Asymptotic analysis of noise sensitivity in a neuronal burster

Bulletin of Mathematical Biology

Volumn 64, Issue 3, 2002, Pages 447-481

  Kuske, R ^a   Baer, S M ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; DENDRITE; MATHEMATICAL COMPUTING; PHYSIOLOGY; STATISTICS;

ACTION POTENTIALS; ANIMALS; DENDRITES; MODELS, NEUROLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; STOCHASTIC PROCESSES;

EID: 0036560602     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1006/bulm.2002.0279     Document Type: Article

References (44)

1. Baer S. M., Rinzel J. Propagation of dendritic spikes mediated by excitable spines: a continuum theory. J. Neurophysiol. 65:1991;874-890.
2. Baer S. M., Zaremba K. R. Bursting oscillations in an idealized model for an activity-dependent spine. Chen L., Ruan S., Zhu J. Advance Topics in Biomathematics. 1998;World Scientific, Singapore.
3. Baer S. M., Erneux T., Rinzel J. The slow passage through a Hopf bifurcation: delay, memory effects and resonance. SIAM J. Appl. Math. 49:1989;55-71.
4. Ben-Jacob E., Bergman D. J., Matkowsky B. J., Schuss Z. The lifetime of oscillatory steady states. Phys. Rev. A. 26:1982;2805-2816.
5. Bertram R., Sherman A. Dynamical complexity and temporal plasticity in pancreatic beta-cells. J. Biosci. 25:2000;197-209.
6. Bertram R., Butte M. J., Kiemel T., Sherman A. Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57:1995;413-439.
7. Chasman L. Research Experience for Undergraduates Project. 2000.
8. Chay T. R., Kang H. S. Role of single-channel stochastic noise on bursting clusters of pancreatic β -cells. Biophys. J. 54:1988;427-435.
9. Del Negro C. A., Hsiao C-F., Chandler S. H., Garfinkel A. Evidence for a novel bursting mechanism in rodent trigeminal neurons. Biophys. J. 75:1998;174-182.
10. De Vries G. Multiple bifurcations in a polynomial model of bursting oscillations. J. Nonlinear Sci. 8:1998;281-316.
11. De Vries G., Sherman A. Channel sharing in pancreatic beta-cells revisited: enhancement of emergent bursting by noise. J. Theor. Biol. 207:2000;513-530.
12. Ermentrout G. B., Kopell N. Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl Math. 46:1986;233-253.
13. Georgiou M., Erneux T. Pulsating laser oscillations depend on extremely-small-amplitude noise. Phys. Rev. A. 45:1992;6636-6642.
14. Golubitsky M., Josic K., Kaper T. J. An unfolding theory approach to bursting in fast-slow systems. Broer H., Krauskopf B., Vegter G. Global Analysis of Dynamical Systems, Festschrift Dedicated to Floris Takens for his 60th Birthday. 2001;Institute of Physics, Bristol.
15. Harris K. M., Kater S. B. Dendritic spines: cellular specializations imparting both stability and flexibility to synaptic function. Annu. Rev. Neurosci. 17:1994;341-371.
16. Hille B. Ionic Channels of Excitable Membranes. 1992;Sinauer, Sunderland.
17. Hughes D., Proctor M. R. E. Chaos and the effect of noise in a model of three-wave mode coupling. Physica D. 46:1990;163-176.
18. Izhikevich E. M. Neural excitability, spiking and bursting. Int. J. Bifurcation Chaos. 10:2000;1171-1266.
19. Keener J., Sneyd J. Mathematical Physiology. 1998;Springer, New York.
20. Kuske R. Probability densities for noisy delay bifurcations. J. Stat. Phys. 96:1999;797-816.
21. Kuske R. Gradient particle solutions of Fokker-Planck equations for noisy delay bifurcations. SIAM J. Sci. Comp. 22:2000;351-367.
22. Kuske R., Papanicolaou G. Invariant measure for noise simplified dynamics. Physica D. 120:1998;255-272.
23. Miller J. P., Rall W., Rinzel J. Synaptic amplification by active membrane in dendritic spines. Brain Res. 325:1985;325-330.
24. Muller D., Toni N., Buchs P. A. Spine changes associated with long-term potentiation. Hippocampus. 10:2000;596-604.
25. Neu J. C. Coupled chemical oscillators. SIAM J. Appl. Math. 37:1979;307-315.
26. Rall W., Agmon-Snir H. Cable theory for dendritic neurons. Koch C., Segev I. Methods in Neuron Modeling. 1998;MIT Press, Cambridge.
27. Rinzel J. A formal classification of bursting mechanisms in excitable systems. Teramoto E., Yamaguti M. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences. 1987;Springer, Berlin.
28. Rinzel J., Baer S. M. Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on fluctuations. Biophys. J. 54:1988.
29. Rinzel J., Troy W. C. Bursting phenomena in a simplified Oregonator flow system model. J. Chem. Phys. 76:1982;1775-1789.
30. Schuss Z. Theory and Applications of Stochastic Differential Equations. 1980;Wiley, New York.
31. Schuss Z., Eisenberg R. Diffusion: a Stochastic Dynamics Approach. 2001.
32. Segev I., Rall W. Computational study of an excitable dendritic spine. J. Neurophysiol. 60:1988;499-523.
33. Sherman A., Rinzel J., Keizer J. Emergence of organized bursting in clusters of pancreatic β -cells by channel sharing. Biophys. J. 54:1988;411-425.
34. Maier R. S., Stein D. L. Limiting exit location distributions in the stochastic exit problem. SIAM J. Appl. Math. 57:1997;752-790.
35. McClintock P. V.E., Moss F. Stochastic postponement of critical onsets in a bistable system. D'Amico A., Mazzetti P. Noise in Physical Systems and 1/f Noise. 1986;Elsevier, Amsterdam.
36. +imaging in spines and fine dendrites of central neurons. Pflugers Arch. 439:1999;201-207.
37. Shardlow T. Stochastic perturbations of the Allen-Cahn equation. Electron. J. Diff. Eqns. 2000:2000;1.
38. Shepherd G. M. The dendritic spine: a multifunctional integrative unit. J. Neurophysiol. 75:1996;2197-2210.
39. Shepherd G. M., Brayton R. K., Miller J. P., Segev I., Rinzel J., Rall W. Signal enhancement in distal cortical dendrites by means of interaction between active dendritic spines. Proc. Natl Acad. Sci. 1985;2192-2195.
40. Stocks N. G., Mannella R., McClintock P. V.E. Influence of random fluctuations on delayed bifurcations: the case of additive white noise. Phys. Rev. A. 40:1989;5361-5369.
41. Stone E., Armbruster D. Noise and O(1) amplitude effects on heteroclinic cycles. Chaos. 9:1999;499.
42. Wang X-J., Rinzel J., Arbib M. Oscillatory and bursting properties of neurons. The Handbook of Brain Theory and Neural Networks. 1995;MIT Press, Cambridge.
43. Wu H.-Y., Baer S. M. Analysis of an excitable dendritic spine with an activity-dependent stem conductance. J. Math. Biol. 36:1998;569-592.
44. Yuste R., Majewska A., Holthoff K. From form to function: calcium compartmentalization in dendritic spines. Nature Neurosci. 7:2000;653-659.