The accessible surface area (ASA) or solvent-accessible surface area (SASA) is the
surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...
of a
biomolecule
A biomolecule or biological molecule is a loosely used term for molecules present in organisms that are essential to one or more typically biological processes, such as cell division, morphogenesis, or development. Biomolecules include large ...
that is accessible to a
solvent. Measurement of ASA is usually described in units of square
angstroms (a standard unit of measurement in
molecular biology). ASA was first described by Lee & Richards in 1971 and is sometimes called the Lee-Richards molecular surface.
ASA is typically calculated using the 'rolling ball' algorithm developed by Shrake & Rupley in 1973.
This algorithm uses a sphere (of solvent) of a particular
radius to 'probe' the surface of the
molecule.
Methods of calculating ASA
Shrake–Rupley algorithm
The Shrake–Rupley algorithm is a numerical method that draws a mesh of points equidistant from each atom of the molecule and uses the number of these points that are solvent accessible to determine the surface area.
The points are drawn at a water molecule's estimated radius beyond the
van der Waals radius, which is effectively similar to ‘rolling a ball’ along the surface. All points are checked against the surface of neighboring atoms to determine whether they are buried or accessible. The number of points accessible is multiplied by the portion of surface area each point represents to calculate the ASA. The choice of the 'probe radius' does have an effect on the observed surface area, as using a smaller probe radius detects more surface details and therefore reports a larger surface. A typical value is 1.4Å, which approximates the radius of a water molecule. Another factor that affects the results is the definition of the VDW radii of the atoms in the molecule under study. For example, the molecule may often lack hydrogen atoms, which are implicit in the structure. The hydrogen atoms may be implicitly included in the atomic radii of the 'heavy' atoms, with a measure called the 'group radii'. In addition, the number of points created on the van der Waals surface of each atom determines another aspect of
discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...
, where more points provide an increased level of detail.
LCPO method
The LCPO method uses a
linear approximation of the
two-body problem
In classical mechanics, the two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles. The problem assumes that the two objects interact only with one another; the only force affecting each ...
for a quicker analytical calculation of ASA.
The approximations used in LCPO result in an error in the range of 1-3 Ų.
Power Diagram method
Recently, a method was presented that calculates ASA fast and analytically using a
power diagram
In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from ...
.
Applications
Accessible surface area is often used when calculating the
transfer free energy required to move a biomolecule from an aqueous solvent to a non-polar solvent, such as a lipid environment. The LCPO method is also used when calculating
implicit solvent Implicit solvation (sometimes termed continuum solvation) is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of ...
effects in the molecular dynamics software package
AMBER.
It is recently suggested that (predicted) accessible surface area can be used to improve
prediction of protein secondary structure.
Relation to solvent-excluded surface
The ASA is closely related to the concept of the solvent-excluded surface (also known as the Connolly's molecular surface area or simply Connolly surface), which is imagined as a cavity in bulk solvent. It is also calculated in practice via a rolling-ball algorithm developed by
Frederic Richards
Frederic Middlebrook Richards (August 19, 1925 – January 11, 2009), commonly referred to as Fred Richards, was an American biochemist and biophysicist known for solving the pioneering crystal structure of the ribonuclease S enzyme in 1967 an ...
and implemented three-dimensionally by Michael Connolly in 1983 and Tim Richmond in 1984. Connolly spent several more years perfecting the method.
See also
*
Implicit solvation Implicit solvation (sometimes termed continuum solvation) is a method to represent solvent as a continuous medium instead of individual “explicit” solvent molecules, most often used in molecular dynamics simulations and in other applications of ...
*
Van der Waals surface
*
VADAR
Volume, Area, Dihedral Angle Reporter (VADAR) is a freely available protein structure validation web server that was developed as a collaboration between Dr. Brian Sykes and Dr. David Wishart at the University of Alberta. VADAR consists of over 1 ...
tool for analyzing peptide and protein structures
*
Relative accessible surface area Relative accessible surface area or relative solvent accessibility (RSA) of a protein residue is a measure of residue solvent exposure. It can be calculated by formula:
\text = \text / \text
where ASA is the solvent accessible surface are ...
Notes
References
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* {{cite journal
, first1=Jan
, last1=Busa
, first2=Jozef
, last2=Dzurina
, first3=Edik
, last3=Hayryan
, title= ARVO: A fortran package for computing the solvent accessible surface area and the excluded volume of overlapping spheres via analytic equations
, journal=Comput. Phys. Commun.
, year=2005
, pages=59–96
, volume=165
, issue=1
, doi=10.1016/j.cpc.2004.08.002
, bibcode=2005CoPhC.165...59B
External links
Network Science, Part 5: Solvent-Accessible Surfaces
is a command line tool in the CCP4 Program Suite for calculating ASA.
NACCESS
solvent accessible area calculations.
FreeSASA
Open source command line tool, C library and Python module for calculating ASA.
Surface Racer
Oleg Tsodikov's Surface Racer program. Solvent accessible and molecular surface area and average curvature calculation. Free for academic use.
ASA.py
— a Python-based implementation of the Shrake-Rupley algorithm.
Michel Sanner's Molecular Surface
– the fastest program to calculate the excluded surface.
pov4grasp
render molecular surfaces.
Molecular Surface Package
— Michael Connolly's program.
Volume Voxelator
— A web-based tool to generate excluded surfaces.
Analytical calculation of the volume and surface of the union of n spheres (Monte-Carlo calculation also provided).
Computing Surface Area and Volume of a Family of 3D Balls.
Calculate solvent accessible surface area of proteins online.
Molecular modelling
Computational chemistry
Molecular dynamics
Protein structure