Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981)

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Accession:42046
... This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior. See paper for details.
Reference:
1 . Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [PubMed]
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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): Depressor scutorum rostralis muscle cell; Abstract Morris-Lecar neuron;
Channel(s): I Calcium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: SNNAP;
Model Concept(s): Bursting; Oscillations; Simplified Models; Invertebrate;
Implementer(s): Av-Ron, Evyatar [eav-ron at uth.tmc.edu];
Search NeuronDB for information about:  I Calcium; I Potassium;
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		>>    module's name: A		>>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
		>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


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

>------------------------------->--------------------------------------->
				>					>
	1			>	A = ssA			(1)	>
				>					>
>------------------------------->--------------------------------------->
>	2			>	        ssA - A			>>
>	-1.0	>IV<		>	dA/dt= ------------	(2)	>
>				>	           tA			>
>------------------------------->--------------------------------------->

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

>----------------------->------------------------------------------------------>
	1		>			1			       >
	-1.2	>h<	>	ssA = --------------------		(1)    >
	9.	>s<	>		+-	     -+ p		       >
	1.0	>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)>
>	0.0	>tx<	>						       >
>----------------------->------------------------------------------------------>
>	2		>	  tx -tn				       >
>	0.0015	>tx<	> tA = -------------------- + tn	            (2)>
>	4.5E-4	>tn<	>	+-	     -+ p			       >
>	-8.7	>h<	>	|     (V-h)/s |				       >
>	1.85	>s<	>	|1 + e        |				       >
>	1.0	>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<	>						       >
>----------------------->------------------------------------------------------>