Series Resistance in Current Clamp

Work through the three demonstrations

Choose the three numbered demonstrations from the popup menu in order. Each view enlarges one graph and shows its relevant controls and summary measurements. Compare all places the passive step, action potential, and EPSP in a compact 2 × 2 layout beside the main teaching conclusions.

In every graph, black is the membrane voltage before electrode distortion, blue is the voltage recorded through the electrode, and the dashed brown trace is the bridge-balanced result when applicable. The lower panel shows the stimulus current. Positive current injected through the electrode is plotted upward; inward excitatory synaptic current is negative and plotted downward.

The shared membrane and electrode models

The same membrane controls apply to all three demonstrations. R_m is the passive leak resistance, C_m is the total membrane capacitance, and V_rest sets the initial equilibrium. In the Hodgkin–Huxley model, the leak reversal potential is recalculated so that the selected V_rest remains stable without an unreported holding current. Because voltage-gated Na⁺ and K⁺ channels also contribute near rest, the HH cell's measured small-signal input resistance need not equal the displayed passive R_m exactly.

The same electrode is also used in all three demonstrations. Series resistance R_s and residual pipette capacitance C_p give an electrode time constant τ_electrode = R_sC_p. During electrode current injection, the measured voltage approaches V_m + I_injR_s. Bridge balance subtracts the selected fraction of this resistive voltage error. C_p neutralization reduces the effective pipette capacitance and therefore shortens τ_electrode.

Reading about bridge balance

Rossant et al. (2012) describe conventional bridge balance in the Abstract and Introduction and illustrate its onset and offset artifacts in Figure 1. Bridge balance subtracts the estimated steady resistive drop, I_injR_s; it does not reverse electrode low-pass filtering. Because a real electrode responds with a finite time constant, instantaneous bridge subtraction can itself create brief transients when current begins or ends. At current onset, for example, the bridge immediately subtracts I_injR_s before the actual electrode voltage has fully developed, producing the downward transient seen here.

1. Passive step: two exponential components

A current step of the selected amplitude and duration drives an isopotential passive membrane with τ_m = R_mC_m. The recording contains the slower membrane response plus the faster electrode component governed by R_sC_p. Compare the raw voltage offset with the bridge-balanced error, and calculate I_injR_s from the displayed settings.

2. Action potential: voltage displacement and filtering

A current step elicits a Hodgkin–Huxley action potential during a 30-ms simulation. The selected R_m, C_m, and V_rest now determine the spike model's passive leak, capacitance, and resting equilibrium as well as the other two protocols. R_s produces an I_injR_s displacement that makes the apparent spike threshold more positive. The finite electrode bandwidth also reduces maximum dV/dt and alters spike peak and half-width. Bridge balance can correct the resistive displacement, but it cannot reconstruct rapid waveform components already lost to low-pass filtering.

3. EPSP: the slow-event comparison

The EPSP is generated by a normalized double-exponential, AMPA-like conductance. Rise τ and decay τ control its kinetics independently; they are exponential time constants rather than a direct 10–90% rise-time measurement. The synaptic current crosses the membrane rather than being injected through the recording electrode, so there is no I_injR_s displacement. When the EPSP changes slowly relative to τ_electrode, its peak and timing are therefore recorded with very little error.

Suggested exercises

1. Set R_s to 5, 10, 25, 50, and 100 MΩ. In Compare all, contrast the passive voltage offset, spike errors, and EPSP peak error.
2. Calculate I_injR_s for both current-step protocols and compare your answers with the displayed voltage displacements.
3. Calculate τ_m and τ_electrode. Use their relative sizes to predict which signals should be distorted most.
4. Vary R_m, C_m, and V_rest. Compare their effects on the passive response, EPSP, and spike threshold or latency.
5. Set bridge balance to 100%, then vary C_p. Which spike errors remain even when the resistive displacement is corrected?
6. Increase C_p neutralization and determine when the spike becomes acceptably accurate.
7. Shorten the EPSP rise and decay constants. At what kinetics does electrode filtering become appreciable?

Scope and references

The passive response and EPSP use a single isopotential membrane. The spike uses the classic Hodgkin–Huxley equations with fixed maximum Na⁺ and K⁺ conductances, while the shared controls set its passive leak resistance, total capacitance, and resting equilibrium. The electrode is represented by one resistance and one residual capacitance; real electrodes can have several time constants and additional nonlinearities. The teaching comparison follows the supplied series-resistance simulation. Bridge balance and capacitive electrode errors are discussed by Rossant et al. (2012), A calibration-free electrode compensation method. The action-potential model follows Hodgkin & Huxley (1952).