Lipid Bilayer-Membrane Protein Coupling - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 80

to the membrane deformation, and many researchers proposed that the free energy
change is contributed due to the elastic bilayer properties. We present here a detailed
analysis of the bilayer's elastic energy, which arises from the consideration of the
mechanical properties of the lipid bilayer. A spontaneous bending near the channel's
edges (as diagrammed in Fig. 5.2 ) is a possible model. The crucial issue is to find
the force which drives the lipid layers inward to bind with the channel's edges. Is it
a harmonic energetic coupling as schematized in Fig. 5.4 ? If so, then we can model
the bilayer-gramicidin A channel coupling through many virtual springs which will
pull both of the lipid layers toward the channel's longitudinal edges. Each lipid
layer then needs to spontaneously bend through a free length, which is proportional
to 2 in each longitudinal edge of the channel, to satisfy the condition of

the hydrophobic bilayer channel coupling as diagrammed in Fig. 5.2 . The bilayer's
elastic property certainly helps the monolayers to spontaneously bend (see Fig. 5.2 ),
but since the bending is permanent, with a high level of stability proportional to the
channel lifetime, the mechanism certainly falls outside simple harmonic coupling.
In this case, the virtual springs presented in Fig. 5.4 need to compress by a length
proportional to their equilibrium lengths. Therefore, the virtual springs do not just
follow the motion of a harmonic oscillator (see Eq. 5.2 ), but rather, higher order
anharmonic terms appear in the potential energy formula in addition to the harmonic
oscillator terms (see Eq. 5.3 ).
The scientific arguments presented here clearly suggest that a brand-new formula
is needed to describe bilayer channel coupling energetics, and one has to include both
harmonic (originating from elastic properties) and anharmonic (originating from
unknown properties) bilayer integral channel coupling terms. We discuss this in the
next section, but first we address the existing bilayer channel coupling energetics
based on the bilayer's mechanical properties, especially bilayer elasticity.

( d 0 − l )/

5.1.3 The Membrane's Elastic Property Contributes
to the Membrane-Membrane Protein Coupling: A Study
Using the Gramicidin A Channel as a Tool

The general or primary function of membrane proteins is to catalyze the selective
transfer of material and information across biological membranes. In the case of cat-
alyzing this transfer, membrane proteins undergo conformational changes, namely:
(a) the opening/closing transitions in ion channels [ 72 , 73 , 88 ] and (b) the shift
in substrate binding site accessibility in conformational carriers and ATP-driven
pumps [ 87 ]. To the extent that these protein conformational changes involve the
protein/bilayer interface, they will perturb the bilayer immediately adjacent to the
protein [ 3 , 20 , 33 , 42 , 76 ], cf. Figs. 4.1 and 5.2 . That is, protein conformational
changes involve not only rearrangements within the protein, but also interactions
with the environment, particularly with the host bilayer. This was discussed in an