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.

util::optional<cv_policy> discretization

Method by which CV boundaries are determined when the cell is discretized. See Discretization and CV policies.

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";

Cable cell probes

Various properties of a a cable cell can be sampled via one of the cable cell specific probe address described below. They fall into two classes: scalar probes are associated with a single real value, such as a membrane voltage or mechanism state value at a particular location; vector probes return multiple values corresponding to a quantity sampled over a whole cell.

The sample data associated with a cable cell probe will either be a double for scalar probes, or a cable_sample_range describing a half-open range of double values:

using cable_sample_range = std::pair<const double*, const double*>

The probe metadata passed to the sampler will be a const pointer to:

  • mlocation for most scalar probes;
  • cable_probe_point_info for point mechanism state queries;
  • mcable_list for most vector queries;
  • std::vector<cable_probe_point_info> for cell-wide point mechanism state queries.

The type cable_probe_point_info holds metadata for a single target on a cell:

struct cable_probe_point_info {
    // Target number of point process instance on cell.
    cell_lid_type target;

    // Number of combined instances at this site.
    unsigned multiplicity;

    // Point on cell morphology where instance is placed.
    mlocation loc;
};

Note that the multiplicity will always be 1 if synapse coalescing is disabled.

Cable cell probes that contingently do not correspond to a valid measurable quantity are ignored: samplers attached to them will receive no values. Mechanism state queries however will throw a cable_cell_error exception at simulation initialization if the requested state variable does not exist on the mechanism.

Cable cell probe addresses that are described by a locset may generate more than one concrete probe: there will be one per location in the locset that is satisfiable. Sampler callback functions can distinguish between different probes with the same address and id by examining their index and/or probe-sepcific metadata found in the probe_metadata parameter.

Membrane voltage

struct cable_probe_membrane_voltage {
    locset locations;
};

Queries cell membrane potential at each site in locations.

  • Sample value: double. Membrane potential in millivolts.
  • Metadata: mlocation. Location of probe.
struct cable_probe_membrane_voltage_cell {};

Queries cell membrane potential across whole cell.

  • Sample value: cable_sample_range. Each value is the average membrane potential in millivolts across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.

Axial current

struct cable_probe_axial_current {
    locset locations;
};

Estimate intracellular current at each site in locations, in the distal direction.

  • Sample value: double. Current in nanoamperes.
  • Metadata: mlocation. Location as of probe.

Transmembrane current

struct cable_probe_ion_current_density {
    locset locations;
    std::string ion;
};

Membrance current density attributed to a particular ion at each site in locations.

  • Sample value: double. Current density in amperes per square metre.
  • Metadata: mlocation. Location of probe.
struct cable_probe_ion_current_cell {
    std::string ion;
};

Membrane current attributed to a particular ion across components of the cell.

  • Sample value: cable_sample_range. Each value is the current in nanoamperes across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.
struct cable_probe_total_ion_current_density {
    locset locations;
};

Membrane current density at given locations _excluding_ capacitive currents.

  • Sample value: double. Current density in amperes per square metre.
  • Metadata: mlocation. Location of probe.
struct cable_probe_total_ion_current_cell {};

Membrane current _excluding_ capacitive currents across components of the cell.

  • Sample value: cable_sample_range. Each value is the current in nanoamperes across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.
struct cable_probe_total_current_cell {};

Total membrance current across components of the cell.

  • Sample value: cable_sample_range. Each value is the current in nanoamperes across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.

Ion concentration

struct cable_probe_ion_int_concentration {
    locset locations;
    std::string ion;
};

Ionic internal concentration of ion at each site in locations.

  • Sample value: double. Ion concentration in millimoles per litre.
  • Metadata: mlocation. Location of probe.
struct cable_probe_ion_int_concentration_cell {
    std::string ion;
};

Ionic external concentration of ion across components of the cell.

  • Sample value: cable_sample_range. Each value is the concentration in millimoles per lire across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.
struct cable_probe_ion_ext_concentration {
    mlocation location;
    std::string ion;
};

Ionic external concentration of ion at each site in locations.

  • Sample value: double. Ion concentration in millimoles per litre.
  • Metadata: mlocation. Location of probe.
struct cable_probe_ion_ext_concentration_cell {
    std::string ion;
};

Ionic external concentration of ion across components of the cell.

