# Example: Rothman_Manis_2003

Note

You can launch an interactive, editable version of this example without installing any local files using the Binder service (although note that at some times this may be slow or fail to open):

## Cochlear neuron model of Rothman & Manis

Rothman JS, Manis PB (2003) The roles potassium currents play in regulating the electrical activity of ventral cochlear nucleus neurons. J Neurophysiol 89:3097-113.

All model types differ only by the maximal conductances.

Adapted from their Neuron implementation by Romain Brette

```from brian2 import *

#defaultclock.dt=0.025*ms # for better precision

'''
Simulation parameters: choose current amplitude and neuron type
(from type1c, type1t, type12, type 21, type2, type2o)
'''
neuron_type = 'type1c'
Ipulse = 250*pA

C = 12*pF
Eh = -43*mV
EK = -70*mV  # -77*mV in mod file
El = -65*mV
ENa = 50*mV
nf = 0.85  # proportion of n vs p kinetics
zss = 0.5  # steady state inactivation of glt
temp = 22.  # temperature in degree celcius
q10 = 3. ** ((temp - 22) / 10.)
# hcno current (octopus cell)
frac = 0.0
qt = 4.5 ** ((temp - 33.) / 10.)

# Maximal conductances of different cell types in nS
maximal_conductances = dict(
type1c=(1000, 150, 0, 0, 0.5, 0, 2),
type1t=(1000, 80, 0, 65, 0.5, 0, 2),
type12=(1000, 150, 20, 0, 2, 0, 2),
type21=(1000, 150, 35, 0, 3.5, 0, 2),
type2=(1000, 150, 200, 0, 20, 0, 2),
type2o=(1000, 150, 600, 0, 0, 40, 2) # octopus cell
)
gnabar, gkhtbar, gkltbar, gkabar, ghbar, gbarno, gl = [x * nS for x in maximal_conductances[neuron_type]]

# Classical Na channel
eqs_na = """
ina = gnabar*m**3*h*(ENa-v) : amp
dm/dt=q10*(minf-m)/mtau : 1
dh/dt=q10*(hinf-h)/htau : 1
minf = 1./(1+exp(-(vu + 38.) / 7.)) : 1
hinf = 1./(1+exp((vu + 65.) / 6.)) : 1
mtau =  ((10. / (5*exp((vu+60.) / 18.) + 36.*exp(-(vu+60.) / 25.))) + 0.04)*ms : second
htau =  ((100. / (7*exp((vu+60.) / 11.) + 10.*exp(-(vu+60.) / 25.))) + 0.6)*ms : second
"""

# KHT channel (delayed-rectifier K+)
eqs_kht = """
ikht = gkhtbar*(nf*n**2 + (1-nf)*p)*(EK-v) : amp
dn/dt=q10*(ninf-n)/ntau : 1
dp/dt=q10*(pinf-p)/ptau : 1
ninf =   (1 + exp(-(vu + 15) / 5.))**-0.5 : 1
pinf =  1. / (1 + exp(-(vu + 23) / 6.)) : 1
ntau =  ((100. / (11*exp((vu+60) / 24.) + 21*exp(-(vu+60) / 23.))) + 0.7)*ms : second
ptau = ((100. / (4*exp((vu+60) / 32.) + 5*exp(-(vu+60) / 22.))) + 5)*ms : second
"""

# Ih channel (subthreshold adaptive, non-inactivating)
eqs_ih = """
ih = ghbar*r*(Eh-v) : amp
dr/dt=q10*(rinf-r)/rtau : 1
rinf = 1. / (1+exp((vu + 76.) / 7.)) : 1
rtau = ((100000. / (237.*exp((vu+60.) / 12.) + 17.*exp(-(vu+60.) / 14.))) + 25.)*ms : second
"""

# KLT channel (low threshold K+)
eqs_klt = """
iklt = gkltbar*w**4*z*(EK-v) : amp
dw/dt=q10*(winf-w)/wtau : 1
dz/dt=q10*(zinf-z)/ztau : 1
winf = (1. / (1 + exp(-(vu + 48.) / 6.)))**0.25 : 1
zinf = zss + ((1.-zss) / (1 + exp((vu + 71.) / 10.))) : 1
wtau = ((100. / (6.*exp((vu+60.) / 6.) + 16.*exp(-(vu+60.) / 45.))) + 1.5)*ms : second
ztau = ((1000. / (exp((vu+60.) / 20.) + exp(-(vu+60.) / 8.))) + 50)*ms : second
"""

# Ka channel (transient K+)
eqs_ka = """
ika = gkabar*a**4*b*c*(EK-v): amp
da/dt=q10*(ainf-a)/atau : 1
db/dt=q10*(binf-b)/btau : 1
dc/dt=q10*(cinf-c)/ctau : 1
ainf = (1. / (1 + exp(-(vu + 31) / 6.)))**0.25 : 1
binf = 1. / (1 + exp((vu + 66) / 7.))**0.5 : 1
cinf = 1. / (1 + exp((vu + 66) / 7.))**0.5 : 1
atau =  ((100. / (7*exp((vu+60) / 14.) + 29*exp(-(vu+60) / 24.))) + 0.1)*ms : second
btau =  ((1000. / (14*exp((vu+60) / 27.) + 29*exp(-(vu+60) / 24.))) + 1)*ms : second
ctau = ((90. / (1 + exp((-66-vu) / 17.))) + 10)*ms : second
"""

# Leak
eqs_leak = """
ileak = gl*(El-v) : amp
"""

# h current for octopus cells
eqs_hcno = """
ihcno = gbarno*(h1*frac + h2*(1-frac))*(Eh-v) : amp
dh1/dt=(hinfno-h1)/tau1 : 1
dh2/dt=(hinfno-h2)/tau2 : 1
hinfno = 1./(1+exp((vu+66.)/7.)) : 1
tau1 = bet1/(qt*0.008*(1+alp1))*ms : second
tau2 = bet2/(qt*0.0029*(1+alp2))*ms : second
alp1 = exp(1e-3*3*(vu+50)*9.648e4/(8.315*(273.16+temp))) : 1
bet1 = exp(1e-3*3*0.3*(vu+50)*9.648e4/(8.315*(273.16+temp))) : 1
alp2 = exp(1e-3*3*(vu+84)*9.648e4/(8.315*(273.16+temp))) : 1
bet2 = exp(1e-3*3*0.6*(vu+84)*9.648e4/(8.315*(273.16+temp))) : 1
"""

eqs = """
dv/dt = (ileak + ina + ikht + iklt + ika + ih + ihcno + I)/C : volt
vu = v/mV : 1  # unitless v
I : amp
"""
eqs += eqs_leak + eqs_ka + eqs_na + eqs_ih + eqs_klt + eqs_kht + eqs_hcno

neuron = NeuronGroup(1, eqs, method='exponential_euler')
neuron.v = El

run(50*ms, report='text')  # Go to rest

M = StateMonitor(neuron, 'v', record=0)
neuron.I = Ipulse

run(100*ms, report='text')

plot(M.t / ms, M[0].v / mV)
xlabel('t (ms)')
ylabel('v (mV)')
show()
```