Force Control for Mechanoinduction of Impedance
Variation in Cellular Organisms
Joo Hoo Nam1 , Peter C Y Chen1⋆ , Zhe Lu2 , Hong Luo3 ,
Ruowen Ge4 and Wei Lin3
1
Department of Mechanical Engineering, National University of Singapore
Department of Mechanical and Industrial Engineering, University of Toronto
3
Singapore Institute of Manufacturing Technology (SIMTech), Singapore
4
Department of Biological Science, National University of Singapore
2
E-mail: ⋆ mpechenp@nus.edu.sg
Abstract.
Constantly exposed to various forms of mechanical forces inherent in their physical
environment (such as gravity, stress induced by fluid flow or cell-cell interactions,
etc.), cellular organisms sense such forces and convert them into biochemical signals
through the processes of mechanosensing and mechanotransduction that eventually
lead to biological changes. The effect of external forces on the internal structures
and activities in a cellular organism may manifest in changes its physical properties,
such as impedance. Studying variation in the impedance of a cellular organism
induced by the application of an external mechanical force represents a meaningful
endeavour (from a biosystems perspective) in exploring the complex mechanosnsing
and mechanotransduction mechanisms that govern the behavior of a cellular organism
under the influence of external mechanical stimuli.
In this paper we describe the development of an explicit force-feedback control
system for exerting an indentation force on a cellular organism while simultaneously
measuring its impedance. To demonstrate the effectiveness of this force-control system,
we have conducted experiments using zebrafish embryos as a test model of a cellular
organism. We report experimental results demonstrating that the application of a
properly controlled external force leads to significant change in the impedance of a
zebrafish embryo. These results offer support for a plausible explanation that activities
of pore canals in the chorion are responsible for the observed change in impedance.
Keywords: Mechanoinduction, micromanipulation, explicit force control, pore canals,
impedance, ion channels, zebrafish embryo.
Submitted to: J. Micromech. Microeng. in August 2009; accepted in November 2009.
Mechanoinduction of impedance variation
2
1. Introduction
Constantly exposed to various forms of mechanical forces inherent in their physical
environment (such as gravity, stress induced by fluid flow or cell-cell interactions,
etc.), cellular organisms sense such forces and convert them into biochemical signals
through the processes of mechanosensing and mechanotransduction that eventually lead
to biological changes. Experiments have shown that cellular organisms may alter their
internal structures and activities in response to external forces. Specific experimental
studies include the myosin-II redistribution in dictyostelium cell when aspirated by
micropipette [1], the remodeling of the actin network in monkey kidney fibroblast under
a lateral deformation [2], the increases in voltage-gated K+ current when an endothelial
cell was stretched [3], and the change in β-actin gene expression of heart and notochord of
a transgenic zebrafish after exposure to simulated microgravity [4]. These experimental
observations suggest that timely application of appropriate external forces may be used
as a means to directly manipulate the dynamics of the internal processes of a cellular
organism, leading to the ultimate objective of mechano-control of biological systems.
The effect of external forces on the internal structures and activities in a cellular
organism may manifest in changes its physical properties. One such property is
the impedance, which is directly related to the ionic movement in the organism.
The initial responses of a cellular organism to an external mechanical force occur at
the cell membrane and mediate many downstream cellular processes, such as DNA
resequencing. Cellular transduction of mechanical forces into electrical signals is a
common mechanosensory process activated in the organism in response to external forces
and often involves mechano-mediated ionic transportation. For example, integrin may
initiate change of intracellular Ca2+ concentration in Madin-Darby canine kidney cells
when the cells are stretched by mechanical forces [5]. It is also generally accepted
that ion channels facilitate ionic movement across biomembranes. Results from several
studies have demonstrated that mechanosensitive ion channels play an important role
in the response of cells to mechanical forces [6]–[12]. Ion channels are proteins that
form the pores within the biomembranes which sense the stress (induced by an external
force) on the cell membrane, and relieve the stress by opening or closing the pores to
change the osmolarity of the membrane.
