# conductance

This document describes the "conductance" C++ class. This class describes objects that are conductances, or populations of ion channels.

This is an abstract class, and concrete implementations of ion channel types need to inherit from this class and define certain attributes like their activation functions.

Abstract | can contain | contained in |
---|---|---|

yes | nothing | compartment |

## Properties¶

`container`

¶

type | default | user-accessible |
---|---|---|

compartment* | NULL | no |

`gbar`

¶

type | default | user-accessible |
---|---|---|

double | 0 | yes |

The maximal conductance of this channel type (in ). This is typically exposed to the user as a parameter to set and modify.

`gbar_next`

¶

type | default | user-accessible |
---|---|---|

double | 0 | no |

`g`

¶

type | default | user-accessible |
---|---|---|

double | 0 | no |

The instantaneous conductance of this channel type.
This is a product of `gbar`

and the activation and
inactivation variables.

`E`

¶

type | default | user-accessible |
---|---|---|

double | 0 | yes |

The reversal potential of this channel type.

`m`

¶

type | default | user-accessible |
---|---|---|

double | 0 | no |

The activation variable of this channel type.

`h`

¶

type | default | user-accessible |
---|---|---|

double | 1 | no |

The inactivation variable of this channel type.

`verbosity`

¶

type | default | user-accessible |
---|---|---|

double | 0 | no |

A flag that tells this channel how verbose it should be.
This should not be exposed to the user, since it it
broadcast to all components from `xolotl.verbosity`

.

## Methods¶

### buildLUT¶

**Function Signature**

```
void buildLUT(double approx_channels)
```

**Description**

This method constructs a look up table (LUT) that is used to estimate and other functions of the voltage. Since these functions are repeatedly evaluated, it is often faster to compute them for some values of the voltage once, store these values in a table, and use this table subsequently. This is an approximation since the voltage is rounded off to the nearest value in the look-up table, uses a little more memory, but can be much faster.

**Code**

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### fast_pow¶

**Function Signature**

```
inline double fast_pow(double x, int a)
```

**Description**

This method is a dirty hack to speed up computing exponents in C++. This requires that the power that a number is raised to be an integer (0-8)

**Code**

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### fast_exp¶

**Function Signature**

```
inline double fast_exp(double x)
```

**Description**

This method constitutes a dirty hack which is a faster way to compute exp(x) but is less precise

**Code**

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### getCurrent¶

**Function Signature**

```
double getCurrent(double V)
```

**Description**

The method returns the current that flows through this channel at this moment.

**Code**

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### checkSolvers¶

**Function Signature**

```
void checkSolvers(int solver_order)
```

**Description**

**Code**

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### mdot¶

**Function Signature**

```
double mdot(double V, double Ca, double m_)
```

**Description**

This method defines the rate of change of the `m`

variable
of this conductance. This definition is used when `integrateMS`

is used.

**Code**

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### hdot¶

**Function Signature**

```
double hdot(double V, double Ca, double h_)
```

**Description**

This method defines the rate of change of the `h`

variable
of this conductance. This definition is used when `integrateMS`

is used.

**Code**

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### m_inf¶

**Function Signature**

```
double m_inf(double V, double Ca)
```

**Description**

This method defines the activation curve of this channel. This is a virtual method, and is meant to be defined in the channel object.

**Code**

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### h_inf¶

**Function Signature**

```
double h_inf(double V, double Ca)
```

**Description**

This method defines the inactivation curve of this channel. This is a virtual method, and is meant to be defined in the channel object.

**Code**

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### tau_m¶

**Function Signature**

```
double tau_m(double V, double Ca)
```

**Description**

This method defines the dependence of the timescale of the activation variable on the voltage of this channel. This is a virtual method, and is meant to be defined in the channel object.

**Code**

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### tau_h¶

**Function Signature**

```
double tau_h(double V, double Ca)
```

**Description**

This method defines the dependence of the timescale of the inactivation variable on the voltage of this channel. This is a virtual method, and is meant to be defined in the channel object.

**Code**

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### gaussrand¶

**Function Signature**

```
double gaussrand()
```

**Description**

This method implements a very fast Gaussian random
number generator. This is much faster than the
built-in generators in the C++ `<random>`

header, and
is copied from Knuth and Marsaglia.

For the original source, see "A Convenient Method for Generating Normal Variables" SIAM Rev., 6(3), 260–264.

**Code**

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### connect¶

**Function Signature**

```
void connect(compartment *pcomp_)
```

**Description**

This method "connects" a conductance object to a compartment
object. This sets the `container`

property of the conductance,
so the channel knows which compartment contains it.

**Code**

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### integrate¶

**Function Signature**

```
void integrate(double V, double Ca)
```

**Description**

This method integrates the conductance object using
the exponential Euler method. This is the default
integration method used by xolotl. If an exact solution
is to be calculated (i.e.,`approx_m = 0`

and `approx_h=0`

)
then `m`

and `h`

are updated using the exponential Euler
equation using function evaluations of the activation
functions at this voltage and Calcium.

Otherwise, the lookup table is used to update `m`

and `h`

in this channel.

Note that this method is defined as virtual, so it can be overridden by integration methods specified in a specific conductance.

**See Also**

**Code**

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### integrateLangevin¶

**Function Signature**

```
void integrateLangevin(double V, double Ca)
```

**Description**

This method integrates the conductance object using the Euler-Maruyama method. The integration method used here is consistent with the methods used in Goldwyn and Shea-Brown 2011 and with Sengupta, Laughlin and Niven

Briefly, this method follows the approximate Langevin formulation of the underlying stochastic system formed by N independent channels that have independent gating kinetics. It can be thought of as the deterministic ODE, with an additive noise term whose variance scales with the inverse square root of the number of channels. The number of channels is computed automatically from the channel density and the area of the compartment.

**Code**

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### integrateMS¶

**Function Signature**

```
void integrateMS(int k, double V, double Ca)
```

**Description**

This method integrates a channel object using a multi-step solver (MS = "multi-step"). The "sub-step" is indicated in the integer k, which is the first input to this method.

The multi-step solver that is used here is a Runge-Kutta 4th order solver. Thus, k can have values up to 4.

Based on `k`

, different elements of the arrays `k_m`

and `k_h`

are calculated and stored. At each step, the derivative functions
`mdot`

and `hdot`

are computed.

**See Also**

**Code**

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