Lipid Bilayer-Membrane Protein Coupling - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 85

exp exp

G def
k B T

− (λ + − λ)

−

F dis

τ ∼ = (5.13)

k B T

F dis here follows from Eq. 5.12 in the elastic bilayer consideration.
In this elastic bilayer deformation energy calculation, the decomposed local
bilayer compression and monolayer bending energy densities are often calculated
considering the bilayer as an almost perfect elastic body. Equation 5.11 provides
only the quadratic energy form of the mismatch d 0 −

l , which is the harmonic energy
coupling term (Eq. 5.3 ). This energy term does not consist of any anharmonic terms,
which are highly needed especially in the case of having a considerable value of
d 0 −

l . Consequently, the lack of presence of nonlinear terms other than the linear
term (proportional to d 0 − l )inthevalueof F dis makes the form of F dis in Eq. 5.12

incomplete and scientifically incorrect. This has been explained in detail in an ear-
lier section, as well as in ([11] in Chap. 4 ) . Therefore, a general form for F dis must
be formulated, using a totally different scientifically acceptable model, considering
all general properties of the lipid bilayer and integral membrane proteins. We have
done so using a screened Coulomb interaction model for calculating the hydrophobic
bilayer-membrane protein coupling energy by including electrical properties of the
lipids and membrane proteins ([ 11 ] in Chap. 4 ) . We explain briefly below.

5.2 Lipid Membrane-Membrane Protein Coupling
Due to Electrical Properties of Lipids and Proteins

In Sect. 5.1 we have discussed how the membrane's elastic properties raise the possi-
bility of conditional mechanical energetic coupling between lipid layers and integral
membrane proteins. We have also found that although the mechanical property of
lipid layers (or generally, the bilayer elasticity) provides important contributions
to the membrane functions, there are even more important biophysical properties,
namely the electrical properties of the membrane constituents and the integral mem-
brane proteins that generate primary effects on most of the membrane transport
properties ([ 11 ] in Chap. 4 ) . Based on this latter publication, it is clear that a tra-
ditional mechanical energetic coupling between the bilayer and membrane proteins
does not contribute the primary regulatory effects on membrane proteins. Instead,
the electrical energetic coupling does so.

5.2.1 Screened Coulomb Potentials and Lennard-Jones
Interactions Between Peptides on Ion Channels
and Lipids in the Membrane: A Study Using Gramicidin A
Channel as a Tool

Using specific 'elastic parameters' in a fluid-like membrane is a good first-order
approximation that works well within the limitations of a linear theory. However,