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The phenomena that emerge from the interaction of the stochastic opening andclosing of ion channels (channel noise) with the non-linear neural dynamics areessential to our understanding of the operation of the nervous system. Theeffects that channel noise can have on neural dynamics are generally studiedusing numerical simulations of stochastic models. Algorithms based on discreteMarkov Chains (MC) seem to be the most reliable and trustworthy, but evenoptimized algorithms come with a non-negligible computational cost. DiffusionApproximation (DA) methods use Stochastic Differential Equations (SDE) toapproximate the behavior of a number of MCs, considerably speeding upsimulation times. However, model comparisons have suggested that DA methods didnot lead to the same results as in MC modeling in terms of channel noisestatistics and effects on excitability. Recently, it was shown that thedifference arose because MCs were modeled with coupled activation subunits,while the DA was modeled using uncoupled activation subunits. Implementationsof DA with coupled subunits, in the context of a specific kinetic scheme,yielded similar results to MC. However, it remained unclear how to generalizethese implementations to different kinetic schemes, or whether they were fasterthan MC algorithms. Additionally, a steady state approximation was used for thestochastic terms, which, as we show here, can introduce significantinaccuracies. We derived the SDE explicitly for any given ion channel kineticscheme. The resulting generic equations were surprisingly simple andinterpretable - allowing an easy and efficient DA implementation. The algorithmwas tested in a voltage clamp simulation and in two different current clampsimulations, yielding the same results as MC modeling. Also, the simulationefficiency of this DA method demonstrated considerable superiority over MCmethods.

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States