Universal Gas Constant (base units)

Capacitance per unit area.

Conductance per unit area.

Universal Gas Constant (milli-)

Scaled by 1000x. Results in output

The independent variable for time, $t$.

Faraday's Constant

The electric charge of one mole of electrons.

Unicode ℱ can be typed by writing \scrF then pressing tab in the Julia REPL, and in many editors.

Examples

julia> Conductor.ℱ
96485.33212331001 C mol^-1

struct CompartmentSystem{T<:Conductor.AbstractDynamics} <: Conductor.AbstractCompartmentSystem

A neuronal compartment.

• voltage::Symbolics.Num: Voltage potential.

• dynamics::Conductor.AbstractDynamics

• capacitance::Union{Nothing, Symbolics.Num}: Membrane capacitance.

• eqs::Vector{Symbolics.Equation}

• iv::Symbolics.Num: Independent variable. Defaults to time, $t$.

• states::Vector{Symbolics.Num}

• ps::Vector{Symbolics.Num}

• observed::Vector{Symbolics.Equation}

• name::Symbol

• systems::Vector{ModelingToolkit.AbstractTimeDependentSystem}

• defaults::Dict

• extensions::Vector{ModelingToolkit.ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.

• synapses::Vector{Synapse{<:ModelingToolkit.AbstractSystem}}

• arbor::Conductor.Arborization

• stimuli::Vector{<:Conductor.StimulusModel}

• geometry::Conductor.Geometry: Morphological geometry of the compartment.

CompartmentSystem(Vₘ, channels, reversals; <keyword arguments>)

Arguments

• capacitance::SpecificCapacitance: The capacitance of the compartment given in Farads per unit area (e.g. µF/cm^2).
• geometry::Geometry: Morphological geometry of the compartment.
• extensions::Vector{ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.
• stimuli::Vector{Equation}:
• name::Symbol: Name of the system.

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

ConductanceSystem(g, ion, gate_vars; <keyword arguments>)

Main constructor for ConductanceSystem.

Arguments

• gbar::Num: Maximum conductance, $\overline{g}$.
• aggregate::Bool: determines 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.

EquilibriumPotential(ion::IonSpecies, val; <keyword arguments>)

An equilibrium (a.k.a. reversal) potential.

Arguments

• dynamic::Bool = false: a dynamic EquilbriumPotential is assumed to vary with time (e.g. derived from the Nernst equation).
• name::Symbol = Symbol("I", Conductor.PERIODIC_SYMBOL[ion]): the symbol to use for the symbolic variable. By default, a lookup table is used to find the ion's symbol on the periodic table of elements.

Gate(
    form::Type{AlphaBeta},
    α,
    β;
    name,
    kwargs...
) -> Gate{AlphaBeta}

Accepts expressions for forward (α) and reverse (β) reaction rates as descriptors for its kinetics.

See also: get_eqs.

Gate(
    form::Type{Conductor.ParameterGate},
    val;
    name,
    kwargs...
) -> Gate{Conductor.ParameterGate}

A static parameter gate with initial value, val.

Gate(
    form::Type{SimpleGate},
    rhs::Symbolics.Num;
    default,
    name,
    kwargs...
) -> Gate{SimpleGate}

Accepts any symbolic expression as an explicit definition of the gate dynamics.

Gate(
    form::Type{SteadyStateTau},
    x∞,
    τₓ;
    name,
    kwargs...
) -> Gate{SteadyStateTau}

Accepts expressions for its steady-state activation, x∞(Vₘ), and the time constant, τₓ(Vₘ), as descriptors for its kinetics.

See also: get_eqs.

struct Gate{T<:Conductor.GateVarForm} <: Conductor.AbstractGatingVariable

Low-level constructor for Gate.

A gate has a single symbolic output and stores properties (passed as a variable length list of keyword arguments). Gate properties are accessible via get and getproperty.

Example

julia> @variables t X(t)
2-element Vector{Num}:
    t
 X(t)

julia> g = Gate{MyGateType}(MyGateType, X, Equation[], prop1 = "foo", prop2 = 62)
Gate{MyGateType}(MyGateType, X(t), Symbolics.Equation[], Dict{Symbol, Any}(:prop2 => 62, :prop1 => "foo"))

julia> (g.prop1, g.prop2)
("foo", 62)

abstract type GateVarForm

Abstract supertype for extending the behavior of Gate.

Stub subtypes of GateVarForm are used as traits when writing new methods that call Gate objects.

Example

struct MyNewGate <: Conductor.GateVarForm end

function Conductor.get_eqs(g::Gate{MyNewGate}, comp::CompartmentSystem)
    # a function that returns a vector of equations defining gate dynamics
end

IonConcentration(ion::IonSpecies, val = nothing; <keyword arguments>)

An intra/extracellular concentration of ions.

Arguments

• location::PrimitiveLocation = Inside: location (Inside or Outside) w.r.t. the parent compartment (intracellular or extracellular).
• dynamic::Bool = false: when false, the concentration will be a static parameter.
• name::Symbol = Conductor.PERIODIC_SYMBOL[ion]: the symbol to use for the symbolic variable. By default, a lookup table is used to find the ion's symbol on the periodic table of elements.

