# Cable cells¶

Warning

The interface for building and modifying cable cell objects will be thoroughly revised in the near future. The documentation here is primarily a place holder.

Cable cells, which use the cell_kind cable, represent morphologically-detailed neurons as 1-d trees, with electrical and biophysical properties mapped onto those trees.

A single cell is represented by an object of type cable_cell. Properties shared by all cable cells, as returned by the recipe get_global_properties method, are described by an object of type cable_cell_global_properties.

## The cable_cell object¶

Cable cells are built up from a series of segment objects, which themselves describe an unbranched component of the cell morphology. These segments are added via the methods:

soma_segment *cable_cell::add_soma(double radius)

Add the soma to the cable cell with the given radius. There can be only one per cell.

The soma segment has index 0, and must be added before any cable segments.

cable_segment *cable_cell::add_cable(cell_lid_type index, Args&&... args)

Add a unbranched section of the cell morphology, with its proximal end attached to the segment given by index. The following arguments are forwarded to the cable_segment constructor.

Segment indices are exactly the order in which they have been added to a cell, counting from zero (for the soma). Both soma_segment and cable_segment are derived from the abstract base class segment.

Todo

Describe cable_segment constructor arguments, unless we get to the replace cell building/morphology implementation first.

Each segment will inherit the electrical properties of the cell, unless otherwise overriden (see below).

## Cell dynamics¶

Each segment in a cell may have attached to it one or more density 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.

Cells may also have point mechanisms, which are added directly to the cable_cell object.

A third type of mechanism, which describes ionic reversal potential behaviour, can be specified for cells or the whole model via cell parameter settings, described below.

Mechanisms are described by a mechanism_desc object. These specify the name of the mechanism (used to find the mechanism in the mechanism catalogue) and parameter values for the mechanism that apply within a segment. A mechanism_desc is effectively a wrapper around a name and a dictionary of parameter/value settings.

Mechanism descriptions can be constructed implicitly from the mechanism name, and mechanism parameter values then set with the set method. Relevant mechanism_desc methods:

mechanism_desc::mechanism_desc(std::string name)

Construct a mechanism description for the mechanism named name.

mechanism_desc &mechanism_desc::set(const std::string &key, double value)

Sets the parameter associated with key in the description. Returns a reference to the mechanism description, so that calls to set can be chained in a single expression.

Density mechanisms are associated with a cable cell object with:

void segment::add_mechanism(mechanism_desc mech)

Point mechanisms, which are associated with connection end points on a cable cell, are attached to a cell with:

void cable_cell::add_synapse(mlocation loc, mechanism_desc mech)

where mlocation is a simple struct holding a segment index and a relative position (from 0, proximal, to 1, distal) along that segment:

## Electrical properities and ion values¶

On each cell segment, electrical and ion properties can be specified by the parameters field, of type cable_cell_local_parameter_set.

The cable_cell_local_parameter_set has the following members, where an empty optional value or missing map key indicates that the corresponding value should be taken from the cell or global parameter set.

class cable_cell_local_parameter_set
std::unordered_map<std::string, cable_cell_ion_data> ion_data

The keys of this map are names of ions, whose parameters will be locally overriden. The struct cable_cell_ion_data has three fields: init_int_concentration, init_ext_concentration, and init_reversal_potential.

Internal and external concentrations are given in millimolars, i.e. mol/m³. Reversal potential is given in millivolts.

util::optional<double> init_membrane_potential

Initial membrane potential in millivolts.

util::optional<double> temperature_K

Local temperature in Kelvin.

util::optional<double> axial_resistivity

Local resistivity of the intracellular medium, in ohm-centimetres.

util::optional<double> membrane_capacitance

Local areal capacitance of the cell membrane, in Farads per square metre.

Default parameters for a cell are given by the default_parameters field in the cable_cell object. This is a value of type cable_cell_parameter_set, which extends cable_cell_local_parameter_set by adding an additional field describing reversal potential computation:

class cable_cell_parameter_set : public cable_cell_local_parameter_set
std::unordered_map<std::string, mechanism_desc> reversal_potential_method

Maps the name of an ion to a ‘reversal potential’ mechanism that describes how it should be computed. When no mechanism is provided for an ionic reversal potential, the reversal potential will be kept at its initial value.

Default parameters for all cells are supplied in the cable_cell_global_properties struct.

## Global properties¶

class cable_cell_global_properties
const mechanism_catalogue *catalogue

All mechanism names refer to mechanism instances in this mechanism catalogue. By default, this is set to point to global_default_catalogue(), the catalogue that contains all mechanisms bundled with Arbor.

double membrane_voltage_limit_mV

If non-zero, check to see if the membrane voltage ever exceeds this value in magnitude during the course of a simulation. If so, throw an exception and abort the simulation.

bool coalesce_synapses

When synapse dynamics are sufficiently simple, the states of synapses within the same discretized element can be combined for better performance. This is true by default.

std::unordered_map<std::string, int> ion_species

Every ion species used by cable cells in the simulation must have an entry in this map, which takes an ion name to its charge, expressed as a multiple of the elementary charge. By default, it is set to include sodium “na” with charge 1, calcium “ca” with charge 2, and potassium “k” with charge 1.

cable_cell_parameter_set default_parameters

The default electrical and physical properties associated with each cable cell, unless overridden locally. In the global properties, every optional field must be given a value, and every ion must have its default values set in default_parameters.ion_data.

add_ion(const std::string &ion_name, int charge, double init_iconc, double init_econc, double init_revpot)

Convenience function for adding a new ion to the global ion_species table, and setting up its default values in the ion_data table.

add_ion(const std::string &ion_name, int charge, double init_iconc, double init_econc, mechanism_desc revpot_mechanism)

As above, but set the initial reversal potential to zero, and use the given mechanism for reversal potential calculation.

For convenience, neuron_parameter_defaults is a predefined cable_cell_local_parameter_set value that holds values that correspond to NEURON defaults. To use these values, assign them to the default_parameters field of the global properties object returned in the recipe.

## Reversal potential dynamics¶

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, a provided mechanism does the work, but it subject to some strict restrictions. 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 given as a POINT mechanism.

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

If a reversal potential mechanism writes to multiple ions, then if the mechanism is given for one of the ions in the global or per-cell parameters, it must be given for all of them.

Arbor’s default catalogue includes a “nernst” reversal potential, which is parameterized over a single ion, and so can be assigned to e.g. calcium in the global parameters via

cable_cell_global_properties gprop;
// ...
gprop.default_parameters.reversal_potential_method["ca"] = "nernst/ca";


This mechanism has global scalar parameters for the gas constant R and Faraday constant F, corresponding to the exact values given by the 2019 redifinition of the SI base units. These values can be changed in a derived mechanism in order to use, for example, older values of these physical constants.

mechanism_catalogue mycat(global_default_catalogue());
mycat.derive("nernst1998", "nernst", {{"R", 8.314472}, {"F", 96485.3415}});

gprop.catalogue = &mycat;
gprop.default_parameters.reversal_potential_method["ca"] = "nernst1998/ca";