Chandler D. (1987). Introduction to modern statistical mechanics..

Conti F, Wanke E. (1975). Channel noise in nerve membranes and lipid bilayers. Quarterly reviews of biophysics. 8 [PubMed]

De Felice LJ, Goolsby WN. (1996). Order from randomness : spontaneous firing from stochastic properties of ion channels. Fluctuations and Order: The New Synthesis..

Fox RF, Lu Yn. (1994). Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 49 [PubMed]

Gillespie DT. (1977). Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry. 81

HODGKIN AL, HUXLEY AF. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology. 117 [PubMed]

• Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
• Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
• Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
• Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]
• Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]

Hille B. (1992). Potassium channels and chloride channels Ionic Channels of Excitable Membrane.

Hines M. (1989). A program for simulation of nerve equations with branching geometries. International journal of bio-medical computing. 24 [PubMed]

Ito H, Ono K, Noma A. (1994). Background conductance attributable to spontaneous opening of muscarinic K+ channels in rabbit sino-atrial node cells. The Journal of physiology. 476 [PubMed]

Kramers HA. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Physica. 7

Lecar H, Nossal R. (1971). Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing. Biophysical journal. 11 [PubMed]

Lecar H, Nossal R. (1971). Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. Biophysical journal. 11 [PubMed]

Press WH, Teukolsky SA, Flannery BP, Vellerling WT. (1992). Numerical Recipes In C: The Art Of Scientific Computing.

Risken H. (1989). The Fokker-Planck Equation (2nd ed).

Rubinstein JT. (1995). Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophysical journal. 68 [PubMed]

Sigworth FJ. (1980). The variance of sodium current fluctuations at the node of Ranvier. The Journal of physiology. 307 [PubMed]

Skaugen E, Walløe L. (1979). Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta physiologica Scandinavica. 107 [PubMed]

Strassberg AF, Defelice LJ. (1993). Limitations of the Hodgkin-Huxley formalism: eects of single channel kinetics on transmembrane voltage dynamics Neural Comput. 5

Tuckwell HC. (1989). Stochastic Processes In The Neurosciences.

Anwar H, Hepburn I, Nedelescu H, Chen W, De Schutter E. (2013). Stochastic calcium mechanisms cause dendritic calcium spike variability. The Journal of neuroscience : the official journal of the Society for Neuroscience. 33 [PubMed]

• Stochastic calcium mechanisms cause dendritic calcium spike variability (Anwar et al. 2013) [Model]

Bruce IC. (2007). Implementation issues in approximate methods for stochastic Hodgkin-Huxley models. Annals of biomedical engineering. 35 [PubMed]

• Implementation issues in approximate methods for stochastic Hodgkin-Huxley models (Bruce 2007) [Model]

Butson CR, Clark GA. (2008). Random noise paradoxically improves light-intensity encoding in Hermissenda photoreceptor network. Journal of neurophysiology. 99 [PubMed]

Cannon RC, O'Donnell C, Nolan MF. (2010). Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes. PLoS computational biology. 6 [PubMed]

• Stochastic ion channels and neuronal morphology (Cannon et al. 2010) [Model]

Carnevale NT, Hines M. (2003). Personal Communication of NEURON bibliography .

Carnevale NT, Morse TM. (1996). Research reports that have used NEURON Web published citations at the NEURON website.

Channell P, Fuwape I, Neiman AB, Shilnikov AL. (2009). Variability of bursting patterns in a neuron model in the presence of noise. Journal of computational neuroscience. 27 [PubMed]

• Reduced leech heart interneuron (Channell et al. 2009) [Model]

Dangerfield CE, Kay D, Burrage K. (2012). Modeling ion channel dynamics through reflected stochastic differential equations Physical review. E, Statistical, nonlinear, and soft matter physics. 85 [PubMed]

• Reflected SDE Hodgkin-Huxley Model (Dangerfield et al. 2012) [Model]

De Schutter E. (1999). Using realistic models to study synaptic integration in cerebellar Purkinje cells. Reviews in the neurosciences. 10 [PubMed]

Diba K, Koch C, Segev I. (2006). Spike propagation in dendrites with stochastic ion channels. Journal of computational neuroscience. 20 [PubMed]

• Spike propagation in dendrites with stochastic ion channels (Diba et al. 2006) [Model]

