Biomedical Engineering Reference
In-Depth Information
containing a particular fraction of the probability of finding the atom and is related
to the mean square displacement of the atom by
B
=(8
/
3)
π
2
<δ
2
>
for the
isotropic (spherical) case. Anisotropic temperature factors may also be supplied in
the form of the principal axes of an ellipsoid. In proteins, B-factors typically range
from 5 to over 60 A
2
, so that the positional uncertainty (
>
0.2 A) is much larger than
the precision that the coordinate entries would lead one to believe.
Crystallization is a process which obliges molecules to come together, forming
interfaces that may have no significance in Nature. One important goal when
interpreting crystal structures of protein complexes is to be able to distinguish
a biological interface from a banal crystal packing interface. Assignments of
biological interfaces given in the PDB file itself are often wrong [
37
,
42
]. The true
interface can be determined by experiments in solution, or by capturing the essential
features of protein-protein interfaces to a sufficient degree that predictions can be
made.
Absolute and relative affinities.
One of the most fundamental biochemical quan-
tities in protein-protein interactions is the affinity. The affinity of an association
reaction
A
+
B → AB
refers to the ratio
K
=
c
AB
/c
A
c
B
,inwhichthe
c
's
refer to the concentration of free
A
, free
B
and of their complex in an equilibrium
aqueous solution. (As the affinity constant K has units of inverse concentration, care
must be taken in comparing values obtained using different concentration scales.)
K
characterizes a given associating system; at a given temperature it is a constant
and constitutes a constraint on the concentrations of the different species. High
values of K indicate a strong tendency for
A
and
B
to form the complex.
Experimental estimates for the affinity are typically obtained from isothermal
titration calorimetry or surface plasmon resonance measurements.
The affinity is related to the free energy change
ΔG
◦
for the association (per
molecule of complex). Under standard state conditions,
ΔG
◦
=
−kT
ln
Kc
,in
which
k
is Boltzmann's constant and
T
the temperature in degrees Kelvin, and the
zero of the free-energy scale is set by the reference concentration
c
, which is usually
specified as 1M, or 1 mole of the component in question per liter of solution. (Recall
that 1 mole is about 6
×
10
23
molecules.) Measured free-energy changes for protein-
protein interactions are generally in the range of about
−
18 kcal/mole [
39
],
from which it can be seen that the concentration at which half the protein is tied up
in complexes ranges from the
μM
to the
fM
range.
Rationalizing the absolute binding free energy is a complex task. Site-directed
mutagenesis consists of changing the amino-acid identity of a single residue in
the wild-type protein sequence (primary structure) to another, usually alanine. The
effect of this mutation on the binding affinity is quantified using the difference in
binding energies
ΔΔG
◦
(note that this corresponds to the logarithm of the ratio
of the corresponding binding affinities). Systematic measurements of
ΔΔG
◦
for
mutating each residue in a single protein-protein complex allows the identification
of so-called
hotspot residues
that contribute disproportionately to the free energy
of association [
50
]. While providing invaluable information on the importance of
specific residues, this technique does not, however, directly convey information on
−
7 to
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