Multiple modes of a conditional neural oscillator (Epstein, Marder 1990)

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Accession:42321
We present a model for a conditional bursting neuron consisting of five conductances: Hodgkin-Huxley type time- and voltage-dependent Na+ and K+ conductances, a calcium activated voltage-dependent K+ conductance, a calcium-inhibited time- and voltage-dependent Ca++ conductance, and a leakage Cl- conductance. Different bursting and silent modes and transitions between them are analyzed in the model and compared to bursting modes in experiment. See the paper for details.
Reference:
1 . Epstein IR, Marder E (1990) Multiple modes of a conditional neural oscillator. Biol Cybern 63:25-34 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Chloride; I Na,t; I K; I Sodium; I Calcium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: SNNAP;
Model Concept(s): Bursting; Invertebrate;
Implementer(s): Baxter, Douglas;
Search NeuronDB for information about:  I Chloride; I Na,t; I K; I Sodium; I Calcium; I Potassium;
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
		>>    module's name: A		>>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
A:		> 	Activation function (time constant method)	>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

>------------------------------->--------------------------------------->
>				>					>
>	1			>	A = ssA			(1)	>
>				>					>
>------------------------------->--------------------------------------->
	2			>	        ssA - A			>
	-1	>IV<		>	dA/dt= ------------	(2)	>
				>	           tA			>
>------------------------------->--------------------------------------->

		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
ssA:		> 	Steady state value for activation		>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

>----------------------->------------------------------------------------------>
	1		>			1			       >
	-42.0	>h<	>	ssA = --------------------		(1)    >
	6.66667	>s<	>		+-	     -+ p		       >
	1	>p<	>		|     (h-V)/s |			       >
			>		|1 + e        |			       >
			>		+-	     -+			       >
			>						       >
>----------------------->------------------------------------------------------>
>	2		>		   1 - An			       >
>	0.0001	>An<	>	ssA = -------------------- + An		       >
>	0.0002	>h<	>		+-	     -+ p		       >
>	0.0003	>s<	>		|     (h-V)/s |			(2)    >
>	0.00004	>p<	>		|1 + e        |			       >
>			>		+-	     -+			       >
>----------------------->------------------------------------------------------>


		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tA:		> 	Time constant for activation			>	
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

>----------------------->------------------------------------------------------>
			>						       >
	1		> tA = tx					    (1)>
	23.5	>tx<	>						       >
>----------------------->------------------------------------------------------>
>	2		>	  tx -tn				       >
>	xxx.xx	>tx<	> tA = -------------------- + tn	            (2)>
>	xxx.xx	>tn<	>	+-	     -+ p			       >
>	xxx.xx	>h<	>	|     (V-h)/s |				       >
>	xxx.xx	>s<	>	|1 + e        |				       >
>	x	>p<	>	+-	     -+				       >
>			>						       >
>----------------------->------------------------------------------------------>
>	3		>	 		tx -tn			       >
>	0.1	>tx<	> tA = ----------------------------------- + tn     (3)>
>	0.2	>tn<	>	+-	     -+p1 +-	       -+p2	       >
>	0.3	>h1<	>	|   (V-h1)/s1 |	  |   (V-h2)/s2 |	       >
>	0.4	>s1<	>	|1+e          |	  |1+e          |	       >
>	1	>p1<	>	+-	     -+	  +-	       -+	       >
>	0.5	>h2<	>						       >
>	0.6	>s2<	>						       >
>	2	>p2<	>						       >
>----------------------->------------------------------------------------------>
>			>	  +--			      -+	       >
>	4		>	  |   1 - rtn		       |	       >
>	xxx.xx	>tx<	> tA = tx | -------------------- + rtn |            (4)>
>	xxx.xx	>rtn<	>	  | +-	          -+ p	       |	       >
>	xxx.xx	>h<	>	  | |     (V-h)/s  |	       |	       >
>	xxx.xx	>s<	>	  | |1 + e         |	       |	       >
>	x	>p<	>	  | +-	          -+           |	       >
>			>	  +-- 			      -+	       >
>			>						       >
>----------------------->------------------------------------------------------>
>			>	+--			                --+    >
>	5		>	| 	1 - rtn		                  |    >
>	xxx.xx	>tx<	> tA=tx | ---------------------------------- +rtn | (5)>
>	xxx.xx	>rtn<	>	| +-	      -+p1+-	      -+p2        |    >
>	xxx.xx	>h1<	>	| |   (V-h1)/s1|  |   (V-h2)/s2|          |    >
>	xxx.xx	>s1<	>	| |1+e         |  |1+e         |          |    >
>	x	>p1<	>	| +-	      -+  +-	      -+          |    >
>	xxx.xx	>h2<	>	+-- 			   	        --+    >
>	xx.xx	>s2<	>						       >
>	x	>p2<	>						       >
>----------------------->------------------------------------------------------>


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