Dynamic Clamp Conductance Injection Software Based on the QNX Real Time Operating System with Error Control and an Implicit Integration Method

Abstract

Dynamic clamp or conductance injection is an electrophysiological method that uses a real-time interface between living cells and a computer to simulate conductance changes in the membrane. To date, the numerical integration methods used for this purpose have been explicit. These methods have an upper bound for the length of the step size when the method becomes numerically unstable. This becomes a practical problem particularly when injecting fast voltage-dependent conductances. Here, we improve the numerical integration of the equations underlying such conductances by implementing an implicit method (Iserles & Norsett, IMA J. Num. Anal. 10:463, 1990), suited for stiff equations. Specifically, this is an A- and L-stable diagonal implicit Runge-Kutta method, which can exploit information about the membrane potential sampled at subintervals of the current update period, which we demonstrate can greatly improve the accuracy and stability of the injected conductance. Furthermore, the integration method let us implement real-time error monitoring.We have built our implementation of this on the QNX microkernel real-time operating system, widely used for high-speed mission-critical real-time applications in industry. Its flexibility and reliability in timing, interrupt control and processor scheduling in multiprocessor systems, and its microkernel architecture (which frees up more CPU time than other comparable systems for running the model), make it an ideal platform for more complex integration methods such as the one we describe. The here offered prospect of an improved accuracy and stability of the conductance injection technique, opens up for analyzing membranes with faster channels than was previously possible.