Studying variation in the impedance of a cellular organism induced by the
application of an external mechanical force could be a meaningful endeavour
(from a biosystems perspective) in exploring the complex mechanosnsing and
mechanotransduction mechanisms that govern the behavior of a cellular organism under
the influence of external mechanical stimuli. One way to conduct such a study is to apply
suitable indentation forces on a cellular organism while measuring its impedance.
Various approaches have been reported in the literature on applying external
mechanical forces on cellular organisms, with magnitude of applied forces ranging from
micro-Newtons to nano-Newtons or even pico-Newtons. An excellent recent review [13]
of this area describes a number of micromanipulation tools and techniques, such as
Mechanoinduction of impedance variation
3
micropipette aspiration, laser trapping, magnetic bead measurement, microcantilever
sensor, micromechanical cell stretching, and electrodeformation (e.g., [2] [14] [15]).
These techniques normally involve deforming a cellular organism and simultaneously
measuring the induced forces. An engineering challenge remains in explicitly controlling
the applied force to achieve force regulation and trajectory tracking. The need for
explicit force control in this type of micromanipulation arises because of the fragility of
cellular organisms and of the possibility that different types of force trajectories may
induce different types of biological behavior in the organism.
A cellular organism normally exhibits a certain mechanical stiffness. Indentation
forces below a certain magnitude may not deform the organism sufficiently to induce
a significant physiological change in the organism. Moreover, two samples of the same
type of organism at differnt developmental stages may exhibit different levels of stiffness,
as is evident, for example, in the case of zebrafish embryos [16]. On the other hand,
too large a force may result in the membrane of the organism being pierced and the
integrity of the organism damaged. Therefore, to study how an externally applied force
may induce variation in the physical properties of a cellular organism requires proper
control of the applied force.
In this paper we describe the development of an explicit force control system for
exerting an indentation force on a cellular organism while simultaneously measuring its
impedance. The system consists of a compound flexure stage to transmit the force from a
voice coil actuator to a micro-indenter. The interaction force between the micro-indenter
and the organism is fed back to the controller by a piezoresistive micro-force sensor.
The impedance is measured with Electrical Impedance Spectroscopy (EIS) technique.
To demonstrate the effectiveness of this force-control system, we conduct experiments
using zebrafish embryo as a test model of a cellular organism. We report experimental
results demonstrating that the application of a properly controlled external force leads
to significant change in the impedance of a zebrafish embryo. These results offer support
for a plausible explanation that activities of pore canals in the chorion are responsible
for the observed change in impedance.
This paper is organized as follows. Section 2 describes the structure of a zebrafish
embryo and the measurement of its impedance. Section 3 presents the explicit forcefeedback control system. Section 4 reports the experimental results and discusses their
implications.
2. Zebrafish Embryo and Its Impedance
Being a vertebrate animal, zebrafish represents a valuable resource for identifying genes
involved in human disease. The zebrafish embryo is translucent, biologically safe, and
easily obtainable. It has become a very useful model system for studying biological
development, and for the exploration of new techniques for force-based micro/biomanipulation (e.g., [14] [17]).
Mechanoinduction of impedance variation
4
2.1. Collection of Zebrafish Embryos
Zebrafish embryos were collected and transferred according to the protocols described
in [18]. The male and female adult zebrafish were separated with a barrier and held
overnight in a tank with egg water (1L of distilled water with 1.5 ml stock salts).
The zebrafish were allowed to breed by removing the barrier the next morning, and
the embryos were collected at the bottom of the tank and transferred to a petri dish
containing E3 Medium (5M NaCl, 4M KCl, 1M MgSO4 , 1M CaCl2 and methylene blue).
The embryos were maintained in the E3 medium at room temperature for six to seven
hours and then transferred to a plastic made test holder; they were at approximately
50% epiboly stage.
2.2. Structure of the Chorion and Ionic Movement
Although it is not clear whether integrin or ion channels exist in the zebrafish chorion,
evidence has shown that ionic activities do occur there [19]. Structurally the zebrafish
chorion consists of three electron-dense layers [20, 21]. The two innermost layers are
penetrated with pore canals. Pore plugs deposited on the individual outer pore openings
(located on outer layer) block the pore canals to the outside environment (as illustrated
in Figure 1). The mechanism of the formation of such plugs remains unknown.
