Cable cells¶
An Arbor cable cell is a full description of a cell with morphology and cell dynamics, where cell dynamics include ion species and their properties, ion channels, synapses, gap junction sites, stimuli and spike detectors. Arbor cable cells are constructed from a morphology and a label dictionary, and provide a rich interface for specifying the cell’s dynamics.
Note
The cable cell does not have one dedicated page, it has a few more! This page describes how to build a full description of a cable cell, based on three components that are broken out into their own pages:
label dictionary that are used to describe locations and regions on a cell;
It can be helpful to consult those pages for some of the sections of this page.
Decoration¶
A cable cell is decorated by specifying the distribution and placement of dynamics on the cell to produce a full description of a cell morphology and its dynamics with all information required to build a standalone single-cell model, or as part of a larger network.
Decoration uses region and locset descriptions, with their respective use for this purpose reflected in the two broad classes of dynamics in Arbor:
Painted dynamics are applied to regions of a cell, and are associated with an area of the membrane or volume of the cable.
Placed dynamics are applied to locations on the cell, and are associated with entities that can be counted.
Threshold detectors (spike detectors).
Painted dynamics¶
Painted dynamics are applied to a subset of the surface and/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 compartments. 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.
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.
Cable properties¶
There are four cable properties that are defined everywhere on all cables:
Vm: Initial membrane voltage [mV].
cm: Membrane capacitance [F/m²].
rL: Axial resistivity of cable [Ω·cm].
tempK: Temperature [Kelvin].
In Python, the cable_cell interface provides the cable_cell.set_properties() method
for setting cell-wide defaults for properties, and the
cable_cell.paint() interface for overriding properties on specific regions.
import arbor
# Load a morphology from file and define basic regions.
tree = arbor.load_swc('granule.swc')
morph = arbor.morphology(tree, spherical_root=True)
labels = arbor.label_dict({'soma': '(tag 1)', 'axon': '(tag 2)', 'dend': '(tag 3)'})
# Create a cable cell.
cell = arbor.cable_cell(morph, labels)
# Set cell-wide properties that will be applied by default to # the entire cell.
cell.set_properties(Vm=-70, cm=0.02, rL=30, tempK=30+273.5)
# Override specific values on the soma and axon
cell.paint('"soma"', Vm=-50, cm=0.01, rL=35)
cell.paint('"axon"', Vm=-60, rL=40)
Discretisation¶
For the purpose of simulation, cable cells are decomposed into discrete subcomponents called control volumes (CVs), following the finite volume method terminology. Each control volume comprises a connected subset of the morphology. Each fork point in the morphology will be the responsibility of a single CV, and as a special case a zero-volume CV can be used to represent a single fork point in isolation.
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 created for every combination of global parameter values.
Take for example a mechanism passive leaky dynamics:
Name:
"passive".Global variable: reversal potential
"el".Range variable: conductance
"g".
# Create pas mechanism with default parameter values (set in NMODL file).
m1 = arbor.mechanism('passive')
# Create default mechanism with custom conductance (range)
m2 = arbor.mechanism('passive', {'g': 0.1})
# Create a new pas mechanism with that changes reversal potential (global)
m3 = arbor.mechanism('passive/el=-45')
# Create an instance of the same mechanism, that also sets conductance (range)
m4 = arbor.mechanism('passive/el=-45', {'g': 0.1})
cell.paint('"soma"', m1)
cell.paint('"soma"', m2) # error: can't place the same mechanism on overlapping regions
cell.paint('"soma"', m3) # error: technically a different mechanism?
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.
Ion |
name |
Valence |
Calcium |
ca |
1 |
Potassium |
k |
1 |
Sodium |
na |
2 |
Each ion species has the following properties:
internal concentration: concentration on interior of the membrane [mM].
external concentration: concentration on exterior of the membrane [mM].
reversal potential: reversal potential [mV].
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.
but it is 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 that 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:
cell = arbor.cable_cell(morph, labels)
# method 1: create the mechanism explicitly.
ca = arbor.mechanism('nernst/x=ca')
cell.set_ion(ion='ca', method=ca)
# method 2: set directly using a string description
cell.set_ion(ion='ca', method='nernst/x=ca')
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:
# cell is an arbor.cable_cell
# It is possible to define all of the initial condition values
# for a ion species.
cell.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.
cell.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 specific locations.
Connection sites¶
Connections (synapses) are instances of NMODL POINT mechanisms. See also Connections.
Gap junction sites¶
See Gap junctions.