{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:11:55Z","timestamp":1775167915237,"version":"3.50.1"},"reference-count":58,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2014,5,1]],"date-time":"2014-05-01T00:00:00Z","timestamp":1398902400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1003551","type":"journal-article","created":{"date-parts":[[2014,5,1]],"date-time":"2014-05-01T20:33:24Z","timestamp":1398976404000},"page":"e1003551","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":57,"title":["Bistable Dynamics Underlying Excitability of Ion Homeostasis in Neuron Models"],"prefix":"10.1371","volume":"10","author":[{"given":"Niklas","family":"H\u00fcbel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eckehard","family":"Sch\u00f6ll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus A.","family":"Dahlem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2014,5,1]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1113\/jphysiol.1952.sp004764","article-title":"A quantitative description of membrane current and its application to conduction and excitation in nerve","volume":"117","author":"AL Hodgkin","year":"1952","journal-title":"J Physiol"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1071\/PP9790337","article-title":"The action potential in <italic>chara corallina<\/italic> III.* the Hodgkin-Huxley parameters for the plasmalemma","volume":"6","author":"MJ Beilby","year":"1979","journal-title":"Funct Plant Biol"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/S0006-3495(80)85016-8","article-title":"Fast sodium current in cardiac muscle. A quantitative description","volume":"32","author":"L Ebihara","year":"1980","journal-title":"Biophys J"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0006-3495(83)84384-7","article-title":"Minimal model for membrane oscillations in the pancreatic beta-cell","volume":"42","author":"TR Chay","year":"1983","journal-title":"Biophys J"},{"key":"ref5","first-page":"100","article-title":"The nature of the oscillatory behaviour in electrical activity from pancreatic beta-cell","volume":"Suppl 10","author":"I Atwater","year":"1980","journal-title":"Horm Metab Res Suppl"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1085\/jgp.201110611","article-title":"Ionic mechanisms and Ca<sup>2<\/sup> dynamics underlying the glucose response of pancreatic <italic>\u03b2<\/italic> cells: a simulation study","volume":"138","author":"CY Cha","year":"2011","journal-title":"J Gen Physiol"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1098\/rstb.1985.0001","article-title":"A model of cardiac electrical activity incorporating ionic pumps and concentration changes","volume":"307","author":"D DiFrancesco","year":"1985","journal-title":"Phil Trans R Soc B"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF02368625","article-title":"Modification of difrancesco-noble equations to simulate the effects of vagal stimulation onin vivo mammalian sinoatrial node electrical activity","volume":"21","author":"S Dokos","year":"1993","journal-title":"Annals of biomedical engineering"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1098\/rsta.2001.0820","article-title":"Models of cardiac ventricular action potentials: iterative interaction between experiment and simulation","volume":"359","author":"D Noble","year":"2001","journal-title":"Phil Trans R Soc A"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1063\/1.166508","article-title":"Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle","volume":"10","author":"H Arce","year":"2000","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1038\/nm.2333","article-title":"The role of spreading depression, spreading depolarization and spreading ischemia in neurological disease","volume":"17","author":"JP Dreier","year":"2011","journal-title":"Nat Med"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1038\/nrneurol.2013.192","article-title":"Cortical spreading depression and migraine","author":"AC Charles","year":"2013","journal-title":"Nat Rev Neurol"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1177\/1073858412453340","article-title":"Is spreading depolarization characterized by an abrupt, massive release of Gibbs free energy from the human brain cortex","volume":"19","author":"JP Dreier","year":"2013","journal-title":"Neuroscientist"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1006\/jtbi.1997.0487","article-title":"A conservation principle and its effect on the formulation of Na-Ca exchanger current in cardiac cells","volume":"189","author":"A Varghese","year":"1997","journal-title":"J Theor Biol"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s002490050254","article-title":"A theory for the membrane potential of living cells","volume":"29","author":"L Endresen","year":"2000","journal-title":"Eur Biophys J"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"3086","DOI":"10.1016\/j.bpj.2009.08.060","article-title":"A novel method to quantify contribution of channels and transporters to membrane potential dynamics","volume":"97","author":"CY Cha","year":"2009","journal-title":"Biophys J"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1152\/jn.2000.84.1.495","article-title":"Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations","volume":"84","author":"H