Miscellaneous active electrical nonlinear devices – circuits – and – Signal converting – shaping – or generating – Amplitude control
Reexamination Certificate
2002-08-28
2004-03-02
Le, Dinh T. (Department: 2816)
Miscellaneous active electrical nonlinear devices, circuits, and
Signal converting, shaping, or generating
Amplitude control
C327S307000
Reexamination Certificate
active
06700427
ABSTRACT:
BACKGROUND
1. Field of the Invention
The present invention relates to voltage clamping circuits that attempt to maintain a desired clamping voltage in the presence of an undesired series resistance. In particular, the present invention relates to voltage clamping circuits that measure ionic current in biological preparations that are compromised by series resistance. The present invention teaches an improved method to compensate for this series resistance which results in wide bandwidth, zero steady-state error, and high stability.
2. Description of the Prior Art
The Voltage Clamp With Series Resistance
FIG. 1
shows a voltage clamp often used to measure ionic current in biological preparations. Referring to
FIG. 1
, a low impedance voltage source
5
generates a command voltage Vc. Voltage source
5
is connected to a biological cell
15
through a single cellular microelectrode, patch electrode or pipette elecrode
10
, the fabrication of which is well known in the art. Electrode
10
has an electrode series resistance Rs, an electrode voltage Vp, and an electrode current Ip. Cell
15
has a membrane capacitance Cm, a membrane voltage Vm, and a membrane current Im. Im is related to cell membrane conductance changes—a key quantity to measure in order to understand the electrophysiology of the cell being studied. The generation of membrane current Im by the cell is modeled in
FIG. 1
by a current source
20
.
If Rs is small enough be ignored, voltage source
5
clamps the membrane voltage Vm at Vc and simultaneously shunts Im which would otherwise flow into Cm. In so doing, Im is measured and characterized as a function of Vm.
In practice the large value of Rs (>10 M&OHgr;) often compromises the effectiveness of the voltage clamp shown in FIG.
1
. First, the bandwidth of the voltage clamp and of the current measurement of Im is limited by an access time constant &tgr;
a
=Rs*Cm, resulting in an uncompensated bandwidth fa=1/&tgr;
a
. The uncompensated bandwidth is often too low to resolve rapidly activating ionic currents. More importantly, the presence of such large Rs values allows Vm to deviate from the desired command voltage Vc due to the finite voltage drop across Rs. Since Im is often a steep nonlinear function of Vm, such voltage deviation will significantly corrupt the measurement of Im.
Series Resistance Compensation
FIG. 2A
shows a common approach to compensate for the effects of series resistance know as standard series resistance compensation (see
Electronic Design of the Patch Clamp
by F. J. Sigworth, 1983, found in
Single-Channel Recording
, edited by B. Sakrann an E. Neher, p.29-32.) in which a scaled value of the measured pipette current is used as positive feedback to reduce the effective value of Rs. Referring to
FIG. 2A
, the voltage clamp of
FIG. 1
is shown with the addition of a current measurement means
25
, a scaler
35
, and a summer
30
. Current measurement means
25
measures the electrode current Ip to produce a measured electrode current Ipmeas. Scaler
35
multiplies Ipmeas by a scale factor &agr;*Rs, where scale factor a ranges from 0 to 1, to produce a standard series resistance compensation signal Vcomp. Summer
30
adds the command voltage Vc to Vcomp, thus forming a positive feedback loop.
The effect of standard series resistance compensation is illustrated in
FIG. 2B
which shows the equivalent circuit of
FIG. 2A
when Vc is set to zero. Referring to
FIG. 2B
, Cm is shown shunted by a resistor Reff given by
R
eff
=(1−&agr;)
R
s
. (E1)
When &agr;=0 Reff=Rs, and as &agr;→1, Reff→0. Therefore the effect of standard series resistance compensation is to reduce the effective value of Rs to Reff, resulting in a compensated time constant &tgr;
comp
=Reff*Cm and a compensated bandwidth fcomp=1/&tgr;
comp
for the voltage clamp. The step response of standard series resistance compensation is shown in FIG.
2
C. Referring to
FIG. 2C
, the response of Vm to a step change in Im is revealed to be an exponential rise (time constant=&tgr;
comp
) with an asymptotic error voltage given by Im*Reff (ideally, if Reff were zero the error voltage would be zero as well). Significantly, the error voltage is reduced—not eliminated—by increasing &agr;, accompanied by a simultaneous increase in the compensated bandwidth.
Limitations of Standard Rs Compensation: Stability Constraints at High &agr; Settings
While it would be desirable to filly compensate for Rs by setting &agr;=1, (giving 0 error volage and infinite bandwidth) stability constraints limit the maximum a attainable before undamped oscillations occur. Sigworth shows that this oscillation is related to limited bandwidth of the current measurement circuitry and stray capacitance effects of the electrode. For a well-damped response the current measurement bandwidth needs to be~ten times the volage clamping bandwidth. Consequently, high voltage clamp bandwidth (&agr;>~0.8) implies very wide current measurement bandwidth that is difficult to achieve in practice.
Even when attempts are made to create a very wide bandwidth current measurement, they are of limited utility due to another factor which reduces stability at high Rs compensation settings: stray capacitance effects of electrode
10
. Electrode
10
has stray capacitance (not modeled in
FIGS. 1 and 2
) which draws current at high frequencies. This current de-stabilizes standard series resistance compensation. (See frequency response analysis in the Appendix of Sherman et. al. 1999. Series Resistance Compensation for Whole-Cell-Patch-Clamp Studies Using a Membrane State Estimator,
Biophys. J
. 77:2590-2601.) For stable series resistance compensation, it is common practice to compensate for the electrode stray capacitance electronically. The effectiveness of electronic capacitance compensation is compromised at high frequencies, due in part to wide bandwidth requirements, this time in the capacitance compensation circuitry itself. In addition, capacitance compensation performs well when used on a lumped shunt capacitance whereas the electrode stray capacitance is in fact distributed along the length of its immersion depth, in ways that are unpredictable and difficult to characterize mathematically. The distributed nature of the electrode capacitance becomes more pronounced at higher frequencies, which compromises the performance of electronic capacitance compensation. This in turn de-stabilizes standard series resistance compensation at high a settings.
In practice, due both to the difficulties of achieving very wide bandwidth current measurement and of achieving accurate capacitance compensation at high bandwidths, standard series resistance compensation is limited to ~90% (&agr;=0.9).
Limitations of Standard Rs Compensation: Lowpass Filtering the Feedback Signal
A common method used to increase the stability of standard Rs compensation is to lowpass filter the signal Vcomp. This approach is used by the Axopatch amplifier series produced by Axon Instruments (Foster City, Calif.), where the “lag” control sets a time constant for a lowpass filter that acts on the Rs compensation signal. While such lowpass filtering avoids high-frequency oscillations, it is of limited utility since the filter then reduces the voltage clamp bandwidth. (See the Theory section of this patent for a discussion of how lowpass filtering relates to and differs from the present invention).
Limitations of Standard Rs Compensation: Excitable Cells—Steady-State Error vs. Bandwidth
When working with excitable cells, such as cardiac myocytes responsible for heartbeat generation or nerve cells responsible for nerve signal propagation, a change in Vm of only a few millivolts leads to an extremely large (>100 fold) and rapid (<300 &mgr;s) increase in Im that underlies the generation of the action potential. Thus, when voltage clamping excitable cells it is necessary to maintain the change of Vm in response to a change in Im at less than a few millivolts within a time wi
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