The voltage clamp technique pioneered by Hodgkin is used to estimate the current flowing through a membrane. The voltage across a membrane can be easily measured simply by placing electrodes on either side of the membrane and measuring the potential difference between them. Voltage measurement can be done non-intrusively - i.e., without disrupting the electrical path. In contrast, current measurement requires the ammeter to be interposed in the current path so as to have the circuit current flowing through it. Therefore, measuring current under different conditions of membrane transport is a little more complicated.
Membrane current reflects the flow of ions across the membrane, and is of fundamental importance for understanding the mechanism of membrane transport. In order to understand how a method was devised to measure membrane current consider the following schematic of the membrane (Figure 1):
Figure 1
Figure 1 shows a membrane separating two chambers (A &B) containing solutions. The solutions contain ions which move through the membrane by different mechanisms. For simplicity, we assume that only one ion species is involved. The ions are driven by a “virtual potential difference” which is the Nernst potential. In a state of equilibrium, the algebraic sum of all the currents is zero and no net current flows outside. To study the transport of the ions across the membrane we would like to measure these currents.
The driving potential is usually due to concentration difference of the ions in the two partitions. The concentration difference may be set up by a combination of several mechanisms, which includes the presence of other ions, active transport, etc.
Electrical Measurements
It is helpful to represent the above schematic in terms of an electrical equivalent which will lead to a method of measuring the electrical currents. As mentioned above the active transport may be regarded as a virtual driving potential (Nernst potential). The actual quantity of ions transported (through the ion specific channels) depends on the number of available channels or in electrical terms the conductance of the mechanism responsible for the active transport. Similarly, the non-specific passive transfer current depends on the passive impedance of the membrane which is mainly capacitive as the lipid membranes act as insulators. Figure 2 shows the electrical equivalent with these elements.
The following notation has been used:
Cm = membrane capacitance
gK = ion specific conductance
EK = apparent driving potential for the transport, Nernst potential
IL = leak current
IK = ion channel current
Figure 2
Using basic electric circuit theory, we can write:
At rest, the capacitance current, IC, is zero. Therefore, IK=IC=0, and the steady state voltage, VAB , measured externally, will equal EK.
If an external ammeter is connected across the membrane then the current IK will flow through the ammeter as shown in Figure 3. If the internal resistance of the ammeter is zero, then the potential difference across the membrane will be rendered zero. There is an effective short-circuit between AB, and VAB = 0. In steady state conditions when there is no change of voltage or current, IC=0, and Im=IK.
Therefore,
This measured current is called the short-circuiting current.
Figure 3
Active current measurement
Figure 4
The Voltage Clamp Arrangement
The above simple system shown in Figure 4 can be improved by using electronic circuitry to automatically adjust the current Im such that the measured voltage VAB becomes zero or any other desired value. A schematic of such a system is illustrated below in Figure 5. The electrical equivalent of the membrane is replaced by the more commonly used representation of a cell or chamber which forms partition A, and surrounded by a bathing solution which forms partition B. The two partitions are electrically accessed by electrodes. The transmembrane voltage referred to as VAB so far, is also called Vm.
Figure 5
Figure 6
Figure 6 shows the same automatic system drawn in terms of actually electronic system blocks. Since the system operates by clamping the membrane voltage to any given value determined by the experimenter, it is called a voltage clamp arrangement. The command voltage or desired membrane voltage is called the clamp voltage because the circuit automatically delivers sufficient current to maintain the transmembrane voltage at that value.
For any given clamp voltage, the following circuit equation can be written:
Vclamp=Vm=EK+IK/gK
The conductance of the membrane to the ion in question can now be calculated as:
In the voltage clamp circuit, Vm and Im are measured. In the single ion case, EK can be measured (Vm measured under open circuit conditions), and IK=Im. Therefore, the conductance can be directly computed.
In the multi-ion case, say when two ions, sodium and potassium are present, assuming independent channels for the two ions, the operational equations are:
Vm = EK + IK/gK = Ena + Ina/ gNa
Im = IK + INa
The separation of the two currents has to be done by suitable design of the experiments.
Speed of response
It is often of interest to study the time course of membrane current changes following changes in voltage or the application of a drug, etc. The above discussion has been mainly with regard to the steady state condition, that is, when the changes have stabilised. Immediately following a change in transmembrane voltage, a current is required to charge the capacitor (Figure 4) to the new voltage. The feedback system gain has be sufficiently high to ensure that the capacitor current can be supplied quickly. If not, the response will be sluggish. The three principal blocks in this system are the voltage amplifier, the voltage comparator, and the voltage-to-current converter. In combination with the membrane they form a negative feedback closed loop system. The gain, K1K2, determines how quickly the system responds to changes in the given command voltage. The smaller the overall gain, the more slowly the system will respond, as well as larger will be the discrepancy between the command voltage and the actual membrane voltage.
Recording
Since both Im and Vm can be measured easily using the voltage clamp circuit, the values are usually digitised and stored in a computer for further analysis. The dynamic response of the system should be designed to be very fast so that changes on the order of milliseconds or less can be easily observed.The following figure shows the block schematic of the voltage clamp experiment. The boxes, H, P and K are electronic circuits, and the box Gm represents the membrane under study. The membrane voltage, Vm is recorded, and a current Is is injected into the membrane. The desired membrane voltage is given as the command voltage Vclamp.
The following figure is another representation of the experimental arrangement with the three electronic circuits shown as boxes. The membrane is shown as a sheet separating the bathing solutions into two chambers. For simplicity, separate electrodes are used for the voltage measurement and current injection.
Notes:
Im = VI /5000
Note on V-to-I converter:
Suresh Devasahayam
July 2004
© Suresh Devasahayam, Department of Bioengineering, Christian Medical College, Vellore