import moose
from pylab import *
# ###########################################
# Neuron models
# ###########################################
## Leaky integrate and fire neuron
Vrest = -65e-3 # V # resting potential
Vt_base = -45e-3 # V # threshold
Vreset = -55e-3 # V # in current steps, Vreset is same as pedestal
R = 1e8 # Ohm
tau = 10e-3 # s
refrT = 2e-3 # s
# ###########################################
# Initialize neuron group
# ###########################################
## two neurons: index 0 will be presynaptic, 1 will be postsynaptic
network = moose.LIF( 'network', 2 );
moose.le( '/network' )
network.vec.Em = Vrest
network.vec.thresh = Vt_base
network.vec.refractoryPeriod = refrT
network.vec.Rm = R
network.vec.vReset = Vreset
network.vec.Cm = tau/R
network.vec.inject = 0.
network.vec.initVm = Vrest
#############################################
# Ca Plasticity parameters: synapses (not for ExcInhNetBase)
#############################################
### Cortical slice values -- Table Suppl 2 in Graupner & Brunel 2012
### Also used in Higgins et al 2014
#tauCa = 22.6936e-3 # s # Ca decay time scale
#tauSyn = 346.3615 # s # synaptic plasticity time scale
### in vitro values in Higgins et al 2014, faster plasticity
#CaPre = 0.56175 # mM
#CaPost = 1.2964 # mM
### in vivo values in Higgins et al 2014, slower plasticity
##CaPre = 0.33705 # mM
##CaPost = 0.74378 # mM
#delayD = 4.6098e-3 # s # CaPre is added to Ca after this delay
## proxy for rise-time of NMDA
#thetaD = 1.0 # mM # depression threshold for Ca
#thetaP = 1.3 # mM # potentiation threshold for Ca
#gammaD = 331.909 # factor for depression term
#gammaP = 725.085 # factor for potentiation term
#J = 5e-3 # V # delta function synapse, adds to Vm
#weight = 0.43 # initial synaptic weight
## gammaP/(gammaP+gammaD) = eq weight w/o noise
## see eqn (22), noiseSD also appears
## but doesn't work here,
## weights away from 0.4 - 0.5 screw up the STDP rule!!
#bistable = True # if bistable is True, use bistable potential for weights
#noisy = False # use noisy weight updates given by noiseSD
#noiseSD = 3.3501 # if noisy, use noiseSD (3.3501 from Higgins et al 2014)
########################################
## DP STDP curve (Fig 2C) values -- Table Suppl 1 in Graupner & Brunel 2012
tauCa = 20e-3 # s # Ca decay time scale
tauSyn = 150.0 # s # synaptic plasticity time scale
CaPre = 1.0 # arb
CaPost = 2.0 # arb
delayD = 13.7e-3 # s # CaPre is added to Ca after this delay
# proxy for rise-time of NMDA
thetaD = 1.0 # mM # depression threshold for Ca
thetaP = 1.3 # mM # potentiation threshold for Ca
gammaD = 200.0 # factor for depression term
gammaP = 321.808 # factor for potentiation term
J = 5e-3 # V # delta function synapse, adds to Vm
weight = 0.5 # initial synaptic weight
# gammaP/(gammaP+gammaD) = eq weight w/o noise
# see eqn (22), noiseSD also appears
# but doesn't work here,
# weights away from 0.4 - 0.5 screw up the STDP rule!!
bistable = True # if bistable is True, use bistable potential for weights
noisy = False # use noisy weight updates given by noiseSD
noiseSD = 2.8284 # if noisy, use noiseSD (3.3501 in Higgins et al 2014)
##########################################
syn = moose.GraupnerBrunel2012CaPlasticitySynHandler( '/network/syn' )
syn.numSynapses = 1 # 1 synapse
# many pre-synaptic inputs can connect to a synapse
# synapse onto postsynaptic neuron
moose.connect( syn, 'activationOut', network.vec[1], 'activation' )
# synapse from presynaptic neuron
moose.connect( network.vec[0],'spikeOut', syn.synapse[0], 'addSpike')
# post-synaptic spikes also needed for STDP
moose.connect( network.vec[1], 'spikeOut', syn, 'addPostSpike')
syn.synapse[0].delay = 0.0
syn.synapse[0].weight = weight
syn.CaInit = 0.0
syn.tauCa = tauCa
syn.tauSyn = tauSyn
syn.CaPre = CaPre
syn.CaPost = CaPost
syn.delayD = delayD
syn.thetaD = thetaD
syn.thetaP = thetaP
syn.gammaD = gammaD
syn.gammaP = gammaP
syn.weightScale = J # weight ~1, weightScale ~ J
# weight*weightScale is activation,
# i.e. delta-fn added to postsynaptic Vm
syn.weightMax = 1.0 # bounds on the weight
syn.weightMin = 0.
