Citation Relationships

Legends: Link to a Model Reference cited by multiple papers


Teka W, Stockton D, Santamaria F (2016) Power-law dynamics of membrane conductances increase spiking diversity in a Hodgkin-Huxley model PLoS Comput Biol 12(3):e1004776

   Hodgkin–Huxley model with fractional gating (Teka et al. 2016)

References and models cited by this paper

References and models that cite this paper

Anastasio TJ (1994) The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biol Cybern 72:69-79 [PubMed]
Bean BP (2007) The action potential in mammalian central neurons. Nat Rev Neurosci 8:451-65 [Journal] [PubMed]
Ben-Avraham D,Havlin S (2000) Diffusion and reactions in fractals and disordered systems
Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent-II Geophys J Int 13:529-539
Deco G, Schürmann B (1998) The coding of information by spiking neurons: an analytical study. Network 9:303-17 [PubMed]
Destexhe A, Mainen ZF, Sejnowski TJ (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1:195-230 [PubMed]
   Application of a common kinetic formalism for synaptic models (Destexhe et al 1994) [Model]
   Kinetic synaptic models applicable to building networks (Destexhe et al 1998) [Model]
Drew PJ, Abbott LF (2006) Models and properties of power-law adaptation in neural systems. J Neurophysiol 96:826-33 [Journal] [PubMed]
Ellerkmann RK, Riazanski V, Elger CE, Urban BW, Beck H (2001) Slow recovery from inactivation regulates the availability of voltage-dependent Na(+) channels in hippocampal granule cells, hilar neurons and basket cells. J Physiol 532:385-97 [PubMed]
Fohlmeister JF (2015) Voltage gating by molecular subunits of Na+ and K+ ion channels: higher-dimensional cubic kinetics, rate constants, and temperature. J Neurophysiol 113:3759-77 [Journal] [PubMed]
Fulinski A,Grzywna Z,Mellor I,Siwy Z,Usherwood PNR (1998) Non-Markovian character of ionic current fluctuations in membrane channels. Physical Review E 58(1):919-24
Gal A, Eytan D, Wallach A, Sandler M, Schiller J, Marom S (2010) Dynamics of excitability over extended timescales in cultured cortical neurons. J Neurosci 30:16332-42 [Journal] [PubMed]
Goychuk I (2014) Life and death of stationary linear response in anomalous continuous time random walk dynamics Communications in Theoretical Physics 62(4):497
Goychuk I, Hänggi P (2002) Ion channel gating: a first-passage time analysis of the Kramers type. Proc Natl Acad Sci U S A 99:3552-6 [Journal] [PubMed]
Goychuk I, Hänggi P (2004) Fractional diffusion modeling of ion channel gating. Phys Rev E Stat Nonlin Soft Matter Phys 70:051915 [Journal] [PubMed]
Hines ML, Carnevale NT (1997) The NEURON simulation environment. Neural Comput 9:1179-209 [PubMed]
Horvath B, Banyasz T, Jian Z, Hegyi B, Kistamas K, Nanasi PP, Izu LT, Chen-Izu Y (2013) Dynamics of the late Na(+) current during cardiac action potential and its contribution to afterdepolarizations. J Mol Cell Cardiol 64:59-68 [Journal] [PubMed]
Hu W, Tian C, Li T, Yang M, Hou H, Shu Y (2009) Distinct contributions of Na(v)1.6 and Na(v)1.2 in action potential initiation and backpropagation. Nat Neurosci 12:996-1002 [Journal] [PubMed]
   Action Potential initiation and backpropagation in Neocortical L5 Pyramidal Neuron (Hu et al. 2009) [Model]
Jin X, Tecuapetla F, Costa RM (2014) Basal ganglia subcircuits distinctively encode the parsing and concatenation of action sequences. Nat Neurosci 17:423-30 [Journal] [PubMed]
Koch C (1999) Biophysics Of Computation: Information Processing in Single Neurons
Li HQ, Chen SH, Zhao HM (1990) Fractal mechanisms for the allosteric effects of proteins and enzymes. Biophys J 58:1313-20 [Journal] [PubMed]
Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335-42 [Journal] [PubMed]
Magin R (2010) Fractional calculus models of complex dynamics in biological tissues Computers Mathematics With Applications 59:1586-1593
Magin RL (2004) Fractional calculus in bioengineering. Crit Rev Biomed Eng 32:1-104 [PubMed]
