COMMENT
Updated Exp2Syn synapse with Mg-blocked nmda channel.
Defaul values of parameters (time constants etc) set to match synaptic channels in
striatal medium spiny neurons (Du et al., 2017; Chapman et al., 2003; Ding et al., 2008).
Robert . Lindroos @ ki . se
original comment:
________________
Two state kinetic scheme synapse described by rise time tau1,
and decay time constant tau2. The normalized peak condunductance is 1.
Decay time MUST be greater than rise time.
The solution of A->G->bath with rate constants 1/tau1 and 1/tau2 is
A = a*exp(-t/tau1) and
G = a*tau2/(tau2-tau1)*(-exp(-t/tau1) + exp(-t/tau2))
where tau1 < tau2
If tau2-tau1 -> 0 then we have a alphasynapse.
and if tau1 -> 0 then we have just single exponential decay.
The factor is evaluated in the
initial block such that an event of weight 1 generates a
peak conductance of 1.
Because the solution is a sum of exponentials, the
coupled equations can be solved as a pair of independent equations
by the more efficient cnexp method.
ENDCOMMENT
NEURON {
POINT_PROCESS adaptive_glutamate_cshom
RANGE tau1_ampa, tau2_ampa, tau1_nmda, tau2_nmda
RANGE erev_ampa, erev_nmda, g, i
NONSPECIFIC_CURRENT i
RANGE i_ampa, i_nmda, g_ampa, g_nmda, I, G, mg, q, alpha, eta
RANGE w0, NMDA_AMPA_ratio
RANGE weight, lthresh_LTP, lthresh_LTD, hthresh_LTP, last_dopamine, lthresh_LTP_min
RANGE hthresh_LTP_const, hthresh_LTP_0, hthresh_max, n, delta, width, steepness_LTP, steepness_LTD
RANGE learning_rate_w_LTP, learning_rate_w_LTD, thresh_LTP_0, learning_rate_thresh_LTP, thresh_LTD_0, learning_rate_thresh_LTD, hthresh_LTP_0
RANGE ca_nmdai_max, cali_max, active_syn_flag, nmda_ca_fraction, delta_LTP
POINTER dopamine, stimulus_flag
USEION ca_nmda READ ca_nmdai WRITE ica_nmda VALENCE 2
USEION cal READ cali VALENCE 2
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (microsiemens)
}
PARAMETER {
erev_ampa = 0.0 (mV)
erev_nmda = 15.0 (mV)
tau1_ampa = 1.9 (ms)
tau2_ampa = 4.8 (ms) : tau2 > tau1
tau1_nmda = 5.52 (ms) : old value was 5.63
tau2_nmda = 231 (ms) : tau2 > tau1
mg = 1 (mM)
alpha = 0.062
q = 2
eta = 18
NMDA_AMPA_ratio = 1
w0 = 0.01
learning_rate_w_LTP = 0.01
learning_rate_w_LTD = 0.01
thresh_LTP_0 = 0.07
thresh_LTD_0 = 0.005
hthresh_LTP_0 = 0.5
hthresh_max = 2.0
lthresh_LTP_min = 0.055
delta = 0.65
width = 0.25
hthresh_LTP_const = 0.05
learning_rate_thresh_LTP = 0.005
learning_rate_thresh_LTD = 0.005
n = 4 : Hill coefficient
steepness_LTP = 0.25
steepness_LTD = 2.5
nmda_ca_fraction = 0.15
ca_nmdai_max = 0
cali_max = 0
active_syn_flag = 1e-6
}
ASSIGNED {
v (mV)
i (nA)
g (uS)
factor_nmda
factor_ampa
i_ampa
i_nmda
g_ampa
g_nmda
block
I
G
stimulus_flag
dopamine
last_dopamine
ica_nmda (nA)
ca_nmdai (mM)
cali (mM)
weight
lthresh_LTP
lthresh_LTD
hthresh_LTP
delta_LTP
}
STATE {
A (uS)
B (uS)
C (uS)
D (uS)
}
INITIAL {
LOCAL tp
if (tau1_nmda/tau2_nmda > .9999) {
tau1_nmda = .9999*tau2_nmda
}
if (tau1_ampa/tau2_ampa > .9999) {
tau1_ampa = .9999*tau2_ampa
}
: NMDA
A = 0
B = 0
tp = (tau1_nmda*tau2_nmda)/(tau2_nmda - tau1_nmda) * log(tau2_nmda/tau1_nmda)
factor_nmda = -exp(-tp/tau1_nmda) + exp(-tp/tau2_nmda)
factor_nmda = 1/factor_nmda
: AMPA
C = 0
D = 0
tp = (tau1_ampa*tau2_ampa)/(tau2_ampa - tau1_ampa) * log(tau2_ampa/tau1_ampa)
factor_ampa = -exp(-tp/tau1_ampa) + exp(-tp/tau2_ampa)
factor_ampa = 1/factor_ampa
weight = w0
lthresh_LTP = thresh_LTP_0
lthresh_LTD = thresh_LTD_0
hthresh_LTP = hthresh_LTP_0
active_syn_flag = 0