IonCurrent(ion::IonSpecies, val = nothing; <keyword arguments>)

An ionic membrane current.

Arguments

• aggregate::Bool = false: aggregate currents are the sum of all conductances (with matched ion species) flowing into the parent compartment. For example, an aggregate IonCurrent for Calcium will be the sum of all other Calcium-permeable currents.
• dynamic::Bool = true: when dynamic == false the IonCurrent will be a static parameter value.
• name::Symbol = Symbol("I", Conductor.PERIODIC_SYMBOL[ion]): the symbol to use for the symbolic variable. By default, a lookup table is used to find the ion's symbol on the periodic table of elements.

Ion species to annotate ConductanceSystem, IonCurrent, IonConcentration, etc. May be one of:

• NonIonic
• Sodium
• Potassium
• Chloride
• Calcium
• Cation
• Anion
• Glutamatergic
• Cholinergic
• AMPA
• NMDA

MembranePotential(V0 = -60mV; <keyword arguments>)

The voltage in an arbitrary compartment.

If V0 == nothing, the default value of the resulting variable will be left unassigned.

Arguments

• dynamic::Bool = true: when false, the voltage will be a static parameter.
• source::PrimitiveSource = Intrinsic: the expected origin of a voltage state. Intrinsic sources are states from the parent compartment. Extrinsic sources come from other compartments (e.g. presynaptic compartments).
• n::Integer = 1: when n > 1, the voltage will be a symbolic array of length n.
• name::Symbol = :Vₘ: the symbol to use for the symbolic variable

MultiCompartment(
    topology::MultiCompartmentTopology;
    extensions,
    name,
    defaults
) -> MultiCompartmentSystem

Basic constructor for a MultiCompartmentSystem.

struct MultiCompartmentSystem <: Conductor.AbstractCompartmentSystem

A neuron with 2+ morphologically connected compartments.

• eqs::Vector{Symbolics.Equation}

• iv::Symbolics.Num: Independent variabe. Defaults to time, $t$.

• states::Vector{Symbolics.Num}

• ps::Vector{Symbolics.Num}

• observed::Vector{Symbolics.Equation}

• name::Symbol

• systems::Vector{ModelingToolkit.AbstractTimeDependentSystem}

• defaults::Dict

• topology::MultiCompartmentTopology

• compartments::Vector{CompartmentSystem}: Individual subcompartments of the neuron.

• extensions::Vector{ModelingToolkit.ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.

struct NeuronalNetworkSystem <: Conductor.AbstractNeuronalNetworkSystem

A network of neurons with synaptic connections.

• eqs::Vector{Symbolics.Equation}

• iv::Symbolics.Num: Independent variabe. Defaults to time, $t$.

• states::Vector

• ps::Vector

• observed::Vector{Symbolics.Equation}

• name::Symbol

• systems::Vector{ModelingToolkit.AbstractTimeDependentSystem}

• defaults::Dict

• topology::NetworkTopology

• reversal_map::Dict

• extensions::Vector{ModelingToolkit.ODESystem}: Additional systems to extend dynamics. Extensions are composed with the parent system during conversion to ODESystem.

NeuronalNetworkSystem(
    topology::NetworkTopology,
    reversal_map
) -> NeuronalNetworkSystem
NeuronalNetworkSystem(
    topology::NetworkTopology,
    reversal_map,
    extensions::Vector{<:ModelingToolkit.AbstractTimeDependentSystem};
    defaults,
    name
) -> NeuronalNetworkSystem

Basic constructor for a NeuronalNetworkSystem.

struct Population{T<:Conductor.AbstractCompartmentSystem}

A population (or small group) of neurons.

A Population is a lazy representation of neurons templated from a single model prototype. Iterating over a Population returns up to n uniquely-named copies of the prototype that are serially numbered and, optionally, namespaced. Parameter values of the replicate neurons can be individually defined by indexed assignment, or applied to the entire group via distributions.

• neurons

• popname: Base name of the population.

• defs: Population defaults

• stimuli: Stimuli applied to select neurons.

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.

Differential with respect to time, $t$.

ExtrinsicPotential(; n = 1, name::Symbol = :Vₓ)

A voltage derived from an external source (i.e. not the parent compartment).

Equivalent to: MembranePotential(nothing; dynamic=true, source=Extrinsic, n=n, name=name)

Arguments

• n::Integer = 1: when n > 1, the voltage will be a symbolic array of length n.
• name::Symbol = :Vₓ: the symbol to use for the symbolic variable

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.

Simulation(
    neuron::Conductor.AbstractCompartmentSystem,
    tspan;
    simplify,
    parallel,
    kwargs...
) -> Any

Compile and run a simulation of a single neuron or network of neurons for a specified duration, time.

If return_system == true, returns a simplified ODESystem instead.

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.

Temperature(temp; <keyword arguments>)

Temperature (in Kelvin)

Arguments

• dynamic::Bool = false: a dynamic Temperature is assumed to vary with time.
• name::Symbol = :T: the symbol to use for the symbolic variable.