Dendritic attenuation

The attenuation of currents traveling along the somatodendritic axis is an intrinsic property of biological neurons and is due to the morphology and cable properties of their dendritic trees. (also see Tran-van-Minh et al, 2015).

In this example, we show:

• How to measure the dendritic, distance-dependent voltage attenuation of a long current pulse injected at the soma.

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

from dendrify import Dendrite, NeuronModel, Soma

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

# Create neuron model
soma = Soma('soma', length=25*um, diameter=25*um)
trunk = Dendrite('trunk', length=100*um, diameter=1.5*um)
prox = Dendrite('prox', length=100*um, diameter=1.2*um)
dist = Dendrite('dist', length=100*um, diameter=1*um)

# Create a neuron group
connections = [(soma, trunk), (trunk, prox), (prox, dist)]
model = NeuronModel(connections, cm=1*uF/(cm**2), gl=50*uS/(cm**2),
                    v_rest=-70*mV, r_axial=400*ohm*cm)
neuron = model.make_neurongroup(1, method='euler')  # no spiking for simplicity

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

# Run simulation
b.run(20*ms)
neuron.I_ext_soma = -10*pA
b.run(500*ms)
neuron.I_ext_soma = 0*pA
b.run(100*ms)

# Analyse and plot results
time = M.t/ms
vs = M.V_soma[0]/mV
vt = M.V_trunk[0]/mV
vp = M.V_prox[0]/mV
vd = M.V_dist[0]/mV
voltages = [vs, vt, vp, vd]
delta_v = [min(v) - v[0] for v in voltages]
ratio = [i/delta_v[0] for i in delta_v]
distances = range(0, 400, 100)
names = ['soma', 'trunk', 'prox', 'dist']

fig, axes = b.subplots(1, 2, figsize=(6, 3))
ax0, ax1 = axes
for i, v in enumerate(voltages):
    ax0.plot(time, v, label=names[i])
ax0.set_ylabel('Voltage (mV)')
ax0.set_xlabel('Time (ms)')
ax0.legend()

ax1.plot(distances, ratio, 'ko-', ms=4)
ax1.set_ylabel(r'$dV_{dend}$ / $dV_{soma}$')
ax1.set_xlabel('Distance from soma (μm)')
ax1.set_yticks(b.arange(.7, 1, .1))

fig.tight_layout()
b.show()