TY - JOUR
T1 - Bursting, beating, and chaos in an excitable membrane model
AU - Chay, T. R.
AU - Rinzel, J.
N1 - Funding Information:
This work was supported by a National Science Foundation grant PCM82 15583 to Dr. T. Chay. Received for publication 23 April 1984 and in final form 2 October 1984.
PY - 1985
Y1 - 1985
N2 - We have studied periodic as well as aperiodic behavior in the self-sustained oscillations exhibited by the Hodgkin-Huxley type model of Chay, T. R., and J. Keizer (Biophys. J., 1983, 42:181–190) for the pancreatic beta-cell. Numerical solutions reveal a variety of patterns as the glucose-dependent parameter kCa is varied. These include regimes of periodic beating (continuous spiking) and bursting modes and, in the transition between these modes, aperiodic responses. Such aperiodic behavior for a nonrandom system has been called deterministic chaos and is characterized by distinguishing features found in previous studies of chaos in nonbiophysical systems and here identified for an (endogenously active) excitable membrane model. To parallel the successful analysis of chaos in other physical/chemical contexts we introduce a simplified, but quantitative, one-variable, discrete-time representation of the dynamics. It describes the evolution of intracellular calcium (which activates a potassium conductance) from one spike upstroke to the next and exhibits the various modes of behavior.
AB - We have studied periodic as well as aperiodic behavior in the self-sustained oscillations exhibited by the Hodgkin-Huxley type model of Chay, T. R., and J. Keizer (Biophys. J., 1983, 42:181–190) for the pancreatic beta-cell. Numerical solutions reveal a variety of patterns as the glucose-dependent parameter kCa is varied. These include regimes of periodic beating (continuous spiking) and bursting modes and, in the transition between these modes, aperiodic responses. Such aperiodic behavior for a nonrandom system has been called deterministic chaos and is characterized by distinguishing features found in previous studies of chaos in nonbiophysical systems and here identified for an (endogenously active) excitable membrane model. To parallel the successful analysis of chaos in other physical/chemical contexts we introduce a simplified, but quantitative, one-variable, discrete-time representation of the dynamics. It describes the evolution of intracellular calcium (which activates a potassium conductance) from one spike upstroke to the next and exhibits the various modes of behavior.
UR - http://www.scopus.com/inward/record.url?scp=0022037388&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0022037388&partnerID=8YFLogxK
U2 - 10.1016/S0006-3495(85)83926-6
DO - 10.1016/S0006-3495(85)83926-6
M3 - Article
C2 - 3884058
AN - SCOPUS:0022037388
SN - 0006-3495
VL - 47
SP - 357
EP - 366
JO - Biophysical journal
JF - Biophysical journal
IS - 3
ER -