Reconfigurable Ion-Channel based Biosensor: Input Excitation Design and
Sahar M.Monfared,Vikram Krishnamurthy Fellow, IEEE,Bruce Cornell
Abstract—This paper considers modeling and signal process-
ing of a biosensor incorporating gramicidin A (gA) ion chan-
nels. The gA ion channel based biosensor provides improved
sensitivity in rapid detection of biological analytes and is easily
adaptable to detect a wide range of analytes. In this paper,
the electrical dynamics of the biosensor are modeled by an
equivalent second order linear system. The chemical dynamics
of the biosensor response to analyte concentration are modeled
by a two-time scale nonlinear system of differential equations.
An optimal input excitation is designed for the biosensor to
minimize the covariance of the channel conductance estimate.
By using the theory of singular perturbation, we show that the
channel conductance varies according to one of three possible
modes depending on the concentration of the analyte present.
A multi-hypothesis testing algorithm is developed to classify
the analyte concentration in the system as null, medium or
high. Finally experimental data collected from the biosensor in
response to various analyte concentrations are used to verify
the modeling of the biosensor as well as the performance of the
multi-hypothesis testing algorithm.
Biological ion channels are water-filled sub-nano-sized
pores formed by protein molecules in the membranes of all
living cells , . Ion channels in cell membranes play a
crucial role in living organisms. They selectively regulate
the flow of ions into and out of a cell and regulate the
cell’s biochemical activities. This paper deals with model-
ing and signal processing of a biosensor that exploits the
selective conductivity of ion channels. Such ion channel
based biosensors can detect target molecular species of
interest across a wide range of applications. These include
medical diagnostics, environmental monitoring and general
The ion-channel based biosensors we focus on are built
using gramicidin A. Gramicidin A was one of the first
antibiotics isolated in the 1940s [7, pp.130] and has a
low molecular weight. In , a novel biosensor, which
incorporates gramicidin A ion channels into an artificial cell
membrane was developed by our coauthor, see , , .
This paper describes how such ion channel biosensors can be
modeled as a stochastic dynamical system, how their input
can be dynamically adapted to minimize the detection error
covariance, and finally how maximum likelihood classifiers
can be used to detect analyte presence and concentration.
The main results of this paper are as follows:
1) Dynamical Response of Biosensor: In Section II the
electrical dynamics of the ion channel biosensor are
modeled by an equivalent second order linear system,
see ,. We then formulate the dynamics of the
biosensor response to analyte concentration as a two-
time scale nonlinear dynamical system. The presence
of analyte decreases the concentration of the dimers
formed in the biosensor, thus decreasing the channel
admittance. In order to study the evolution of the
channel admittance in response to the introduction of
analyte, the chemical kinetics of the biosensor are mod-
eled as a singularly perturbed system, see also ,.
The channel concentration evolves according to three
regimes depending on the concentration of the analyte
in the system.
2) Optimal Input Design: An input controller is designed
to optimize the input excitation to the biosensor, by
minimizing the covariance of the biosensor impedance
estimate, see . The optimal input excitation is
found to be independent of channel conductance. As
a result we can decouple the biosensor input design
problem from the analyte concentration classification.
3) Analyte Concentration Classification: The final con-
tribution of the paper is to devise a multi-hypothesis
Kalman filtering algorithm to classify the concentration
of the analyte present in the system as null, medium or
high. The derived equations, describing the evolution
of the channel conductance as a function of analyte
concentration, is used in this stage.
The remainder of this paper is organized as follows. Section
II describes the construction of the biosensor as well as the
electrical and chemical modeling of the biosensor. Section
III focuses on optimal input excitation design as well as
the maximum likelihood classifier algorithm. Section IV
includes an experimental study of the classification algorithm
described in Section III on the actual ion channel biosensor,
using Streptavidin as analyte and Biotin as binding site.
