Playing around with synapses

In this little section, you should examine the time courses of the different synaptic types. In the file below, I describe a simple active cell that synapses onto a passive compartment V_post. There are 5 different synaptic currents simulated (the depressed synapse is among them). The equations are based on the models presented in the Destexhe et al paper. Here is the ODE file

 
# Synapse exercises
# presynaptic cell
v'=-(gna*h*m^3*(v-ena)+gk*n^4*(v-ek)+gl*(v-el) -i-ip*heav(t-ton)*heav(toff-t))/c
m'=am(v)*(1-m)-bm(v)*m
h'=ah(v)*(1-h)-bh(v)*h
n'=an(v)*(1-n)-bn(v)*n
# post synaptic cell
vpost'=-.2*(vpost-vp0)-iampa-igaba-inmda-igabb-idep
# transmitter released
trans=tmax/(1+exp(-(v-2)/5))
# synaptic types
s_ampa'=al_ampa*trans*(1-s_ampa) -s_ampa*bet_ampa
s_nmda'=al_nmda*trans*(1-s_nmda) -s_nmda*bet_nmda
s_gaba'=al_gaba*trans*(1-s_gaba) -s_gaba*bet_gaba
r'=al_gabb*trans*(1-r) -r*bet_gabb
s_gabb'=k3*r-k4*s_gabb
# depressed AMPA synapse
s_dep'=al_ampa*trans*(1-s_dep-xx) -s_dep*bet_ampa
xx'=s_dep*bet_ampa-beta2*xx
# synaptic currents
idep=g_dep*s_dep*(vpost-vex)
iampa=g_ampa*s_ampa*(vpost-vex)
inmda=g_nmda*s_nmda*(vpost-vex)/(1+exp(-.062*vpost)*(mg/3.57))
igaba=g_gaba*s_gaba*(vpost-vin)
igabb=g_gabb*(s_gabb^4/(s_gaba^4+kd))*(vpost-ek)
# make them plottable
aux i_ampa=iampa
aux i_nmda=inmda
aux i_gaba=igaba
aux i_gabb=igabb
aux i_dep=idep
# functions
am(v)=.32*(54+v)/(1-exp(-(v+54)/4))
bm(v)=.28*(v+27)/(exp((v+27)/5)-1)
ah(v)=.128*exp(-(50+v)/18)
bh(v)=4/(1+exp(-(v+27)/5))
an(v)=.032*(v+52)/(1-exp(-(v+52)/5))
bn(v)=.5*exp(-(57+v)/40)
# parameters
par ek=-100,ena=50,el=-67,vp0=-70
par gl=.1,gk=80,gna=100
par c=1,i=0
par bet_ampa=.19,al_ampa=1.1, g_ampa=.038
par bet_nmda=.0066,al_nmda=.072, g_nmda=.0,mg=0
par bet_gaba=.18,al_gaba=5, g_gaba=.0
par bet_gabb=.0012,al_gabb=.09, k3=.18,k4=.034,kd=4,g_gabb=.0
par g_dep=0.0,beta2=.01
par tmax=3.2, vex=0,vin=-80
par ton=0,toff=10,ip=1
init v=-67.68,m=.0128,h=1,n=.0332,vpost=-70
@ method=qualrk,toler=.0001,total=40,dt=.25
@ xhi=40,yp=vpost,ylo=-72,yhi=-62
done

The file is set up to simulate 40 msec of time. The presynaptic cell is injected with a small or large pulse of current to elicit either 1 or many action potentials. The parameter ip controlls the magnitude of ther current. To get 1 presynaptic spike set ip=1 and to get 4 presynaptic spikes, set it to 35. The conductance parameters are g_ampa, g_nmda, g_gaba, g_gabb, g_dep for each of the four types and depressed AMPA synapse. The graph is set up to show the post-synaptic cell which is passive and receives a synapse from the presynaptic cell with magnitude $0.038\ mS/cm^2.$ (This strange number results in 1 nS of conductance for a 10 by 10 micron cylinder.)

Exercises

1.

Run the given ODE file and simulate the effects of a single AMPA spike and on the same graph the GABA-A and the depressed synapse. (Make sure you set the non-active synaptic conductances to 0 and the active conductance to 0.038.) Although the amplitude of the conductances for both the AMPA and the GABA-A synapse are close, there is greater depolarization due to the AMPA synapse. Why? Does synaptic depression have an effect on the AMPA single spike response?

2.

Look at the response to NMDA synapses (in zero magnesium - the parameter mg=0) and to GABA-B synapses. Why is the response to NMDA small? Why is the GABA-B response almost no-existent?

3.

Set ip=35 to give a burst of action potentials. Compare the AMPA and the depressed AMPA. What is the difference?

4.

Set the time of integration to 1000 msec. Set the x-axis length to be 1000 and the y-axis window between -75 and -60. Now reintegrate the equations and look at the responses to GABA-B and NMDA synapses. Why is the GABA-B so much larger with a burst of action potentials?

5.

Now set all the synapses to zero except for the NMDA synapse. Set the total integration time to 500. Set the magnesium mg=1. Integrate the equations and take note of the NMDA current by plotting I_NMDA. Now change the resting potential of the post-synaptic cell by changing the parameter vp0. Change the initial value of the post-synaptic voltage to the resting potential. Change it to -60, -50, -30, -10, 0. Plot the peak NMDA current. Why is it non-monotonic? How would the peak NMDA current change if you block magnesium and change the resting potential of the cell?