Figure 1. Structure of the zebrafish chorion (adapted from [21]). Z1: outer layer, Z2:
middle layer, Z3: inner layer, P: pore canal, PP: pore plug.
2.3. Impedance Measurement
The amount of electrical charges on the surface of the chorion depends on the ion
concentration on the membrane. The Gouy-Chapman theory [22] suggests that such
surface charges lead to the formation of a double layer whose function is similar to that
of a parallel plate capacitor. When a voltage is supplied via the electrodes, the positive
ions on the membrane tend to balance out the negative charges on one of the electrodes.
This process continues until an equilibrium in electrical charges is established. Figure
2 shows a parallel-RC circuit model of a zebrafish embryo.
5
Mechanoinduction of impedance variation
V◦
Zebrafish
embryo
Vm
Im
R
C
Figure 2. Parallel-RC circuit model and circuit for measuring impedance.
We used the technique of Electrical Impedance Spectroscopy (EIS) to measure the
impedance [23], as is illustrated in Figure 2. We applied an AC potential Vm to the
embryo and measured the current Im flowing through it. When excited by an sinusoidal
voltage Vm (t) = V0 sin(ωt), where V0 is the amplitude of the excitation and the ω is
the radial frequency, the response current Im (due to the membrane capacitance) will
be at the same frequency ω but shifted in phase φ and with an amplitude I0 , i.e.,
Im (t) = I0 sin (ωt − φ). By Ohm’s law, the impedance of the system can be calculated
as:
Vm (t)
V0 sin(ωt)
Z0 sin(ωt)
(1)
Zm (t) =
=
=
Im (t)
I0 sin(ωt − φ)
sin(ωt − φ)
Therefore, the impedance can be expressed in term of Z0 = V0 /I0 and a phase shift φ.
The embryo was half immersed in E3 medium in order to minimize the short-circuit
effect of the solution. The negative electrode (immersed in the solution) made contact
with the embryo on the bottom pole while the positive electrode made contact on the
top pole. Both electrodes were Ag-AgCl wires, made from a pure Ag wire (with a
diameter of 0.2 mm) soaked in household bleach for 15 to 30 minutes [24]. To determine
the impedance using Equation (1) requires the measurement of Vm and Im . When no
voltage is applied, the circuit carries a current (i.e., the so-called current offset bias) due
to inherent noise induced by the measuring equipment. This current offset bias was first
measured and used to calibrate the subsequent measured current when a voltage was
applied. The embryo was then excited by an 1V, 10Hz sinusoidal voltage applied through
an analog Input/Output multifunctional card (Model NI6024E, National Instrument).
Both Vm and Im were measured at a sampling frequency of 10kHz by a 24-bit analog
input module (Model NI9219, National Instrument).
3. Force Control for Mechanoinduction
Piercing the chorion of a zebrafish embryo with a micropipette typically requires a force
in the order of 1 mN [25]. This, however, is not a universal threshold since different
zebrafish embryos have different mechanical properties; even for the same embryo, the
thickness of the chorion will change as the embryo evolves from one developmental
6
Mechanoinduction of impedance variation
stage to the next [16]. To study how an externally applied force may induce variation in
impedance of an embryo, the indentation force must be sufficiently large to induce an
observable response, yet not excessive so as to reduce the risk of piercing the chorion.
To achieve this requires proper sensing and control of the applied force, as in many areas
of micromanipulation [26].
Figure 3 illustrates the overall system for exerting forces on an embryo. The
system consists of a voice-coil actuator for force generation, a flexure stage for force
transmission, a micropipette equipped with a force sensor for applying a prescribed
force on the embryo.
Voice Coil Actuator
from DC Current Source
Flexure Stage
Position Encoder
Movable
Platform
to Force
Transducer
to Position
Transducer
Negative
Electrode
Micro-Indenter
with Force
Sensor
Embryo Holder
Positive Electrode
Figure 3. System for exerting an indentation force on an embryo.