  • Sample value: cable_sample_range. Each value is the concentration in millimoles per lire across an unbranched component of the cell, as determined by the discretization.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.

Mechanism state

struct cable_probe_density_state {
    locset locations;
    std::string mechanism;
    std::string state;
};

Value of state variable in a density mechanism in each site in locations. If the mechanism is not defined at a particular site, that site is ignored.

  • Sample value: double. State variable value.
  • Metadata: mlocation. Location as given in the probe address.
struct cable_probe_density_state_cell {
    std::string mechanism;
    std::string state;
};

Value of state variable in adensity mechanism across components of the cell.

  • Sample value: cable_sample_range. State variable values from the mechanism across unbranched components of the cell, as determined by the discretization and mechanism extent.
  • Metadata: mcable_list. Each cable in the cable list describes the unbranched component for the corresponding sample value.
struct cable_probe_point_state {
    cell_lid_type target;
    std::string mechanism;
    std::string state;
};

Value of state variable in a point mechanism associated with the given target. If the mechanism is not associated with this target, the probe is ignored.

  • Sample value: double. State variable value.
  • Metadata: cable_probe_point_info. Target number, multiplicity and location.
struct cable_probe_point_state_cell {
    std::string mechanism;
    std::string state;
};

Value of state variable in a point mechanism for each of the targets in the cell with which it is associated.

  • Sample value: cable_sample_range. State variable values at each associated target.
  • Metadata: std::vector<cable_probe_point_info>. Target metadata for each associated target.

Discretization and CV policies

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.

The CVs are uniquely determined by a set of B of mlocation boundary points. For each non-terminal point h in B, there is a CV comprising the points {xh ≤ x and ¬∃ y ∈ B s.t h < y < x}, where < and ≤ refer to the geometrical partial order of locations on the morphology. A fork point is owned by a CV if and only if all of its corresponding representative locations are in the CV.

The set of boundary points used by the simulator is determined by a CV policy. These are objects of type cv_policy, which has the following public methods:

class cv_policy
locset cv_boundary_points(const cable_cell&) const

Return a locset describing the boundary points for CVs on the given cell.

region domain() const

Give the subset of a cell morphology on which this policy has been declared, as a morphological region expression.

Specific CV policy objects are created by functions described below (strictly speaking, these are class constructors for classes are implicit converted to cv_policy objects). These all take a region parameter that restrict the domain of applicability of that policy; this facility is useful for specifying differing discretizations on different parts of a cell morphology. When a CV policy is constrained in this manner, the boundary of the domain will always constitute part of the CV boundary point set.

CV policies can be combined with + and | operators. For two policies A and B, A + B is a policy which gives boundary points from both A and B, while A | B is a policy which gives all the boundary points from B together with those from A which do not within the domain of B. The domain of A + B and A | B is the union of the domains of A and B.

cv_policy_single

cv_policy_single(region domain = reg::all())

Use one CV for the whole cell, or one for each connected component of the supplied domain.

cv_policy_explicit

cv_policy_explicit(locset locs, region domain = reg::all())

Use the points given by locs for CV boundaries, optionally restricted to the supplied domain.

cv_policy_every_sample

cv_policy_every_sample(region domain = reg::all())

Use every sample point in the morpholgy definition as a CV boundary, optionally restricted to the supplied domain. Each fork point in the domain is represented by a trivial CV.

cv_policy_fixed_per_branch

cv_policy_fixed_per_branch(unsigned cv_per_branch, region domain, cv_policy_flag::value flags = cv_policy_flag::none);

cv_policy_fixed_per_branch(unsigned cv_per_branch, cv_policy_flag::value flags = cv_policy_flag::none):

For each branch in each connected component of the domain (or the whole cell, if no domain is given), evenly distribute boundary points along the branch so as to produce exactly cv_per_branch CVs.

By default, CVs will terminate at branch ends. If the flag cv_policy_flag::interior_forks is given, fork points will be included in non-trivial, branched CVs and CVs covering terminal points in the morphology will be half-sized.

cv_policy_max_extent

cv_policy_max_extent(double max_extent, region domain, cv_policy_flag::value flags = cv_policy_flag::none);

cv_policy_max_extent(double max_extent, cv_policy_flag::value flags = cv_policy_flag::none):

As for cv_policy_fixed_per_branch, save that the number of CVs on any given branch will be chosen to be the smallest number that ensures no CV will have an extent on the branch longer than max_extent micrometres.