Nicotinic control of dopamine release in nucleus accumbens (Maex et al. 2014)

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Accession:228337
Minimal model of the VTA (ventral segmental area) representing two (GABA versus dopamine) neuron populations and two subtypes of nicotinic receptors (alpha4beta2 versus alpha7). The model is used to tell apart circuit from receptor mechanisms in the nicotinic control of dopamine release and its pharmacological manipulation.
Reference:
1 . Maex R, Grinevich VP, Grinevich V, Budygin E, Bencherif M, Gutkin B (2014) Understanding the role a7 nicotinic receptors play in dopamine efflux in nucleus accumbens. ACS Chem Neurosci 5:1032-40 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neural mass; Channel/Receptor;
Brain Region(s)/Organism: Basal ganglia;
Cell Type(s): Ventral tegmental area dopamine neuron;
Channel(s):
Gap Junctions:
Receptor(s): Nicotinic;
Gene(s):
Transmitter(s): Acetylcholine; Dopamine; Gaba; Glutamate;
Simulation Environment: XPP;
Model Concept(s): Schizophrenia; Addiction; Volume transmission; Neuromodulation; Pathophysiology; Rate-coding model neurons; Simplified Models;
Implementer(s): Maex, Reinoud [reinoud at bbf.uia.ac.be];
Search NeuronDB for information about:  Nicotinic; Acetylcholine; Dopamine; Gaba; Glutamate;
# XPP scripts for supplementary Figure S4A right of 
# Maex R, Grinevich VP, Grinevich V, Budygin E, Bencherif M, Gutkin B (2014)
# Understanding the role a7 nicotinic receptors play in dopamine efflux
# in nucleus accumbens. ACS Chemical Neuroscience 5, 1032-1040.
#
# Activation model of Figure 3B; varying the dose of TC-7020.

# Output is accumbal dopamine concentration in microM.


# Naming conventions 
#
# V_      = membrane voltage of (neuron or neuron population)
# R_      = release of (transmitter)
# C_      = concentration of (transmitter)
# I_      = membrane current of (channel or receptor)
# P_      = presynatic membrane current of (receptor)
# tau_    = time-constant of
# tmin_ = minimum value of time-constant of
# tmax_ = maximum value of time-constant of
# inf_    = steady-state value of
# act_    = level of activation of (receptor)
# des_    = level of desensitisation of (receptor)
# w_      = weight of
# EC50_   = halfmax concentration of steady-state response
# Ktau_   = halfmax concentration of time-constant
# stim_   = stimulation by

# glu  = glutamate or glu-ergic neuron (population)
# dop  = dopamine or dopamine-ergic neuron (population)
# gab  = gaba or gaba-ergic neuron (population)
# ach  = acetylcholine
# nic  = nicotine
# a7   = alpha7-type nicACh receptor
# a4b2 = alpha4-beta2-type nicACh receptor
# bas  = basal
#


# Units 
# time seconds
# concentration microMolar (nanoMolar in printed figures)


# Transfer functions (input-output) 
# sigmoid
f(x) = 1/(1 + exp(-x)) 
# halfwave rectification
hwr(x) = heav(x) * x    
# clipped at 0 and 1
clip(x) = (1 + (x-1) * (heav (1-x))) * heav(x) 
# Hill equation
# Hill(x,K,n) = 1 / (1 + (K/x)^n)
Hill(x,K,n) = x^n / (x^n + K^n) 
# competitive Hill ---THIS IS NEW and allows for competitive inhibition between up to three compounds --- 
compHill(x,y,z,wx,wy,wz,Kx,Ky,Kz,n) = \
  (wx * x^n/(x^n + Kx^n * (1 + (y/Ky)^n + (z/Kz)^n))) + \
  (wy * y^n/(y^n + Ky^n * (1 + (x/Kx)^n + (z/Kz)^n))) + \
  (wz * z^n/(z^n + Kz^n * (1 + (x/Kx)^n + (y/Ky)^n)))
# rectangular pulse
rect_pulse(t,from,to,amp) = amp * (heav (t-from) - heav (t-to))



