Chandler D (1987) Introduction to modern statistical mechanics.

Conti F, Wanke E (1975) Channel noise in nerve membranes and lipid bilayers. Q Rev Biophys 8:451-506 [PubMed]

De Felice LJ, Goolsby WN (1996) Order from randomness : spontaneous firing from stochastic properties of ion channels. Fluctuations and Order: The New Synthesis., Millonas M, ed. pp.331

Fox RF, Lu Yn (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:3421-3431 [PubMed]

Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry 81:2340-2361

Hille B (1992) Potassium channels and chloride channels Ionic Channels of Excitable Membrane, Hille B, ed. pp.115

Hines M (1989) A program for simulation of nerve equations with branching geometries. Int J Biomed Comput 24:55-68 [PubMed]

HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

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

Ito H, Ono K, Noma A (1994) Background conductance attributable to spontaneous opening of muscarinic K+ channels in rabbit sino-atrial node cells. J Physiol 476:55-68 [PubMed]

Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284

Lecar H, Nossal R (1971) Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing. Biophys J 11:1048-67 [Journal] [PubMed]

Lecar H, Nossal R (1971) Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. Biophys J 11:1068-84 [Journal] [PubMed]

Press WH, Teukolsky SA, Vellerling WT, Flannery BP (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. Biophys J 68:779-85 [Journal] [PubMed]

Sigworth FJ (1980) The variance of sodium current fluctuations at the node of Ranvier. J Physiol 307:97-129 [PubMed]

Skaugen E, Walløe L (1979) Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol Scand 107:343-63 [Journal] [PubMed]

Strassberg AF, Defelice LJ (1993) Limitations of the Hodgkin-Huxley formalism: eects of single channel kinetics on transmembrane voltage dynamics Neural Comput 5:843-855

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. J Neurosci 33:15848-67 [Journal] [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. Ann Biomed Eng 35:315-8; author reply 319 [Journal] [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. J Neurophysiol 99:146-54 [Journal] [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 Comput Biol [Journal] [PubMed]

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

Carnevale NT, Morse TM (1996-2009) Research reports that have used NEURON Web published citations at the NEURON website [Journal]

Channell P, Fuwape I, Neiman AB, Shilnikov AL (2009) Variability of bursting patterns in a neuron model in the presence of noise. J Comput Neurosci 27:527-42 [Journal] [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 Phys Rev E 85(5):051907 [Journal] [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. Rev Neurosci 10:233-45 [PubMed]

Diba K, Koch C, Segev I (2006) Spike propagation in dendrites with stochastic ion channels. J Comput Neurosci 20:77-84 [Journal] [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 Comput Biol 5:e1000290 [Journal] [PubMed]

Ermentrout GB, Terman DH (2010) Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics, Antman SS:Marsden JE:Sirovich L:Wiggins, ed. pp.1 [Journal]

•	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. Phys Rev E Stat Nonlin Soft Matter Phys 83:041908 [Journal] [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 Comput Biol 7:e1002247 [Journal] [PubMed]

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

Hales JP, Lin CS, Bostock H (2004) Variations in excitability of single human motor axons, related to stochastic properties of nodal sodium channels. J Physiol 559:953-64 [Journal] [PubMed]

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

Kitano K, Fukai T (2007) Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies. J Comput Neurosci 23:237-50 [Journal] [PubMed]

Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation. PLoS Comput Biol 7:e1001102 [Journal] [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. Ann Biomed Eng 30:578-87 [PubMed]

Nguyen V, Mathias R, Smith GD (2005) A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bull Math Biol 67:393-432 [Journal] [PubMed]

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

Platkiewicz J, Brette R (2010) A threshold equation for action potential initiation. PLoS Comput Biol 6:e1000850 [Journal] [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. J Comput Neurosci 21:271-92 [Journal] [PubMed]

Rowat P (2007) Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing. Neural Comput 19:1215-50 [Journal] [PubMed]

Rowat PF, Elson RC (2004) State-dependent effects of Na channel noise on neuronal burst generation. J Comput Neurosci 16:87-112 [Journal] [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. Neurosci Res 41:161-83 [PubMed]

Schmerl BA, McDonnell MD (2013) Channel noise induced stochastic facilitation in an auditory brainstem neuron model Physical Review E 88:052722 [Journal] [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. J Comput Neurosci 31:647-66 [Journal] [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. J Comput Neurosci 9:133-48 [PubMed]

Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of Computational Modelling in Neuroscience, Cambridge University Press :1-401 [Journal]

•	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. Biophys J 88:85-95 [Journal] [PubMed]