Biology Reference
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equally spaced sub-conductance states of a single channel (
Rahman and Taylor,
2009
). For IP
3
R, sub-conductance states are rare (
Rahman and Taylor, 2009
), allow-
ing the simplest possible scheme, a switch between a single closed (C) and open (O)
state (C
O) with arbitrarily chosen rate constants (e.g., 100 s
1
), to be used for the
initial idealization (
Qin, 2004
). Beginning with this simple scheme does not compro-
mise later analyses thatmight revealmore complex relationships between several open
and closed states. Direct comparison of raw traces with their idealized versions is
essential at this stage to confirm the fidelity of the idealization procedure.
Hitherto, the analysis, has considered only the amplitudes of the currents, the
next step considers the durations of these events in records from single channels.
This provides the opportunity to resolve di
$
erent open and closed states and
possible relationships between them, leading to plausible gating schemes. The
distribution of lifetimes of a single state of a channel is described by a single
exponential (Colquhoun, 1994). The analysis attempts iteratively to establish, for
each potential gating scheme (beginning with the simplest, C
V
O), the number of
exponential functions required to describe the closed and open lifetimes derived
from the idealization procedure. A maximum interval likelihood method (MIL) is
used to fit the lifetimes with pdfs (
Qin et al., 1996, 1997, 2000
). During this fitting
process, a dead-time of 200
m
s (twice the sampling interval) is retrospectively
imposed for the correction of missed events (
Sivilotti, 2010
).
Dwell-time histograms are generated and displayed with logarithmic abscissa
and square root ordinate (
Fig. 4
D) (
Sigworth and Sine, 1987
) and fitted by a
mixture of exponential pdfs, defined in the function f(t)as
$
X
n
a
i
t
i
fðtÞ¼
exp t=t
i
ð
Þ
ð3Þ
i¼
1
where a
i
is the fractional area occupied by the ith component in the distribution, such
that the areas corresponding to all components sum to unity, and
t
i
is the time
constant for the ith component. The mean life-time (
t
) is given by the following
equation:
X
n
i¼
1
a
i
t
i
t ¼
ð
Þ
ð4Þ
The Sigworth-Sine transformation (
Fig. 4
D) allows a single plot clearly to display
dwell-times spanning several orders of magnitude. Individual exponential compo-
nents of the distribution can be directly identified from the peaks of the distribution.
After iterative exploration of alternative gating schemes, the log likelihood ratio
(Colquhoun, 1994) is used to identify the scheme that best fits the data. The chosen
scheme is then used to reidealize the raw data to provide the final gating para-
meters (mean life-times and P
o
). Although these are the methods we have used to
address the gating of IP
3
R(
Rahman et al., 2009
), more sophisticated approaches
exploit the additional information that lurks in the correlations that exist between
transitions (
McManus et al., 1985
).
