Cable cell decoration

The distribution and placement of dynamics on a cable cell is called the decor of a cell. A decor is composed of individual decorations, which associate a property or dynamic process with a region or locset. The choice of region or locset is reflected in the two broad classes of dynamics on cable cells:

Decorations are described by a decor object in Arbor. It provides facilities for

  • setting properties defined over the whole cell;

  • descriptions of dynamics applied to regions and locsets.

Painted dynamics

Painted dynamics are applied to a subset of the surface or volume of cells. They can be specified at three different levels:

  • globally: a global default for all cells in a model.

  • per-cell: override the global defaults for a specific cell.

  • per-region: specialize on specific cell regions.

This hierarchical approach for resolving parameters and properties allows us to, for example, define a global default value for calcium concentration, then provide a different values on specific cell regions.

Some dynamics, such as membrane capacitance and the initial concentration of ion species must be defined for all CVs. Others need only be applied where they are present, for example ion channels. The types of dynamics, and where they can be defined, are tabulated below.

Painted property resolution options.

region

cell

global

cable properties

ion initial conditions

density mechanism

ion rev pot mechanism

ion valence

If a property is defined at multiple levels, the most local definition will be chosen: a cell-local definition will override a global definition, and a definition on a region will override any cell-local or global definition on that region.

Warning

If a property is defined on two regions that overlap, it is not possible to deterministically choose the correct definition, and an error will be raised during model instantiation.

1. Cable properties

There are four cable properties that must be defined everywhere on a cell:

  • Vm: Initial membrane voltage [mV].

  • cm: Membrane capacitance [F/m²].

  • rL: Axial resistivity of cable [Ω·cm].

  • tempK: Temperature [Kelvin].

Each of the cable properties can be defined as a cell-wide default, that is then specialised on specific regions.

Note

In Python, the decor interface provides the decor.set_properties() method for setting cell-wide defaults for properties, and the decor.paint() interface for overriding properties on specific regions.

import arbor

# Create an empty decor.
decor = arbor.decor()

# Set cell-wide properties that will be applied by default to the entire cell.
decor.set_properties(Vm=-70, cm=0.02, rL=30, tempK=30+273.5)

# Override specific values on regions named "soma" and "axon".
decor.paint('"soma"', Vm=-50, cm=0.01, rL=35)
decor.paint('"axon"', Vm=-60, rL=40)

3. Density mechanisms

Regions can have density mechanisms defined over their extents. Density mechanisms are NMODL mechanisms which describe biophysical processes. These are processes that are distributed in space, but whose behaviour is defined purely by the state of the cell and the process at any given point.

The most common use for density mechanisms is to describe ion channel dynamics, for example the hh and pas mechanisms provided by NEURON and Arbor, which model classic Hodgkin-Huxley and passive leaky currents respectively.

Mechanisms have two types of parameters that can be set by users

  • Global parameters are a single scalar value that is the same everywhere a mechanism is defined.

  • Range parameters can vary spatially.

Every mechanism is described by a string with its name, and an optional list of key-value pairs that define its range parameters.

Because a global parameter is fixed over the entire spatial extent of a density mechanism, a new mechanism has to be created for every combination of global parameter values.

Take for example the built-in mechanism for passive leaky dynamics:

  • Name: "pas"

  • Global variable: reversal potential "e".

  • Range variable: conductance "g".

# Create passive mechanism with default parameter values (set in NMODL file).
m1 = arbor.mechanism('pas')

# Create mechanism with custom conductance (range)
m2 = arbor.mechanism('pas', {'g': 0.1})

# Create a new passive mechanism with that changes reversal potential (global)
m3 = arbor.mechanism('pas/e=-45')

# Create an instance of the same mechanism, that also sets conductance (range)
m4 = arbor.mechanism('pas/e=-45', {'g': 0.1})

decor = arbor.decor()
decor.paint('"soma"', m1)
decor.paint('"soma"', m2) # error: can't place the same mechanism on overlapping regions
decor.paint('"soma"', m3) # error: can't have overlap between two instances of a mechanism
                          #        with different values for a global parameter.

4. Ion species

Arbor allows arbitrary ion species to be defined, to extend the default calcium, potassium and sodium ion species. A ion species is defined globally by its name and valence, which can’t be overridden at cell or region level.

Default ion species in Arbor

Ion

name

Valence

Calcium

ca

2

Potassium

k

1

Sodium

na

1

Each ion species has the following properties:

  1. internal concentration: concentration on interior of the membrane [mM].

