Analyzing Neuronal Networks Using Discrete-Time Dynamics.
We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect's Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.
Ahn
Sungwoo
S
Department of Mathematics, Ohio State University, Columbus, Ohio 43210.
Smith
Brian H
BH
Borisyuk
Alla
A
Terman
David
D
Trends Neurosci. 1996 May;19(5):202-8
8723208
J Neurophysiol. 1996 Sep;76(3):2049-70
8890314
Annu Rev Neurosci. 1999;22:487-509
10202546
Neuron. 2005 Nov 23;48(4):661-73
16301181
Nat Neurosci. 1999 Jan;2(1):74-8
10195183
Cell. 2000 Jul 21;102(2):147-59
10943836
Nature. 1999 Dec 9;402(6762):664-8
10604472
Annu Rev Neurosci. 2001;24:263-97
11283312
J Comput Neurosci. 1994 Jun;1(1-2):11-38
8792223
J Physiol. 1952 Aug;117(4):500-44
12991237
J Neurophysiol. 1999 Jul;82(1):382-97
10400966
Science. 1998 Feb 27;279(5355):1351-5
9478895
Neuron. 2004 May 13;42(3):437-49
15134640
Nat Neurosci. 1999 Nov;2(11):1003-9
10526340
Proc Natl Acad Sci U S A. 1999 Nov 9;96(23):13480-5
10557346
Neuron. 2008 Jul 10;59(1):110-24
18614033
Annu Rev Neurosci. 2006;29:163-201
16776583
Semin Cell Dev Biol. 2006 Aug;17(4):433-42
16766212
Trends Neurosci. 1994 May;17(5):199-208
7520202
Neuron. 2004 Dec 2;44(5):865-76
15572116
Neuron. 2006 Aug 3;51(3):351-8
16880129
J Neurosci. 2003 Jun 15;23(12):5370-80
12832563
Eur J Neurosci. 2003 Oct;18(8):2119-32
14622173
Learn Mem. 1998 May-Jun;5(1-2):146-56
10454379
Neuron. 2004 Sep 30;44(1):31-48
15450158
Proc Natl Acad Sci U S A. 2004 Jul 13;101(28):10476-81
15232007
Science. 1988 Dec 23;242(4886):1654-64
3059497
Proc Natl Acad Sci U S A. 1995 Jun 6;92(12):5577-81
7777551
Science. 2001 Feb 2;291(5505):889-94
11157170
Neuron. 2001 May;30(2):553-67
11395014
J Neurosci. 2006 Feb 8;26(6):1663-8
16467512
Curr Opin Neurobiol. 2006 Aug;16(4):429-34
16822662
Proc Natl Acad Sci U S A. 1994 Oct 25;91(22):10586-90
7937997
Biophys J. 1983 May;42(2):181-90
6305437
Biophys J. 1985 Mar;47(3):357-66
3884058
Neuron. 2001 May;30(2):569-81
11395015
Neural Comput. 2004 May;16(5):999-1012
15070507
Nat Neurosci. 2003 Nov;6(11):1224-9
14566341
Physica D. 2008 Mar;237(3):324-338
18443649
Prog Neurobiol. 1997 Mar;51(4):457-81
9106902
Trends Neurosci. 2002 Oct;25(10):525-31
12220881
J Neurosci. 2009 Aug 19;29(33):10191-202
19692594