Ex19: Gap Junctions

Electrical synapses (gap junctions) between cells

Model: Gap Junctions

Demonstrates <electricalConnection> — bidirectional electrical coupling between cells via gap junctions with linear conductance: \(I_{gap} = g_{gap}(V_{pre} - V_{post})\).

The cells are FitzHugh-Nagumo oscillators.

---

1. Define FHN Cell in TVBO

from tvbo import SimulationExperiment

exp = SimulationExperiment.from_string("""
label: "NeuroML Ex19: FHN with Gap Junctions"
dynamics:
  name: FitzHughNagumo
  parameters:
    I: { value: 0.8 }
  state_variables:
    V:
      equation: { rhs: "V - V**3/3 - W + I" }
      initial_value: 0.0
      variable_of_interest: true
    W:
      equation: { rhs: "0.08*(V + 0.7 - 0.8*W)" }
      initial_value: 0.0
network:
  number_of_nodes: 1
integration:
  method: euler
  step_size: 0.01
  duration: 200.0
  time_scale: s
""")
print(f"Model: {exp.dynamics.name}")

Model: FitzHughNagumo

2. Render LEMS XML

xml = exp.render("lems")
print(xml[:1200])

<Lems>

  <!-- Tell jLEMS/jNeuroML which component is the simulation entry point. -->
  <Target component="sim_NeuroML_Ex19__FHN_with_Gap_Junctions"/>

  <!-- ════════════════════════════════════════════════════════════════
       Dimensions & Units (inline — no external includes needed)
       ════════════════════════════════════════════════════════════════ -->

  <!-- Dimensions -->
  <Dimension name="none"/>
  <Dimension name="time" t="1"/>
  <Dimension name="voltage" m="1" l="2" t="-3" i="-1"/>
  <Dimension name="per_time" t="-1"/>
  <Dimension name="conductance" m="-1" l="-2" t="3" i="2"/>
  <Dimension name="capacitance" m="-1" l="-2" t="4" i="2"/>
  <Dimension name="current" i="1"/>
  <Dimension name="resistance" m="1" l="2" t="-3" i="-2"/>
  <Dimension name="concentration" l="-3" n="1"/>
  <Dimension name="substance" n="1"/>
  <Dimension name="charge" t="1" i="1"/>
  <Dimension name="temperature" k="1"/>

  <!-- Units -->
  <Unit symbol="s" dimension="time" power="0"/>
  <Unit symbol="ms" dimension="time" power="-3"/>
  <Unit symbol="us" dimension="time" power="-6"/>
  <Unit symbol="V" dimension="voltage" power="0"/>
  <Unit symbol="mV" dimension="voltage" power="-3"/>
  <U

3. Run Reference

import sys, os
sys.path.insert(0, os.path.dirname(os.path.abspath(".")))
from _nml_helpers import run_lems_example

ref_outputs = run_lems_example("LEMS_NML2_Ex19_GapJunctions.xml")
for name, arr in ref_outputs.items():
    print(f"  {name}: shape={arr.shape}")

  ex19_v.dat: shape=(70001, 3)

4. Run TVBO

import numpy as np

result = exp.run("neuroml")
da = result.integration.data
tvbo_arr = np.column_stack([da.coords['time'].values, da.values])
print(f"TVBO: shape={tvbo_arr.shape}")

TVBO: shape=(20001, 3)

5. Plot Reference

import matplotlib.pyplot as plt
import numpy as np

for name, ref_arr in ref_outputs.items():
    t = ref_arr[:, 0] * 1000
    fig, ax = plt.subplots(figsize=(10, 4))
    for i in range(1, min(ref_arr.shape[1], 6)):
        ax.plot(t, ref_arr[:, i] * 1000, alpha=0.8, label=f'Cell {i}')
    ax.set_xlabel("Time (ms)")
    ax.set_ylabel("Voltage (mV)")
    ax.set_title(f"Ex19: Gap Junctions — {name}")
    ax.legend(fontsize=7)
    ax.grid(True, alpha=0.3)
    plt.tight_layout()
    plt.show()

Gap Junctions

Electrical synapses (electricalConnection) are NeuroML-native network features. TVBO represents the FHN cell dynamics; the gap junction coupling is handled by the NeuroML adapter.