syn.noisy = noisy
syn.noiseSD = noiseSD
syn.bistable = bistable
# ###########################################
# Setting up tables
# ###########################################
Vms = moose.Table( '/plotVms', 2 )
moose.connect( network, 'VmOut', Vms, 'input', 'OneToOne')
spikes = moose.Table( '/plotSpikes', 2 )
moose.connect( network, 'spikeOut', spikes, 'input', 'OneToOne')
CaTable = moose.Table( '/plotCa', 1 )
moose.connect( CaTable, 'requestOut', syn, 'getCa')
WtTable = moose.Table( '/plotWeight', 1 )
moose.connect( WtTable, 'requestOut', syn.synapse[0], 'getWeight')
# ###########################################
# Simulate the STDP curve with spaced pre-post spike pairs
# ###########################################
dt = 1e-3 # s
# moose simulation
moose.useClock( 0, '/network/syn', 'process' )
moose.useClock( 1, '/network', 'process' )
moose.useClock( 2, '/plotSpikes', 'process' )
moose.useClock( 3, '/plotVms', 'process' )
moose.useClock( 3, '/plotCa', 'process' )
moose.useClock( 3, '/plotWeight', 'process' )
moose.setClock( 0, dt )
moose.setClock( 1, dt )
moose.setClock( 2, dt )
moose.setClock( 3, dt )
moose.setClock( 9, dt )
moose.reinit()
# function to make the aPlus and aMinus settle to equilibrium values
settletime = 100e-3 # s
[docs]def reset_settle():
"""
Call this between every pre-post pair
to reset the neurons and make them settle to rest.
"""
syn.synapse[0].weight = weight
syn.Ca = 0.0
moose.start(settletime)
# Ca gets a jump at pre-spike+delayD
# So this event can occur during settletime
# So set Ca and weight once more after settletime
syn.synapse[0].weight = weight
syn.Ca = 0.0
# function to inject a sharp current pulse to make neuron spike
# immediately at a given time step
[docs]def make_neuron_spike(nrnidx,I=1e-7,duration=1e-3):
"""
Inject a brief current pulse to
make a neuron spike
"""
network.vec[nrnidx].inject = I
moose.start(duration)
network.vec[nrnidx].inject = 0.
[docs]def main():
"""
Simulate a pseudo-STDP protocol and plot the STDP kernel
that emerges from Ca plasticity of Graupner and Brunel 2012.
Author: Aditya Gilra, NCBS, Bangalore, October, 2014.
"""
dwlist_neg = []
