XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6.

# Theta neuron model 50e and 20i cells with all-to-all 
# connectivity and periodic input to both the e- and i-cells
#
# Parameters
par I_e=0.4,I_i=0
par tauz=50,gz=.5
par sige=0.5,sigi=.01
par gie=3,gei=.4,gii=0.15,gee=2,
par taue=1,taui=3
#
# Periodic stimuli description with parameters
E(t)=heav(t-t_on)*heav(stim+t_on-t)
PO(t)=heav(d-t)
P(t)=PO(mod(t,per))
z'=(-z+p(t))/tau
I_x(t)=Ampx*z*E(t)
I_y(t)=Ampy*z*E(t)
par Ampx=70,Ampy=10,d=1,per=25,tau=20
par t_on=0,stim=1000
#
# ODEs for e-cells(x), i-cells(y) and adaptation(z)
x[0..49]'=1-cos(x[j])+(1+cos(x[j]))*(I_e+I_x(t)-gz*z[j]-gie*si+gee*se+sige*we[j])
z[0..49]'=sd(x[j])-z[j]/tauz
y[0..19]'=1-cos(y[j])+(1+cos(y[j]))*(I_i+I_y(t)-gii*si+gei*se+sigi*wi[j])
#
global 1 x[0..49]-pi {x[j]=-pi;out_put=1}
global 1 y[0..19]-pi {y[j]=-pi;out_put=1}
# Synapses
se'=sum(0,49)of(sd(shift(x0,i')))/50-se/taue
si'=sum(0,19)of(sd(shift(y0,i')))/20-si/taui
#
#Initial conditions
x[0..49](0)=ran(1)*2*pi-pi
y[0..19](0)=ran(1)*2*pi-pi
wiener we[0..49]
wiener wi[0..19]
sd(x)=exp(-b*(1-cos(x-2.5)))*b
par b=100
aux swgt=.8*se+.2*si
aux per_input=I_x(t)
@ dt=0.02,nOut=10
@ meth=euler,total=1400,trans=400,maxstor=1000000
@ yp=se,xlo=400,xhi=1400,ylo=0,yhi=.5
done

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Model :

