Series Resistance in Voltage Clamp

Work through the three demonstrations

Choose the numbered demonstrations from the popup menu or use the arrow buttons. Compare all places the voltage step, synaptic current, and I–V relations beside the main conclusions. The recording electrode and membrane-property controls apply throughout.

The shared voltage-clamp model

The amplifier controls the membrane through series resistance R_s. With outward-positive current, actual membrane voltage is V_m = V_command − IR_s. The effective clamp speed also depends on C_m. The compensation control is an intentionally idealized reduction of effective R_s; real amplifier compensation can introduce ringing or instability, which is outside this simulation.

1. Voltage step: settling and capacitive current

Compare V_command with actual V_m. A finite R_s prevents an instantaneous voltage change, producing a capacitive current that decays as the membrane approaches its steady voltage. Increase R_s or C_m to slow the clamp. The dashed current is the ideal steady membrane current and deliberately excludes an instantaneous ideal capacitive impulse.

2. Synaptic current: when does R_s matter?

The event is a normalized double-exponential conductance with reversal potential E_syn, peak g_syn, τ_rise, and τ_decay. The displayed current is baseline-subtracted. Try an excitatory miniature at V_hold = −70 mV and E_syn = 0 mV, then an inhibitory miniature at V_hold = 0 mV and E_syn = −70 mV. Error depends on the resulting current, not simply on whether the recording is in voltage clamp.

3. I–V relations: separate holding and synaptic currents

The upper panel shows the steady holding current needed to maintain each command voltage. Its ideal I–V relation crosses zero at V_rest. Finite R_s reduces the actual voltage excursion and makes the measured relation pivot around V_rest. Purple points use nominal V_command; teal points use the actual baseline voltage V_baseline = V_command − I_holdR_s,eff.

The lower panel shows the synaptic current after subtracting the holding current. The AMPAR (linear) model represents an ohmic AMPA-receptor conductance: its ideal synaptic I–V relation is a straight line crossing zero at E_syn. During the response, additional current through R_s moves V_m away from both V_command and its baseline value. The corrected voltage coordinate therefore uses the total current during the response: V_response = V_command − I_{total,response}R_s,eff.

The CP-AMPAR (inwardly rectifying) option represents calcium-permeable, commonly GluA2-lacking AMPA receptors. Intracellular polyamines increasingly block these receptors at positive potentials, suppressing outward current and producing inward rectification. The simulation uses a qualitative voltage-dependent rectification factor to demonstrate how R_s error can displace or obscure that shape; it is not a quantitative kinetic fit to Lalanne et al. Mode 3 treats g_syn as a steady open conductance at the sampled point. C_m and synaptic kinetics determine how quickly that state is approached but do not change these steady I–V relations.

Suggested exercises

1. Calculate the initial current and steady voltage error for a voltage step using Ohm's law. Compare your result with the displayed values.
2. Set R_s to 5, 25, 50, and 100 MΩ. Determine when a 1-nS synaptic event first exceeds a 1-mV clamp error.
3. Keep g_syn fixed while changing V_hold and E_syn. Explain the error from driving force and current amplitude.
4. At +30 mV, calculate I_holdR_s and predict the baseline membrane voltage before reading the I–V summary.
5. Explain why the holding-current relation pivots around V_rest, whereas the linear synaptic relation reverses at E_syn.
6. Compare the AMPAR and CP-AMPAR models. Why can plotting current against nominal command voltage misrepresent CP-AMPAR rectification?

Scope and references

This is a single-compartment teaching model. It omits spatial voltage escape, imperfect R_s estimates, noise, amplifier saturation, and instability from aggressive compensation. Series-resistance correction follows the Ohm's-law treatment described by Traynelis (1998) and the classical analysis of Moore, Hines & Harris (1984). Direct measurements of somatic voltage-clamp error are discussed by Williams & Mitchell (2008) and Gray & Santin (2023). The positive-voltage I–V correction is motivated by Lalanne et al. (2016).