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normal modes in this limit are found by diagonalizing the friction-weighted force
constant matrix,
U
−
1/ 2
−
1/ 2
=
ζ
ζ
.
(7.44)
U
In such a case, the system does not oscillate, but displacements from the
equilibrium conformation will relax along the eigenvectors of
U
with relaxation
constants given by the corresponding eigenvalues. This technique has been used
to calculate scattering functions of proteins, and to investigate the sources behind
damping in global protein motions (Hinsen
et al.
, 2000).
7.3. Applications
7.3.1.
Membrane proteins
Membrane proteins are typically composed of three domains: an extracellular
(EC) domain exposed to the periplasm, an intracellular/cytoplasmic (IC or CP)
domain buried in the cytoplasm, and a transmembrane (TM) domain embedded
in the lipid bilayer. Some membrane proteins, known as receptors, are involved
in signal transmission via recognition and binding of substrate/ligand to the EC
domain, which triggers conformational changes in the CP domain. The allosteric
coupling between different domains or the concerted motions, permit the
protein to recognize, bind or translocate substrates. Other membrane proteins
serve as ion channels or substrate transport. Permeations of ions and/or substrates
thus require collective relaxation mechanism or cooperative motions, which are
usually amenable to ENMs. Here we focus on recent progress made in
delineating the dynamics of four groups of membrane proteins, potassium
channels, acetylcholine receptors, rhodopsin and mechanosensitive channels
using ENM-based methods.
Potassium channels
:
Common gating mechanism observed in different
potassium channels
.
The TM domain of K
+
channels is composed of a bundle
of eight α−helices contributed by four identical monomers (Fig. 7.2). At the
center of these helices is a narrow
selectivity filter
(towards the EC region),
followed by a large cavity in the middle, and a long gating region, also called
pore
, that connects to the CP region (Fig. 7.3a). MD studies have provided us
with insights in to the mechanism of function at the selectivity filter, including
the preferential selectivity of potassium over sodium (Shrivastava & Sansom,
2000; Shrivastava
et al.
, 2002; Bernèche & Roux, 2000) and the free energy