id
name
time
substance
extent
volume
area
length

L3V1

type	FunctionDefinitions [10]	name	math
FunctionDefinition	max max <functionDefinition id="max" name="minimum"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> x </ci> </bvar> <bvar> <ci> y </ci> </bvar> <piecewise> <piece> <ci> x </ci> <apply> <gt/> <ci> x </ci> <ci> y </ci> </apply> </piece> <otherwise> <ci> y </ci> </otherwise> </piecewise> </lambda> </math> </functionDefinition>	minimum	$x y x x y y$
FunctionDefinition	min min <functionDefinition id="min" name="maximum"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> x </ci> </bvar> <bvar> <ci> y </ci> </bvar> <piecewise> <piece> <ci> x </ci> <apply> <lt/> <ci> x </ci> <ci> y </ci> </apply> </piece> <otherwise> <ci> y </ci> </otherwise> </piecewise> </lambda> </math> </functionDefinition>	maximum	$x y x x y y$
FunctionDefinition	heav heav <functionDefinition id="heav" name="heavyside"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> x </ci> </bvar> <piecewise> <piece> <cn type="integer"> 0 </cn> <apply> <lt/> <ci> x </ci> <cn type="integer"> 0 </cn> </apply> </piece> <piece> <cn> 0.5 </cn> <apply> <eq/> <ci> x </ci> <cn type="integer"> 0 </cn> </apply> </piece> <piece> <cn type="integer"> 1 </cn> <apply> <gt/> <ci> x </ci> <cn type="integer"> 0 </cn> </apply> </piece> <otherwise> <cn type="integer"> 0 </cn> </otherwise> </piecewise> </lambda> </math> </functionDefinition>	heavyside	$x 0 x 0 0.5 x 0 1 x 0 0$
FunctionDefinition	mod mod <functionDefinition id="mod" name="modulo"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> x </ci> </bvar> <bvar> <ci> y </ci> </bvar> <piecewise> <piece> <apply> <minus/> <ci> x </ci> <apply> <times/> <ci> y </ci> <apply> <ceiling/> <apply> <divide/> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <xor/> <apply> <lt/> <ci> x </ci> <cn type="integer"> 0 </cn> </apply> <apply> <lt/> <ci> y </ci> <cn type="integer"> 0 </cn> </apply> </apply> </piece> <otherwise> <apply> <minus/> <ci> x </ci> <apply> <times/> <ci> y </ci> <apply> <floor/> <apply> <divide/> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </lambda> </math> </functionDefinition>	modulo	$x y x y x y x 0 y 0 x y x y$
FunctionDefinition	e e <functionDefinition id="e"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> t </ci> </bvar> <bvar> <ci> stim </ci> </bvar> <bvar> <ci> t_on </ci> </bvar> <apply> <times/> <apply> <ci> heav </ci> <apply> <minus/> <ci> t </ci> <ci> t_on </ci> </apply> </apply> <apply> <ci> heav </ci> <apply> <minus/> <apply> <plus/> <ci> stim </ci> <ci> t_on </ci> </apply> <ci> t </ci> </apply> </apply> </apply> </lambda> </math> </functionDefinition>		$t stim t_on heav t t_on heav stim t_on t$
FunctionDefinition	po po <functionDefinition id="po"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> t </ci> </bvar> <bvar> <ci> d </ci> </bvar> <apply> <ci> heav </ci> <apply> <minus/> <ci> d </ci> <ci> t </ci> </apply> </apply> </lambda> </math> </functionDefinition>		$t d heav d t$
FunctionDefinition	p p <functionDefinition id="p"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> t </ci> </bvar> <bvar> <ci> per </ci> </bvar> <apply> <ci> po </ci> <apply> <ci> mod </ci> <ci> t </ci> <ci> per </ci> </apply> </apply> </lambda> </math> </functionDefinition>		$t per po mod t per$
FunctionDefinition	i_x i_x <functionDefinition id="i_x"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> t </ci> </bvar> <bvar> <ci> ampx </ci> </bvar> <bvar> <ci> stim </ci> </bvar> <bvar> <ci> t_on </ci> </bvar> <bvar> <ci> z </ci> </bvar> <apply> <times/> <ci> ampx </ci> <ci> z </ci> <apply> <ci> e </ci> <ci> t </ci> <ci> t_on </ci> <ci> stim </ci> </apply> </apply> </lambda> </math> </functionDefinition>		$t ampx stim t_on z ampx z e t t_on stim$
FunctionDefinition	i_y i_y <functionDefinition id="i_y"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> t </ci> </bvar> <bvar> <ci> ampy </ci> </bvar> <bvar> <ci> stim </ci> </bvar> <bvar> <ci> t_on </ci> </bvar> <bvar> <ci> z </ci> </bvar> <apply> <times/> <ci> ampy </ci> <ci> z </ci> <apply> <ci> e </ci> <ci> t </ci> <ci> t_on </ci> <ci> stim </ci> </apply> </apply> </lambda> </math> </functionDefinition>		$t ampy stim t_on z ampy z e t t_on stim$
FunctionDefinition	sd sd <functionDefinition id="sd"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <lambda> <bvar> <ci> x </ci> </bvar> <bvar> <ci> b </ci> </bvar> <apply> <times/> <apply> <exp/> <apply> <times/> <apply> <minus/> <ci> b </ci> </apply> <apply> <minus/> <cn type="integer"> 1 </cn> <apply> <cos/> <apply> <minus/> <ci> x </ci> <cn> 2.5 </cn> </apply> </apply> </apply> </apply> </apply> <ci> b </ci> </apply> </lambda> </math> </functionDefinition>		$x b b 1 x 2.5 b$

