Biology Reference
In-Depth Information
3.2.3
Theoretical Versus Experimental Hydrophobicity
Standardization also enables quantitative comparison of both distributions. This
analysis can be based on the following definition of distance entropy proposed by
Kulback and Leibler (Nalewajski 2006 ) :
Pi
()
DPQ
(||
)
=
Pi
()log
KL
2
Qi
()
i
where P(i) denotes the observed probability (hydrophobicity density) as applied to
the i -th residue, while Q(i) denotes the expected (target distribution) hydrophobicity
for the same residue.
Two target (reference) distributions are considered when interpreting D KL values.
It should be noted that since D KL expresses entropy, only a relative comparison between
pairs of distributions can be meaningful in this scope. Hence, one D KL value re fl ects
the distance between observed (O) and theoretical (T) distributions, while another
value is derived as the distance between observed (O) and random (R) distributions.
Random distribution can be obtained by assigning equal hydrophobicity to each resi-
due (thus, R i = 1/N, where N is the number of residues in the polypeptide chain).
To simplify the notation, the following comparison between observed and theo-
retically expected distributions is introduced (Banach and Roterman 2009 ) :
N
O
OT
/
=
O
log
i
i
2
T
i
=
1
i
Consequently, the distance between observed and random distributions is given as:
N
O
OR
/
=
O
log
i
i
2
R
i
=
1
i
The relation between O/T and O/R is taken as a classification criterion when
determining whether a given protein is structurally accordant with the theoretical
model. If O/T is greater than O/R, the protein does not conform to the model. We
are currently developing computational tools which will enable us to objectively
quantify (cluster analysis) the degree of accordance based on cluster analysis.
1 G85 exhibits far greater discordance between O and T than the protein presented
in Fig. 3.1c . This discordance appears to result from distortions caused by the presence
of an external molecule (Table 3.1 ).
An important question arises: why do some proteins exhibit significant struc-
tural discordance between theoretical expectations and observed properties of their
hydrophobic cores?
 
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