tsodyks facilitating example

This scripts simulates two neurons. One is driven with dc-input and connected to the other one with a facilitating tsodyks synapse. The membrane potential trace of the second neuron is recorded.

This example reproduces figure 1B of Tsodyks et al. (1998) Neural Networks with Dynamic Synapses. Neural computation, http://dx.doi.org/10.1162/089976698300017502 This example is analog to tsodyks_depressing.py, except that different synapse parameters are used. Here, a small facilitation parameter U causes a slow saturation of the synaptic efficacy (Eq. 2.2), enabling a facilitating behavior.

First, we import all necessary modules for simulation and plotting.

import nest
import nest.voltage_trace
import pylab
from numpy import exp

Second, the simulation parameters are assigned to variables. The neuron and synapse parameters are stored into a dictionary.

h = 0.1    # simulation step size (ms)
Tau = 40.    # membrane time constant
Theta = 15.    # threshold
E_L = 0.     # reset potential of membrane potential
R = 1.     # membrane resistance (GOhm)
C = Tau / R  # Tau (ms)/R in NEST units
TauR = 2.     # refractory time
Tau_psc = 1.5    # time constant of PSC (= Tau_inact)
Tau_rec = 130.   # recovery time
Tau_fac = 530.   # facilitation time
U = 0.03   # facilitation parameter U
A = 1540.  # PSC weight in pA
f = 20. / 1000.  # frequency in Hz converted to 1/ms
Tend = 1200.  # simulation time
TIstart = 50.    # start time of dc
TIend = 1050.  # end time of dc
I0 = Theta * C / Tau / (1 - exp(-(1 / f - TauR) / Tau))  # dc amplitude

neuron_param = {"tau_m": Tau,
                "t_ref": TauR,
                "tau_syn_ex": Tau_psc,
                "tau_syn_in": Tau_psc,
                "C_m": C,
                "V_reset": E_L,
                "E_L": E_L,
                "V_m": E_L,
                "V_th": Theta}

syn_param = {"tau_psc": Tau_psc,
             "tau_rec": Tau_rec,
             "tau_fac": Tau_fac,
             "U": U,
             "delay": 0.1,
             "weight": A,
             "u": 0.0,
             "x": 1.0}

Third, we reset the kernel and set the resolution using SetKernelStatus.

nest.SetKernelStatus({"resolution": h})

Fourth, the nodes are created using Create. We store the returned handles in variables for later reference.

neurons = nest.Create("iaf_psc_exp", 2)
dc_gen = nest.Create("dc_generator")
volts = nest.Create("voltmeter")

Fifth, the iaf_psc_exp-neurons, the dc_generator and the voltmeter are configured using SetStatus, which expects a list of node handles and a parameter dictionary or a list of parameter dictionaries.

nest.SetStatus(neurons, neuron_param)
nest.SetStatus(dc_gen, {"amplitude": I0, "start": TIstart, "stop": TIend})
nest.SetStatus(volts, {"label": "voltmeter", "withtime": True, "withgid": True,
                       "interval": 1.})

Sixth, the dc_generator is connected to the first neuron (neurons[0]) and the voltmeter is connected to the second neuron (neurons[1]). The command Connect has different variants. Plain Connect just takes the handles of pre- and post-synaptic nodes and uses the default values for weight and delay. Note that the connection direction for the voltmeter reflects the signal flow in the simulation kernel, because it observes the neuron instead of receiving events from it.

nest.Connect(dc_gen, [neurons[0]])
nest.Connect(volts, [neurons[1]])

Seventh, the first neuron (neurons[0]) is connected to the second neuron (neurons[1]). The command CopyModel copies the tsodyks_synapse model to the new name syn with parameters syn_param. The manually defined model syn is used in the connection routine via the syn_spec parameter.

nest.CopyModel("tsodyks_synapse", "syn", syn_param)
nest.Connect([neurons[0]], [neurons[1]], syn_spec="syn")

Finally, we simulate the configuration using the command Simulate, where the simulation time Tend is passed as the argument. We plot the target neuron's membrane potential as a function of time.