ConductanceSystem

A ConductanceSystem describes the state- and time-dependence of a conductance (i.e. classically g, the inverse of resistance; typically measured in Siemens). It can be used to model the conductance associated with ionic membrane currents, synaptic currents, and axial currents that flow between connected neuronal compartments. By default, a Conductance System is composed of zero or more gates and a parameter for the maximum conductance value ($\overline{g}$). The output of a ConductanceSystem is equal to the the product of each individual gate and $\overline{g}$.

To model sodium conductance in a Hodgkin-Huxley model:

using Conductor, ModelingToolkit, Unitful
import Unitful: mV, mS, cm

Vₘ = ParentScope(MembranePotential())

nav_kinetics = [
    Gate(AlphaBeta,
         ifelse(Vₘ == -40.0, 1.0, (0.1*(Vₘ + 40.0))/(1.0 - exp(-(Vₘ + 40.0)/10.0))),
         4.0*exp(-(Vₘ + 65.0)/18.0), p = 3, name = :m)
    Gate(AlphaBeta,
         0.07*exp(-(Vₘ+65.0)/20.0),
         1.0/(1.0 + exp(-(Vₘ + 35.0)/10.0)), name = :h)]

@named NaV = IonChannel(Sodium, nav_kinetics, max_g = 120mS/cm^2)

equations(NaV) # includes: g(t) ~ gbar*(m(t)^3)*h(t)

\[ \begin{align} \frac{\mathrm{d} m\left( t \right)}{\mathrm{d}t} =& \left( 1 - m\left( t \right) \right) \mathrm{ifelse}\left( 1, \frac{0.1 \left( 40 + V_m\left( t \right) \right)}{1 - e^{0.1 \left( -40 - V_m\left( t \right) \right)}}; \left( V_m\left( t \right) = -40 \right) \right) - 4 m\left( t \right) e^{0.055556 \left( -65 - V_m\left( t \right) \right)} \\ \frac{\mathrm{d} h\left( t \right)}{\mathrm{d}t} =& \frac{ - h\left( t \right)}{1 + e^{0.1 \left( -35 - V_m\left( t \right) \right)}} + 0.07 \left( 1 - h\left( t \right) \right) e^{0.05 \left( -65 - V_m\left( t \right) \right)} \\ g\left( t \right) =& \left( m\left( t \right) \right)^{3} gbar h\left( t \right) \end{align} \]

Conductor.ConductanceSystem — Type

struct ConductanceSystem{T<:Conductor.ConductanceModel} <: Conductor.AbstractConductanceSystem

A model of conductance.

eqs
iv: Independent variable. Defaults to time, $t$.
states
ps
observed
name
systems
defaults
output: Conductance, $g$, of the system.
gbar: Maximum conductance, $\overline{g}$.
ion: Permeability of the conductance.
model
gate_vars: Gating variables.
extensions: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.

inputs

source

Conductor.IonChannel — Function

IonChannel(ion, gate_vars; <keyword arguments>)

An ionic membrane conductance.

Arguments

max_g: Default value for maximum conductance, $\overline{g}$.
extensions::Vector{ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.
defaults::Dict: Default values for states and parameters.
name::Symbol: Name of the system.

source

Conductor.AxialConductance — Function

AxialConductance(gate_vars; <keyword arguments>)

A non-specific conductance between morphologically contiguous compartments.

Arguments

max_g: Maximum conductance, $\overline{g}$.
extensions::Vector{ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.
defaults::Dict: Default values for states and parameters.
name::Symbol: Name of the system.

source

Conductor.SynapticChannel — Function

SynapticChannel(ion, gate_vars; <keyword arguments>)

A synaptically activated conductance. Depends on extrinsic (i.e. presynaptic) state.

Arguments

max_g: Maximum conductance, $\overline{g}$.
extensions::Vector{ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.
aggregate::Bool: whether the Conductance model should aggregate extrinsic sources of state instead of integrating them independently. Defaults to false.
defaults::Dict: Default values for states and parameters.
name::Symbol: Name of the system.

source