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 ...

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 developmental biology, development. Biom ...

that is accessible to a

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

. Measurement of ASA is usually described in units of square angstroms (a standard unit of measurement in

molecular biology Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and phys ...

). 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 In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...

to 'probe' the surface of the

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...

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 numerica ...

, 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 Å².

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 effects in the molecular dynamics software package

AMBER Amber is fossilized tree resin that has been appreciated for its color and natural beauty since Neolithic times. Much valued from antiquity to the present as a gemstone, amber is made into a variety of decorative objects."Amber" (2004). In M ...

. 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.

Notes

References

* * * * * * * * * * * * * * * * {{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