of the molecular surface
over the accessible surface or the van der Waals surface is its
ability to visualize the shape complementarity at interfaces:Having read an early protein-protein docking paper by Wodak and
Janin (1978a), I studied the bptitrypsin interface. Tom Ferrin,
Tack Kuntz and I made a 16mm film of this interface, which was
widely shown. Kuntz and I also studied protein packing defects or
cavities (Connolly, 1981a), which were better visualized by the
molecular surface than with the original Lee & Richards'
accessible surface (Lee & Richards, 1971). Interior cavities
were identified by an automatic algorithm that clustered together
nearby surface points. Some packing defects were connected for the
external surface by narrow tunnels. Not being able to
algorithmically define the limits of such invaginations, I decided
that it would be necessary to select which points belonged to an
invagination by hand. This Handle program (Connolly,
1981a) never got to your point of actually being able to
interactively select points, but it continued to be used at
U.C.S.F. after I completed my degree and left, because of its
ability to display huge numbers of surface points.At U.C.S.F. Jeff Blaney applied MS to model the binding of
thyroxine to prealbumin (Blaney, Jorgensen, Connolly, Ferrin,
Langridge, Oatley, Burridge and Blake, 1982), and Paul Weiner
computed the electrostatic potential with the probe center associated
with each surface point and colored the points accordingly (Weiner,
Langridge, Blaney, Schaeffer and Kollman, 1982).Before leaving U.C.S.F., I rewrote MS in Fortran 77. This was
not done by running the original Ratfor code through the Ratfor
pre-processor, but rather by hand. The purpose of this rewrite was
to make the program more portable, since with the time (1981), the
operating system of choice for DEC's VAX-11780 was VMS, not UNIX.
The Fortran 77 version of MS was tested in the National Resource
for Computation in Chemistry at Lawrence Berkeley Laboratory, with
the help of Art Olson and T.J. O'Donnell, using GRAMPS (O'Donnell
and Olson, 1981). It was then mailed towards the Quantum Chemistry
Program Exchange, where it became program #429 (Connolly,
1981b).Solvent-accessible and molecular surface areas have been
computed by many methods. While the original Lee & Richards'
method computed areas by multiplying available arc lengths by the
spacing between the planes, the Shrake and Rupley (1973) method
placed 92 points on the expanded atomic sphere and determined which
points were available to solvent (i.e., not inside any other
expanded sphere). The first application of solvent-accessibility to
nucleic acids was made by Alden and Kim (1979). The areas computed
depend not only upon the method, but also upon the van der Waals
radii used. For my own work, I have taken nucleic acid radii from
Alden and Kim (1979) and protein atom radii from McCammon, Wolynes
and Karplus (1979). The areas computed by means of surface points,
even if closely spaced, are not very accurate. In order to attack
this problem, the GEPOL program has been developed (Pascual-Ahuir,
Silla, Tomasi and Bonaccorsi, 1987; Pascual-Ahuir and Silla, 1990;
Silla, Villar, Nilsson, Pascual-Ahuir and Tapia, 1990; Silla,
Tu–—n and Pascual-Ahuir, 1991; Pascual-Ahuir, Silla,
Tu–—n, 1994). In order to combat the slowness of
numerical surface area methods, an analytical approximation to your
available surface areas has been developed (Wodak and Janin,
1980). Another approach to increasing computational efficiency has
been to vectorize the calculation (Wang and Levinthal, 1991). Le
Grand and Merz (1993) have developed a rapid approximation to
molecular surface area extending the Shrake & Rupley method and
using look-up tables. A recent area method for personal computers
has been described in both hardcopy (Pacios, 1994) and online form
(Pacios, 1995) from the Journal of Molecular Modeling.The term buried surface area has two related meanings: (a) the
surface buried away from solvent when the protein folds, and (b)
the surface buried away from solvent when two proteins or subunits
associate to form a complex. The thermodynamic importance of buried
hydrophobic surface area has been investigated by Chothia (1974,
1976) and the surface buried in interfaces has also been
investigated (Chothia and Janin, 1975; Lesk, Janin, Wodak and
Chothia, 1985). Recently Pattabiraman, Ward and Fleming (1995) have
introduced something they call the occluded
surface.Faster (than MS) dot surface algorithms have been developed by
Pearl and Honegger (1983), and (Moon and Howe, 1989). The latter
algorithm has been re-coded by Silicon Graphics as an Explorer
module and is also called ATOMICSURF.Spline curves passing through the molecular surface points have
been computed by Colloc'h and Mornon (1988; 1990). Perrot and
Maigret (1990) have developed a program MSEED that rolls the probe
sphere continuously over the outer surface of the protein. It gains
considerably in speed over algorithms that try to place the sphere
tangent to all triples of neighboring spheres, with the expense of
missing interior cavities. However, for most applications, the
interior cavity surfaces are not needed.While a numerical method samples the surface at a finite number
of discrete points, cubes, triangles or plane curves, an analytical
method describes the surface as a collection of pieces of spheres,
each defined by the center,
Office 2010 Discount, radius, and arcs forming the boundary.
