Top

Journal of Computational Neuroscience

Published in:

01-10-2011

The variance of phase-resetting curves

Authors: G. Bard Ermentrout, Bryce Beverlin II, Todd Troyer, Theoden I. Netoff

Published in: Journal of Computational Neuroscience | Issue 2/2011

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Phase resetting curves (PRCs) provide a measure of the sensitivity of oscillators to perturbations. In a noisy environment, these curves are themselves very noisy. Using perturbation theory, we compute the mean and the variance for PRCs for arbitrary limit cycle oscillators when the noise is small. Phase resetting curves and phase dependent variance are fit to experimental data and the variance is computed using an ad-hoc method. The theoretical curves of this phase dependent method match both simulations and experimental data significantly better than an ad-hoc method. A dual cell network simulation is compared to predictions using the analytical phase dependent variance estimation presented in this paper. We also discuss how entrainment of a neuron to a periodic pulse depends on the noise amplitude.

previous article Erratum to: Journal of Computational Neuroscience, DOI 10.1007/s10827-010-0303-y and DOI 10.1007/s10827-010-0304-x

next article Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Abouzeid, A., & Ermentrout, B. (2009). Type-ii phase resetting curve is optimal for stochastic synchrony. Physical Review E, 80, 011911.CrossRef

Achuthan, S., & Canavier, C. C. (2009). Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. The Journal of Neuroscience, 29(16), 5218–5233.PubMedCrossRef

Ariaratnam, J. T., & Strogatz, S. H. (2001). Phase diagram for the winfree model of coupled nonlinear oscillators. Physical Review Letters, 86, 4278–4281.PubMedCrossRef

Brown, E., Moehlis, J., & Holmes, P. (2004). On the phase reduction and response dynamics of neural oscillator populations. Neural Computation, 16, 673–715.PubMedCrossRef

Dorval, A. D., Christini, D. J., & White, J. A. (2001). Real-time linux dynamic clamp: A fast and flexible way to construct virtual ion channels in living cells. Annals of Biomedical Engineering, 29, 897–907.PubMedCrossRef

Ermentrout, B., & Saunders, D. (2006). Phase resetting and coupling of noisy neural oscillators. Journal of Computational Neuroscience, 20, 179–190.PubMedCrossRef

Forger, D. B., & Paydarfar, D. (2004). Starting, stopping, and resetting biological oscillators: In search of optimum perturbations. Journal of Theoretical Biology, 230, 521–532.PubMedCrossRef

Galan, R. F., Ermentrout, G. B., & Urban, N. N. (2005). Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Physical Review Letters, 94, 158101.PubMedCrossRef

Gardiner, C. W. (2004). Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer Series in Synergetics (Vol. 13). Berlin: Springer.

Goel, P., & Ermentrout, B. (2002). Synchrony, stability, and firing patterns in pulse-coupled oscillators. Physica D, 163(3), 191–216.CrossRef

Golomb, D., & Amitai, Y. (1997). Propagating neuronal discharges in neocortical slices: Computational and experimental study. Journal of Neurophysiology, 78, 1199–1211.PubMed

Guevara, M. R., & Glass, L. (1982). Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias. Journal of Mathematical Biology, 14, 1–23.PubMedCrossRef

Harris, J. J., & Stocker, H. (1998). Handbook of mathematics and computational science. New York: Springer.CrossRef

Ito, K. (1946). On a stochastic integral equation. Proceedings of the Japan Academy, 22, 32–35.CrossRef

Kloeden, P. E., & Platen, E. (1992). Numerical solution of stochastic differential equations. Applications of Mathematics (New York) (Vol. 23). Berlin: Springer.

Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Dover Publications.

Ly, C., & Ermentrout, G. B. (2009). Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli. Journal of Computational Neuroscience, 26, 425–443.PubMedCrossRef

Ly, C., & Ermentrout, G. B. (2010). Coupling regularizes individual units in noisy populations. Physical Review E, 81, 11911.CrossRef

Netoff, T. I., Acker, C. D., Bettencourt, J. C., & White, J. A. (2005a). Beyond two-cell networks: Experimental measurement of neuronal responses to multiple synaptic inputs. Journal of Computational Neuroscience, 18, 287–295.PubMedCrossRef

Netoff, T. I., Banks, M. I., Dorval, A. D., Acker, C. D., Haas, J. S., Kopell, N., et al. (2005b). Synchronization in hybrid neuronal networks of the hippocampal formation. Journal of Neurophysiology, 93, 1197–1208.PubMedCrossRef

Neu, J. C. (1979). Coupled chemical oscillators. SIAM Journal on Applied Mathematics, 37(2), 307–315.CrossRef

Pervouchine, D. D., Netoff, T. I., Rotstein, H. G., White, J. A., Cunningham, M. O., Whittington, M. A., et al. (2006). Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus. Neural Computation, 18, 2617–2650.PubMedCrossRef

Plackett, R. L. (1983). Karl pearson and the chi-squared test. International Statistical Review, 51, 59–72.CrossRef

Preyer, A., & Butera, R. (2005). Neuronal oscillators in aplysia californica that demonstrate weak coupling in vitro. Physical Review Letters, 95(13), 138103.PubMedCrossRef

Reyes, A. D., & Fetz, E. E. (1993). Effects of transient depolarizing potentials on the firing rate of cat neocortical neurons. Journal of Neurophysiology, 69, 1673–1683.PubMed

Stoop, R., Schindler, K., & Bunimovich, L. A. (2000). Neocortical networks of pyramidal neurons: From local locking and chaos to macroscopic chaos and synchronization. Nonlinearity, 13, 1515–1529.CrossRef

Torben-Nielsen, B., Uusisaari, M., & Stiefel, K. (2010). A comparison of methods to determine neuronal phase-response curves. Frontiers in Neuroinformatics, 4(6).

Welch, B. L. (1947). The generalization of student’s problem when several different population variances are involved. Biometrika, 34, 28–35.PubMed

Winfree, A. T. (1967). Biological rhythms and the behavior of populations of coupled oscillators. Journal of Theoretical Biology, 16, 15–42.PubMedCrossRef

Title: The variance of phase-resetting curves
Authors: G. Bard Ermentrout
Bryce Beverlin II
Todd Troyer
Theoden I. Netoff
Publication date: 01-10-2011
Publisher: Springer US
Published in: Journal of Computational Neuroscience / Issue 2/2011
Print ISSN: 0929-5313
Electronic ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-010-0305-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 2/2011

Automatic classification and robust identification of vestibulo-ocular reflex responses: from theory to practice

The Wagon Wheel Illusions and models of orientation selection

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

In vivo conditions influence the coding of stimulus features by bursts of action potentials

Reduced order modeling of passive and quasi-active dendrites for nervous system simulation

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

Premium Partner