Magin RL (2004) Fractional calculus in bioengineering Critical Reviews™in Biomedical Engineering
Magin RL (2012) Fractional calculus in bioengineering: a tool to model complex dynamics Carpathian Control Conference (ICCC), 13th International, Magin RL, ed.
Mainardi F,Gorenflo R (2000) On Mittag-Leffler-type functions in fractional evolution processes Journal of Computational and Applied Mathematics 118(1-2):283-99
Marinov TM, Ramirez N, Santamaria F (2013) FRACTIONAL INTEGRATION TOOLBOX. Fract Calc Appl Anal 16:670-681 [Journal] [PubMed]
Mercik S, Weron K (2001) Stochastic origins of the long-range correlations of ionic current fluctuations in membrane channels. Phys Rev E Stat Nonlin Soft Matter Phys 63:051910 [Journal] [PubMed]
Miller MN, Okaty BW, Nelson SB (2008) Region-specific spike-frequency acceleration in layer 5 pyramidal neurons mediated by Kv1 subunits. J Neurosci 28:13716-26 [Journal] [PubMed]
Modeldb (2016) [Internet]. Available from: https:--senselab.med.yale.edu-ModelDB-default.cshtml
Nagy A,Sweilam N (2014) An efficient method for solving fractional Hodgkin–Huxley model Physics Letters A 378(30):1980-4
Naundorf B, Wolf F, Volgushev M (2006) Unique features of action potential initiation in cortical neurons. Nature 440:1060-3 [Journal] [PubMed]
Oldham KB, Spanier J (2006) The fractional calculus: theory and applications of differentiation and integration to arbitrary order.
Pozzorini C, Naud R, Mensi S, Gerstner W (2013) Temporal whitening by power-law adaptation in neocortical neurons. Nat Neurosci 16:942-8 [Journal] [PubMed]
Qu Z, Xie LH, Olcese R, Karagueuzian HS, Chen PS, Garfinkel A, Weiss JN (2013) Early afterdepolarizations in cardiac myocytes: beyond reduced repolarization reserve. Cardiovasc Res 99:6-15 [Journal] [PubMed]
Santamaria F,Bower JM (2009) Hodgkin–Huxley Models Encyclopedia of Neuroscience, Squire LR, ed. pp.1173
Sheffield ME, Best TK, Mensh BD, Kath WL, Spruston N (2011) Slow integration leads to persistent action potential firing in distal axons of coupled interneurons. Nat Neurosci 14:200-7 [Journal] [PubMed]
Sherief H,El-Sayed AMA,Behiry SH,Raslan WE (2012) Using Fractional Derivatives to Generalize the Hodgkin– Huxley Model Fractional Dynamics and Control, Baleanu D:Machado JAT:Luo ACJ, ed. pp.275
Soudry D, Meir R (2012) Conductance-based neuron models and the slow dynamics of excitability. Front Comput Neurosci 6:4 [Journal] [PubMed]
Stockton DB, Santamaria F (2015) NeuroManager: a workflow analysis based simulation management engine for computational neuroscience. Front Neuroinform 9:24 [Journal] [PubMed]
   NeuroManager: a workflow analysis based simulation management engine (Stockton & Santamaria 2015) [Model]
Teka W, Marinov TM, Santamaria F (2014) Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model. PLoS Comput Biol 10:e1003526 [Journal] [PubMed]
   Fractional leaky integrate-and-fire model (Teka et al. 2014) [Model]
Trombin F, Gnatkovsky V, de Curtis M (2011) Changes in action potential features during focal seizure discharges in the entorhinal cortex of the in vitro isolated guinea pig brain. J Neurophysiol 106:1411-23 [Journal] [PubMed]
Uebachs M, Schaub C, Perez-Reyes E, Beck H (2006) T-type Ca2+ channels encode prior neuronal activity as modulated recovery rates. J Physiol 571:519-36 [Journal] [PubMed]
Wawrzkiewicz A, Pawelek K, Borys P, Dworakowska B, Grzywna ZJ (2012) On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory. Eur Biophys J 41:505-26 [Journal] [PubMed]
Weinberg SH (2015) Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model. PLoS One 10:e0126629 [Journal] [PubMed]
Yang Y, Adowski T, Ramamurthy B, Neef A, Xu-Friedman MA (2015) High-speed dynamic-clamp interface. J Neurophysiol 113:2713-20 [Journal] [PubMed]
Mondal A, Upadhyay RK (2018) Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking Nonlinear Dynamics 91:1275-1288 [Journal]
(48 refs)