Model: Kinetic Scheme Ion Channels
This example demonstrates ionChannelKS — ion channels defined by Markov state transitions between open/closed states. The k_vh channel uses a vHalfTransition with rates:
\[r_{f0} = \frac{\exp(z\gamma(v - v_{Half})/k_{te})}{\tau}, \quad
r_{r0} = \frac{\exp(-z(1-\gamma)(v - v_{Half})/k_{te})}{\tau}\]
\[r_f = \frac{1}{1/r_{f0} + \tau_{Min}}, \quad
r_r = \frac{1}{1/r_{r0} + \tau_{Min}}\]
where \(k_{te} = 25.3\,\text{mV}\) . The cell has a standard HH Na channel (\(m^3 h\) ) and the KS K channel (\(n\) , instances=1):
\[C\frac{dv}{dt} = -g_{Na}m^3 h(v - E_{Na}) - g_K n(v - E_K) + I_{\text{ext}}\]
By annotating the dynamics with iri: neuroml:pointCellCondBased and structuring the ion channels as components (including ionChannelKS with gateKS and vHalfTransition), TVBO emits standard NeuroML2 types that preserve the jLEMS child-before-parent RK4 evaluation order — giving exact numerical identity.
1. Define in TVBO
from tvbo import SimulationExperiment# Ex4 parameters: pointCellCondBased, C=1pF # Na: 6000 channels × 20pS, erev=50mV (standard HH rates) # K (k_vh): 1800 channels × 8pS, erev=-77mV (KS vHalfTransition) = SimulationExperiment.from_string(""" label: "NeuroML Ex4: KS Channels" dynamics: name: HH_KineticScheme iri: neuroml:pointCellCondBased description: > Cell with HH Na channel and kinetic-scheme K channel, matching NeuroML2 Ex4. parameters: C: { value: 1, description: "nml:1pF" } v0: { value: -65, description: "nml:-65mV" } thresh: { value: -20, description: "nml:-20mV" } pulse_delay: { value: 100, description: "nml:100ms" } pulse_duration: { value: 100, description: "nml:100ms" } I_amp: { value: 0.005, description: "nml:0.005 nA" } components: na: name: na iri: neuroml:ionChannelHH parameters: conductance: { value: 20, description: "nml:20pS" } number: { value: 6000 } erev: { value: 50, description: "nml:50mV" } components: m: name: m iri: neuroml:gateHHrates parameters: instances: { value: 3 } components: forwardRate: name: forwardRate iri: neuroml:HHExpLinearRate parameters: rate: { value: 1, description: "nml:1per_ms" } midpoint: { value: -40, description: "nml:-40mV" } scale: { value: 10, description: "nml:10mV" } reverseRate: name: reverseRate iri: neuroml:HHExpRate parameters: rate: { value: 4, description: "nml:4per_ms" } midpoint: { value: -65, description: "nml:-65mV" } scale: { value: -18, description: "nml:-18mV" } h: name: h iri: neuroml:gateHHrates parameters: instances: { value: 1 } components: forwardRate: name: forwardRate iri: neuroml:HHExpRate parameters: rate: { value: 0.07, description: "nml:0.07per_ms" } midpoint: { value: -65, description: "nml:-65mV" } scale: { value: -20, description: "nml:-20mV" } reverseRate: name: reverseRate iri: neuroml:HHSigmoidRate parameters: rate: { value: 1, description: "nml:1per_ms" } midpoint: { value: -35, description: "nml:-35mV" } scale: { value: 10, description: "nml:10mV" } k_vh: name: k_vh iri: neuroml:ionChannelKS parameters: conductance: { value: 8, description: "nml:8pS" } number: { value: 1800 } erev: { value: -77, description: "nml:-77mV" } components: n: name: n iri: neuroml:gateKS parameters: instances: { value: 1 } components: c1: name: c1 iri: neuroml:closedState o1: name: o1 iri: neuroml:openState vh1: name: vh1 iri: neuroml:vHalfTransition parameters: from: { value: 0, description: "nml:c1" } to: { value: 0, description: "nml:o1" } vHalf: { value: 0, description: "nml:0mV" } z: { value: 1.5 } gamma: { value: 0.75 } tau: { value: 3.2, description: "nml:3.2ms" } tauMin: { value: 0.3, description: "nml:0.3ms" } integration: step_size: 0.01 duration: 300.0 time_scale: ms """ )print (f"Model: { exp. dynamics. name} " )print (f"IRI: { exp. dynamics. iri} " )print (f"Components: { list (exp.dynamics.components.keys())} " )
Model: HH_KineticScheme
IRI: neuroml:pointCellCondBased
Components: ['k_vh', 'na']
This example uses iri: neuroml:ionChannelKS with gateKS containing closedState, openState, and vHalfTransition sub-components. TVBO’s adapter emits these as standard NeuroML2 XML elements — no need to flatten the Markov scheme into ODEs. This gives exact numerical identity with the reference simulation at the original step size (0.01 ms).
