Bistable Dynamics Underlying Excitability of Ion Homeostasis in Neuron Models

PLoS Computational Biology

Volumn 10, Issue 5, 2014, Pages

  Hübel, Niklas ^a   Schöll, Eckehard ^a   Dahlem, Markus A ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN; ELECTROPHYSIOLOGY; IONS; METABOLISM; NEURONS; PUMPS;

ACTION-POTENTIALS; BISTABLE DYNAMICS; CHEMICAL ENERGY; ENERGY REQUIREMENTS; HODGKIN-HUXLEY FORMALISM; ION CONCENTRATIONS; ION GRADIENTS; ION HOMEOSTASIS; NEURON MODELING; TRANSMEMBRANES;

FREE ENERGY;

ADENOSINE TRIPHOSPHATASE (POTASSIUM SODIUM); ION CHANNEL; ION;

ARTICLE; BIOPHYSICS; CONCENTRATION RESPONSE; DYNAMICS; ENERGY METABOLISM; HODGKIN HUXLEY EQUATION; IONIC BALANCE; MATHEMATICAL MODEL; METABOLIC PARAMETERS; MIGRAINE; NERVE CELL MODEL; NERVE POTENTIAL; NEUROSCIENCE; PHENOTYPE; PROTEIN FUNCTION; ACTION POTENTIAL; ANIMAL; BIOLOGICAL MODEL; CHANNEL GATING; COMPUTER SIMULATION; HOMEOSTASIS; HUMAN; MEMBRANE POTENTIAL; METABOLISM; NERVE CELL; PHYSIOLOGY;

ACTION POTENTIALS; ANIMALS; COMPUTER SIMULATION; ENERGY METABOLISM; HOMEOSTASIS; HUMANS; ION CHANNEL GATING; IONS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURONS; SODIUM-POTASSIUM-EXCHANGING ATPASE;

EID: 84900449012     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1003551     Document Type: Article

References (58)