Kager","year":"2000","journal-title":"J Neurophysiol"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/A:1008924227961","article-title":"Osmotic forces and gap junctions in spreading depression: a computational model","volume":"10","author":"BE Shapiro","year":"2001","journal-title":"J Comput Neurosci"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1140\/epjst\/e2007-00214-8","article-title":"Cortical spreading depression: An enigma","volume":"147","author":"RM Miura","year":"2007","journal-title":"Eur Phys J Spec Top"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10827-008-0083-9","article-title":"Computer simulations of neuron-glia interactions mediated by ion flux","volume":"25","author":"GG Somjen","year":"2008","journal-title":"J Comput Neurosci"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"e22127","DOI":"10.1371\/journal.pone.0022127","article-title":"Neural dynamics during anoxia and the \u201cwave of death\u201d","volume":"6","author":"BJ Zandt","year":"2011","journal-title":"PLoS ONE"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"e70469","DOI":"10.1371\/journal.pone.0070469","article-title":"A mathematical model of the metabolic and perfusion effects on cortical spreading depression","volume":"8","author":"JC Chang","year":"2013","journal-title":"PLoS ONE"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10827-008-0132-4","article-title":"The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics","volume":"26","author":"JR Cressman Jr","year":"2009","journal-title":"J Comput Neurosci"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s10867-010-9212-6","article-title":"Ion concentration dynamics as a mechanism for neural bursting","volume":"37","author":"E Barreto","year":"2010","journal-title":"J Biol Phys"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"e1002664","DOI":"10.1371\/journal.pcbi.1002664","article-title":"Spontaneous excitation patterns computed for axons with injury-like impairments of sodium channels and Na\/K pumps","volume":"8","author":"N Yu","year":"2012","journal-title":"PLoS Comput Biol"},{"key":"ref26","first-page":"1","article-title":"Coupled left-shift of Nav channels: modeling the Na-loading and dysfunctional excitability of damaged axons","author":"PA Boucher","year":"2012","journal-title":"J Comp Neurosci"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1177\/1073858408317955","article-title":"Potassium Dynamics in the Epileptic Cortex: New Insights on an Old Topic","volume":"14","author":"F Fr\u00f6hlich","year":"2008","journal-title":"Neuroscientist"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"031922","DOI":"10.1103\/PhysRevE.74.031922","article-title":"Coexistence of tonic firing and bursting in cortical neurons","volume":"74","author":"F Fr\u00f6hlich","year":"2006","journal-title":"Phys Rev E"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1152\/jn.00529.2003","article-title":"Potassium model for slow (2\u20133 Hz) in vivo neocortical paroxysmal oscillations","volume":"92","author":"M Bazhenov","year":"2004","journal-title":"J Neurophysiol"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0006-3495(83)84408-7","article-title":"Two stable steady states in the Hodgkin-Huxley axons","volume":"41","author":"K Aihara","year":"1983","journal-title":"Biophys J"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1011250329341","article-title":"Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions","volume":"11","author":"PJ Hahn","year":"2001","journal-title":"J Comput Neurosci"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.jtbi.2009.01.032","article-title":"The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: A computational study","volume":"258","author":"G Florence","year":"2009","journal-title":"J Theor Biol"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10827-008-0132-4","article-title":"The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics","volume":"26","author":"JR Cressman Jr","year":"2009","journal-title":"J Comput Neurosci"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"2773","DOI":"10.1007\/s11538-011-9647-3","article-title":"A continuum neural model for the instigation and propagation of cortical spreading depression","volume":"73","author":"W Yao","year":"2011","journal-title":"Bull Math Biol"},{"key":"ref35","unstructured":"Rinzel J, Ermentrout GB (1989) Analysis of neural excitability and oscillations. In: Koch C, Segev I, editors, Methods in neuronal modeling, Cambridge, MA: MIT Press. pp. 251\u2013291."},{"key":"ref36","doi-asserted-by":"crossref","unstructured":"Ermentrout GB, Terman D (2010) Mathematical Foundations of Neuroscience. Springer.","DOI":"10.1007\/978-0-387-87708-2"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1111\/j.1460-9568.2012.08107.x","article-title":"The extracellular matrix and diffusion barriers in focal cortical dysplasias","volume":"36","author":"J Zamecnik","year":"2012","journal-title":"Eur J Neurosci"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1126\/science.1241224","article-title":"Sleep drives metabolite clearance from the adult brain","volume":"342","author":"L Xie","year":"2013","journal-title":"Science"},{"key":"ref39","unstructured":"Doedel EJ, Oldeman BE (2009) Auto-07P: Continuation and bifurcation software for ordinary differential equations. Concordia University, Montreal, Canada."