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Fidelity of voltage clamps of Purkinje cells

Constructing a realistic model of a neuron relies on the availability of high quality data, especially from voltage-clamp experiments. However, once constructed, the model itself can be used to explore the likely value of the voltage-clamp experiments themselves. For example, using voltage-clamp techniques, Regehr [10] have recently proposed that Na+ channels are present in the (distal) dendrite as well as the soma of the Purkinje cell. They based this claim on the fact that they could measure fast inward currents with whole-cell patch clamps of axotomized Purkinje cells under conditions of good voltage control in the soma. However, it has been suggested that in these experiments the soma itself may not have been adequately clamped [12].

Using the model, we have found that the presence of active dendritic membrane had a dramatic effect on the electrotonic length of the Purkinje cell and thus the ability to achieve an adequate space clamp [7]. Passive membrane models predict that Purkinje cells are electrotonically compact, with a length of ≈ 0.3 X [11]. Rapp et al. [8] have pointed out that the large synaptic input the Purkinje cell receives could increase this length by a factor of 2.4. Our model shows that during a dendritic spike the electrotonic distance to the top of the dendrite increased by a factor of 3 compared with a passive membrane dendrite. Between spikes the length was also increased, but less. Thus the state of activation of the dendritic channels also made a significant difference in the electrotonic length of the dendrite. Similarly, activation of dendritic channels also caused a very bad space clamp, especially in the depolarizing direction. We have assumed that the application of Cs⁺ externally and EGTA internally blocked most K⁺ currents completely [1]. If this was not the case, K⁺ currents would contribute only a small conductance compared with the CaP conductance and similar results would be obtained.

Our results suggest that space clamp is extremely bad in adult Purkinje cells, with a significant divergence from the holding potential at only 50 μm from the soma for depolarizing potentials. Therefore it is possible that the Na⁺ currents recorded by Regehr et al. [10] are carried by Na⁺ channels located in the very proximal parts of the main dendrite. In our present model, we have confined Na⁺ channels to the soma, because several other studies, including TTX binding [6], dendritic patch recordings (ibid.), and imaging with a fluorescent Na⁺ indicator [4] demonstrated Na⁺ channels only on the soma and axon of the Purkinje cell.

Using the model, we can predict that space clamps could be somewhat improved if Ca²⁺ channels were also blocked, but this was not the case in most reported whole-cell patchclamp studies [3, 5, 9, 10]. Note that if the CaP channel does not inactivate, as has been reported by [13], one cannot remove the Ca²⁺ conductance by steady depolarization as has been claimed in some studies [5]. In dissociated Purkinje cells, where large parts of the dendritic tree may be amputated, space clamp can also assumed to be better. Thus the “whole-cell” patch-clamp method may be appropriate to measure ionic currents in soma and proximal dendrite in dissociated, cultured Purkinje cells. Equations for several channels used in our model were based on this approach [2, 3, 9].

Finally, our ultimate objective in constructing this model was to explore synaptic influences on Purkinje cell firing patterns.

EFFECT ON VOLTAGE-CLAMP EXPERIMENTS

Ultimately, the significance of active membrane properties on the electrotonic length of a Purkinje cell is related to its integration of synaptic input. That is the subject of the accompanying paper. However, the electrotonic structure of the Purkinje cell is also relevant to the feasibility and interpretation of voltage-clamp experiments. Recently several groups have reported results of whole-cell patch clamps of Purkinje cells [2, 3, 5, 9, 10]. An important question in interpreting the data from such studies is whether an adequate space clamp was achieved [7].

To test the general difficulty of having a good space clamp of a cell the size and complexity of the Purkinje cell we simulated a voltage clamp in our basic model. The results shown in Fig. 13 clearly indicate that it is very difficult and likely impossible to establish a good space clamp of an adult Purkinje cell.

To model voltage clamps under conditions similar to the ones used by experimentalists [5] we simulated external Cs²⁺ block of Kdr, KM, and Kh channels [1] and inactivation of all Ca²⁺-activated K⁺ channels because of the presence of ethylene glycolbis(β -aminoethyl ether)-N,N,N,N-tetraacetic acid (EGTA) in the internal solution. The model was clamped at four voltages [-100 mV, -68 mV (resting potential), -40 mV, and +40 mV] and allowed to stabilize to a steady state, which took about one simulated second. The space clamp was always bad, because the cell was never isopotential (even at -68 mV the distal spiny dendrite had a potential of -67.47 mV). The clamp was, however, especially bad in the depolarized direction. Any step above -50 mV resulted in activation of the Ca²⁺ channels in the model, causing a clear spike in the dendrites Fig. 13A and B). In the steady state, the distal dendrite had potentials that diverged up to ±40 mV from the holding potential in the soma, because the CaP channel did not inactivate completely. The model did not achieve a steady state for voltage steps between -50 and -25 mV because the membrane potential oscillated in the whole dendritic tree.

Figure 13C shows the membrane potential at increasing distances from the soma for different control voltages. It demonstrates that even the proximal dendrite was not clamped well. During depolarizing voltage-clamp steps the membrane potential differed from the holding potential by ≥10 mV at a distance of only 25 μm from the soma.

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