  2. external concentration: concentration on exterior of the membrane [mM].

  3. reversal potential: reversal potential [mV].

  4. reversal potential mechanism: method for calculating reversal potential.

Properties 1, 2 and 3 must be defined, and are used as the initial values for each quantity at the start of the simulation. They are specified globally, then specialized at cell and region level.

The reversal potential of an ion species is calculated by an optional reversal potential mechanism. If no reversal potential mechanism is specified for an ion species, the initial reversal potential values are maintained for the course of a simulation. Otherwise, the mechanism does the work.

Reversal potential mechanisms are density mechanisms subject to some strict restrictions. Specifically, a reversal potential mechanism described in NMODL:

  • May not maintain any STATE variables.

  • Can only write to the “eX” value associated with an ion.

  • Can not be a POINT mechanism.

Essentially, reversal potential mechanisms must be pure functions of cellular and ionic state.

Note

Arbor imposes greater restrictions on mechanisms that update ionic reversal potentials than NEURON. Doing so simplifies reasoning about interactions between mechanisms that share ionic species, by virtue of having one mechanism, and one mechanism only, that calculates reversal potentials according to concentrations that the other mechanisms use and modify.

If a reversal potential mechanism writes to multiple ions, it must be given for either no ions, or all of the ions it writes.

Arbor’s default catalogue includes a nernst reversal potential, which is parameterized over a single ion. For example, to bind it to the calcium ion at the cell level using the Python interface:

decor = arbor.decor()

# Method 1: create the mechanism explicitly.
ca = arbor.mechanism('nernst/x=ca')
decor.set_ion(ion='ca', method=ca)

# Method 2: set directly using a string description.
decor.set_ion(ion='ca', method='nernst/x=ca')

cell = arbor.cable_cell(morph, labels, decor)

The NMODL code for the Nernst mechanism can be used as a guide for how to calculate reversal potentials.

While the reversal potential mechanism must be the same for a whole cell, the initial concentrations and reversal potential can be localized for regions using the paint interface:

# decor is an arbor.decor

# It is possible to define all of the initial condition values
# for a ion species.
decor.paint('(tag 1)', arbor.ion('ca', int_con=2e-4, ext_con=2.5, rev_pot=114))

# Alternatively, one can selectively overwrite the global defaults.
decor.paint('(tag 2)', arbor.ion('ca', rev_pot=126)

Placed dynamics

Placed dynamics are discrete countable items that affect or record the dynamics of a cell, and are assigned to locsets. Because locsets can contain multiple locations on the cell, and the exact number of these locations can not be known until the model is built, each placed dynamic is given a string label, used to refer to the group of items on the underlying locset.

1. Connection sites

Connections (synapses) are instances of NMODL POINT mechanisms. See also connection.

2. Gap junction sites

See gap junction.

3. Threshold detectors (spike detectors).

4. Stimuli

A current stimulus is a DC or sinusoidal current of fixed frequency with a time-varying amplitude governed by a piecewise-linear envelope.

The stimulus is described by three parameters: a sequence of points (ti, ai) describing the envelope, where the times ti are in milliseconds and the amplitudes ai are in nanoamperes; a frequency in kilohertz, where a value of zero denotes DC; and the phase in radians at time zero.

The stimulus starts at the first timepoint t0 with amplitude a0, and the amplitude is then interpolated linearly between successive points. The last envelope point (tn, an) describes a constant amplitude an from the time tn onwards.

Stimulus objects in the C++ and Python interfaces have simple constructors for describing constant stimuli and constant amplitude stimuli restricted to a fixed time interval.

# Constant stimulus, amplitude 10 nA.
decor.place('(root)', arbor.iclamp(10), "iclamp0")

# Constant amplitude 10 nA stimulus at 20 Hz, with initial phase of π/4 radians.
decor.place('(root)', arbor.iclamp(10, frequency=0.020, phasce=math.pi/4), "iclamp1")

# Stimulus at 1 kHz, amplitude 10 nA, for 40 ms starting at t = 30 ms.
decor.place('(root)', arbor.iclamp(30, 40, 10, frequency=1), "iclamp2")

# Piecewise linear stimulus with amplitude ranging from 0 nA to 10 nA,
# starting at t = 30 ms and stopping at t = 50 ms.
decor.place('(root)', arbor.iclamp([(30, 0), (37, 10), (43, 8), (50, 0)], "iclamp3")

5. Probes

API