Membrane Capacitance Measurements Revisited: Dependence of Capacitance Value on Measurement Method in Nonisopotential Neurons

Abstract

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Contamination of current-clamp measurement of neuron capacitance by voltage-dependent phenomena

“…In the past, achieving this goal has been attempted by performing current steps from relatively negative membrane potentials (typically Ϫ50 mV), on the assumption that most depolarization-activated conductances will be inactive in this membrane potential range, and by blocking the hyperpolarization-activated current I h with cesium (see, e.g., Golowasch et al 2009). However, to our knowledge whether neuron responses under these conditions are nonetheless contaminated by voltage-dependent phenomena has not been tested.…”

“…These potentials included the Ϫ50 to Ϫ60 mV range used in previous work measuring PY neuron capacitance (Golowasch et al 2009). The amplitude of the voltage responses of the neurons to identical current steps changed considerably as V ssc was varied from Ϫ95 mV to Ϫ50 mV ( Fig.…”

“…Inset: 3 cycles of the neuron's response during the pulse train at Ϫ50 mV. Pulse train response amplitude was greater at Ϫ95 mV than at Ϫ50 mV [the membrane potential at which capacitance measurements are typically made (Golowasch et al 2009)], indicating that input resistance (R N ) was greater at Ϫ95 mV. from t ϭ 0 to 990 ms were fit (see Fig.…”

“…Multiple electrical techniques for neuron capacitance measurement have been described. Capacitance can be measured in voltage clamp by integrating or fitting the currents that occur with step or ramp changes in voltage (Golowasch et al 2009;Haedo and Golowasch 2006;Iwasaki et al 2008;Khorkova and Golowasch 2007;Pineda et al 2008;Royeck et al 2008) or in current clamp by fitting the voltage responses to step changes in current (Arsenault et al 2011;Firestein and Werblin 1987;Liao and Lee 2011;Major et al 1993;Roth and Häusser 2001;Szabo et al 2010). Current-clamp techniques are most accurate for neurons with extended morphologies or nonuniform conductance distributions (nonisopotential neurons) (Golowasch et al 2009), the case for essentially all neurons.…”

“…In nonisopotential neurons with only passive (non-voltagedependent) electrical properties, and in which the dendritic compartment dominates neuron response (see Fig. 3 of Golowasch et al 2009), the slowest of these terms can be used to estimate neuron capacitance and resistance. The faster terms arise from current flow through the neuron's branches (Major et al 1993) and can be used to estimate neuron electrotonic length (Rall 1977).…”