**From:** Clayton (*clj_at_jjwater.info*)

**Date:** Mon Jul 23 2012 - 10:08:35 CDT

**Next message:**David Minh: "Re: Negative surface area?"**Previous message:**Jesper Sørensen: "Re: secondary structure restraints in coarse grain"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

NAMD 2.9 had been calculating negative solvent accessible surface areas

for some molecules when when using the Generalized Born Implicit Solvent

algorithm. It is not immediately obvious when this happens because the

SASA is only used internally, as one of the values used in determining

the total electrostatic force (the "ELECT" value reported in the .out

file). I have done some research, picked apart the source code, and

found the problem.

NAMD uses the Linear Combination of Pairwise Overlaps method to

approximate the surface area of molecules. This method models each atom

as a hard sphere, and geometrically calculates the area of each sphere,

then how much of the area of any given sphere is buried inside another.

*>From the paper in which this method was first proposed (Jo¨rg Weiser,
*

Peter S. Shenkin, W. Clark Still, Approximate Atomic Surfaces from

Linear Combinations of Pairwise Overlaps (LCPO), 1998), the formula used

for this is shown in the attached image. A rigid mathematical

derivation seems excessive here, but the meaning of each term is

simple. Ai is the SASA of an individual atom modeled as a hard sphere

i. The first term is simply the area of sphere i. The second term

calculates from the radii and distance between centers of neighbouring

spheres (possibly two spheres of arbitrary size j and k, for this

example), how much surfaces area of sphere i is buried inside its

neighbours, j and k. However, it is possible for spheres j and k to

overlap each other inside i, and in the second term, the area buried

inside both j and k is subtracted twice, which underestimates Ai. The

third term calculates how much area of i is subtracted twice in this

way, and corrects this. Lastly, it is easy to draw three spheres, i, j,

and k, such that j and k both overlap with i, and with each other, but

none of the overlap of j and k is inside i, regardless of how large the

overlap is between j and k. As the distance between i and its two

neighbours decreases, and also as the distance between j and k

decreases, the percentage of the overlap between j and k that is inside

i increases, and fourth term accounts for this. The constants P1

through P4 are constants which are specific to each possible number of

large neighbours for hybridization of each element.

NAMD uses exactly the formula from this paper, and has, at the end of

the source code file "ComputeLCPO.c", a structure which contains all of

the P1 - P4 values for it will need, which are copied exactly from the

appendix of the aforementioned paper. Obviously, for every atom type,

the area of the hard sphere model buried inside neighbors can not exceed

the total area of that sphere. However, the P1 and P2 values for sp3

hybridized N with one large neighbour are such that this is precisely

what NAMD calculates. The P1 value is an order of magnitude smaller

than the P2 value, which makes no physical sense. NAMD subtracts as

"buried" area more area than there is in total for sp3 N with one

neighbour by nearly a factor of 10.

Weiser, Shenkin, and Still calculate these P values three different ways

for each atom, and the numbers they show in the appendix for the very

same atom's P1 value that were arrived at using the other two methods

are entirely sensible. Each is larger than magnitude, but of opposite

sign, from the corresponding P2 value, and an order of magnitude larger

than this value. If one changes the exponent from -2 to -1, this value

will be very close to what was obtained using the other two methods, but

slightly smaller, which is consistent with P1 values obtained using this

method for every other atom in the table. It seems extremely likely

that this is simply a typo in the exponent. However, it may call the

whole table into question. I have tried to contact the authors of the

paper, but haven't heard back.

In any case, the surface area which NAMD calculates for any molecule

containing an sp3 N with one neighbour will be underestimated, and can

be negative if such N atoms make up a large percentage of the area of

the molecule.

**Next message:**David Minh: "Re: Negative surface area?"**Previous message:**Jesper Sørensen: "Re: secondary structure restraints in coarse grain"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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