Sorry I may not say it clear.
depression and facilitation are the final result I want. Depression, Facilitation, Depression Recovery and Facilitation Recovery are the constants defined by hoc file. So I have four parameters to control the overall plasticity (Dep for Depression, DepR for Depression Recovery, Fac for Facilitation and FacR for Facilitation Recovery).
PSP_final = PSP * plasticity (PSP for the postsynaptic potential which is dependent on time)
plasticity = D * F (D for depression and F for facilitation. they are the results I want to get from the differential equations)
D' = DepR*(1-plasticity)-Dep*PSP_final
F' = Fac*PSP_final - FacR(1-plasticity)
for now I only consider either depression or facilitation. so it could be simplified as
D' = DepR*(1-D)-Dep*PSP_final = DepR*(1-D)-Dep*D*PSP
F' = Fac*PSP_final-FacR(1-F)=Fac*F*PSP-FacR(1-F)
when DepR and FacR is 0 which means there is no recovery, the equations would be
D' = -Dep*D*PSP
F' = Fac*F*PSP
which is all right as you point it out the result is
D = exp(-Dep*exp(t-tsyn))
F = exp(Fac*exp(t-tsyn))
I just could not get it right for the recovery part. To make it clear, I'll rewrite the equations I want to resolve are:
D' = DepR*(1-D)-Dep*D*PSP
F' = Fac*F*PSP-FacR(1-F)
In these two equations, D and F are to be solved. DepR, Dep, Fac and FacR are constants. I'm a bit confused with the presence of v in these equations. The results of D with nonzero Dep and DepR should be sawtooth-shaped with damping amplitude to a plateau decided by DepR.
I didnt change the color so a bit uneasy to see. The upper trace is the spikes, the middle trace is D (for depression) with a smaller DepR and the lower trace is D with the same Dep and a bigger DepR. PSP is zero when there is no spike delivered to the postsynaptic neuron.
So when a spike arrives, the synapse depresses, but between spikes, the synapse would get some recovery from the depression. The results were done in MATLAB and now I need to build up a larger network so turn to NEURON.
Sorry I've got loads of problems. I've been stuck here for over a week now and catching up to a deadline so really need your help. Thanks a lot!
Last edited by yj232 on Mon Jun 27, 2011 6:38 am, edited 3 times in total.