Can the Structure of the Hydrophobic Core Determine the Complexation Site? - Identification of Ligand Binding Site and Protein-Protein Interaction Area - page 42

The su H coefficient (aggregate Gauss function value for all N points) is applied
to normalize the distribution.

3.2.2 Observed (Empirical) Hydrophobicity Distribution

The probabilistic distribution of hydrophobicity can be understood as a reference
structure, determining the “idealized” shape of the protein's hydrophobic core.
It should be noted that the actual structure of the core may not fully correspond to
this idealized model. In an actual protein the observed hydrophobicity distribution
can be established on the basis of the locations of hydrophobic and hydrophilic resi-
dues, according to the function proposed by Levitt ( 1976 ) . Levitt's function enables
us to calculate the potency of hydrophobic interactions between specific residues
relative to their mutual distance and their own hydrophobicity. It is given as:

⎧

⎛ ⎛

2

⎞ ⎞

4 6 8

r

⎛⎞ ⎛⎞ r ⎛⎞ ⎛⎞ r r

1

( )

⎪

ij ij ij ij

HH

r r

f rr c

+ ⎜ 1 − ⎜ 7 − 9 + 5 − ⎟ ⎟ , ≤

1

⎪

∑

⎜⎟

⎜⎟ ⎜⎟ ⎜⎟

i j

⎜ ⎟

ij

e

⎜ 2 c ⎟

H = ⎝⎠ ⎝⎠ c ⎝⎠ ⎝⎠ c c

⎨

⎝ ⎝ ⎠ ⎠

i

e
sum

H

j ⎪

0, forr > c

⎩

ij

where

e
H denotes the experimentally observed hydrophobicity density at a certain
point (specifically, at the position of the effective atom of the i-th residue).
Hydrophobic interactions can be aggregated in a distance-dependent form (as given
in the formula) with cutoff distance c equal to 9 Å (as proposed by Levitt). This
aggregate value acts as a normalizing factor for the distribution. Values

r r

HH
express the hydrophobicity of the i-th and j-th residues respectively (following the
scale presented in Brylinski et al. ( 2007a ) ).
Good agreement between both distributions is observed in globular proteins
which possess a highly regular hydrophobic core localized centrally in the protein
body with hydrophilic residues exposed on the surface. Hydrophobicity density
decreases in accordance with the Gauss function, reaching values close to zero on
the protein surface, which is why the molecule remains soluble.
H r coefficients are used to express the hydrophobicity of each amino acid (any
scale can be applied here). The r values determine distances between pairs of inter-
acting residues (specifically, between their effective atoms whose positions are
derived by averaging out the locations of all atoms belonging to side chains). c is the
cutoff distance for hydrophobic interactions, which - following (Levitt 1976 ) - was
taken as 9 Å. Introducing this value into the idealized hydrophobicity distribution
broadens the area in which the molecule “perceives” hydrophobic interactions.
The normalization coefficient enables us to interpret values of the presented func-
tion as the likelihood that hydrophobic conditions will be encountered at specific

,

i j