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0 20 40 60 80 100
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (ms)
ˆ
G
c
(nS)
0 20 40 60 80 100
−150
−100
−50
0
50
100
150
Time (ms)
Input (mV), Output (pA)
A
B
Input Voltage
Output Current
I/V
LSPE
Figure 5: A) Sinusoidal voltage response (120 mV peak-
to-peak, 10 Hz, 0 mV DC offset) of the nanopore system
model. B) A comparison of the LPSE and I/V methods for
generating
b
G
c
. The voltage sign change at 50 ms causes
a step change in G
c
from 1/3 to 2/9 nS. The I/V method
does not generate accurate estimates, whereas the LSPE al-
gorithm does track the change in G
c
.
uses fixed-length windows of past data to generate
the estimated conductance value. Future work will
explore improving the algorithm’s performance by
varying the window length based on detected rates of
change of the data (Jiang and Zhang, 2004), and by
incorporating forgetting-factors in the sequential im-
plementation (Ljung and Gunnarsson, 1990). Also,
an offline implementation that makes use of future
windows to compute the estimate will be developed
to further improve the detection resolution of rapid
DNA-protein dissociation events that follow voltage
changes in active control experiments (Wilson et al.,
2009), (Olasagasti et al., 2010).
The cited advantage of AC-signal detection (ab-
sent DC bias) is that nanopore/analyte interactions
can be measured while reducing the effects of elec-
troosmosis, electrophoresis, and protein deformation
that accompany large DC biases (Ervin et al., 2008).
In (Ervin et al., 2008), custom hardware (lock-in am-
plifier) and software permit high frequency (10–20
mV, 1–2 kHz f
w
) sinusoidal voltage inputs. The LSPE
derived here cannot track G
c
at sinusoidal frequencies
above 50 Hz (data not shown). Future work will ex-
plore if and how well the LSPE estimate may track
the presence of DNA in the pore at sinusoidal volt-
ages around 0 mV (no DC bias), at 5–50 Hz frequen-
cies, as an alternative to the high frequency method in
(Ervin et al., 2008).
REFERENCES
Bates, M., Burns, M., and Meller, A. (2003). Dynamics
of DNA molecules in a membrane channel probed
by active control techniques. Biophysical Journal,
84:2366–2372.
Benner, S., Chen, R. J. A., Wilson, N. A., Abu-Shumays,
R., Hurt, N., Lieberman, K. R., Deamer, D. W., Dun-
bar, W. B., and Akeson, M. (2007). Sequence-specific
detection of individual DNA polymerase complexes in
real time using a nanopore. Nature Nanotechnology,
2:718–724.
Boyd, S. P. and Vandenberghe, L. (2004). Convex Optimiza-
tion. Cambridge University Press.
Ervin, E. N., Kawano, R., White, R., and White, H. (2008).
Simultaneous alternating and direct current readout
of protein ion channel blocking events using glass
nanopore membranes. Anal. Chem, 80(6):2069–2076.
Garalde, D. R., Maitra, R. D., O’Donnell, C. R., Wang,
G., and Dunbar, W. B. (2011). Modeling the biolog-
ical nanopore instrument for biomolecular state esti-
mation. IEEE Trans. on Control Systems Technology,
in preparation.
Goodwin, G. C., Middleton, R. H., and Poor, H. V. (1992).
High-speed digital signal processing and control. Pro-
ceedings of the IEEE, 80(2):240–259.
Jiang, J. and Zhang, Y. (2004). A novel variable-length
sliding window blockwise least-squares algorithm for
on-line estimation of time-varying parameters. Inter-
national Journal of Adaptive Control and Signal Pro-
cessing, 18(6):505–521.
Katz, E. and Willner, I. (2003). Probing biomolecular inter-
actions at conductive and semiconductive surfaces by
impedance spectroscopy: Routes to impedimetric im-
munosensors, DNA-sensors, and enzyme biosensors.
Electroanalysis, 15(11):913–947.
Ljung, L. and Gunnarsson, S. (1990). Adaptation and track-
ing in system identification—a survey. Automatica,
26(1):7–21.
Olasagasti, F., Lieberman, K. R., Benner, S., Cherf, G. M.,
Dahl, J. M., Deamer, D. W., and Akeson, M. (2010).
Replication of individual DNA molecules under elec-
tronic control using a protein nanopore. Nature Nan-
otechnology, 5(11):798–806.
Wilson, N. A., Abu-Shumays, R., Gyarfas, B., Wang, H.,
Lieberman, K. R., Akeson, M., and Dunbar, W. B.
(2009). Electronic control of DNA polymerase bind-
ing and unbinding to single DNA molecules. ACS
Nano, 3:995–1003.
LEAST-SQUARES ESTIMATION OF NANOPORE CHANNEL CONDUCTANCE IN VOLTAGE-VARYING
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