The Activity Phase of Postsynaptic Neurons in a Simplified Rhythmic Network
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Many inhibitory rhythmic networks produce activity in a range of frequencies. The relative phase of activity between neurons in these networks is often a determinant of the network output. This relative phase is determined by the interaction between synaptic inputs to the neurons and their intrinsic properties. We show, in a simplified network consisting of an oscillator inhibiting a follower neuron, how the interaction between synaptic depression and a transient potassium current in the follower neuron determines the activity phase of this neuron. We derive a mathematical expression to determine at what phase of the oscillation the follower neuron becomes active. This expression can be used to understand which parameters determine the phase of activity of the follower as the frequency of the oscillator is changed. We show that in the presence of synaptic depression, there can be three distinct frequency intervals, in which the phase of the follower neuron is determined by different sets of parameters. Alternatively, when the synapse is not depressing, only one set of parameters determines the phase of activity at all frequencies.
- Ahissar E, Sosnik R, Haidarliu S (2000) Transformation from temporal to rate coding in a somatosensory thalamocortical pathway. Nature 406: 302–306. CrossRef
- Bartos M, Manor Y, Nadim F, Marder E, Nussbaum M(1999) Coordination of fast and slow rhythmic neuronal circuits. J. Neurosci. 19: 2247–2256.
- Bose A, Manor Y, Nadim F (2001) Bistable oscillations arising from synaptic depression. SIAM J. Appl. Math. 62: 706–727.
- Buchholtz F, Golowasch J, Epstein I, Marder E (1992) Mathematical model of an identified stomatogastric ganglion neuron. J. Neurophysiol. 67: 332–340.
- Connor JA, Stevens CF (1971) Voltage clamp studies of a transient outward membrane current in gastropod neural somata. J. Physiol. (Lond.) 213: 21–30.
- Connor JA, Walter D, McKowan R (1977) Neural repetitive firing: Modifications of the hodgkin-huxley axon suggested by experimental results from crustacean axons. Biophys. J. 18: 81–102.
- DiCaprio R, Jordan G, Hampton T (1997) Maintenance of motor pattern phase relationships in the ventilatory system of the crab. J. Exp. Biol. 200: 963–974.
- Ermentrout GB (2002) Simulating, Analyzing and Animating Dynamical Systems: A Gued to XPPAUT for Researchers and Students. SIAM, Philadelphia.
- Harris-Warrick R, Coniglio L, Barazangi N, Guckenheimer J, Gueron S (1995) Dopamine modulation of transient potassium current evokes phase shifts in a central pattern generator network. J. Neurosci. 15: 342–358.
- Hess D, Manira A (2001) Characterization of a high-voltageactivated ia current with a role in spike timing and locomotor pattern generation. Proc. Nat. Acad. Sci. 98(9): 5276–5281. CrossRef
- Hooper SL (1997a) Phase maintenance in the pyloric pattern of the lobster (panulirus interruptus) stomatogastric ganglion. J. Comput. Neurosci. 4: 191–205. CrossRef
- Hooper SL (1997b) The pyloric pattern of the lobster (panulirus interruptus) stomatogastric ganglion comprises two phasemaintaining subsets. J. Comput. Neurosci. 4: 207–219. CrossRef
- Hsiao C, Chandler S (1995) Characteristics of a fast transient outward current in guinea pig trigeminal motoneurons. Brain. Res. 695: 217–26. CrossRef
- Laurent G, Wehr M, Davidowitz H (1996) Temporal representations of odors in an olfactory network. J. Neurosci. 16: 3837–3847.
- Manor Y, Bose A, Booth V, Nadim F (2003) The contribution of synaptic depression to phase maintenance in a model rhythmic network. J. Neurophysiol. 90, 3513–3528.
- Marder E, Calabrese R (1996) Principles of rhythmic motor pattern generation. Physiol. Rev. 76, 687–717.
- Mishchenko EF, Rozov NK (1980). Differential Equations with Small Parameters and Relaxation Oscillators. Plenum Press, New York.
- Morris C, Lecar H (1981) Voltage oscillations in the barnicle giant muscle fiber. Biophys. J. 35: 193–213.
- O'Keefe J, Recce ML (1993) Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3: 317–330.
- Pearson K, Iles J (1970) Discharge patterns of coxal levator and depressor motoneurons of the cockroach, periplaneta americana. J. Exp. Biol. 52: 139–165.
- Rinzel J, Ermentrout G(1997) In: C. Koch and I. Segev, eds., Methods in Neuronal Modeling: From Synapses to Networks, MIT Press, Cambridge, MA, pp. 135–170.
- Rush M, Rinzel J (1995) The potassium a-current, lowfiring rates and rebound excitation in hodgkin-huxley models. Bull. Math. Biol. 57: 899–929.
- Skinner F, Mulloney B (1998) Intersegmental coordination of limb movements during locomotion: Mathematical models predict circuits that drive swimmeret beating.J. Neurosci. 18: 3831–3842.
- Storm J (1990) Potassium currents in hippocampal pyramidal cells. Prog. Brain Res. 83: 161–187.
- Thompson S (1977) Three pharmacologically distinct potassium channels in molluscan neurones. J. Physiol. 265: 465–488.
- The Activity Phase of Postsynaptic Neurons in a Simplified Rhythmic Network
Journal of Computational Neuroscience
Volume 17, Issue 2 , pp 245-261
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- synaptic depression
- phase maintenance
- central pattern generator
- Industry Sectors
- Author Affiliations
- 1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
- 2. Life Sciences Department, Ben-Gurion University of the Negev and Zlotowski Center for Neuroscience, Beer-Sheva, Israel, 84105
- 3. Department of Biological Sciences, Rutgers University, Newark, NJ, 07102, USA