Citation Relationships



Goldwyn JH, Shea-Brown E (2011) The what and where of adding channel noise to the Hodgkin-Huxley equations. PLoS Comput Biol 7:e1002247 [PubMed]

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

   Stochastic versions of the Hodgkin-Huxley equations (Goldwyn, Shea-Brown 2011)

References and models cited by this paper

References and models that cite this paper

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 [Journal] [PubMed]

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

Bruce IC (2009) Evaluation of stochastic differential equation approximation of ion channel gating models. Ann Biomed Eng 37:824-38 [Journal] [PubMed]

   Evaluation of stochastic diff. eq. approximation of ion channel gating models (Bruce 2009) [Model]

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 [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]

Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71:3013-21 [Journal] [PubMed]

   Spontaneous firing caused by stochastic channel gating (Chow, White 1996) [Model]

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 [Journal] [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 [Journal] [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 [Journal] [PubMed]

Faisal AA, Laughlin SB (2007) Stochastic simulations on the reliability of action potential propagation in thin axons. PLoS Comput Biol 3:e79 [Journal] [PubMed]

Faisal AA, Selen LP, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292-303 [Journal] [PubMed]

Finke C, Vollmer J, Postnova S, Braun HA (2008) Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations. Math Biosci 214:109-21 [Journal] [PubMed]

Fox RF (1997) Stochastic versions of the Hodgkin-Huxley equations. Biophys J 72:2068-74 [Journal] [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 [Journal] [PubMed]

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

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]

   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]

Imennov NS, Rubinstein JT (2009) Stochastic population model for electrical stimulation of the auditory nerve. IEEE Trans Biomed Eng 56:2493-501 [Journal] [PubMed]

Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]

   Artificial neuron model (Izhikevich 2003, 2004, 2007) [Model]

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 [Journal] [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 [Journal] [PubMed]

Keener JP (2009) Invariant manifold reductions for Markovian ion channel dynamics. J Math Biol 58:447-57 [Journal] [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 [Journal] [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 [Journal] [PubMed]

Liebovitch LS, Scheurle D, Rusek M, Zochowski M (2001) Fractal methods to analyze ion channel kinetics. Methods 24:359-75 [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]

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 [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]

Saarinen A, Linne ML, Yli-Harja O (2008) Stochastic differential equation model for cerebellar granule cell excitability. PLoS Comput Biol 4:e1000004 [Journal] [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 [Journal] [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 [Journal] [PubMed]

Shuai JW, Jung P (2002) Optimal intracellular calcium signaling. Phys Rev Lett 88:068102 [Journal] [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]

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 [Journal] [PubMed]

Wang M, Hou Z, Xin H (2004) Double-system-size resonance for spiking activity of coupled Hodgkin-Huxley neurons. Chemphyschem 5:1602-5 [Journal] [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 [Journal] [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 [Journal] [PubMed]

Dangerfield CE, Kay D, Burrage K (2012) Modeling ion channel dynamics through reflected stochastic differential equations Phys Rev E 85(5):051907 [Journal]

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

Kilinc D, Demir A (2017) Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques. IEEE Trans Biomed Circuits Syst 11:958-974 [Journal] [PubMed]

   A neuronal circuit simulator for non Monte Carlo analysis of neuronal noise (Kilinc & Demir 2018) [Model]

Kilinc D,Demir A (2015) Simulation of noise in neurons and neuronal circuits Proceedings of the IEEE/ACM international conference on computer-aided design (ICCAD) :589-596 [Journal]

   A neuronal circuit simulator for non Monte Carlo analysis of neuronal noise (Kilinc & Demir 2018) [Model]

Schmandt NT, Galán RF (2012) Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating. Phys Rev Lett 109:118101 [Journal] [PubMed]

   Markov Chain-based Stochastic Shielding Hodgkin Huxley Model (Schmandt, Galan 2012) [Model]

Schmerl BA, McDonnell MD (2013) Channel noise induced stochastic facilitation in an auditory brainstem neuron model Physical Review E 88:052722 [Journal]

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

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