last_dopamine = 0
}
BREAKPOINT {
SOLVE state METHOD cnexp
: NMDA
g_nmda = (B - A)*weight*NMDA_AMPA_ratio
block = MgBlock()
i_nmda = g_nmda * (v - erev_nmda) * block
ica_nmda = nmda_ca_fraction*i_nmda
i_nmda = (1 - nmda_ca_fraction)*i_nmda
: AMPA
g_ampa = (D - C)*weight
i_ampa = g_ampa * (v - erev_ampa)
: total current
G = g_ampa + g_nmda
I = i_ampa
i = I
if (stimulus_flag == 1) {
ca_nmdai_max = max(ca_nmdai, ca_nmdai_max)
cali_max = max(cali, cali_max)
last_dopamine = dopamine
} else {
if (last_dopamine == 1 && active_syn_flag == 1) {
delta_LTP = sigmoidal(ca_nmdai_max, lthresh_LTP, steepness_LTP) * (1 - sigmoidal(ca_nmdai_max, lthresh_LTP, steepness_LTP))
weight = weight + learning_rate_w_LTP * delta_LTP
lthresh_LTP = lthresh_LTP + learning_rate_thresh_LTP * delta_LTP * (1 - 2*sigmoidal(ca_nmdai_max, lthresh_LTP, steepness_LTP))
} else if (last_dopamine == -1 && active_syn_flag == 1) {
weight = weight - learning_rate_w_LTD * cali_max * sigmoidal(cali_max, lthresh_LTD, steepness_LTD) * weight
lthresh_LTP = lthresh_LTP - learning_rate_thresh_LTP * (lthresh_LTP - lthresh_LTP_min)
}
last_dopamine = dopamine
reset_max()
}
: delta_LTP = lthresh(ca_nmdai_max, lthresh_LTP, steepness_LTP) * hthresh(ca_nmdai_max, lthresh_LTP, steepness_LTP)
: weight = weight + learning_rate_w_LTP * lthresh(ca_nmdai_max, lthresh_LTP, steepness_LTP) * hthresh(ca_nmdai_max, hthresh_LTP, steepness_LTP)
: lthresh_LTP = lthresh_LTP + learning_rate_thresh_LTP * delta_LTP * (1 - 2*sigmoid(ca_nmdai_max, lthresh_LTP, steepness_LTP))
: lthresh_LTP = max(lthresh_LTP, lthresh_LTP_min)
:lthresh_LTP = lthresh_LTP + learning_rate_thresh_LTP * lthresh(ca_nmdai_max, lthresh_LTP, steepness_LTP)* ((ca_nmdai_max-width)* delta - lthresh_LTP)
:lthresh_LTD = lthresh_LTD + learning_rate_thresh_LTD *lthresh(ca_nmdai_max, lthresh_LTP, steepness_LTP) * (cali_max*delta - lthresh_LTD)
:hthresh_LTP = lthresh_LTP + width
: weight = weight - learning_rate_w_LTD * cali_max * lthresh(cali_max, lthresh_LTD, steepness_LTD) * weight
: lthresh_LTP = lthresh_LTP - learning_rate_thresh_LTP * lthresh(cali_max, lthresh_LTD, steepness_LTD)*(lthresh_LTP - max(ca_nmdai_max, lthresh_LTP_min))
: lthresh_LTP = max(lthresh_LTP, lthresh_LTP_min)
:lthresh_LTP = lthresh_LTP - learning_rate_thresh_LTP *lthresh(cali_max, lthresh_LTD, steepness_LTD)*(lthresh_LTP - max(ca_nmdai_max, lthresh_LTP_min))
:lthresh_LTD = lthresh_LTD - learning_rate_thresh_LTD *lthresh(cali_max, lthresh_LTD, steepness_LTD)*(lthresh_LTD - delta*cali_max)
:hthresh_LTP = lthresh_LTP + width
}
DERIVATIVE state {
A' = -A/tau1_nmda*q
B' = -B/tau2_nmda*q
C' = -C/tau1_ampa
D' = -D/tau2_ampa
}
NET_RECEIVE(dummy (uS)) {
active_syn_flag = 1
A = A + factor_nmda
B = B + factor_nmda
C = C + factor_ampa
D = D + factor_ampa
}
FUNCTION MgBlock() {
MgBlock = 1 / (1 + mg * eta * exp(-alpha * v) )
}
FUNCTION lthresh(conc, KD, steepness) {
: lthresh = conc^n/(KD^n + conc^n)
lthresh = sigmoidal(conc,KD, steepness)
}
FUNCTION hthresh(conc, KD, steepness) {
: hthresh = KD^n/(KD^n + conc^n)
hthresh = 1 - sigmoidal(conc, KD, steepness)
}
FUNCTION reset_max() {
ca_nmdai_max = 0
cali_max = 0
active_syn_flag = 0
}
FUNCTION max(current, maximum) {
if (current>maximum) {
max = current
} else {
max = maximum
}
}
FUNCTION min(current, minimum) {
if (current<minimum) {
min = current
} else {
min = minimum
}
}
FUNCTION sigmoidal(x, x_offset, s) {
sigmoidal = 1/(1+exp(-s *(x - x_offset)))
}