# THE MODEL (some of this code is based on Graupner & Gutkin)

# We now have two neuron populations sharing inputs from
# glu neurons (mostly a7-driven) and through a4b2 receptors.
# The parameter coefficients r and s specify the balance 
# between these inputs.


   par s=0,r=0.7

# the dynamics of the dopaminergic neuron population V_dop

   V_dop' = (-V_dop - I_gab + hwr (I_basDop + s*I_glu + r*I_b2)) / tau_Vdop

   par tau_Vdop=0.02,I_basDop=0.1
   aux aux_hwr=hwr (I_basDop + s*I_glu + r*I_b2)


# the dynamics of the gaba-ergic neuron population V_gab

   V_gab' = (-V_gab + hwr ((1-s)*I_glu + (1-r)*I_b2)) / tau_Vgab

   par tau_Vgab=0.02


# the (stationary) glutamatergic input I_glu to dopamine (and GABA) neurons

   I_glu = w_glu * clip (V_glu + P_glu)

   par w_glu=1,V_glu=0.1


# the (varying) gaba-ergic input I_gab to dopamine neurons

   I_gab = w_gab * clip (V_gab + I_basGab)

   aux auxI_gab=I_gab
   par w_gab=1.5 
   par I_basGab=-0.05
   aux auxI_gab=I_gab

# the presynaptic facilitation of glu input to dopamine (and GABA) neurons

   P_glu = P_a7


# the dynamics of presynaptic a7 receptors (same single variable for 
# glu inputs to dopamine cells in VTA and medium spiny neurons in striatum)

   P_a7 = act_a7 * (1 - des_a7)
   aux auxP_a7=P_a7
   aux auxact_a7=act_a7
   aux auxsen_a7=1-des_a7


#   /* activation of alpha7 */

   act_a7' = (- act_a7 + inf_actA7) / tau_actA7

   inf_actA7 = compHill(C_ach,    C_nic,        C_agA7, \
                            1, w_actNicA7,   w_actAgA7, \
                   EC50_A7ach, EC50_A7nic,   EC50_A7ag, Hill_actA7)


   par EC50_A7=80
   par EC50_A7ach=68
   par EC50_A7nic=13
   par Hill_actA7=1.73
   par EC50_A7ag=0.03 
   par w_actNicA7=0.8 
   par w_actAgA7=0.3
   par tau_actA7=0.005


#   /* desensitisation of alpha7 */

   des_a7' = (- des_a7 + inf_desA7) / tau_desA7

   inf_desA7 = compHill(    0,      C_nic,      C_agA7, \
                            1,          1,           1, \
                            1, IC50_A7nic,   IC50_A7ag, Hill_desA7)

   par IC50_A7nic=1.3
   par Hill_desA7=2

   par IC50_A7ag=0.002

   tau_desA7 = tmin_desA7 + \ 
               tmax_desA7 * (1 - inf_desA7)
   aux aux_tdA7=tau_desA7

   par tmin_desA7=0.05
   par tmax_desA7=120


# the dynamics of somatic a4b2 receptors on the soma/dendrite of dopamine neurons

   I_b2 = act_b2 * (1 - des_b2)

   aux auxI_b2=I_b2
   aux auxact_b2=act_b2
   aux auxsen_b2=1-des_b2


#   /* activation of alpha4beta2 */

   act_b2' = (- act_b2 + inf_actB2) / tau_actB2

   inf_actB2 = compHill(C_ach,      C_nic,        C_agB2, \
                            1, w_actNicB2,   w_actAgB2, \
                   EC50_B2ach, EC50_B2nic,   EC50_B2ag, Hill_actB2)


   par EC50_actB2=30
   par EC50_B2ach=30
   par EC50_B2ag=30
   par EC50_B2nic=0.23
   par Hill_actB2=1.05
   par w_actNicB2=2
   par w_actAgB2=1
   par tau_actB2=0.005


