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# -*- coding: utf-8 -*-
"""
Model of TRPM8-dependent dynamic response accompanying the publication:
TRPM8-DEPENDENT DYNAMIC RESPONSE IN A MATHEMATICAL MODEL OF COLD THERMORECEPTOR
Olivares, E. et al.
Submitted to PLoS One, July 2015
"""
import numpy as np
import matplotlib.pyplot as plt
import scipy.signal
import time as time_comp
#fixed (common) parameters
Ed = 50. ; Er = -90.; Em8 = 0.; El = -70.
tsd = 10.; tsr = 24.; tr = 1.5
ssd = 0.1; sd = 0.25; sr = 0.25
Vhsd = -40.; Vhd = -25.; Vhr = -25.
zm8 = 0.65; C = 67.; DE = 9000
Kcam8 = 0.0005; d = 1.
D = 0.5; twn = 1.
eta = 0.012; kappa = 0.18; F = 96500; R = 8.314
#parameters Sets (Table 1 of paper)
Params=np.loadtxt('parameters.txt')
Param_indx=[7,28,54,92,103,134,157,158,168,185,212,215,227,272,275,289,293,311,323,339]
#Temperature protocols
TempTrace1=np.loadtxt('short_pulses.txt',skiprows=1)
TempTrace2=np.loadtxt('temp_steps.txt',skiprows=1)
[gm8, gl, tca, tdv, pca, gsd, gsr, gd, gr, dvmin, dvmax] = [0,0,0,0,0,0,0,0,0,0,0]
rho = lambda x: 1.3**((x-25)/10)
phi = lambda x: 3.**((x-25)/10)
def integ_step(Var, dt, temp, accel):
r = rho(temp)
f = phi(temp)
[v,ar,asd,asr,ca, dv, iwn]=Var
ad = 1./(1+np.exp(-sd*(v-Vhd)))
isd = r*gsd*asd*(v-Ed)
dvinf = dvmin + (dvmax-dvmin)*ca/(ca + Kcam8)
vhm8 = (C*R*(temp) -DE)/(zm8*F)*1000.
am8 = 1./(1+np.exp(-zm8*F /(R*(temp+273.15)) *(v - vhm8 - dv)/1000.))
im8 = gm8*am8*(v-Em8)
Imemb=isd + r*gd*ad*(v - Ed) + r*(gr*ar + gsr*(asr**2)/(asr**2+0.4**2))*(v-Er) \
+ im8 + gl*(v - El) + iwn
arinf = 1./(1+np.exp(-sr*(v-Vhr)));
asdinf = 1./(1+np.exp(-ssd*(v-Vhsd)));
Delta=np.array([-Imemb,
f*(arinf - ar)/tr,
f*(asdinf - asd)/tsd,
f*(-eta*isd - kappa*asr)/tsr,
-accel*(pca*10.0*im8/(2*F*d) + ca/tca), # 10.0 is a correction factor for units
(dvinf-dv)/tdv,
-iwn + D*np.random.normal(0)/np.sqrt(dt)])
return Delta
#Implementacion de Metodo de Euler Maruyama
def EulerV(integ_step,X,N,dt,temp): #Voltage trace at a fixed temperature
datos = np.zeros((7,N))
#First an adaptation run
for i in np.arange(15000/dt):
X += + dt * integ_step(X, dt, temp, 100)
#Then the real run
datos[:,0] = X
i=1
# while i<N/4:
# #Metodo de Euler. Otros metodos mas sofisticados se pueden implementar sobre la base de HyB()
# datos[:,i]=datos[:,i-1] + dt * integ_step(datos[:,i-1], dt, temp, 100)
# i+=1
while i<N:
#Metodo de Euler. Otros metodos mas sofisticados se pueden implementar sobre la base de HyB()
datos[:,i]=datos[:,i-1] + dt * integ_step(datos[:,i-1], dt, temp, 1)
i+=1
return datos
def EulerS(integ_step,X,N,dt,temp): #No voltage trace, only spikes
datos = X
i=1
firing = 0
thresh=-30
spikes=[]