type	Parameters [35]	name	constant	value	unit	derived unit
Parameter	i_e i_e <parameter id="i_e" name="i_e = 0.4" value="0.4" constant="false"/>	i_e = 0.4	F	0.4		None
Parameter	i_i i_i <parameter id="i_i" name="i_i = 0" value="0" constant="false"/>	i_i = 0	F	0.0		None
Parameter	tauz tauz <parameter id="tauz" name="tauz = 50" value="50" constant="false"/>	tauz = 50	F	50.0		None
Parameter	gz gz <parameter id="gz" name="gz = .5" value="0.5" constant="false"/>	gz = .5	F	0.5		None
Parameter	sige sige <parameter id="sige" name="sige = 0.5" value="0.5" constant="false"/>	sige = 0.5	F	0.5		None
Parameter	sigi sigi <parameter id="sigi" name="sigi = .01" value="0.01" constant="false"/>	sigi = .01	F	0.01		None
Parameter	gie gie <parameter id="gie" name="gie = 3" value="3" constant="false"/>	gie = 3	F	3.0		None
Parameter	gei gei <parameter id="gei" name="gei = .4" value="0.4" constant="false"/>	gei = .4	F	0.4		None
Parameter	gii gii <parameter id="gii" name="gii = 0.15" value="0.15" constant="false"/>	gii = 0.15	F	0.15		None
Parameter	gee gee <parameter id="gee" name="gee = 2" value="2" constant="false"/>	gee = 2	F	2.0		None
Parameter	taue taue <parameter id="taue" name="taue = 1" value="1" constant="false"/>	taue = 1	F	1.0		None
Parameter	taui taui <parameter id="taui" name="taui = 3" value="3" constant="false"/>	taui = 3	F	3.0		None
Parameter	ampx ampx <parameter id="ampx" name="ampx = 70" value="70" constant="false"/>	ampx = 70	F	70.0		None
Parameter	ampy ampy <parameter id="ampy" name="ampy = 10" value="10" constant="false"/>	ampy = 10	F	10.0		None
Parameter	d d <parameter id="d" name="d = 1" value="1" constant="false"/>	d = 1	F	1.0		None
Parameter	per per <parameter id="per" name="per = 25" value="25" constant="false"/>	per = 25	F	25.0		None
Parameter	tau tau <parameter id="tau" name="tau = 20" value="20" constant="false"/>	tau = 20	F	20.0		None
Parameter	t_on t_on <parameter id="t_on" name="t_on = 0" value="0" constant="false"/>	t_on = 0	F	0.0		None
Parameter	stim stim <parameter id="stim" name="stim = 1000" value="1000" constant="false"/>	stim = 1000	F	1000.0		None
Parameter		x[0..49]	F	0.0		None
Parameter		y[0..19]	F	0.0		None
Parameter			T	0.0		None
Parameter			T	0.0		None
Parameter	b b <parameter id="b" name="b = 100" value="100" constant="false"/>	b = 100	F	100.0		None
Parameter		x[0..49] = ran(1)2pi-pi	T	0.0	dimensionless	None
Parameter		y[0..19] = ran(1)2pi-pi	T	0.0	dimensionless	None
Parameter	z z <parameter id="z" value="0" units="dimensionless" constant="false"/>		F	0.0	dimensionless	None
Parameter			F	0.0	dimensionless	None
Parameter			F	0.0	dimensionless	None
Parameter			F	0.0	dimensionless	None
Parameter	se se <parameter id="se" value="0" units="dimensionless" constant="false"/>		F	0.0	dimensionless	None
Parameter	si si <parameter id="si" value="0" units="dimensionless" constant="false"/>		F	0.0	dimensionless	None
Parameter	swgt swgt <parameter id="swgt" value="0" units="dimensionless" constant="false"/>		F	0.0	dimensionless	None
Parameter	per_input per_input <parameter id="per_input" value="0" units="dimensionless" constant="false"/>		F	0.0	dimensionless	None
Parameter	t t <parameter id="t" name="model time" value="0" units="dimensionless" constant="false"/>	model time	F	0.0	dimensionless	None

type	InitialAssignments [2]	name		assignment	derived units	sbo	cvterm
InitialAssignment			=	$ran 1 2$	None
InitialAssignment			=	$ran 1 2$	None

type	Rules [9]		assignment	derived units
Rule	d z/dt z <rateRule variable="z"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <divide/> <apply> <plus/> <apply> <minus/> <ci> z </ci> </apply> <apply> <ci> p </ci> <ci> t </ci> <ci> per </ci> </apply> </apply> <ci> tau </ci> </apply> </math> </rateRule>	=	$z p t per tau$	None
Rule		=	None	$None$
Rule		=	None	$None$
Rule		=	None	$None$
Rule	d se/dt se <rateRule variable="se"/>	=	None	$None$
Rule	d si/dt si <rateRule variable="si"/>	=	None	$None$
Rule	swgt swgt <assignmentRule variable="swgt"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <plus/> <apply> <times/> <cn> 0.8 </cn> <ci> se </ci> </apply> <apply> <times/> <cn> 0.2 </cn> <ci> si </ci> </apply> </apply> </math> </assignmentRule>	=	$0.8 se 0.2 si$	None
Rule	per_input per_input <assignmentRule variable="per_input"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <ci> i_x </ci> <ci> t </ci> <ci> ampx </ci> <ci> stim </ci> <ci> t_on </ci> <ci> z </ci> </apply> </math> </assignmentRule>	=	$i_x t ampx stim t_on z$	None
Rule	t t <assignmentRule variable="t"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <csymbol encoding="text" definitionURL="http://www.sbml.org/sbml/symbols/time"> time </csymbol> </math> </assignmentRule>	=	$time$	None

type	Events [2]	name	trigger	priority	delay	assignments	sbo	cvterm
Event	e0 e0 <event id="e0" useValuesFromTriggerTime="true"> <trigger initialValue="false" persistent="true"/> <listOfEventAssignments> <eventAssignment> <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <minus/> <pi/> </apply> </math> </eventAssignment> <eventAssignment variable="out_put"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <cn type="integer"> 1 </cn> </math> </eventAssignment> </listOfEventAssignments> </event>		None initialValue = False persistent = True			= out_put = $1$
Event	e1 e1 <event id="e1" useValuesFromTriggerTime="true"> <trigger initialValue="false" persistent="true"/> <listOfEventAssignments> <eventAssignment> <math xmlns="http://www.w3.org/1998/Math/MathML"> <apply> <minus/> <pi/> </apply> </math> </eventAssignment> <eventAssignment variable="out_put"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <cn type="integer"> 1 </cn> </math> </eventAssignment> </listOfEventAssignments> </event>		None initialValue = False persistent = True			= out_put = $1$