II. MODELING THE DYNAMICS OF THE ION CHANNEL
The construction of the ion channel biosensor developed
by  involves sophisticated concepts in biochemistry. How-
ever, for our purposes its operation can be simply described
as follows. First an artificial ‘tethered’ lipid monolayer is
constructed containing tethered gramicidin channels. ‘Teth-
ered’ means that the inner layer of the membrane is fixed to
a gold substrate (using a disulphide bond) and is no longer
mobile. Then a second outer mobile monolayer comprising
of lipids and gramicidin channels is introduced. These com-
ponents “self-assemble” in water to form a lipid bilayer that
mimics a cell membrane. The lipid bilayer is 4nm thick and
is tethered 4nm away from the gold electrode. A voltage of
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n→∞Pactive mode(n) = 1 for all possible active modes. Empirical
measurements produced according to a possible mode of the system are
used in the classification algorithm.
1) → 1 as time progresses, while lim
2 or 3) → 0. The first and second subplots of Fig.4 show
that the lim
n→∞(Pactive mode(n) = 3) → 0 very fast when the
analyte concentration is medium or high, where as it takes
longer for lim
n→∞(Pactive mode(n) = 2 or 3) → 0 when the
active mode is either 3 or 2. This is due to the closeness
of the dimer concentration decay regime when the analyte
concentration is medium or high. Where null analyte concen-
tration results in a constant dimer concentration profile the
medium and high analyte concentrations cause exponential
decay regimes with different decay constant depending on
the analyte concentration.
n→∞(Pactive mode(n) =
This paper presents mathematical modeling of a novel
ion channel based biosensor. The electrical dynamics of the
biosensor are modeled by a second order linear system.
Furthermore, the chemical kinetics of the biosensor are
modeled as a two-timescale nonlinear dynamical system.
Using asymptotic methods such as singular perturbation
theory, an analytical equation expressing the evolution of
the dimer concentration with time as a function of analyte
concentration is derived. Kalman filters are used to classify
the analyte concentration. Also an optimal input voltage
is designed for the biosensor to minimize the covariance
of the estimation error. It is discovered that the optimal
input properties are independent of the channel conductance,
which allows the decoupling of the optimal input design and
the analyte concentration classification problem. A multi-
hypothesis testing algorithm is devised to classify the analyte
concentration as null, medium or high using the noisy
measurements from the sensor.
 S.H. Chung, O. Anderson, and V. Krishnamurthy, editors. Biologi-
cal Membrane Ion Channels: Dynamics, Structure and Applications.
 B. Cornell. Optical biosensors: Present and future, page 457. Elsevier,
 B. Cornell, V.L. Braach-Maksvytis, L.G. King, P.D. Osman, B. Ra-
guse, L. Wieczorek, and R.J. Pace. A biosensor that uses ion-channel
switches. Nature, 387:580–583, 1997.
 B. Cornell, G. Krishna, P. Osman, R. Pace, and L. Wieczorek. Tethered
bilayer lipid membranes as a support for membrane-active peptides.
Biochemical Society Transactions, 29(4):613–617, 2001.
 G.Q. Dong, L. Jakobowski, M.A.J. Iafolla, and D.R. McMillen.
Simplification of stochastic chemical reaction models with fast and
slow dynamics. Journal of Biological Physics, 33(1):67–95, Feb 2007.
 S. Fekri, M. Athans, and A. Pascoal. Issues, progress, and new results
in robust adaptive control. International Journal of Adaptive Control
and Signal Processing, 20(10):519–579, Aug 2006.
 A. Finkelstein. Water Movement through Lipid Bilayers, Pores and
Plasma Membranes. Wiley-Interscience, 1987.
 B. Hille. Ionic Channels of Excitable Membranes. Sinauer Associates,
Inc., Sunderland, MA., 3 edition, 2001.
 H.K. Khalil. Nonlinear Systems. Prentice Hall, 3 edition, 2002.
 L. Ljung. System Identification. Prentice Hall, 2 edition, 1999.
 F. Separovic and B. Cornell.
device. In S.H. Chung, O. Andersen, and V. Krishnamurthy, editors,
Biological Membrane Ion Channels, pages 595–621. Springer-Verlag,
 S.J. Spencer. Numerical modelling of the ambri membrane biosensor.
Technical Report DMS-C/96/16, CSIRO dms, 1996.
 G. Woodhouse, L. King, L. Wieczorek, P. Osman, and B.Cornell. The
ion channel swtich biosensor. Journal of Molecular Recognition, 12(5),
Gated ion channel-based biosensor