## Simultaneous equations in python

When Python is the interpreter, what is a good
design for the interface to the basic NEURON
concepts.

Moderator: hines

catharina
Posts: 13
Joined: Tue May 30, 2017 9:42 am

### Simultaneous equations in python

Hi,

I want to construct a network of pyramdial cells and interneuron. Therefore I have chosen to use a cell template similar to this one https://senselab.med.yale.edu/modeldb/S ... del=222321. Right now I am trying to construct cell templates in python that are similar to the original ones but use the same mechanisms. However I am having trouble including the mechanisms for the Na-K pump nakpump.mod. This mechanism needs a stability function that recaclulates sodium and potassium conductances and the maximal flux of the pump. This is done by defining simultaneous equations. The function is called once before the simulation is run. Here is the code of the original implementation in hoc:

Code: Select all

``````proc pyramstab() {
access psoma
rm=\$1
init()
vrest = -70

dr_na = vrest-ena
dr_k = vrest-ek

eqinit()
depvar gna, gk
eqn gk:: gk = 1/rm - gna
eqn gna:: gna = (-dr_k*(3/2)*gk)/dr_na
solve()
forall gk_leak=gk
forall gna_leak=gna

p_k=(1+km_k_nakpump/ko)^(-2)
p_na=(1+km_na_nakpump/nai)^(-3)
p_tot=p_k*p_na
forall imax_nakpump = (-gna_leak*dr_na)/(3*p_tot)
}``````
I have tried to write my own version of this function in python. However because the eqn, eqinit() and solve() is not available in python, I do solve the equations and call my function at every time step before I call h.steprun(). This is the code:

Code: Select all

``````def stab(celllist):
rm=5e3
vrest = -70

for nn in range(len(celllist)): # for each cell calculate and assign gk_leak, gna_leak and imax_nakpump
dr_na = vrest-celllist[nn].soma.ena
dr_k = vrest-celllist[nn].soma.ek

gk=(2*dr_na)/((3*dr_k-2*dr_na)*rm) # equations solved for gk and gna, see EqnSolve.nb
gna=(3*dr_k)/((3*dr_k-2*dr_na)*rm)
for ss in celllist[nn].sections:
ss.gk_leak=gk
ss.gna_leak=gna

p_k=(1+celllist[nn].soma.km_k_nakpump/celllist[nn].soma.ko)**(-2)
p_na=(1+celllist[nn].soma.km_na_nakpump/celllist[nn].soma.nai)**(-3)
p_tot=p_k*p_na
for ss in celllist[nn].sections:
ss.imax_nakpump = (-ss.gna_leak*dr_na)/(3*p_tot)
return``````
The problem is that this appaerently does not work the same way as the implementation in hoc does. Now, I am aware that it is because the equations are not defined as simultanous ones in NEURON and hence are not solved parallel to the cable equation. Does anyone know how I can define simultaneous equations in python or how I could work around it? If anyone knows an example where this was done, it would also help me?

I would appreciate any help!

Best, Cathi
catharina
Posts: 13
Joined: Tue May 30, 2017 9:42 am

### Re: Simultaneous equations in python

It took me a while but I finally found a way to work around it.

That's the code I add in python:

Code: Select all

``````h('objref celllist,N')
h.celllist=h.List()
for elem in celllist:
h.celllist.append(elem)

h('proc hstab() {\n\
for nn=0,1 {\n\
rm=5e3\n\
vrest = -70\n\
//print nn\n\
dr_na = vrest-celllist.object(nn).soma.ena\n\
dr_k = vrest-celllist.object(nn).soma.ek\n\
eqinit()\n\
depvar gna, gk\n\
eqn gk:: gk = 1/rm - gna\n\
eqn gna:: gna = (-dr_k*(3/2)*gk)/dr_na\n\
solve()\n\
for ii=0,2 {\n\
celllist.o(nn).sections[ii].gk_leak=gk\n\
celllist.o(nn).sections[ii].gna_leak=gna}\n\
p_k=(1+celllist.object(nn).soma.km_k_nakpump/celllist.object(nn).soma.ko)^(-2)\n\
p_na=(1+celllist.object(nn).soma.km_na_nakpump/celllist.object(nn).soma.nai)^(-3)\n\
p_tot=p_k*p_na\n\
for ii=0,2 {\n\
celllist.o(nn).sections[ii].imax_nakpump= (-celllist.o(nn).sections[ii].gna_leak*dr_na)/(3*p_tot)\n\
}}}')``````
It's not nice but it works. =D Still I think it would be kind of nice to know how to do that directly from python.
ted
Site Admin
Posts: 5819
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
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### Re: Simultaneous equations in python

hoc's simultaneous equation feature is not required to deal with a system of two linear equations in two unknowns--a bit of algebra is sufficient to solve first for gk, then for gna (or vice-versa).
catharina
Posts: 13
Joined: Tue May 30, 2017 9:42 am

### Re: Simultaneous equations in python

Yes, that's what I tried first, see the second block of code I posted. However this doesn't give the same results as the hoc functions. So in this case the stability functions in hoc do ensure that the resting potential stays constant, but the python function doesn't.
ted
Site Admin
Posts: 5819
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: Simultaneous equations in python

catharina wrote:However this doesn't give the same results as the hoc functions. So in this case the stability functions in hoc do ensure that the resting potential stays constant, but the python function doesn't.
You're saying that your model implementation in Python produces the same results as the original hoc implementation does, as long as your Python implementation uses the "stability functions" implemented in hoc?