},{"key":"ref40","doi-asserted-by":"crossref","unstructured":"Kuznetsov YA (1995) Elements of Applied Bifurcation Theory. New York: Springer.","DOI":"10.1007\/978-1-4757-2421-9"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1126\/science.1094442","article-title":"Uses and abuses of mathematics in biology","volume":"303","author":"RM May","year":"2004","journal-title":"Science"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0006-8993(98)00812-9","article-title":"Inhibition of major cationic inward currents prevents spreading depression-like hypoxic depolarization in rat hippocampal tissue slices","volume":"812","author":"M Muller","year":"1998","journal-title":"Brain Res"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1111\/head.12156","article-title":"Migraine Genetics - A Review: Part I","volume":"53","author":"S Silberstein","year":"2013","journal-title":"Headache"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1111\/head.12169","article-title":"Migraine Genetics: Part II","volume":"53","author":"SD Silberstein","year":"2013","journal-title":"Headache"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1002\/andp.200410087","article-title":"Reaction-diffusion waves in neuronal tissue and the window of cortical excitability","volume":"13","author":"MA Dahlem","year":"2004","journal-title":"Ann Phys"},{"key":"ref46","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0006-3495(61)86902-6","article-title":"Impulses and physiological states in theoretical models of nerve membrane","volume":"1","author":"R FitzHugh","year":"1961","journal-title":"Biophys J"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"2061","DOI":"10.1109\/JRPROC.1962.288235","article-title":"An active pulse transmission line simulating nerve axon","volume":"50","author":"J Nagumo","year":"1962","journal-title":"Proc IRE"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1088\/0034-4885\/61\/4\/002","article-title":"Neural networks as spatio-temporal pattern-forming systems","volume":"61","author":"GB Ermentrout","year":"1998","journal-title":"Rep Prog Phys"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.jtbi.2007.11.019","article-title":"Efficient control of transient wave forms to prevent spreading depolarizations","volume":"251","author":"MA Dahlem","year":"2008","journal-title":"J Theo Biol"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"026110","DOI":"10.1063\/1.2937120","article-title":"Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke","volume":"18","author":"MA Dahlem","year":"2008","journal-title":"Chaos"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"e5007","DOI":"10.1371\/journal.pone.0005007","article-title":"Migraine aura: retracting particle-like waves in weakly susceptible cortex","volume":"4","author":"MA Dahlem","year":"2009","journal-title":"PLoS ONE"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"031921","DOI":"10.1103\/PhysRevE.80.031921","article-title":"Dynamical structures in binary media of potassium-driven neurons","volume":"80","author":"DE Postnov","year":"2009","journal-title":"Phys Rev E"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.physd.2009.08.009","article-title":"Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves","volume":"239","author":"MA Dahlem","year":"2010","journal-title":"Physica D"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"015110","DOI":"10.1063\/1.3096411","article-title":"Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time delayed feedback","volume":"19","author":"FM Schneider","year":"2009","journal-title":"Chaos"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/2190-8567-3-7","article-title":"Transient localized wave patterns and their application to migraine","volume":"3","author":"MA Dahlem","year":"2013","journal-title":"J Math Neurosci"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.brainres.2011.10.001","article-title":"Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression","volume":"1434","author":"DE Postnov","year":"2012","journal-title":"Brain Res"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"046101","DOI":"10.1063\/1.4813815","article-title":"Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine","volume":"23","author":"MA Dahlem","year":"2013","journal-title":"Chaos"},{"key":"ref58","first-page":"282","article-title":"Towards dynamical network biomarkers in neuromodulation of episodic migraine","volume":"4","author":"MA Dahlem","year":"2013","journal-title":"Transl Neuroscie"}],"container-title":["PLoS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1003551","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T01:49:28Z","timestamp":1565401768000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1003551"}},"subtitle":[],"editor":[{"given":"Lyle J.","family":"Graham","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2014,5,1]]},"references-count":58,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2014,5,1]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1003551","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,1]]}}}