Simulating ion channel noise in an auditory brainstem neuron model (Schmerl & McDonnell 2013)

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" ... Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. ..." Preprint available at
1 . Schmerl BA, McDonnell MD (2013) Channel noise induced stochastic facilitation in an auditory brainstem neuron model Physical Review E 88:052722 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Channel/Receptor;
Brain Region(s)/Organism: Auditory brainstem;
Cell Type(s): Cochlear nucleus bushy GLU cell; CN stellate cell; Ventral cochlear nucleus T stellate (chopper) neuron; Hodgkin-Huxley neuron;
Channel(s): I h; I Sodium; I Potassium;
Gap Junctions:
Gene(s): Kv1.1 KCNA1; Kv3.1 KCNC1;
Simulation Environment: MATLAB;
Model Concept(s): Bursting; Ion Channel Kinetics; Action Potentials; Methods; Noise Sensitivity; Bifurcation; Audition;
Search NeuronDB for information about:  Cochlear nucleus bushy GLU cell; I h; I Sodium; I Potassium;
Readme file:

This is an implementation of the ion-channel noise method of Fox and Lu, as described 
by Goldwyn and Shea-Brown, applied to the Hodgkin-Huxley model and to the 
Rothman-Manis model of VCN neurons, as examples.

Reference: Brett A. Schmerl and Mark D. McDonnell, "Channel noise induced stochastic 
facilitation in an auditory brainstem neuron model", Physical Review E 88:052722, 2013
( Preprint available at http:/

The following files have been uploaded to ModelDB:

SchmerlMcDonnell_Driver.m -- this script can be modified by the user to control the 
inputs and simulation conditions, and select from amongst the four example neuron models 
implemented, i,e. Hodgkin-Huxley, Rothman-Manis Type I-II, Rothman-Manis Type I-C,
Rothman-Manis Type II.

EulerMaruyama.m -- function that controls the updating of all variables for the next time step

UpdateEquations.m -- function that calculates the RHS of differential equations

UpdateDiffusionMatrixSquareRoot.m -- function that calculates the matrix square root
needed to obtain the diffusion matrix

UpdateDriftAndOccupancies.m -- function that updates the transition matrix and

Params_HodgkinHuxley.m -- parameters for the Hodgkin-Huxley model

Params_RothmanManisTypeII.m  -- parameters for the Rothman-Manis Type II model

Params_RothmanManisTypeI_C.m  -- parameters for the Rothman-Manis Type I-C model

Params_RothmanManisTypeI_II.m  -- parameters for the Rothman-Manis Type I-II model


Running SchmerlMcDonnell_Driver.m from the command line will, by default, solve the
deterministic version of the Hodgkin-Huxley model with an input current of 7.2 microAmps,
for 10000 channels, over a simulation duration of 400 ms, with initial conditions given in 
Params_HodgkinHuxley.m. The solution for the membrane potential will be plotted against
time. The user can edit SchmerlMcDonnell_Driver.m to change the model, to use the SSE
stochastic model, and to change the input current, simulation duration, and number of

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