2. Render LEMS XML
= exp.render("lems" )for line in xml.split(' \n ' ):= line.strip()if any (tag in line_stripped for tag in ['<ionChannel' , '<gateHH' , '<gateKS' ,'<pointCell' , '<channelPopulation' , '<closedState' , '<openState' ,'<vHalfTransition' , '<pulseGenerator' , 'Rate type=' , '<Include' ]):print (line_stripped)
<Include file="Cells.xml"/>
<Include file="Networks.xml"/>
<Include file="Simulation.xml"/>
<ionChannelKS id="k_vh" conductance="8pS">
<gateKS id="n" instances="1">
<closedState id="c1"/>
<openState id="o1"/>
<vHalfTransition from="c1" to="o1" vHalf="0mV" z="1.5" gamma="0.75" tau="3.2ms" tauMin="0.3ms"/>
<ionChannelHH id="na" conductance="20pS">
<gateHHrates id="h" instances="1">
<forwardRate type="HHExpRate" rate="0.07per_ms" midpoint="-65mV" scale="-20mV"/>
<reverseRate type="HHSigmoidRate" rate="1per_ms" midpoint="-35mV" scale="10mV"/>
<gateHHrates id="m" instances="3">
<forwardRate type="HHExpLinearRate" rate="1per_ms" midpoint="-40mV" scale="10mV"/>
<reverseRate type="HHExpRate" rate="4per_ms" midpoint="-65mV" scale="-18mV"/>
<pointCellCondBased id="HH_KineticScheme" C="1pF" v0="-65mV" thresh="-20mV">
<channelPopulation id="k_vh_pop" ionChannel="k_vh" number="1800" erev="-77mV"/>
<channelPopulation id="na_pop" ionChannel="na" number="6000" erev="50mV"/>
<pulseGenerator id="pulseGen1" delay="100ms" duration="100ms" amplitude="0.005 nA"/>
3. Run Reference
import sys, os0 , os.path.dirname(os.path.abspath("." )))from _nml_helpers import run_lems_example= run_lems_example("LEMS_NML2_Ex4_KS.xml" )for name, arr in ref_outputs.items():print (f" { name} : shape= { arr. shape} " )
auto.dat: shape=(30001, 7)
4. Run TVBO Version
import numpy as np= exp.run("neuroml" )= result.integration.data= da.coords['time' ].values= da.sel(variable= 'v' ).values= np.column_stack([time, v_data])print (f"TVBO: shape= { tvbo_arr. shape} , t=[ { tvbo_arr[0 ,0 ]:.4f} , { tvbo_arr[- 1 ,0 ]:.4f} ]" )
TVBO: shape=(30001, 2), t=[0.0000, 0.3000]
5. Numerical Comparison
from _nml_helpers import compare_tracesimport numpy as np= list (ref_outputs.values())[0 ]= ref_arr[:, [0 , 1 ]]= tvbo_arr[:, [0 , 1 ]]= ['time' , 'v' ], tvbo_cols= ['time' , 'v' ])
v: RMSE=0.000000 max_err=0.000000 corr=1.000000 ✅
{'v': {'rmse': np.float64(1.6799752492306732e-21),
'max_err': np.float64(2.168404344971009e-19),
'corr': np.float64(0.9999999999999998),
'close': True}}
6. Plot
from _nml_helpers import plot_comparison= ['time' , 'v' ], tvbo_cols= ['time' , 'v' ],= "Ex4: KS Channels — NeuroML vs TVBO" ,= 1.0 , time_unit= "s" ,
