A simple hardware model for the direct observation of voltage-clamp performance under realistic conditions

The use of control theory for the design of voltage clamp systems: a simple and standardized procedure for evaluating system parameters

Voltage clamp (VC) instruments are closed-loop control systems based on electronic feedback. Such feedback systems can be described in the framework of control theory. We used a mathematical approach based on control theory to improve the performance of VC systems. This approach considerably simplifies the design and optimal tuning of these systems, as is demonstrated for a standard two electrode and a time-sharing single electrode clamp system. The major advantage of this approach and the consequent optimization procedure is that only proportional-integral controllers for VC systems must be used. As a consequence, the design of such VC systems is solely based on the time constants of the clamp circuit. In our approach, the 'symmetrical optimum' rule was applied for the first time to VC systems. This yields optimized systems with respect to speed of response and clamp accuracy. An empirical procedure has been derived from this theoretical approach which allows the optimal tuning of VC instruments based on PI controllers while running an experiment.

Two-compartment model for whole-cell data analysis and transient compensation

Recording and analysis of neuronal patch-clamp data involve many assumptions about membrane properties and cell morphology. Some of these assumptions introduce large errors or oversimplifications into the results. In particular, dendritic branching with high intracellular resistance leads to difficulty with capacitance calculation and transient subtraction, and may significantly distort measured currents. A two-compartment model, presented in detail here, provides a simple method of reducing many of these problems for the relatively simple case of cultured neurons studied with whole-cell patch electrodes. Some passive membrane properties may be accurately calculated, and the results may be used to correct recorded currents for resulting series resistance, intracellular resistance, and capacitive transient errors. The model may be tailored to particular cell types or experimental conditions. Programs to implement the algorithms are available from http://www.its.caltech.edu/ approximately nadeau/Rscomp.html.

A furosemide-sensitive K+-Cl- cotransporter counteracts intracellular Cl- accumulation and depletion in cultured rat midbrain neurons

Efficacy of postsynaptic inhibition through GABAA receptors in the mammalian brain depends on the maintenance of a Cl- gradient for hyperpolarizing Cl- currents. We have taken advantage of the reduced complexity under which Cl- regulation can be investigated in cultured neurons as opposed to neurons in other in vitro preparations of the mammalian brain. Tightseal whole-cell recording of spontaneous GABAA receptor-mediated postsynaptic currents suggested that an outward Cl- transport reduced dendritic [Cl-]i if the somata of cells were loaded with Cl- via the patch pipette. We determined dendritic and somatic reversal potentials of Cl- currents induced by focally applied GABA to calculate [Cl-]i during variation of [K+]o and [Cl-] in the patch pipette. [Cl-]i and [K+]o were tightly coupled by a furosemide-sensitive K+-Cl- cotransport. Thermodynamic considerations excluded the significant contribution of a Na+-K+-Cl- cotransporter to the net Cl- transport. We conclude that under conditions of normal [K+]o the K+-Cl- cotransporter helps to maintain [Cl-]i at low levels, whereas under pathological conditions, under which [K+]o remains elevated because of neuronal hyperactivity, the cotransporter accumulates Cl- in neurons, thereby further enhancing neuronal excitability.

Switched single-electrode voltage-clamp amplifiers allow precise measurement of gap junction conductance

Measurement of gap junction conductance (gj) with patch-clamp amplifiers can, due to series resistance problems, be subject to considerable errors when large currents are measured. Formulas developed to correct for these errors unfortunately depend on exact estimates of series resistance, which are not always easy to obtain. Discontinuous single-electrode voltage-clamp amplifiers (DSEVCs) were shown to overcome series resistance problems in single whole cell recording. With the use of two synchronized DSEVCs, the simulated gj in a model circuit can be measured with a maximum error of <5% in all recording situations investigated (series resistance, 5-47 MOmega; membrane resistance, 20-1,000 MOmega; gj, 1-100 nS). At a very low gj of 100 pS, the error sometimes exceeded 5% (maximum of 15%), but the error was always <5% when membrane resistance was >100 MOmega. The precision of the measurements is independent of series resistance, membrane resistance, and gj. Consequently, it is possible to calculate gj directly from Ohm's law, i.e., without using correction formulas. Our results suggest that DSEVCs should be used to measure gj if large currents must be recorded, i.e., if cells are well coupled or if membrane resistance is low.