t0=time_comp.time()
#First an adaptation run
while i*dt<20000:
if i%100000==0:
print "*ADAPTATION* t=",i*dt,"real t=",time_comp.time()-t0,"remaining=",(N-i)*(time_comp.time()-t0)/i
datos += + dt * integ_step(datos, dt, temp[i], 100)
if (firing==0)*(datos[0]>thresh):
spikes.append(i*dt)
firing=1
if firing*(datos[0]<thresh):
firing=0
i+=1
while i<N:
if i%100000==0:
print "t=",i*dt,"real t=",time_comp.time()-t0,"remaining=",(N-i)*(time_comp.time()-t0)/i
datos += + dt * integ_step(datos, dt, temp[i], 1)
if (firing==0)*(datos[0]>thresh):
spikes.append(i*dt)
firing=1
if firing*(datos[0]<thresh):
firing=0
i+=1
return np.array(spikes)
#Simulacion
def simulation(ParamSet=185,Temp=33.5):
dt=0.05
if isinstance(Temp,(float,int)):
tEnd=4000
time= np.arange(0, tEnd, dt)
Temp_t=Temp*np.ones_like(time)
elif type(Temp)==np.ndarray:
tEnd=Temp[-1,0]*1000
time= np.arange(0, tEnd, dt)
Temp_t=np.interp(time,Temp[:,0]*1000,Temp[:,1])
else:
return 0
P_ind=Param_indx.index(ParamSet)
global gm8, gl, tca, tdv, pca, gsd, gsr, gd, gr, dvmin, dvmax
[gm8, gl, tca, tdv, pca, gsd, gsr, gd, gr, dvmin, dvmax]=Params[P_ind]
#In Neuron conductances are S/cm2, so we need to correct to mS/cm2
gm8*=1000;gl*=1000;gsd*=1000;gsr*=1000;gd*=1000;gr*=1000
N = time.size
#initial conditions
v=-65
r = rho(Temp_t[0])
f = phi(Temp_t[0])
ad = 1./(1+np.exp(-sd*(v-Vhd)));
ar = 1./(1+np.exp(-sr*(v-Vhr)));
asd = 1./(1+np.exp(-ssd*(v-Vhsd)));
asr = -eta*r*gsd*asd*(v - Ed)/kappa;
dv = (37-Temp_t[0])*5.
vhm8 = (C*R*(Temp_t[0]) -DE)/(zm8*F)*1000.
am8 = 1./(1+np.exp(-zm8*F /(R*(Temp_t[0]+273.15)) *(v - vhm8 - dv)/1000))
im8 = gm8*am8*(v-Em8)
ca = -pca*10*im8/(2*F*d)*tca
dv = dvmin + (dvmax-dvmin)*ca/(ca + Kcam8)
# print vhm8,am8,ca,dv
iwn = 0
X=np.array([v,ar,asd,asr,ca, dv,iwn])
if isinstance(Temp,(float,int)):
return time,EulerV(integ_step,X,N,dt,Temp)
else:
return time,Temp_t,EulerS(integ_step,X,N,dt,Temp_t)
if __name__=='__main__':
plt.figure(1,figsize=(8,12))
plt.clf()
p=1
for T in (34,30,26.,22.):
print "Simulating temp=",T
time,Vars = simulation(ParamSet=293,Temp=T)
plt.subplot(4,1,p)
plt.plot(time,Vars[0,:],'k')
plt.ylabel('Voltage (mV)')
plt.text(3500,0,u'%.2g °C'%T,bbox=dict(facecolor='white'))
if p==4:
plt.xlabel('Time (ms)')
p+=1
time,temp,spikes=simulation(ParamSet=158,Temp=TempTrace1)
plt.figure(2,figsize=(12,8))
plt.clf()
plt.subplot(311)
plt.plot(time,temp,'k')
plt.ylabel(u'Temp (°C)')
plt.subplot(312)
plt.hist(spikes,bins=np.arange(0,time[-1],1000))
plt.ylim((0,70))
plt.ylabel('Rate (/s)')
plt.subplot(313)
plt.plot(spikes[1:],np.diff(spikes),'k.')
plt.yscale('log')
plt.ylim((10,3000))
plt.ylabel('ISIs (ms)')
plt.xlabel('Time (ms)')
plt.show()