Hodgkin-Huxley current models¶

The module myokit.lib.hh contains functions for working with Hodgkin-Huxley models of ion channel currents.

The class HHModel can be used to extract a current model from a Myokit: model.
By fixing the voltage and all other states that aren’t part of the current: model a linear system is created.
Fast simulations can then be performed using the: AnalyticalSimulation class, which is particularly useful when trying to estimate a current model’s parameters from a piecewise-linear voltage protocol (e.g. a voltage step protocol).

In addition, several methods are provided to find and manipulate Hodgkin-Huxley style gating variables.

Analytical simulation¶

class myokit.lib.hh.HHModel(model, states, parameters=None, current=None, vm=None)¶

Represents a Hodgkin-Huxley (HH)-style model of an ion channel, extracted from a myokit.Model.

The class assumes the HH model can be (re)written as:

I = prod(x[i]**n[i]) * f(V, p)
dot(x[i]) = (x_inf[i](V, p) - x[i]) / tau_x[i](V, p)

for any number of states x[i] with steady-state x_inf[i] and time constant tau_x[i], where V is the membrane potential, p is a set of parameters, f is an arbitrary function (for example g_max * (V - E_rev)).

The model variables to treat as parameter are specified by the user when the model is created. Any other variables, for example state variables such as intercellular calcium or constants such as temperature, are fixed when the current model is created and can no longer be changed. Initial values written as expressions are evaluated when the model is made.

The current variable is optional.

Arguments:

model: The myokit.Model to extract a current model from.
states: An ordered list of state variables (or state variable names) from model. All remaining state variables will be frozen in place.
parameters=None: A list of parameters to maintain in their symbolic form.
current=None: The current model’s current variable, or None.
vm=None: The variable indicating membrane potential. If set to None (default) the method will search for a variable with the label membrane_potential.

Example:

import myokit
import myokit.lib.hh as hh

# Load a model from disk
model = myokit.load_model('some-model.mmt')

# Select the relevant states and parameters
states = [
    'ina.C1',
    'ina.C2',
    'ina.O',
    ...
    ]
parameters = [
    'ina.p1',
    'ina.p2',
    ...
    ]
current = 'ina.INa'

# Extract an ion current model
mm = hh.HHModel(model, states, parameters, current)

Alternatively, a HHModel can be constructed based on a single component using the method from_component():

import myokit
import myokit.lib.hh as hh

# Load a model from disk
model = myokit.load_model('some-model.mmt')

# Extract a Hodgkin-Huxley style channel model
mm = hh.HHModel.from_component(model.get('ina'))

current()¶: Returns the name of the current variable used by this model, or None if no current variable was specified.

default_membrane_potential()¶: Returns this HH model’s default membrane potential value.

default_parameters()¶: Returns this HH model’s default parameter values

default_state()¶: Returns this HH model’s default state values.

static from_component(component, states=None, parameters=None, current=None, vm=None)¶

Creates a current model from a component, using the following rules:

Every state in the component is a state in the current model.

Every (non-nested) constant in the component is a parameter.

The component should contain exactly one non-nested intermediary variable whose value depends on the model states, this will be used as the current variable.

The model contains a variable labeled “membrane_potential”.

Any of the automatically set variables can be overridden using the keyword arguments states, parameters, current and vm.

The parameters, if determined automatically, will be specified in alphabetical order (using a natural sort).

function()¶

Returns a function that evaluates the state values at any time.

The returned function has the signature:

f(y0, t, p1, p2, p3, ..., V) --> (states, current)

where y0 is a sequence containing the state values at time 0, where t is a scalar or numpy array of times at which to evaluate, where p1, p2, p3, ... are the model parameters, and where V is the membrane potential.

The function output is always a tuple (states, current). If t is a single time, then states will be a list of values (one per model state) and current will be a scalar (or None if no current variable was specified). If t is a numpy array of times then states will be a list of numpy arrays, and current will be a numpy array (or None if no current variable was specified).

membrane_potential()¶: Returns the name of the membrane potential variable used by this model.

parameters()¶: Returns the names of the parameter variables used by this model.

reduced_model()¶: Returns a reduced myokit.Model, containing only the parts necessary to calculate the specified states and current.

states()¶: Returns the names of the state variables used by this model.

steady_state(membrane_potential=None, parameters=None)¶

Returns the steady state solution for this model.