3.1. Force Generation
A linear voice coil actuator (Model LA-05-000A, BEI) drives the movable platform
directly (as illustrated in Figure 3). The actuator consists of a magnetic coil secured
to the base and a movable core fixed to the moving platform of the flexure stage. A
precision DC current source (Model 6220, Keithley Instrument) supplies the current to
the actuator. A current flowing through the coil produces a magnetic field, causing the
core and movable platform to move forward or backward.
3.2. Force Transmission
A compound flexure stage transmits forces in rectilinear motion. Figure 4(a) illustrates
the structure of this stage. Secured to the base by four M3 screws, the stage consists
of a movable platform supported by four leaf springs which can be collectively modeled
as a single spring with an effective stiffness Kf = Eb(d/L)3 , since the springs have the
same geometry and are made of the same material.
The maximum displacement Xm of the movable platform can be computed as
Xm = 2σm L2 /3Ed, where E is the Young’s modulus, b, d and L are the width, thickness
7
Mechanoinduction of impedance variation
(a)
(b)
Figure 4. The flexure stage. (a) Structure. (b) Results of calibration.
and length of the leaf spring respectively, and σm is tensile yield strength [27]. The stage
was designed to have a maximum movement of 1.1 mm. Due to the maximum output
of the DC current source being 104 mA, which is equivalent to a driving force of 59.8
mN, the maximum displacement of the moving platform is 170 µm.
The stage was calibrated to determine the stiffness of the compound springs. Forces
incremented with a step of 57.5 µN were applied to the movable platform through
the voice-coil actuator, and the corresponding deflections X0 of the movable platform
were measured using a position encoder (Model M2000, MicroE System) attached to
the moving platform with a resolution of 0.5 µm. The displacement signals were
collected by connecting the encoder to a digital I/O transducer (Model NI9401, National
Instrument). LabVIEW was used to implement the DAQ operation. Five results of the
calibration (shown in Figure 4(b)) indicate a linear relationship between the applied
force and the deflection. From these results, the stiffness Kf of the compound springs
were estimated to be 380 N/m.
3.3. Force Sensing and Control
The force to be exerted on an embryo is in the order of hundreds of micro-Newtons. A
micro-indenter was used to exert such a force on the embryo. A modified commercial
one-axis piezoresistive micro-force sensor (Model AE801, SensorOne Technologies
Corporation) was used to sense the exerted force. The modification of the sensor
involved bonding a micro-indenter, which was cut from a micropipette, to the free end
of the sensor beam along its centerline [25]. The micro-indenter was fixed to the force
transmission stage with a customized sensor holder as shown in Figure 3.
To achieve a stable interaction force that tracks closely a desired force trajectory, an
explicit force controller was designed based on a mass-spring-damper dynamics model of
the system, as shown in Figure 5, where I is the input current to the voice-coil actuator,
and F is the output force from the voice-coil actuator directly driving the flexure stage.
The values for the parameters in the model are listed in Table 1. The closed-loop control
system is shown in Figure 6, where the force controller was synthesized using the method
8
Mechanoinduction of impedance variation
of control-law partitioning [28]. Using this method, the controller was decomposed into
a model-based portion and a servo portion, with the former making use of the dynamics
model shown in Figure 5, and the latter having a proportional-derivative-integral (PID)
control structure with Kp = 200, Kd = 28 and Ki = 12. These PID gains were chosen to
achieve good tracking performance of the closed-loop system with respect to step signals
that characterize desired force trajectories in cell-indentation experiments. Figure 7
shows the response of the system with respect to a typical desired force trajectory. It
can be seen that the force controller produced satisfactory force-tracking performance.
Figure 5. Dynamics model of the flexure stage.
Table 1. Values of system parameters.