For the reentrant surface, pieces of tori are also included. The
analytical surface may be either slower or faster to compute than a
numerical surface, depending on the fineness of the numerical
surface. An advantage of an analytical method is that atomic
available areas and the solvent-excluded volume are represented as
formulas that can be differentiated. A number of researchers have
computed area and volume derivatives: (Richmond, 1984; Perrot,
Cheng, Gibson, Vila, Palmer, Nayeem,
Microsoft Office Ultimate 2007, Maigret and Scheraga,
Windows 7 Professional Product Key, 1992;
Gogonea and Osawa, 1994b; Sridharan, Nicholls and Sharp, 1994).My early analytical molecular surface algorithm suffered from an
inability to deal with self-intersecting surfaces (Connolly,1983a,
1983b), a problem that I was able to solve only partially in later
work (Connolly, 1985). Even the rewriting of my molecular surface software programs
in C (Connolly, 1993) has not eliminated these problems. Better
methods for dealing with self-intersecting surfaces, cusps and
singularities have been developed by Michel
Sanner and colleagues (Sanner, 1992; Sanner, Olson and Spehner,
1995; Sanner, Olson and Spehner, 1996) and by Gogonea and Osawa
(1994a). Another robustness problem has been dealing with the
situation where the probe sphere is simultaneously tangent to four
atoms. This situation has been successfully dealt with by Eisenhaber and Argos (1993). Fast and parallel methods for
computing molecular surfaces have been developed at UNC (Varshney and Brooks,
1993; Varshney, Brooks and Wright,
Office 2010 Home And Business, 1994; Varshney, Brooks,
Richardson, Wright and Manocha, 1995). The UNC Computer Science
department has a history of parallel computation in their Pixel-Planes
project.Modern interactive graphics systems have the ability to rotate
and render polyhedral surfaces in authentic time. Therefore, the most
practical molecular surface representation is the polyhedral
molecular surface (Connolly, 1985; Zauhar and Morgan, 1990; Weber,
Morgantini, Fluekiger and Roch, 1989; Weber and Morgantini, 1990;
Weber, Fluekiger and Field, 1990; Zhexin, Yunyu, Yingwu, 1995). A
recent triangulation algorithm, SMART, has curved
triangles that lie on the actual spherical-toroidal molecular
surface (Zauhar, 1995). Recent polyhedral surface generators have
used algorithms based upon a cubical grid (Lorensen and Cline,
1987; Heiden, Goetze and Brickmann, 1993; Eisenhaber, Lijnzaad,
Argos, Sander and Scharf, 1995). The Darmstadt
group has displayed their surfaces in conjunction with a
modeling program called MolCad. You and Bashford (1994) have
developed an algorithm for identifying which points on a cubical
grid lie inside the protein's solvent-excluded volume.There are alternative ways to smooth a molecular surface besides
rolling a probe sphere over it (Agishtein, 1992). Blinn (1982) used
Gaussian densities to blend the atoms together. The results of this
work can be seen during the DNA segment on Carl Sagan's Cosmos
public television series. Purvis and Culberson (1986) also used
Gaussians, but with electrostatic coloring.
[ 1. Introduction ] [ 2. Physical Molecular Models ] [ 3. Electron Density Fitting ] [ 4. Molecular Graphics ] [ *** five.
Solvent-Accessible Surfaces *** ] [ 6.
Molecular Surface Graphics ] [ 7.
Molecular Volume and Protein Packing ] [ 8. Shapes of Small Molecules and Proteins ] [
9. Structure-based Drug Design ] [ 10. Protein-Protein Interactions ] [ 11. Surface Biology, Chemistry and
Physics ] [ 12. Bibliography
]
All material in ths article Copyright © 1996 by Michael L. Connolly
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