2.3 Measuring issues

2.3.4 Voltage/current clamping/patching

The very common measuring method reveals some fundamental differences between the electric behavior of conductors and living matter. ”The reason for voltage-clamping the axon is threefold: (1) By keeping the voltage constant, one can eliminate the capacitive current, that is, IC=C⁢d⁢Vd⁢t=0; (2) by keeping the voltage constant, one can measure the time-dependent characteristics of ion conductances without the influence of voltage-dependent parameters; and (3) by inserting two silver wire electrodes into the axon, one can space-clamp it so that the whole length of the axon is isopotential (silver wires short-circuit the interior of the axon).” [2] That is: (1) the experimenter wants to make sure that d⁢Vd⁢t does not change. A late consequence of choosing a wrong R⁢C oscillator model. In the wrong model, the integrator, integrating the currents can be done and the voltage gradient has no role. In the correct model, the diffferentiator, the gradient controls neuron’s operation. (2) Clamping introduces extra current (not measured) to the neuronal circuit. From the known relations in Ohm’s law, we use the fixed voltage and the sum of the ’real’ current plus the ’foreign’ current, and attribute the observed deviation to that the conductance changed. Actually, the measurement device is not appropriate for that purpose. (3) As we discussed, the ion current is flowing on the thin layer on the internal surface of the axon. There are no charge carriers to deliver the potential from those electrodes to the stream of ions (the ions are pressed to the wall of the axon and the dielectric layer repulses the carriers). This effect is why Hodgkin and Huxley experienced [9] a time delay between a voltage and the current: the axon is not equipotential because it is not a conventional conductor. Again, physiology is resetting the clock: (1) they want to believe that voltage gradients have no role and so they eliminate it (2) the do not want to understand that voltage and current are not independent from the charge and the measuring device changes the measured value (3) they do not want to accept that the charge carrier and the charge transmission mechanism, and because of that, the behavior of the biological systems, are different from those in classical electronics. The low speed of ions hinderts the fundamental understanding, mainly of the temporal operation.

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Figure 2.4: (Fig. 6.1 in [2]) ”Schematic diagram of the two-wire voltage-clamp experiments on the squid axon. One wire is used for monitoring the membrane potential and the other for passing current. The voltage clamp amplifier injects or withdraws charges from the interior of the squid axon in order to hold the membrane voltage constant (voltage is clamped at the command voltage, VC).”
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Figure 2.5: ”The negative feedback mechanism of the voltage clamp. Membrane potential (Vm) is measured by one amplifier connected to an intracellular electrode and an extracellular electrode in the bath. The membrane potential signal is displayed on an oscilloscope and is also fed into the negative terminal of the voltage-clamp feedback amplifier. The command potential, which is selected by the experimenter and can be of any desired amplitude and waveform, is fed into the positive terminal of the feedback amplifier. The feedback amplifier then subtracts the membrane potential from the command potential and amplifies any difference between these two signals. The voltage output of the amplifier is connected to the internal current electrode, a thin wire that runs the length of the axon core. The negative feedback ensures that the voltage output of the amplifier drives a current across the resistance of the current electrode that alters the membrane voltage to minimize any difference between Vm and the command potential. To accurately measure the current-voltage relationship of the cell membrane, the membrane potential must be uniform along the entire surface of the axon. This is made possible by the highly conductive internal current electrode, which short-circuits the axoplasmic resistance, reducing axial resistance to zero. This low-resistance pathway eliminates all variations in electrical potential along the axon core.” (Fig. 7.2 of [41])
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Figure 2.6: Simulating a voltage clamped neuron by the program GENESYS [113], Fig. 4.7. The figure clearly shows that the source of the ”K conductance” and ”K current” is the ”injection current”. The rising edge of the current triggers an action potential (note the very sharp gradient at t=2) and then (as the negative feedback is defined) the injecting current is converted to ”K current” (as mis-identified: a real current, but from an external force) compensates for the biological current (aka the current that produces on the AIS an AP). If one assumes that the voltage in the system is constant, one can calculate conductance a IU. However, I=Ib⁢i⁢o⁢l⁢o⁢g⁢i⁢c⁢a⁢l+Ie⁢x⁢t⁢e⁢r⁢n⁢a. By beliving the fallacy that I=Ib⁢i⁢o⁢l⁢o⁢g⁢i⁢c⁢a⁢l, one (mis)identifies the introduced external current as a change in the neuron’s conduction. Simply, a measurement design error. ”The construction is different” in biology.

Notice two of the common fallacies in the figure. ”The highly conductive internal current electrode, which short-circuits the axoplasmic resistance, reducing axial resistance to zero”. First, the current flows in the <1⁢n⁢m thick layer on the internal surface of the membrane instead of inside the axon. The electrode keeps only the potential of the ”bulk” constant, unless the internal electrode fits perfectly (with better than the mentioned size accuracy) into the tube. Furthermore, the membrane’s surface can open/close ion channels in its wall, adding foreign current that causes a change in the value of the command potential. Second, there are two feedback amplifiers of the figure: the natural one (see Fig. 1.8) and the feedback in the clamp instrument. As we discussed, only the steady-state measurements can be accurate. The control voltage that is ”selected by the experimenter and can be of any desired amplitude and waveform”, is misleading: when using non-constant waveform, the system is not in steady state.

See Figure 1.8: ”Any conductor that has a linear current-voltage (I-V) curve is said to be ohmic. Not all conductors have linear I-V curves. Most neurons, for example, have nonlinear or nonohmic I-V relations.” The neuron is not a simple conductor. ”Only a narrow region of the V-I or I-V curves of a neuron can usually be considered ohmic.” [2], page 488. When studying its behavior using ’foreign’ voltage or current, outside that narrow region. The measuring procedure may trigger neuron’s own electric processes, and the careless experimenter observes that – from his point of view – ’foreign’ contribution as a deviation from the ohmic relations. See examples in section 3.2. ”The construction is different from anything we have yet tested in the physical laboratory” [12]; we need to use different methods for that different construction.