Parameter Meaning
M
Kc
Kf
Bf
K1
K2
K3
B2
B3
Mass of movable platform, including microindenter holder and voice-coil movable core
Force sensitivity of voice-coil actuator
Stiffness of compound spring
Damping coefficient of flexure stage
stiffness of environment (i.e., embryo)
stiffness of environment
stiffness of environment
Damping coefficient of environment
Damping coefficient of environment
Value
0.08kg
0.575N/A
380N/m
0.1Ns/m
0.53 N/m
0.22 N/m
0.22 N/m
0.22 Ns/m
4.4 Ns/m
4. Results and Discussion
A zebrafish embryo in its natural state of development exhibits an intrinsic impedance
due to various factors, such as the ionic activities on the electron-dense membrane and
other background currents. Figure 8 shows the measured impedance of an unperturbed
Mechanoinduction of impedance variation
9
Figure 6. Closed-loop force control system
Figure 7. Response of the PID controlled system
embryo. The initial sharp drop in impedance shown in the figure is due to the fact that,
before the electrodes made contact with the chorion, the magnitude of the measured
current was negligible; the calculated impedance, as a consequence, was extremely
large. Once the electrodes made contact with the chorion, current flowed through the
measurement circuit (as shown in Figure 2), and a stable measured impedance was
obtained.
Figure 8. Measured impedance of an unperturbed zebrafish embryo.
Mechanoinduction of impedance variation
10
To investigate the effect of an externally applied force on the impedance of an
embryo, the micro-indenter was controlled to exert a force of 100 µN for about 600
seconds on the chorion of an initially unperturbed embryo. This force was sufficiently
large to induce a change in the impedance of the embryo yet still substantially below
the force threshold that may pierce the chorion. This experiment was repeated on a
number of embryos. Figures 9 and 10 show two typical results. These results indicate
that application of an external force on the chorion led to a noticeable change in the
impedance of the embryo. Such changes were observed to occur upon a delay (of about
200 seconds for the cases shown in Figures 9 and 10) after the force was applied.
Figure 9. The impedance dropped after force applied at around 600sec.
Figure 10. The impedance increased after force applied at around 600sec.
The exact mechanism by which an external force (exerted on a zebrafish embryo)
causing the measured impedance of the embryo to change is not yet known. The
activities of ionic movement across the chorion may offer an explanation. At a given
voltage, the change in the measured current may be due to the influx and/or efflux of
certain ions across the chorion, due to the effect of the external force on the pore canals
in the chorion, as discussed below.
Mechanoinduction of impedance variation
11
The equilibrium in electrical charges on the chorion when a voltage is first applied
(as discussed in Section 2) can be observed in Figures 9–10, where the measured
impedance stabilizes after 300 seconds. It is possible that subsequent application of
an external force on the chorion dislodges the pore plugs from the outer layer, thus
providing a passageway for ions to move across the chorion. Such transportation of
ions leads to fluctuation in ion concentration on the external surface of the chorion,
resulting in a net change in the amount of charges and hence the change in impedance
as demonstrated in Figures 9 and 10. The change in impedance depends on the influx
or efflux of the ions since ions diffuse from high to low concentration region; an influx is
indicated by a decrease in impedance, while an efflux by an increase in impedance. The
observed delay (upon application of force) before change in impedance occurred may
be attributed to the double-layer capacity, as is illustrated in Figure 2 and discussed in
Section 2.
The experimental results that we have reported provide evidence that the
application of an external force leads to observable change in the impedance of a zebrafish
embryo. Such evidence offers support for a plausible explanation that the pore canals
behave in some way similar to (non-selective) mechanosensitive ion channels, and are
responsible for the observed change in impedance. Further research beyond these initial
results are needed to develop a better understanding of the mechanism linking the change
in ion concentration on the chorion surface directly to the pore canal activities induced
by an external force. An immediate consequence of understanding this mechanism is
the ability to engineer new techniques to manipulate the activities of ionic movement
across biomembranes by direct control of external forces.
Acknowledgments
The authors acknowledge the financial support from the Singapore Ministry of
Education under research grant R-265000249112, and would like to thank Mr. Yan Tie
and Mr. Subhas Balan from the Department of Biological Science, National University
of Singapore, for preparation of the zebrafish embryos.
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