Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

被引:54
作者
Gu, Huaguang [1 ]
机构
[1] Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China
基金
中国国家自然科学基金;
关键词
BIFURCATION SCENARIOS; FIRING PATTERNS; NERVE INJURY; DYNAMICS; PAIN; RAT; SYNCHRONIZATION; DISCHARGES; PACEMAKER; RESONANCE;
D O I
10.1371/journal.pone.0081759
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.
引用
收藏
页数:12
相关论文
共 56 条
[1]   PERIODIC AND NON-PERIODIC RESPONSES OF A PERIODICALLY FORCED HODGKIN-HUXLEY OSCILLATOR [J].
AIHARA, K ;
MATSUMOTO, G ;
IKEGAYA, Y .
JOURNAL OF THEORETICAL BIOLOGY, 1984, 109 (02) :249-269
[2]   Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model [J].
Barrio, Roberto ;
Shilnikov, Andrey .
JOURNAL OF MATHEMATICAL NEUROSCIENCE, 2011, 1
[3]   Mesoscale and clusters of synchrony in networks of bursting neurons [J].
Belykh, Igor ;
Hasler, Martin .
CHAOS, 2011, 21 (01)
[4]   A PERIPHERAL MONONEUROPATHY IN RAT THAT PRODUCES DISORDERS OF PAIN SENSATION LIKE THOSE SEEN IN MAN [J].
BENNETT, GJ ;
XIE, YK .
PAIN, 1988, 33 (01) :87-107
[5]   OSCILLATION AND NOISE DETERMINE SIGNAL-TRANSDUCTION IN SHARK MULTIMODAL SENSORY CELLS [J].
BRAUN, HA ;
WISSING, H ;
SCHAFER, K ;
HIRSCH, MC .
NATURE, 1994, 367 (6460) :270-273
[6]   Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model [J].
Braun, Hans A. ;
Schwabedal, Justus ;
Dewald, Mathias ;
Finke, Christian ;
Postnova, Svetlana ;
Huber, Martin T. ;
Wollweber, Bastian ;
Schneider, Horst ;
Hirsch, Martin C. ;
Voigt, Karlheinz ;
Feudel, Ulrike ;
Moss, Frank .
CHAOS, 2011, 21 (04)
[7]   Origin of bursting through homoclinic spike adding in a neuron model [J].
Channell, Paul ;
Cymbalyuk, Gennady ;
Shilnikov, Andrey .
PHYSICAL REVIEW LETTERS, 2007, 98 (13)
[8]   Transitions to synchrony in coupled bursting neurons [J].
Dhamala, M ;
Jirsa, VK ;
Ding, MZ .
PHYSICAL REVIEW LETTERS, 2004, 92 (02) :4
[9]   Spontaneous pain, both neuropathic and inflammatory, is related to frequency of spontaneous firing in intact C-fiber nociceptors [J].
Djouhri, L ;
Koutsikou, S ;
Fang, X ;
McMullan, S ;
Lawson, SN .
JOURNAL OF NEUROSCIENCE, 2006, 26 (04) :1281-1292
[10]   Ectopic discharges trigger sympathetic sprouting in rat dorsal root ganglia following peripheral nerve injury [J].
Dong, CH ;
Xie, ZL ;
Fan, JY ;
Xie, YK .
SCIENCE IN CHINA SERIES C-LIFE SCIENCES, 2002, 45 (02) :191-200