Lipid Bilayer-Membrane Protein Coupling - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 93

independent probability corresponding to a specific energy state and transition prob-
ability between different energy states follow a straight-forward statistical mechani-
cal formalism but a feasible physical analysis of the problem has just been published
([11] in Chap. 4 ) . We wish to address that here first.

5.3.1 Analysis of the Alamethicin Channel Experiments

It is generally known that alamethicin channels may exist with different current
levels, due to the varied number of participating alamethicin monomers. The current
flowing through an alamethicin channel is directly proportional to the cross-sectional
area of the cylindrical structure representing the channel. The model diagrams pre-
sented in Figs. 5.8 , 5.9 , 5.10 clearly address this possibility. It is also possible that any
channel undergoes transitions between different structures and consequently the cur-
rent through that channel undergoes transitions between different current levels. The
current trace across a membrane doped with alamethicin channels shows all these
features. Fig. 5.11 shows such a membrane current due to the presence of alamethicin
channels inside the membrane. Detailed experimental techniques will be discussed
in the next section and can be found in the literature [ 12 ].
We need to develop a unique phenomenological treatment to understand the vari-
ous current transitions through alamethicin channels, as shown in Fig. 5.11 [ 12 ]. This
is done below.
The probability ( W i ) of an alamethicin channel having a current level i is estimated

as:

A i

i = 0

W i =

A nc ,

(5.22)

A i +

where A i denotes the area under the peak in the current level histogram (see
Fig. 5.11 c) representing a current level i ( i

= , , , ,..., , +

1isthe
maximal number of current levels in the experiment) and A nc is the area under the
peak representing the baseline (no channels). The probability of the channel having
a current level i , relative to the baseline, is given by

0 1 2 3 n where n

exp

G nc → i
k B T

A i
A nc =

W i
W nc =

− r i = , (5.23)

G nc → i (which still needs to be normalized by the alamethicin monomer
concentration in the bilayer) is the free energy of the channel in current level i
relative to the baseline, T is the temperature in kelvin, and k B is Boltzmann's constant.

where

G nc → i is, in fact, a measure of the change in the bilayer deformation energy required
to form an alamethicin channel in a bilayer membrane.
It turns out to be helpful to consider the probability of having a current level,
relative to the baseline