This model provides a natural 14-dimensional Langevin dynamics for the Hodgkin Huxley system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 dimensional state space (1 dimension for voltage, 5 for potassium and 8 for sodium) and 14 × 28 noise coefficient matrix S. In [Pu and Thomas (2020) Neural Computation] we show that this 14 x 28 dimensional model is pathwise equivalent to the 14 x 11 dimensional Langevin model proposed in [Fox and Lu (1994) Phys Rev E], as well as an 14 x 14 model described in [Orio and Soudry (2012) PLoS One]. Unlike Fox and Lu's model, our construction does not require a matrix root extraction step, and runs significantly faster. Unlike Orio and Soudry's model, each directed edge acts as an independent noise source, which facilitates the application of stochastic shielding methods for even greater simulation speed. For comparison, we provide implementations of the following models: 1. Discrete-state Markov chain model (slow, but provides the "gold standard" model), adapted from [Goldwyn and Shea-Brown (2011) PLoS Comp. Biol.] 2. 14 x 11 Langevin model from [Fox and Lu (1994) Phys. Rev. E]. (We implement versions with three different boundary conditions: open boundaries, reflecting boundaries, and resampling/rejection at the boundaries.) 3. 4 x 3 Langevin model from [Fox (1997) Biophys. J.] 4. 14 x 13 Langevin model from [Goldwyn and Shea (2011) PLoS Comp. Biol.] 5. 14 x 14 Langevin model from [Dangerfield et al (2012) Phys. Rev. E] 6. 14 x 14 Langevin model from [Orio and Soudry (2012) PLoS One] 7. 14 x 28 Langevin model from [Pu and Thomas (2020) Neural Computation] implemented both with and without stochastic shielding 8. 14 x 0 deterministic HH model (also from [Pu and Thomas (2020) Neural Computation], with the full 14 dimensional state space but no noise) The Read_me.md file provides more detailed simulations. To cite the code: Pu, Shusen, and Peter J. Thomas. "Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics." Neural Computation 32, 1775–1835 (2020)
Model Type: Neuron or other electrically excitable cell
Region(s) or Organism(s): Generic
Cell Type(s): Hodgkin-Huxley neuron
Currents: I K; I Na, leak
Model Concept(s): Stochastic simulation
Simulation Environment: MATLAB
References:
Pu S, Thomas PJ. (2020). Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics Neural Computation. 32