Chemistry Reference
In-Depth Information
Approaches involving Diffusion Constant
Diffusion NMR related binding studies have two main lines of application, One
application is more qualitative, related to the screening of complex mixtures or
individual molecules, commonly with the purpose of identifying potential new
drug compounds, and another, more quantitative, regarding the determination of
association constants [35].
Diffusion is the random translational motion of molecules or ions driven by their
internal kinetic energy [35, 43, 44] and it is related to molecular size, as becomes
apparent from the Stokes-Einstein equation (Eq. 5)
D =
k
B
T/
f
(5)
where D is the diffusion coefficient,
k
B
is the Boltzmann constant, T is the
temperature, and
f
is the friction coefficient. For spherical entities the friction
factor
f
is given by
f
= 6πηr
H
(6)
in which η is the viscosity of the solution and r
H
is the hydrodynamic (or Stokes)
radius of the particle. The Stokes-Einstein equation relates the translational
diffusion coefficient at infinite dilution of a spherical particle to its hydrodynamic
radius. Thus, from simple equations it is possible to relate experimental diffusion
coefficients to molecular radii, Simplicity is the basis for extensive usage [27].
Pulsed field gradient NMR spectroscopy (PFG-NMR) can be used to measure
translational diffusion of molecules and also offer an alternative ligand-based
approach for studying ligand-protein binding, It can be used for both qualitative
and quantitative analysis [27, 35, 45]. The concept of this methodology is very
simple and is based on the fact that the diffusion coefficient of a molecule is
changed upon addition of another molecule when there is interaction between
them [27, 35]. Thus, when a small molecule binds to a large receptor, its diffusion
coefficient decreases according to the macromolecule magnitude. It means that
the small molecule will have the diffusion coefficient of the large receptor, at least
for some time, and if we consider the fast exchange limit, its observed diffusion
coefficient (D
obs
) is described by
