Slow spillover component

[shyam_u2]

I trying to modify Exp2Syn.mod to include a second, slow decay constant, tau3, that contributes to 10% of peak amplitude.
How do I change the existing Exp2Syn.mod to model the slow decay constant ?

Code: Select all

COMMENT
     2 Two state kinetic scheme synapse described by rise time tau1,
     3 and decay time constant tau2. The normalized peak condunductance is 1.
     4 Decay time MUST be greater than rise time.
     5 
     6 The solution of A->G->bath with rate constants 1/tau1 and 1/tau2 is
     7  A = a*exp(-t/tau1) and
     8  G = a*tau2/(tau2-tau1)*(-exp(-t/tau1) + exp(-t/tau2))
     9 	where tau1 < tau2
    10 
    11 If tau2-tau1 -> 0 then we have a alphasynapse.
    12 and if tau1 -> 0 then we have just single exponential decay.
    13 
    14 The factor is evaluated in the
    15 initial block such that an event of weight 1 generates a
    16 peak conductance of 1.
    17 
    18 Because the solution is a sum of exponentials, the
    19 coupled equations can be solved as a pair of independent equations
    20 by the more efficient cnexp method.
    21 
    22 ENDCOMMENT
    23 
    24 NEURON {
    25 	POINT_PROCESS Exp2Syn
    26 	RANGE tau1, tau2, e, i
    27 	NONSPECIFIC_CURRENT i
    28 
    29 	RANGE g
    30 }
    31 
    32 UNITS {
    33 	(nA) = (nanoamp)
    34 	(mV) = (millivolt)
    35 	(uS) = (microsiemens)
    36 }
    37 
    38 PARAMETER {
    39 	tau1=.1 (ms) <1e-9,1e9>
    40 	tau2 = 10 (ms) <1e-9,1e9>
    41 	e=0	(mV)
    42 }
    43 
    44 ASSIGNED {
    45 	v (mV)
    46 	i (nA)
    47 	g (uS)
    48 	factor
    49 }
    50 
    51 STATE {
    52 	A (uS)
    53 	B (uS)
    54 }
    55 
    56 INITIAL {
    57 	LOCAL tp
    58 	if (tau1/tau2 > .9999) {
    59 		tau1 = .9999*tau2
    60 	}
    61 	A = 0
    62 	B = 0
    63 	tp = (tau1*tau2)/(tau2 - tau1) * log(tau2/tau1)
    64 	factor = -exp(-tp/tau1) + exp(-tp/tau2)
    65 	factor = 1/factor
    66 }
    67 
    68 BREAKPOINT {
    69 	SOLVE state METHOD cnexp
    70 	g = B - A
    71 	i = g*(v - e)
    72 }
    73 
    74 DERIVATIVE state {
    75 	A' = -A/tau1
    76 	B' = -B/tau2
    77 }
    78 
    79 NET_RECEIVE(weight (uS)) {
    80 	A = A + weight*factor
    81 	B = B + weight*factor
    82 }

[ted]

The first step is to provide a complete mathematical description of what you have in mind. What is needed is a set of differential equations that specify the dynamics of all states, a set of algebraic equations that relate channel conductances to these states, definitions of all parameters and state variables, and an explicit statement of what happens when a new input event arrives..

[ted]

Some clarification is probably in order.

There is no simple modification to Exp2Syn that will accomplish your goal. The set of ODEs that will provide what you need depends on the empirical basis of what you have in mind. From a mechanistic perspective, you clearly do not want a three transition scheme of the form
R + L -> O1 -> O2 -> R
where R is the fraction of channels that are closed, O1 and O2 are the fractions that are in open states, and L is the ligand (neurotransmitter). Instead something more like this pair of transitions would be more appropriate
Rj + Lj <-> Oj
Rx + Lx <-> Ox
where the subscripts j and x mean "junctional" and "extrajunctional", respectively, and the rise of Lx following presynaptic activation is somewhat slower than the time course of Lj. You could approximate this very easily by using a pair of Exp2Syns--one to represent what happens at the synaptic junction, and another with slower tau1 and tau2 that represents what happens to extrajunctional channels.

An alternative would be to take a purely phenomenological approach and describe the time course of synaptic conductance as
exp(t/tau1) - k*exp(t/tau2) - (1-k)*exp(t/tau3)
where tau1 > tau2 > tau3 and 0<=k<=1. This doesn't take the slower rise of extrajunctional transmitter into account, but it would be a more appropriate strategy if your modeling is based on experimental data that provides estimates of tau1, 2, and 3, and k.