Chemistry Reference
In-Depth Information
The reaction may be thought of as a stochastic process, which generates a random
sequence of microscopic pulses of ionic current. The pattern of current
fluctuations
induced by the transient occupancy of the pore by a diffusingmolecule is an electrical
signature of the molecular interactions that occur inside the protein channel [89].
The magnitude of the current decrease re
ects the extent to which the channel is
blocked by the translocating molecule, while the duration of the current pulse refers
to the strength of interactions between the molecule and the amino acids lining
the pore. This approach, known as the molecular Coulter counter, provides rapid
and accurate characterization in real-time of molecules interacting with single
ion channels [90, 91]. The passage of carbohydrates [92], nucleic acids [93], and
antibiotics [94], could be resolved on a single molecular level.
Statistical analysis of the ligand-binding events can be undertaken by computing
the autocorrelation of the current
fluctuations. For a simple two-state Markovian
process, the autocorrelation takes the form of a single exponential, and the
inverse of the relaxation time is a linear function of the association (closing) and
dissociation (opening) rate constants, k
ass
and k
diss
, respectively. In practice, a similar
but more convenient approach consists of converting time-dependent
fluctuating
current into a frequency domain by using power spectrum analysis [94]. Spectra of
the ligand-induced current
fluctuations can be described by a single Lorentzian
function (the Fourier transform of an exponential is a Lorentzian function) of
the form:
2
4
s
t
S
ð
w
Þ¼
;
ð
7
:
7
Þ
1
þ
w
2
t
2
2
where
t
is the relaxation time of the reaction, and
s
is the variance. Expressions of
t
2
and
s
as a function of the binding rate constants are represented as follows:
Þ
1
t ¼ð
k
ass
C
þ
k
diss
;
ð
7
:
8
Þ
2
N
ðD
i
Þ
Ck
ass
k
diss
2
s
¼
;
ð
7
:
9
Þ
2
ð
k
ass
C
þ
k
diss
Þ
where C is the ligand concentration, N is the total number of channels and
D
i is the
current through one channel.
7.5.4
Facilitated Translocation of Sugars through Bacterial Porins
The outer cell membrane of bacteria is permeable to smaller solutes below a
molecular weight of about 400 Da. Such substances can freely permeate under a
concentration gradient through general diffusion porins. However, under conditions
of lownutrients the simple diffusion process is too slow and the bacterial cells need to
enhance the ef
ciency of translocation. For this purpose, channels speci
c for a
certain compound are present in the outer cell wall. The most extensively studied
examples of speci
c porins are the maltooligosaccharide-speci
c channel LamB, also
