# ClC2-VClamp-Prescott
# Written by Steve Prescott, 2012
# from Ratte and Prescott (ClC-2 channels regulate neuronal excitability, not intracellular chloride levels. J Neurosci 2011; 31: 15838-15843)
# This is the code for voltage clamp simulations
# Designed for XPPAUT
v=va+vb*heav(t>tb)+vc*heav(t>tc)
# specify changes in command voltage... this sequence steps from -70 to +60 to -90
param va=-70, vb=130, vc=-150
# specify time of steps (in ms)
param tb=2000, tc=4000
aux v_=v
# other equations are like in code for current clamp, except that Cli also depends on intracellular dialysis in this code
# synaptic excitation and adaptation have been removed. Ina, IK, and Ileak have been left but are irrelevant unless you wish to measure them
# outputs of interest are intracellular chloride Cli and Iclc2.
# synaptic inhibition is intact so that one can apply a chloride load
dw/dt = phi*(winf(V)-w)/tauw(V)
w(0)=0.000025
minf(v)=.5*(1+tanh((v-v1)/v2))
winf(v)=.5*(1+tanh((v-v3)/v4))
tauw(v)=1/cosh((v-v3)/(2*v4))
param vk=-90,vl=-70,vna=45
param gk=20,gl=1,gna=20
param v1=-1.2,v2=18
# v1 and v2 correspond to beta_m and gamma_m in paper
param v3=-9,v4=10
# v3 and v4 correspond to beta_w and gamma_w in paper
param phi=.25,cap=2
# SYNAPTIC INHIBITION
# Here is the second WIENER VARIABLE... gives Ornstein-Uhlenbeck process for synaptic inhibition
wiener nz2
aux ginh_=(ginh*inorm+ginh_avg)*irect*(0+oninh(t)+offinh(t))
dginh/dt=-ginh/tau_inh+scale_inh*nz2
inorm=sqrt(2/tau_inh)
irect=heav((ginh*inorm+ginh_avg)>0)
par scale_inh=0
par tau_inh=10
par ginh_avg=1
# See below for reversal potentials associated with chloride
oninh(t)=heav(t>=tst_oninh)*1
offinh(t)=heav(t>(tst_oninh+tr_offinh))*(-1)
param tst_oninh=0,tr_offinh=4000
# to give non-noisy gaba application
# set scale_inh to 0
# set intensity by ginh_avg
# set duration (onset and offset) by tst_oninh and tr_offinh
# currently set to have open gaba channels during voltage command step to 0 mV, and then they close during step to -90 mV
# ClC-2
# parameters based on Staley 94 J Neurophysiol paper
# voltage-dependence is relative to Ecl, which is how you get rectification
dp/dt = (pinf(V)-p)/taup
pinf(V)=1/(1+exp((vcl-betap-v)/gammap))
param betap=15, gammap=-14
# v1/2 (i.e. betap) and vslope (gammaP) taken from Staley 94, tau is an estimate from that same paper.
param taup=300
# estimate (slow) tau from Zuniga et al. 2004 J Physiol, at body temp (which is what Staley used in 94)
p(0)=0
# instead of using original rectification strategy, you can get simple rectification with the following param
# betap=0 (centers curve on vcl), gammap=-0.0001 (makes the curve very steep), taup=0.1 (makes activation instantaneous)
aux Iclc2 = gclc*p*(V-Vcl)
param gclc=0
# CHLORIDE HANDLING
# GHK equation, where 4 is for ratio of Cl to bicarb flux
Vgaba = 1000*R*Tem/F*ln((4*cli+bicarb*11.8)/(4*clo+bicarb*25))
# bicarb can be set to 1 or 0 to include or exclude bicarbonate component
param bicarb=1
# Nernst equations
vbicarb = 1000*R*Tem/F*ln((bicarb*11.8)/(bicarb*25))
Vcl = 1000*R*Tem/F*ln(cli/clo)
aux vcl_=vcl
aux vgaba_=vgaba
param F=96485, R=8.3, Tem=310
param clo=120
cli(0)=6
x = (Vbicarb-Vgaba)/(Vbicarb-Vcl)
# based on ginh(v-vgaba) = x*ginh(v-vcl) + (1-x)ginh(v-vbicarb), re-arrange to find x, which apportions to current (ion flux) attributable to each ion species
aux x_ = x
# Next line updates intracellular chloride concentration, including intracellular dialysis from recording pipette
dcli/dt = SAvol*((ginh*inorm+ginh_avg)*irect*x*(0+oninh(t)+offinh(t))*(v-Vcl)+gkcc2*(Vk-Vcl)+gclc*p*(V-Vcl))/F+(pip_cl-cli)/tau_pip
# note for gaba current that driving force is calculated as v-Vcl and is multiplied by x in order to isolate chloride component of the total current.
param pip_cl=4, tau_pip=1000
param gkcc2=.7
aux Ikcc2 = gkcc2*(Vk-Vcl)
# Note that kcc2 does not appear in current balance equation because it is electroneutral (i.e. Cl and K flux cancel each other out)
# SHAPE
# for sphere: vol=(4/3)*pi*(ra^3), SA=4*pi*(ra^2), SA/vol=3/ra
# for a cylinder: vol=pi*h*(ra^2), SA=2*pi*ra*(ra+h), SA/vol=(2/ra)+(2/h) -> Sa/vol=2/ra if you exlclude ends...assume it is connected to adjoining cylinders
# Therefore, shape = 3 for sphere; =2 for cylinder without ends
param shape=3
!SAvol=shape/(10*ra)
# note because of units, factor of 10 is applied to denominator (convert mm to cm to get cm^3 for dealing with volumes)
# Radius now specified in mm, 6.3 microns ->0.0063 mm,
param ra=.0063
# this radius gives surface area (of sphere) of 5x10^-6 cm^2
# Adjust to simulate cylindrical dendrite
# PRACTICAL DETAILS FOR XPP
@ total=20000,dt=.1,xlo=-100,xhi=60,ylo=-.125,yhi=.6,xp=v,yp=w
@ meth=Euler
# ALWAYS USE EULER METHOD WITH NOISE PROCESSES (although there are no such mechanisms in this code
@ dsmin=1e-5,dsmax=.1,parmin=0,parmax=80, autoxmin=0,autoxmax=80,autoymin=-80,autoymax=40
@ MAXSTOR=1000000
done