Accessible surface area

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, where more points provide an increased level of detail.

The LCPO method uses a linear approximation of the two-body problem for a quicker analytical calculation of ASA.{{cite journal |vauthors=Weiser J, Shenkin PS, Still WC |title=Approximate atomic surfaces from linear combinations of pairwise overlaps (LCPO)

|journal=Journal of Computational Chemistry |volume=20 |issue=2 |pages=217–230 |year=1999 |doi=10.1002/(SICI)1096-987X(19990130)20:2<217::AID-JCC4>3.0.CO;2-A}} The approximations used in LCPO result in an error in the range of 1-3 Ų.

Recently{{When|date=September 2022}}, a method was presented that calculates ASA fast and analytically using a power diagram.{{cite journal |vauthors=Klenin K, Tristram F, Strunk T, Wenzel W |title=Derivatives of molecular surface area and volume: Simple and exact analytical formulas|journal=Journal of Computational Chemistry |volume=32 |issue=12 |pages=2647–2653 |year=2011 |doi=10.1002/jcc.21844|pmid=21656788|s2cid=27143042|url=https://publikationen.bibliothek.kit.edu/110084051/150300225 }}

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.

It is recently{{When|date=September 2022}} suggested that (predicted) accessible surface area can be used to improve prediction of protein secondary structure.{{Cite journal | last1 = Momen-Roknabadi | first1 = A | last2 = Sadeghi | year = 2008 | first2 = M | last3 = Pezeshk | first3 = H | last4 = Marashi | first4 = SA | title = Impact of residue accessible surface area on the prediction of protein secondary structures | journal = BMC Bioinformatics | volume = 9 | page = 357 | pmid = 18759992 | pmc = 2553345 | doi = 10.1186/1471-2105-9-357 | doi-access = free }}{{Cite journal | doi = 10.1002/prot.20441 | last1 = Adamczak | first1 = R | last2 = Porollo | first2 = A | last3 = Meller | first3 = J. | year = 2005 | title = Combining prediction of secondary structure and solvent accessibility in proteins | journal = Proteins | volume = 59 | issue = 3| pages = 467–75 | pmid = 15768403 | s2cid = 13267624 }}

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{{cite journal | last1 = Richards | first1 = FM. | year = 1977 | title = Areas, volumes, packing and protein structure | journal = Annu Rev Biophys Bioeng | volume = 6 | pages = 151–176 | doi = 10.1146/annurev.bb.06.060177.001055 | pmid = 326146 }} and implemented three-dimensionally by Michael Connolly in 1983{{cite journal | last1 = Connolly | first1 = M. L. | year = 1983| title = Analytical molecular surface calculation | journal = J Appl Crystallogr | volume = 16 | issue = 5| pages = 548–558 | doi = 10.1107/S0021889883010985 | bibcode = 1983JApCr..16..548C }} and Tim Richmond in 1984.{{cite journal | last1 = Richmond | first1 = T. J. | year = 1984| title = Solvent accessible surface area and excluded volume in proteins. Analytical equations for overlapping spheres and implications for the hydrophobic effect | journal = J Mol Biol | volume = 178 | issue = 1| pages = 63–89 | doi = 10.1016/0022-2836(84)90231-6 | pmid = 6548264 }} Connolly spent several more years perfecting the method.{{cite journal | last1 = Connolly | first1 = M. L. | year = 1993| title = The molecular surface package | journal = J Mol Graphics | volume = 11 | issue = 2| pages = 139–141 | doi = 10.1016/0263-7855(93)87010-3 | pmid = 8347567 }}

• Implicit solvation
• Van der Waals surface
• VADAR tool for analyzing peptide and protein structures
• Relative accessible surface area

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• [https://web.archive.org/web/20061114140809/http://www.netsci.org/Science/Compchem/feature14e.html Network Science, Part 5: Solvent-Accessible Surfaces]
• [http://www.ccp4.ac.uk/dist/html/areaimol.html AREAIMOL] is a command line tool in the CCP4 Program Suite for calculating ASA.
• [http://wolf.bi.umist.ac.uk/naccess/ NACCESS] solvent accessible area calculations.
• [https://freesasa.github.io/ FreeSASA] Open source command line tool, C library and Python module for calculating ASA.
• [https://web.archive.org/web/20150327001936/http://pharmacy.mc.uky.edu/faculty/tsodikov/software.php Surface Racer] Oleg Tsodikov's Surface Racer program. Solvent accessible and molecular surface area and average curvature calculation. Free for academic use.
• [http://boscoh.com/protein/asapy ASA.py] — a Python-based implementation of the Shrake-Rupley algorithm.
• [https://web.archive.org/web/20061016175607/http://www.scripps.edu/~sanner/html/msms_home.html Michel Sanner's Molecular Surface] – the fastest program to calculate the excluded surface.
• [http://pov4grasp.free.fr/news.php pov4grasp] render molecular surfaces.
• [https://web.archive.org/web/20130819171544/http://biohedron.drupalgardens.com/ Molecular Surface Package] — Michael Connolly's program.
• [http://geometry.molmovdb.org/3v/ Volume Voxelator] — A web-based tool to generate excluded surfaces.
• [http://petitjeanmichel.free.fr/itoweb.petitjean.spheres.html ASV freeware] Analytical calculation of the volume and surface of the union of n spheres (Monte-Carlo calculation also provided).
• [https://sbl.inria.fr/doc/Space_filling_model_surface_volume-user-manual.html Vorlume] Computing Surface Area and Volume of a Family of 3D Balls.
• [http://curie.utmb.edu/getarea.html GetArea] Calculate solvent accessible surface area of proteins online.
• [https://www.bionanoinfo.com/proms/ ProMS] ProMS - Protein Molecular Surface Calculator

Category:Molecular modelling

Category:Computational chemistry

Category:Molecular dynamics

Category:Protein structure