Alzubaidi H, Gilsing H, Shardlow T (2010) Stochastic Methods in Neuroscience, Laing C:Lord G, ed. pp.344 Austin TD (2008) The emergence of the deterministic Hodgkin–Huxley equations as a limit from the underlying stochastic ion-channel mechanism Ann Appl Probab 18:1279-1325 Bruce IC (2007) Implementation issues in approximate methods for stochastic Hodgkin-Huxley models. Ann Biomed Eng 35:315-8; author reply 319 [PubMed] Bruce IC (2009) Evaluation of stochastic differential equation approximation of ion channel gating models. Ann Biomed Eng 37:824-38 [Journal] [PubMed] Brunel N, Chance FS, Fourcaud N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86:2186-9 [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] Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71:3013-21 [PubMed] Clay JR (1998) Excitability of the squid giant axon revisited. J Neurophysiol 80:903-13 [Journal] [PubMed] Clay JR (2005) Axonal excitability revisited. Prog Biophys Mol Biol 88:59-90 [PubMed] Cudmore RH, Fronzaroli-Molinieres L, Giraud P, Debanne D (2010) Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current. J Neurosci 30:12885-95 [PubMed] Dayan P, Abbott LF (2001) Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems De Vries G, Sherman A (2000) Channel sharing in pancreatic beta-cells revisited: enhancement of emergent bursting by noise. J Theor Biol 207:513-30 [PubMed] Faisal AA, Laughlin SB (2007) Stochastic simulations on the reliability of action potential propagation in thin axons. PLoS Comput Biol 3:e79-39 [PubMed] Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292-303 [PubMed] Finke C, Vollmer J, Postnova S, Braun HA () Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations. Math Biosci 214:109-21 [PubMed] Fox RF (1997) Stochastic versions of the Hodgkin-Huxley equations. Biophys J 72:2068-74 [PubMed] 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] Freidlin M, Wentzell A (1998) Random Perturbations of Dynamical Systems Gardiner CW (2004) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Springer Series in Synergetics, 3rd ed. GERSTEIN GL, MANDELBROT B (1964) RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophys J 4:41-68 [PubMed] Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry 81:2340-2361 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 [PubMed] Higham DJ (2001) An algorithmic introduction to numerical simulation of stochastic differential equation Siam Review 43:525-546 Hille B (2001) Ionic Channels of Excitable Membranes Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM (2004) ModelDB: A Database to Support Computational Neuroscience. J Comput Neurosci 17:7-11 [Journal] [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] Imennov NS, Rubinstein JT (2009) Stochastic population model for electrical stimulation of the auditory nerve. IEEE Trans Biomed Eng 56:2493-501 [PubMed] Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal] Jo J, Kang H, Choi MY, Koh DS (2005) How noise and coupling induce bursting action potentials in pancreatic {beta}-cells. Biophys J 89:1534-42 [PubMed] Johnston D, Wu SMS (1995) Foundations of Cellular Neurophysiology
with simulations and illustrations by Richard Gray Foundations of Cellular Neurophysiology Jones SW (2006) Are rate constants constant? J Physiol 571:502 [PubMed] Keener JP (2009) Invariant manifold reductions for Markovian ion channel dynamics. J Math Biol 58:447-57 [PubMed] Keleshian AM, Edeson RO, Liu GJ, Madsen BW (2000) Evidence for cooperativity between nicotinic acetylcholine receptors in patch clamp records. Biophys J 78:1-12 [PubMed] Laing C, Lord G (2009) Stochastic Methods in Neuroscience Li YX, Rinzel J (1994) Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166:461-73 [PubMed] Liebovitch LS, Scheurle D, Rusek M, Zochowski M (2001) Fractal methods to analyze ion channel kinetics. Methods 24:359-75 [PubMed] Linaro D, Storace M, Giugliano M (2011) Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation PLOS 7:e1001102 [Journal] [PubMed] 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] Pakdaman K, Thieullen M, Wainrib G (2010) Fluid limit theorems for stochastic hybrid systems with application to neuron models Adv Appl Probab 42(3):761-794 Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1988) Numerical recipes in C: the art of scientific computing Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition, Segev I, Koch C, ed. pp.251 Rolls ET, Deco G (2010) The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function 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 [PubMed] Rowat PF, Elson RC () State-dependent effects of Na channel noise on neuronal burst generation. J Comput Neurosci 16:87-112 [PubMed] Saarinen A, Linne ML, Yli-Harja O (2008) Stochastic differential equation model for cerebellar granule cell excitability. PLoS Comput Biol 4:e1000004 [PubMed] Sato D, Xie LH, Nguyen TP, Weiss JN, Qu Z (2010) Irregularly appearing early afterdepolarizations in cardiac myocytes: random fluctuations or dynamical chaos? Biophys J 99:765-73 [PubMed] Schneidman E, Freedman B, Segev I (1998) Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput 10:1679-703 [PubMed] Sengupta B, Laughlin SB, Niven JE (2010) Comparison of Langevin and Markov channel noise models for neuronal signal generation. Phys Rev E Stat Nonlin Soft Matter Phys 81:011918 [PubMed] Shuai JW, Jung P (2002) Optimal intracellular calcium signaling. Phys Rev Lett 88:068102-75 [PubMed] Skaugen E, Walloe L (1979) Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol Scand 107:343-63 [PubMed] Tuckwell HC (1988) Introduction To Theoretical Neurobiology: Vol 1, Linear Cable Theory And Dendritic Structure Vandenberg CA, Bezanilla F (1991) A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophys J 60:1511-33 [PubMed] Wang M, Hou Z, Xin H (2004) Double-system-size resonance for spiking activity of coupled Hodgkin-Huxley neurons. Chemphyschem 5:1602-5 [PubMed] White JA, Klink R, Alonso A, Kay AR (1998) Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J Neurophysiol 80:262-9 [Journal] [PubMed] White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:131-7 [PubMed] Woloshyn R (1999) http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/FORTRAN/mtfort90.f Mersenne twister implemented in FORTRAN Woo J, Miller CA, Abbas PJ (2010) The dependence of auditory nerve rate adaptation on electric stimulus parameters, electrode position, and fiber diameter: a computer model study. J Assoc Res Otolaryngol 11:283-96 [PubMed] Zeng S, Jung P (2004) Mechanism for neuronal spike generation by small and large ion channel clusters. Phys Rev E Stat Nonlin Soft Matter Phys 70:011903 [PubMed] | 