#   /* desensitisation */

   des_b2' = (- des_b2 + inf_desB2) / tau_desB2

   inf_desB2 = Hill (C_nic + C_agB2, EC50_desB2, Hill_desB2)

   tau_desB2 = tmin_desB2 + \ 
               tmax_desB2 * Hill (Ktau_desB2, C_nic + C_agB2, Htau_desB2)

   aux aux_tdB2=tau_desB2

   par EC50_desB2=0.061
   par Hill_desB2=0.5
   par tmin_desB2=0.5
   par tmax_desB2=600
   par Ktau_desB2=0.11
   par Htau_desB2=3


# the dynamics of dopamine release AND RE-UPTAKE
# This is a bit complicated because for a fair comparison, all dopamine levels
# are normalized to the same fixed baseline (about 50 nanoMolar). Hence we assume
# that homeostatic mechanisms are at work that keep the baseline fixed under variable
# parameter conditions (mostly varying cholinergic tones).

   R_dop' = (C_basDop * (1 + (V_dop-ss_Vdop) / ss_Vdop) - R_dop) / tau_Rdop - R_dop * Vmax_Rdop / (R_dop + EC50_Rdop)

   par tau_Rdop=0.2,P_a7bas=0.01
   par C_basDop=0.1
# the following values are from Chen and Budygin 2007
   par Vmax_Rdop=1.3
   par EC50_Rdop=0.2


# the physiological (ach) and pharmacological (nic, specific a7 and a4b2 agonists) stimuli

#  /* acetylcoline */
   par C_ach=0

#   /* nicotine */
   stim_nic = bas_nic + rect_pulse (t, 66, 67, dose_Nic)

   par dose_nic=1

# we now simulate an alpha function as a second-order ode
# the alpha-function is area normalized
# to calculate its peak, take amplitude and divide by 10*e

   C_nic_nic' = (-C_nic_nic + stim_nic)/tau1_nic
   C_nic' = (-C_nic + C_nic_nic)/tau2_nic

   par tau1_nic=10,tau2_nic=10,bas_nic=0 

#   /* alpha7 agonist */

   stim_a7 = rect_pulse (t, 36, 37, dose_Aga7)

# THIS IS THE PARAMETER VARIED IN THE FIGURE
#   par dose_Aga7=0.1
#   par dose_Aga7=0.3
   par dose_Aga7=0.5
#   par dose_Aga7=1.0
#   par dose_Aga7=2.0

   C_agA7A7' = (-C_agA7A7 + stim_a7) / tau1_agA7
   C_agA7' = (-C_agA7 + C_agA7A7) / tau2_agA7

   par tau1_agA7=10,tau2_agA7=100

#   /* alpha4 beta2 agonist */

   stim_b2 = rect_pulse (t, 60, 61, 0)
   C_agB2' = (-C_agB2 + stim_b2) / tau_agB2

   par tau_agB2=10


# /* calculating the steady-states (in reverse order) */
    ss_Ib2 = compHill(   C_ach,          0,           0, \
                            1, w_actNicB2,   w_actAgB2, \
                   EC50_B2ach, EC50_B2nic,   EC50_B2ag, Hill_actB2)
    ss_Pa7 = compHill(   C_ach,          0,           0, \
                            1, w_actNicA7,   w_actAgA7, \
                   EC50_A7ach, EC50_A7nic,   EC50_A7ag, Hill_actA7)
    ss_Pglu = ss_Pa7
    ss_Iglu = w_glu * clip (V_glu + ss_Pglu)
    ss_Vgab = hwr ((1-s)*ss_Iglu + (1-r)*ss_Ib2)
    ss_Igab = w_gab * clip (ss_Vgab + I_basGab)
    ss_Vdop = - ss_Igab + hwr (I_basDop + s*ss_Iglu + r*ss_Ib2)
# aux auxss_Vdop=ss_Vdop


# the initial conditions
act_a7(0)=0
des_a7(0)=0
act_b2(0)=0
des_b2(0)=0
V_dop(0)=0
V_gab(0)=0
C_nic(0)=bas_nic
C_nic_nic(0)=bas_nic


# the numerical parameters
@ MAXSTOR=500000
@ BOUNDS=1e+8
@ DT=0.005
@ TOTAL=150
@ xlo=20
@ xhi=120
@ ylo=0
@ yhi=0.12
@ METHOD=rk
@ NJMP=20
@ YP=r_dop
done


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