Membrane-Embedded Channel of Bacteriophage Phi29 DNA-Packaging Motor for Translocation and Sensing of Double-Stranded DNA - Nanopores: Sensing and Fundamental Biological Interactions - page 86

4.4.3 Current-Voltage Relationship of Single
(or Multiple) Connector Channels

The application of a ramping potential (2.2 mV s 1 ) from 100 mV to +100 mV to

the BLM containing a single (or multiple) connector channel revealed a perfectly
linear I-V relationship, thereby demonstrating well-behaved, uniform conductance
of the channel. The current traces from one, two and three connector insertions
are shown in Fig. 4.5a in the presence of 5 mM Tris (pH 7.8)/2 M NaCl. Increased
number of connectors correlated to greater slopes but identical conductance per
channel, further demonstrating the uniform size and stability of the phi29 connector
channels in the BLM.
In addition to number of connector channels, the conductance also depends on
the ion concentration and ion species (Fig. 4.6 ). From the I-V slope, the conduc-
tance in 0.5 M NaCl, 1.0 M NaCl, 1.5 M NaCl and 2.0 M NaCl were determined
to be 1.75 0.05 nS, respec-

tively, demonstrating the expected increase in conductance with an increase in salt
concentration (Fig. 4.6a, c ). The conductance values were higher at equal concen-
trations of KCl compared to NaCl as follows: at 0.5 M KCl, 1.0 M KCl, 1.5 M KCl
and 2.0 M KCl, the conductance were 2.70

0.11 nS, 3.03 0.02 nS, 4.07 0.26 nS, and 4.60

0.21 nS, 4.65 0.11 nS, 6.23 0.32

nS, and 7.83 0.20 nS, respectively (Fig. 4.6b, d ).

4.4.4 An Analytical Expression for Determining the Number
of Connectors Inserted in the Lipid Bilayer

The conductance of the membrane/connector complex, G m can be calculated using
two approaches: (1) The step size of the current jump upon connector insertion under
a specific voltage in real time. In this case, the ratio of the measured current to the
applied voltage represents the conductance value. (2) The slope of the current trace
under a ramp voltage [ 48 ]. The second approach gives a more accurate value, since
the slope contains numerous data points and also accounts for effects, such as changes
in surface potentials of Ag/AgCl electrodes as well as membrane contact potentials.
The conductance of one channel in the BLM, G c can be obtained readily using
the same approaches. Since phi29 connector channels are of uniform size and
are stable under a wide range of salt concentrations, a linear relationship is there-
fore expected between the conductance of the membrane/connector and the number
of connectors in the BLM (Fig. 4.6c, d ). Indeed a linear relationship is obtained
in both NaCl and KCl buffers. Table 4.1 shows the results of calculating single
channel conductance using the discrete current steps.
Generally, if G m and G c are known, the number of connectors ( N ) incorporated
in a membrane can be deduced as follows [ 48 ]:

G m
G c

N ¼ (4.1)