Equation for Single compartment models with external input

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Equation for Single compartment models with external input

Postby homerobse » Thu Jun 08, 2017 6:45 pm

Hello! I am struggling to find what exactly are the equations that NEURON integrates when I create a section with just one segment, insert hh, insert Exp2Syn and insert IClamp.

Code: Select all
soma = h.Section(name='soma')
soma2 = h.Section(name='soma2')

soma.insert('hh')
soma2.insert('hh')

syn = h.Exp2Syn(0.5, sec=soma2)
syn.e = 0
syn.tau1 = 1
syn.tau2 = 3

net_con = h.NetCon(soma(0.5)._ref_v, syn, 0, 5, 0.07)

stim = h.IClamp(soma(0.5))
stim.delay = 1
stim.dur = 5
stim.amp = 20


I have read many parts of Hines & Carnevale 1997 at https://www.neuron.yale.edu/neuron/static/papers/nc97/nctoc.htm), but I still don't understand how does neuron compute the voltage in the compartment including synapses and external inputs like IClamp. Is it including it at the equation 2 on the right side of the equal sign in this part of the explanation https://www.neuron.yale.edu/neuron/static/papers/nc97/nc3p1.htm ?

I mean: c dv/dt + i_ion = sum[(v_k-v_j)/r_jk] + Isyn + Iext . Is that it?

And what happens in the case of a single compartment, as the case I illustrated? Is (v_k-v_j)/r_jk=0 in this case?
homerobse
 
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Re: Equation for Single compartment models with external inp

Postby ted » Tue Jun 27, 2017 11:57 am

The discretized cable equation (Equation 2 in that paper) is the key. Currents produced by synapses and other point sources attached to a compartment, such as current or voltage clamps, are added to the right hand side of Equation 2.
what happens in the case of a single compartment . . . Is (v_k-v_j)/r_jk=0
Yes. There can be no current flow between compartments if there is only a single compartment.
ted
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Re: Equation for Single compartment models with external inp

Postby homerobse » Tue Jun 27, 2017 2:44 pm

Thank you very much!
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