Dudman JT, Nolan MF. (2009). Stochastically gating ion channels enable patterned spike firing through activity-dependent modulation of spike probability. PLoS computational biology. 5 [PubMed]

Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35

• Mathematical Foundations of Neuroscience (Ermentrout and Terman 2010) [Model]

Goldwyn JH, Imennov NS, Famulare M, Shea-Brown E. (2011). Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons. Physical review. E, Statistical, nonlinear, and soft matter physics. 83 [PubMed]

• On stochastic diff. eq. models for ion channel noise in Hodgkin-Huxley neurons (Goldwyn et al. 2010) [Model]

Goldwyn JH, Shea-Brown E. (2011). The what and where of adding channel noise to the Hodgkin-Huxley equations. PLoS computational biology. 7 [PubMed]

• Stochastic versions of the Hodgkin-Huxley equations (Goldwyn, Shea-Brown 2011) [Model]
• Stochastic versions of the Hodgkin-Huxley equations (Goldwyn, Shea-Brown 2011) (pylab) [Model]

Hales JP, Lin CS, Bostock H. (2004). Variations in excitability of single human motor axons, related to stochastic properties of nodal sodium channels. The Journal of physiology. 559 [PubMed]

Kitano K, Fukai T. (2007). Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies. Journal of computational neuroscience. 23 [PubMed]

Linaro D, Storace M, Giugliano M. (2011). Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation. PLoS computational biology. 7 [PubMed]

• Accurate and fast simulation of channel noise in conductance-based model neurons (Linaro et al 2011) [Model]

Mino H, Rubinstein JT, White JA. (2002). Comparison of algorithms for the simulation of action potentials with stochastic sodium channels. Annals of biomedical engineering. 30 [PubMed]

Nguyen V, Mathias R, Smith GD. (2005). A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bulletin of mathematical biology. 67 [PubMed]

• Stochastic automata network Markov model descriptors of coupled Ca2+ channels (Nguyen et al. 2005) [Model]

Orio P, Soudry D. (2012). Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states. PloS one. 7 [PubMed]

• Simple and accurate Diffusion Approximation algor. for stochastic ion channels (Orio & Soudry 2012) [Model]

Platkiewicz J, Brette R. (2010). A threshold equation for action potential initiation. PLoS computational biology. 6 [PubMed]

• A threshold equation for action potential initiation (Platkiewicz & Brette 2010) [Model]

Rotstein HG, Oppermann T, White JA, Kopell N. (2006). The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells. Journal of computational neuroscience. 21 [PubMed]

Rowat P. (2007). Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing. Neural computation. 19 [PubMed]

Rowat PF, Elson RC. (2004). State-dependent effects of Na channel noise on neuronal burst generation. Journal of computational neuroscience. 16 [PubMed]

Savtchenko LP, Gogan P, Tyc-Dumont S. (2001). Dendritic spatial flicker of local membrane potential due to channel noise and probabilistic firing of hippocampal neurons in culture. Neuroscience research. 41 [PubMed]

Schmerl BA, McDonnell MD. (2013). Channel noise induced stochastic facilitation in an auditory brainstem neuron model Physical review. E, Statistical, nonlinear, and soft matter physics. 88 [PubMed]

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

Stanley DA, Bardakjian BL, Spano ML, Ditto WL. (2011). Stochastic amplification of calcium-activated potassium currents in Ca2+ microdomains. Journal of computational neuroscience. 31 [PubMed]

• CA1 pyramidal: Stochastic amplification of KCa in Ca2+ microdomains (Stanley et al. 2011) [Model]

Steinmetz PN, Manwani A, Koch C, London M, Segev I. (2000). Subthreshold voltage noise due to channel fluctuations in active neuronal membranes. Journal of computational neuroscience. 9 [PubMed]

Sterratt DC, Graham B, Gillies A, Willshaw D. (2011). Principles of Computational Modelling in Neuroscience, Cambridge University Press.

• Principles of Computational Modelling in Neuroscience (Book) (Sterratt et al. 2011) [Model]

Tanskanen AJ, Greenstein JL, O'Rourke B, Winslow RL. (2005). The role of stochastic and modal gating of cardiac L-type Ca2+ channels on early after-depolarizations. Biophysical journal. 88 [PubMed]