Biomedical Engineering Reference
In-Depth Information
a ligand-protein complex possible. The magnitude of this free energy cost has been much debated
in the literature. Explicit calculations show that it varies only slightly with molecular weight, but
an important problem for the estimation of
G
transl+rot
is that it depends on the “tightness” of the
ligand-protein complex. A tighter complex leads to a greater loss of freedom of movement and thus
to a more negative
T
Δ
G
transl+rot
range from 12 kJ/mol for a “loose” complex to
45 kJ/mol for a tightly bound complex. Whatever the exact magnitude of
Δ
S. Most estimates of
Δ
G
transl+rot
is in a particular
case, it is a very signii cant energy to overcome by the favorable binding forces. Consider a ligand with
an afi nity (
K
i
) of 1 nM corresponding to
Δ
G
of −53.4 kJ/mol at 310 K (Section 1.2). In order to end up
with this free energy difference between the bound and unbound states, the favorable binding forces
must produce not only 53.4 kJ/mol of ligand-protein binding energy but in addition 12-45 kJ/mol of
free energy is required to make the association possible. It should be noted that this free energy cost
of ligand-protein association is always present and cannot be reduced by ligand design. However, the
exact value of
Δ
G
values. To a i rst approxi-
mation it cancels out when comparing the afi nities of different ligands to the same receptor.
Δ
G
transl+rot
is only important for predictions of “absolute”
Δ
1.3.2
D
G
conf
—C
ONFORMATIONAL
C
HANGES
OF
L
IGAND
AND
R
ECEPTOR
The restriction of motions that are accounted for in
G
transl+rot
described above refer to the “overall”
motion of the molecule. However, there is an additional type of motion, which is more or less frozen
upon ligand binding. Most ligand molecules are l exible, which means that in the aqueous phase outside
the binding cavity in the protein, the ligand undergoes conformational changes by rotation about single
bonds. For example, the dihedral angles in hydrocarbon chains changes between gauche and anti
conformations resulting in a mixture of ligand conformations, i.e. different ligand shapes. A ligand
generally binds to a protein in a single well-dei ned conformation that positions functional groups
used for binding in appropriate locations in space for interactions with their binding partners in the
protein. This implies that the motions corresponding to the conformational freedom in aqueous solu-
tion are to a large extent frozen in the binding site. As discussed above for
Δ
Δ
G
transl+rot
, this leads to a
decrease in the entropy (conformational entropy) giving a more negative
Δ
S
and
T
Δ
S
and thus a free
energy cost for binding. The magnitude of
S
conf
has been estimated to be 1-6 kJ/mol
per restricted internal rotation and depends on the “tightness” of the ligand-protein complex as in the
case of
Δ
G
conf
due to
T
Δ
G
transl+rot
(Section 1.3.1).
A second energy contribution to
Δ
G
conf
comes from changes in ligand conformation between
aqueous solution and ligand-protein complex. Comparisons of ligand conformations observed in
x-ray structures of ligand-protein complexes and ligand conformations in aqueous phase (as calcu-
lated by state-of-the-art computational methods) show that a ligand in general does not bind to the
protein in its preferred conformation (lowest energy conformation) in aqueous solution. An example
of this is shown in Figure 1.4. Palmitic acid prefers the well-known all-anti (zigzag) conformation
of the hydrocarbon chain in aqueous solution, but binds to the adipocyte lipid-binding protein with
an afi nity (
K
i
) of 77 nM in a signii cantly folded conformation. The energy required for palmitic
acid to adopt the binding conformation has been calculated to be 10.5 kJ/mol. This conformational
energy penalty is detrimental to binding and has the effect of increasing the
K
i
value in comparison
to a case in which the ligand binds in its preferred conformation in aqueous solution.
As shown in Section 1.2, a conformational energy penalty of 5.9 kJ/mol corresponds to a decrease
in afi nity (increase of
K
i
) by a factor of 10. For each additional 5.9 kJ/mol of conformational energy
penalty, the afi nity decreases further by a factor of 10. It is consequently of high importance in the
design of new ligands using x-ray determined protein structures (see Chapter 2) or pharmacoph-
ore models (see Chapter 3) to avoid introducing signii cant conformational energy penalties in the
designed ligands. Calculations of the conformational energy penalties for ligands in a series of x-ray
structures of ligand-protein complexes indicate that these energy penalties in general are below
13 kJ/mol. This may be used as a rule of thumb in ligand design. In this context, it is important to
Δ