Arguments:

membrane_potential: The value to use for the membrane potential, or None to use the value from the original myokit.Model.
parameters: The values to use for the parameters, given in the order they were originally specified in (if the model was created using from_component(), this will be alphabetical order), or None to use the values from the original model.

Returns a list of steady state values.

class myokit.lib.hh.HHModelError(message)¶: Raised for issues with constructing or using a LinearModel.

class myokit.lib.hh.AnalyticalSimulation(model, protocol=None)¶

Analytically evaluates a HHModel’s state for a given set of points in time.

Each simulation object maintains an internal state consisting of

The current simulation time
The current state
The default state

When a simulation is created, the simulation time is set to zero and both the current and default state are initialized using the HHModel. After each call to run() the time and current state are updated, so that each successive call to run continues where the previous simulation left off.

A protocol can be used to set the membrane potential during the simulation, or the membrane potential can be adjusted manually between runs.

Example:

import myokit
import myokit.lib.hh as hh

# Create an ion current model
m = myokit.load_model('luo-1991.mmt')
m = hh.HHModel.from_component(m.get('ina'))

# Create an analytical simulation object
s = hh.AnalyticalSimulation(m)

# Run a simulation
s.set_membrane_potential(-30)
d = s.run(10)

# Show the results
import matplotlib.pyplot as plt
plt.figure()
plt.subplot(211)
for state in m.states():
    plt.plot(d.time(), d[state], label=state)
plt.legend(loc='center right')
plt.subplot(212)
plt.plot(d.time(), d[m.current()])
plt.show()

default_state()¶: Returns the default state used by this simulation.

membrane_potential()¶: Returns the currently set membrane potential.

parameters()¶: Returns the currently set parameter values.

pre(duration)¶

Performs an unlogged simulation for duration time units and uses the final state as the new default state.

After the simulation:

The simulation time is not affected
The current state and the default state are updated to the final state reached in the simulation.

Calls to reset() after using pre() will set the current state to this new default state.

reset()¶

Resets the simulation:

The time variable is set to zero.
The state is set to the default state.

run(duration, log=None, log_interval=0.01, log_times=None)¶

Runs a simulation for duration time units.

After the simulation:

The simulation time will be increased by duration time units.
The simulation state will be updated to the last reached state.

Arguments:

duration: The number of time units to simulate.
log: A log from a previous run can be passed in, in which case the results will be appended to this one.
log_interval: The time between logged points.
log_times: A pre-defined sequence of times to log at. If set, log_interval will be ignored.

Returns a myokit.DataLog with the simulation results.

set_constant(variable, value)¶: Updates a single parameter to a new value.

set_default_state(state)¶: Changes this simulation’s default state.

set_membrane_potential(v)¶: Changes the membrane potential used in this simulation.

set_parameters(parameters)¶: Changes the parameter values used in this simulation.

set_state(state)¶: Changes the initial state used by in this simulation.

solve(times)¶

Evaluates and returns the states at the given times.

In contrast to run(), this method simply evaluates the states (and current) at the given times, using the last known settings for the state and membrane potential. It does not use a protocol and does not take into account the simulation time. After running this method, the state and simulation time are not updated.

Arguments:

times: A series of times, where each time must be some t >= 0.

For models with a current variable, this method returns a tuple (state, current) where state is a matrix of shape (len(states), len(times)) and current is a vector of length len(times).

For models without a current variable, only state is returned.

state()¶: Returns the initial state used by this simulation.

Finding and manipulating HH-states¶

myokit.lib.hh.convert_hh_states_to_inf_tau_form(model, v=None)¶

Scans a myokit.Model for Hodgkin-Huxley style states written in “alpha-beta form”, and converts them to “inf-tau form”.

For any state x written in the form dot(x) = alpha * (1 - x) - beta * x this method will calculate the steady state and time constant, and add variables for both. Next, the state RHS will be replaced by an expression of the form dot(x) = (x_inf - x) / tau_x, where x_inf and tau_x are the new variables.

Myokit :: API and User Guide

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Hodgkin-Huxley current models¶

Analytical simulation¶

Finding and manipulating HH-states¶