Biomedical Engineering Reference
In-Depth Information
the correlations and dependencies that may exist between the residues of a binding
patch [
55
].
Residue conservation.
Bioinformatics and molecular dynamics investigations
have shown that residue conservation and dynamics are distinct in the interface
region compared to the surface as a whole [
46
,
63
], and that the interface core,
as opposed to the rim, appears to have a particular importance [
5
,
17
]. Hotspot
residues may also be interpreted in light of the degree of conservation seen at
these positions in the protein sequence. Such conservation refers implicitly to a
classification of known proteins sharing a common ancestor and similar structures,
and, importantly, function. The latter is particularly important for assessing protein-
protein interactions, as function is predicated on the character of the partner protein
as well. For analyses of residue conservation, sequences of related proteins from
different organisms must be gathered and aligned; this step involves positing that
the interaction and the interface are conserved in the different organisms (further
discussion on this point can be found elsewhere [
43
,
54
,
66
]). After alignment,
an estimation of the degree of conservation can be made at each position. Amino
acids that are critical to the stability of a complex are often found to be more or
less invariant (conserved) [
35
]. A common way of assessing this conservation is
through the Shannon entropy
s
calculated for each position
i
in the alignment, using
the frequencies of appearance of the 20 natural amino-acids (aa) at that position:
s
i
=
−
aa
f
i,aa
ln
f
i,aa
. Positions at which an amino acid is more conserved
exhibit a more peaked distribution, with a consequently lower entropy. Indirect
prediction of hotspot residues from measures of residue conservation can thus
help rationalize the affinity of a protein-protein interaction. We shall also see that
certain geometric constructions can help unravel the relationship between residue
conservation and structural features of a complex.
1.2.1.2
Physical Modeling of Macromolecules
The biological, biochemical, and biophysical data just presented can be approached
by different theoretical means. A classical approach is to use physical chemical
modeling of the atomic interactions in the system.
Energy functions and forcefields.
The set of coordinates of all particles in the
system constitutes the configuration
X
. Statistical mechanics shows how knowledge
of the potential energy
E
(
X
) of the macromolecular system can be used to deduce
relative probabilities of different configurations of the system via the Boltzmann
factor
exp
−E
(
X
)
/kT
. High potential energies are associated with low probability
configurations, and vice versa.
It is thus important to be able to calculate the potential energy as accurately
as possible. It is currently difficult to envision ab initio quantum mechanical
approaches to modelling entire proteins and their dynamics. Thankfully, empirical
forcefield approaches using the classical approximation can provide remarkably
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