In this example, we will take the model from Figure 1
and actually add the kinetics. We will then add 4 synapses whose
conductances and whose onsets can be individually set (although they
will all have the same time courses). The object of this little
exercise is to explore thresholds and timing of synapses. The file is
called `trcomp4.ode` and you should integrate it at least for 80
msec. I have used alpha functions for the synapses since there is no
post-synaptic cell and these fire only once.
The sodium and potassium dynamics are
those of Traub's cortical cell model. The parameters you will vary
are called `gsyn1,gsyn2,gsynb,gsyns` which are the conductances
for the two apical dendrite compartments, the basal dendrite
compartment, and the soma compartment. The other parameters of
interest are `ts,tb,t1,t2` which are the onset times of the 4
synapses. The voltages are `v, va1,va2,vb` for the soma, the two
apical dendrites, and the basal dendrite. I have chosen the coupling
between the compartments for you for the purposes of this exercise.
Here are some things to do:

- 1.
- Find the minimum value of the synaptic conductance on each compartment in order to elicit a spike at the soma.
- 2.
- Fix the conductance on the basal dendrite to be below the
threshold to elicit a spike. Now increase the conductance on the
terminal apical dendrite (labeled
`gsyn2`) until the two of them elicit a spike. - 3.
- With the paired synapses of the above, alter the timing by
increasing
`t2`from 5 to higher values. How close do the two stimuli have to be to elicit a spike. Increase the conductance`gsyn2`and repeat this. - 4.
- Note that the alpha functions are normalized so that their
integral in time is 1. Set all the synaptic conductances to 0 except
`gsyn2.`Make a table showing the minimum conductance to elicit a spike at the soma as a function of`tau_s`the time constant of the synapse. Try fast synapses`tau_s=5`and slow`tau_s=40`as well as those in between. - 5.
- Hold
`gsyn2=4.`Now vary`tau_s`from 1 msec (really fast) to 20 msec. Which stimulus evokes the most action potentials.

# traub sodium and potassium kinetics and 3 compartments with synapses # v va1,va2,vb v'=-(gna*h*m^3*(v-ena)+gk*n^4*(v-ek)+gl*(v-el)+gas*(v-va1)+gbs*(v-vb)+\ alphas(t)*(v-vsyn))/c va1'=-(gl*(va1-el)+g21*(va1-va2)+gsa*(va1-v)+alpha1(t)*(va1-vsyn))/c va2'=-(gl*(va2-el)+g12*(va2-va1)+alpha2(t)*(va2-vsyn))/c vb'=-(gl*(vb-el)+gsb*(vb-v)+alphab(t)*(vb-vsyn))/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 init v=-67,va1=-67,va2=-67,vb=-67,m=0,n=0,h=1 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) par ek=-100,ena=50,el=-67 par gl=.1,gk=80,gna=100 par c=1,i=0 par gsyns=0,gsynb=0,gsyn1=0,gsyn2=0,vsyn=0 par ts=5,tb=5,t1=5,t2=5 par tau_s=5 par g12=2,g21=1,gsa=.5,gas=2,gbs=2,gsb=.5 alpha(t)=t*exp(-t/tau_s)/(tau_s^2) alpha1(t)=gsyn1*alpha(max(t-t1,0)) alpha2(t)=gsyn2*alpha(max(t-t2,0)) alphab(t)=gsynb*alpha(max(t-tb,0)) alphas(t)=gsyns*alpha(max(t-ts,0)) @ dt=.25,meth=qualrk,total=80,xhi=80,ylo=-80,yhi=25 done