ddt = 2e-3 # s
# since CaPlasticitySynHandler is event based
# multiple pairs are needed for Ca to be registered above threshold
# Values from Fig 2, last line of legend
numpairs = 60 # number of spike parts per deltat
t_between_pairs = 1.0 # time between each spike pair
t_extent = 100e-3 # s # STDP kernel extent,
# t_extent > t_between_pairs/2 inverts pre-post pairing!
# dt = tpost - tpre
# negative dt corresponds to post before pre
print('-----------------------------------------------')
for deltat in arange(t_extent,0.0,-ddt):
reset_settle()
for i in range(numpairs):
# post neuron spike
make_neuron_spike(1)
moose.start(deltat)
# pre neuron spike after deltat
make_neuron_spike(0)
moose.start(t_between_pairs) # weight changes after pre-spike+delayD
# must run for at least delayD after pre-spike
dw = ( syn.synapse[0].weight - weight ) / weight
print(('post before pre, dt = %1.3f s, dw/w = %1.3f'%(-deltat,dw)))
dwlist_neg.append(dw)
print('-----------------------------------------------')
# positive dt corresponds to pre before post
dwlist_pos = []
for deltat in arange(ddt,t_extent+ddt,ddt):
reset_settle()
for i in range(numpairs):
# pre neuron spike
make_neuron_spike(0)
moose.start(deltat)
# post neuron spike after deltat
make_neuron_spike(1)
moose.start(t_between_pairs)
dw = ( syn.synapse[0].weight - weight ) / weight
print(('pre before post, dt = %1.3f s, dw/w = %1.3f'%(deltat,dw)))
dwlist_pos.append(dw)
print('-----------------------------------------------')
print(('Each of the above pre-post pairs was repeated',\
numpairs,'times, with',t_between_pairs,'s between pairs.'))
print()
print('Due to event based updates, Ca decays suddenly at events:')
print('pre-spike, pre-spike + delayD, and post-spike;')
print('apart from the usual CaPre and CaPost jumps at')
print('pre-spike + delayD and post-spike respectively.')
print('Because of the event based update, multiple pre-post pairs are used.')
print()
print('If you reduce the t_between_pairs,')
print(' you\'ll see potentiation for the LTD part without using any triplet rule!')
print()
print("If you turn on noise, the weights fluctuate too much,")
print(" not sure if there's a bug in my noise implementation.")
print('-----------------------------------------------')
# ###########################################
# Plot the simulated Vm-s and STDP curve
# ###########################################
# insert spikes so that Vm reset doesn't look weird
Vmseries0 = Vms.vec[0].vector
numsteps = len(Vmseries0)
for t in spikes.vec[0].vector:
Vmseries0[int(t/dt)-1] = 30e-3 # V
Vmseries1 = Vms.vec[1].vector
for t in spikes.vec[1].vector:
Vmseries1[int(t/dt)-1] = 30e-3 # V
timeseries = linspace(0.,1000*numsteps*dt,numsteps)
# Voltage plots
figure(facecolor='w')
plot(timeseries,Vmseries0,color='r') # pre neuron's vm
plot(timeseries,Vmseries1,color='b') # post neuron's vm
xlabel('time (ms)')
ylabel('Vm (V)')
title("pre (r) and post (b) neurons' Vm")
# Ca plots for the synapse
figure(facecolor='w')
plot(timeseries,CaTable.vector[:len(timeseries)],color='r')
plot((timeseries[0],timeseries[-1]),(thetaP,thetaP),color='k',\
linestyle='dashed',label='pot thresh')
plot((timeseries[0],timeseries[-1]),(thetaD,thetaD),color='b',\
linestyle='dashed',label='dep thresh')
legend()
xlabel('time (ms)')
ylabel('Ca (arb)')
title("Ca conc in the synapse")
# Weight plots for the synapse
figure(facecolor='w')
plot(timeseries,WtTable.vector[:len(timeseries)],color='r')
xlabel('time (ms)')
ylabel('Efficacy')
title("Efficacy of the synapse")
# STDP curve
fig = figure(facecolor='w')
ax = fig.add_subplot(111)
ax.plot(arange(-t_extent,0,ddt)*1000,array(dwlist_neg),'.-r')
ax.plot(arange(ddt,(t_extent+ddt),ddt)*1000,array(dwlist_pos),'.-b')
xmin,xmax = ax.get_xlim()
ymin,ymax = ax.get_ylim()
ax.set_xticks([xmin,0,xmax])
ax.set_yticks([ymin,0,ymax])
ax.plot((0,0),(ymin,ymax),linestyle='dashed',color='k')
ax.plot((xmin,xmax),(0,0),linestyle='dashed',color='k')
ax.set_xlabel('$t_{post}-t_{pre}$ (ms)')
ax.set_ylabel('$\Delta w / w$')
fig.tight_layout()
#fig.subplots_adjust(hspace=0.3,wspace=0.5) # use after tight_layout()
show()
if __name__ == '__main__':
main()