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where pri:ai(r) is the number of protein atoms of type j at distance r. This procedure assures that no solvent volume effects were introduced into the reference number densities. Table 1 lists the average occurrences of protein atom types found in a spherical reference volume with radius 12 Á. Interestingly, the relative average occurrence of protein atoms of type j is the same in a sphere ofradius 6 Á, using the same midpoints. However, while the 12 Á, sphere shows a Gaussian distribution of occurrences, the average number of the 6 Á, sphere shows a highly fluctuating occurrence pattern as illustrated in Figure 2. The finding that the average number densities in the 6 and 12 Á, radius spheres are comparable suggests that the 12 Á, sphere contains mostly protein atoms that are not part of the protein surface.

Using Ref2 the PMF can be calculated as

Vol cor r

fopígW-fopbuik)

number of occurences

Figure 2. Histogram of occurrences of the protein type CP in a database of 697 protein crystal structures (see Reference 27) in spheres with radius 12 A (black) and 6 A (white). The latter is scaled by a factor of 8 to account for the volume difference between the spheres.

number of occurences

Figure 2. Histogram of occurrences of the protein type CP in a database of 697 protein crystal structures (see Reference 27) in spheres with radius 12 A (black) and 6 A (white). The latter is scaled by a factor of 8 to account for the volume difference between the spheres.

Reference state 3

A more solvent independent reference state (Ref3) is defined by applying a correction factor to pijbulk (Equation 5).

where p -W is defined in Equation 5 and p^i is defined as : P(r)dr

Pbulk =

prot p ( r) is the number density of protein atoms of any type in spherical shells that are entirely filled with protein atoms at the distance r (Equation 7). p(r) represents an average overprotein structures in the database. p' (p) designates the number density of protein atoms of any type at the distance r from a ligand atom of type i in a particular protein-ligand complex. p W is defined

Table 1. Average occurrence of protein atoms in a sphere of given radiusa

Protein Average occurrence in a Average occurrence in a atom type 12 A, reference sphere 6 A, reference sphereb

CF

84.8

83.8

CP

121.9

119.4

cF

33.7

32.7

cP

10.5

11.9

CO

4.1

4.8

CN

3.0

2.9

NC

4.6

4.9

ND

59.5

57.3

NR

2.9

4.3

OC

7.9

9.9

OA

55.3

54.9

OD

8.9

10.6

SA

1.3

1. 0

a The atom types correspond to the protein atom types defined by Muegge and Martin [27]. The average occurrences are calculated by using the same set of 697 protein complexes used by Muegge and Martin to derive the PMF [27]. One test sphere is used per protein structure only. The midpoint of the sphere is set in the midpoint of the protein located by an iterative numerical procedure. For a sphere of 12 A, radius an optimal occurrence of protein heavy atoms of 400 is found. In case more or less than 400 protein heavy atoms are found in the sphere, a volume correction factor is used to scale the number of occurrences of particular protein atom types up or down (Equation 8). It accounts for the ratio of the actual and optimal numbers of heavy atoms in the sphere.

b The average occurrence is scaled up by a factor 8 to reflect the fact that the volume of a sphere of radius 6 A, is eight times smaller than that of 12 A, radius.

as number density of protein atoms in a spherical reference sphere of radius R around a ligand atom of type i by

Pbulk pR flR

0 0

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