1. Hodgkin AL, Huxley AF, (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117: 500.
2. Beilby MJ, Coster HGL, (1979) The action potential in chara corallina III.* the Hodgkin-Huxley parameters for the plasmalemma. Funct Plant Biol 6: 337-353.
3. Ebihara L, Johnson E, (1980) Fast sodium current in cardiac muscle. A quantitative description. Biophys J 32: 779-790.
4. Chay TR, Keizer J, (1983) Minimal model for membrane oscillations in the pancreatic beta-cell. Biophys J 42: 181-190.
5. Atwater I, Dawson CM, Scott A, Eddlestone G, Rojas E, (1980) The nature of the oscillatory behaviour in electrical activity from pancreatic beta-cell. Horm Metab Res Suppl Suppl 10: 100-107.
6. Cha CY, Nakamura Y, Himeno Y, Wang J, Fujimoto S, et al. (2011) Ionic mechanisms and Ca2 dynamics underlying the glucose response of pancreatic β cells: a simulation study. J Gen Physiol 138: 21-37.
7. DiFrancesco D, Noble D, (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil Trans R Soc B 307: 353-398.
8. Dokos S, Celler B, Lovell N, (1993) Modification of difrancesco-noble equations to simulate the effects of vagal stimulation onin vivo mammalian sinoatrial node electrical activity. Annals of biomedical engineering 21: 321-335.
9. Noble D, Rudy Y, (2001) Models of cardiac ventricular action potentials: iterative interaction between experiment and simulation. Phil Trans R Soc A 359: 1127-1142.
10. Arce H, Xu A, González H, Guevara MR, (2000) Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle. Chaos: An Interdisciplinary Journal of Nonlinear Science 10: 411-426.
11. Dreier JP, (2011) The role of spreading depression, spreading depolarization and spreading ischemia in neurological disease. Nat Med 17: 439-447.
12. Charles AC, Baca SM, (2013) Cortical spreading depression and migraine. Nat Rev Neurol pp. 637-44 doi:10.1038/nrneurol.2013.192.
13. Dreier JP, Isele TM, Reiffurth C, Kirov SA, Dahlem MA, et al. (2013) Is spreading depolarization characterized by an abrupt, massive release of Gibbs free energy from the human brain cortex? Neuroscientist 19: 25-42.
14. Varghese A, Sell GR, (1997) A conservation principle and its effect on the formulation of Na-Ca exchanger current in cardiac cells. J Theor Biol 189: 33-40.
15. Endresen L, Hall K, Høye J, Myrheim J, (2000) A theory for the membrane potential of living cells. Eur Biophys J 29: 90-103.
16. Cha CY, Himeno Y, Shimayoshi T, Amano A, Noma A, (2009) A novel method to quantify contribution of channels and transporters to membrane potential dynamics. Biophys J 97: 3086-3094.
17. Kager H, Wadman WJ, Somjen GG, (2000) Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J Neurophysiol 84: 495-512.
18. Shapiro BE, (2001) Osmotic forces and gap junctions in spreading depression: a computational model. J Comput Neurosci 10: 99-120.
19. Miura RM, Huang H, Wylie JJ, (2007) Cortical spreading depression: An enigma. Eur Phys J Spec Top 147: 287-302.
20. Somjen GG, Kager H, Wadman WJ, (2008) Computer simulations of neuron-glia interactions mediated by ion flux. J Comput Neurosci 25: 349-365.
21. Zandt BJ, ten Haken B, van Dijk JG, van Putten MJ, (2011) Neural dynamics during anoxia and the "wave of death". PLoS ONE 6: e22127.
22. Chang JC, Brennan KC, He D, Huang H, Miura RM, et al. (2013) A mathematical model of the metabolic and perfusion effects on cortical spreading depression. PLoS ONE 8: e70469.
23. Cressman JR Jr, Ullah G, Ziburkus J, Schiff SJ, Barreto E, (2009) The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. J Comput Neurosci 26: 159-170.
24. Barreto E, Cressman JR, (2010) Ion concentration dynamics as a mechanism for neural bursting. J Biol Phys 37: 361-373.
25. Yu N, Morris CE, Joos B, Longtin A, (2012) Spontaneous excitation patterns computed for axons with injury-like impairments of sodium channels and Na/K pumps. PLoS Comput Biol 8: e1002664.
26. Boucher PA, Joós B, Morris CE, (2012) Coupled left-shift of Nav channels: modeling the Na-loading and dysfunctional excitability of damaged axons. J Comp Neurosci pp. 1-19.
27. Fröhlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ, (2008) Potassium Dynamics in the Epileptic Cortex: New Insights on an Old Topic. Neuroscientist 14: 422-433.
28. Fröhlich F, Bazhenov M, (2006) Coexistence of tonic firing and bursting in cortical neurons. Phys Rev E 74: 031922.
29. Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ, (2004) Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations. J Neurophysiol 92: 1116-1132.
30. Aihara K, Matsumoto G, (1983) Two stable steady states in the Hodgkin-Huxley axons. Biophys J 41: 87-89.
31. Hahn PJ, Durand DM, (2001) Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions. J Comput Neurosci 11: 5-18.
32. Florence G, Dahlem MA, Almeida ACG, Bassani JWM, Kurths J, (2009) The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: A computational study. J Theor Biol 258: 219.
33. Cressman JR Jr, Ullah G, Ziburkus J, Schiff SJ, Barreto E, (2009) The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. J Comput Neurosci 26: 159-170.
34. Yao W, Huang H, Miura RM, (2011) A continuum neural model for the instigation and propagation of cortical spreading depression. Bull Math Biol 73: 2773-2790.
35. 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. 251-291.
36. Ermentrout GB, Terman D (2010) Mathematical Foundations of Neuroscience. Springer.
37. Zamecnik J, Homola A, Cicanic M, Kuncova K, Marusic P, et al. (2012) The extracellular matrix and diffusion barriers in focal cortical dysplasias. Eur J Neurosci 36: 2017-2024.
38. Xie L, Kang H, Xu Q, Chen MJ, Liao Y, et al. (2013) Sleep drives metabolite clearance from the adult brain. Science 342: 373-377.
39. Doedel EJ, Oldeman BE (2009) Auto-07P: Continuation and bifurcation software for ordinary differential equations. Concordia University, Montreal, Canada.
40. Kuznetsov YA (1995) Elements of Applied Bifurcation Theory. New York: Springer.
41. May RM, (2004) Uses and abuses of mathematics in biology. Science 303: 790-793.
42. Muller M, Somjen GG, (1998) Inhibition of major cationic inward currents prevents spreading depression-like hypoxic depolarization in rat hippocampal tissue slices. Brain Res 812: 1-13.
43. Silberstein S, Dodick D, (2013) Migraine Genetics- A Review: Part I. Headache 53: 1207-17.
44. Silberstein SD, Dodick DW, (2013) Migraine Genetics: Part II. Headache 53: 1218-29 doi:10.1111/head.12169.
45. Dahlem MA, Müller SC, (2004) Reaction-diffusion waves in neuronal tissue and the window of cortical excitability. Ann Phys 13: 442-449.
46. FitzHugh R, (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1: 445-466.
47. Nagumo J, Arimoto S, Yoshizawa S, (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50: 2061-2070.
48. Ermentrout GB, (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61: 353-430.
49. Dahlem MA, Schneider FM, Schöll E, (2008) Efficient control of transient wave forms to prevent spreading depolarizations. J Theo Biol 251: 202-209.
50. Dahlem MA, Schneider FM, Schöll E, (2008) Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke. Chaos 18: 026110.
51. Dahlem MA, Hadjikhani N, (2009) Migraine aura: retracting particle-like waves in weakly susceptible cortex. PLoS ONE 4: e5007.
52. Postnov DE, Müller F, Schuppner RB, Schimansky-Geier L, (2009) Dynamical structures in binary media of potassium-driven neurons. Phys Rev E 80: 031921.
53. Dahlem MA, Graf R, Strong AJ, Dreier JP, Dahlem YA, et al. (2010) Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves. Physica D 239: 889-903.
54. Schneider FM, Schöll E, Dahlem MA, (2009) Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time delayed feedback. Chaos 19: 015110.
55. Dahlem MA, Isele TM, (2013) Transient localized wave patterns and their application to migraine. J Math Neurosci 3: 7.
56. Postnov DE, Postnov DD, Schimansky-Geier L, (2012) Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression. Brain Res 1434: 200-211.
57. Dahlem MA, (2013) Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine. Chaos 23: 046101.
58. Dahlem MA, Rode S, May A, Fujiwara N, Hirata Y, et al. (2013) Towards dynamical network biomarkers in neuromodulation of episodic migraine. Transl Neuroscie 4: 282-294.