Back-propagating dSpikes

An important property of biological neurons is that action potentials (APs) initiated in the axon can invade the soma and nearby dendrites and propagate backwards toward the dendritic tips. The transmission efficacy of these back-propagating action potentials (bAPs) relies on the dendritic morphology and the presence of dendritic voltage-gated ion channels.

In Dendrify, to achieve this behavior one needs to first recreate a more realistic somatic AP shape by using the second_reset and spike_width arguments in make_neurongroup. In this way, the somatic voltage can be first reset to a more positive value and then below threshold. This allows the passive depolarization of proximal dendrites in responses to somatic APs. If dendrites are also equipped with active ionic mechanisms, this depolarization can trigger the spontaneous generation of dendritic bAPs.

In this example we show:

  • How to implement back-propagating dSpikes in Dendrify.

  • How to achieve a more realistic somatic AP shape in I&F models, that is essential for the generation of bAPs.

Important

Notice that when a second_reset is used, the make_neurongroup method returns an additional object which is Brian’s Synapses. If your simulation code uses Brian’s Networks feature, this additional object should be added to the network as well (also shown in the example below).

import brian2 as b
from brian2.units import cm, ms, mV, nS, ohm, pA, uF, um, uS

from dendrify import Dendrite, NeuronModel, Soma

b.prefs.codegen.target = 'numpy'  # faster for simple simulations

# Create neuron model
soma = Soma('soma', model='leakyIF', length=25*um, diameter=25*um)
trunk = Dendrite('trunk', length=100*um, diameter=2.5*um)
prox = Dendrite('prox', length=100*um, diameter=1*um)
dist = Dendrite('dist', length=100*um, diameter=0.5*um)

trunk.dspikes('Na', g_rise=22*nS, g_fall=14*nS)
prox.dspikes('Na', g_rise=9*nS, g_fall=5.7*nS)
dist.dspikes('Na', g_rise=3.7*nS, g_fall=2.4*nS)

con = [(soma, trunk, 15*nS), (trunk, prox, 6*nS), (prox, dist, 2*nS)]
model = NeuronModel(con, cm=1*uF/(cm**2), gl=40*uS/(cm**2),
                    v_rest=-65*mV, r_axial=150*ohm*cm,
                    scale_factor=2.8, spine_factor=1.5)
model.config_dspikes('Na', threshold=-35*mV,
                     duration_rise=1.2*ms, duration_fall=2.4*ms,
                     offset_fall=0.2*ms, refractory=5*ms,
                     reversal_rise='E_Na', reversal_fall='E_K')

# Make a new neurongroup
neuron, ap_reset = model.make_neurongroup(1, method='euler',
                                          threshold='V_soma > -40*mV',
                                          reset='V_soma = 40*mV',
                                          second_reset='V_soma=-55*mV',
                                          spike_width=0.8*ms,
                                          refractory=4*ms)

# Record voltages
vars = ['V_soma', 'V_trunk', 'V_prox', 'V_dist']
M = b.StateMonitor(neuron, vars, record=True)

# Run simulation
net = b.Network(neuron, ap_reset, M)
net.run(10*ms)
neuron.I_ext_soma = 115*pA
net.run(100*ms)
neuron.I_ext_soma = 0*pA
net.run(60*ms)

# Visualize results
fig, axes = b.subplots(2, 1, figsize=(6, 5))
ax0, ax1 = axes

ax0.plot(M.t/ms, M.V_soma[0]/mV, label='soma', zorder=3)
ax0.plot(M.t/ms, M.V_trunk[0]/mV, label='trunk')
ax0.plot(M.t/ms, M.V_prox[0]/mV, label='prox')
ax0.plot(M.t/ms, M.V_dist[0]/mV, label='dist')
ax0.set_ylabel('Voltage (mV)')
ax0.legend()

ax1.plot(M.t/ms, M.V_soma[0]/mV, zorder=3)
ax1.plot(M.t/ms, M.V_trunk[0]/mV)
ax1.plot(M.t/ms, M.V_prox[0]/mV)
ax1.plot(M.t/ms, M.V_dist[0]/mV)
ax1.set_title('(Zoomed)', y=1, pad=-12, fontsize=10)
ax1.set_xlabel('Time (ms)')
ax1.set_ylabel('Voltage (mV)')
ax1.set_xlim(50, 120)

fig.tight_layout()
b.show()
../_images/comp_backprop.png