brainmodels.synapses.AMPA

class brainmodels.synapses.AMPA(pre, post, conn, delay=0.0, g_max=0.42, E=0.0, alpha=0.98, beta=0.18, T=0.5, T_duration=0.5, method='exponential_euler', **kwargs)[source]

AMPA conductance-based synapse model.

Model Descriptions

AMPA receptor is an ionotropic receptor, which is an ion channel. When it is bound by neurotransmitters, it will immediately open the ion channel, causing the change of membrane potential of postsynaptic neurons.

A classical model is to use the Markov process to model ion channel switch. Here \(g\) represents the probability of channel opening, \(1-g\) represents the probability of ion channel closing, and \(\alpha\) and \(\beta\) are the transition probability. Because neurotransmitters can open ion channels, the transfer probability from \(1-g\) to \(g\) is affected by the concentration of neurotransmitters. We denote the concentration of neurotransmitters as \([T]\) and get the following Markov process.

../../_images/synapse_markov.png

We obtained the following formula when describing the process by a differential equation.

\[\frac{ds}{dt} =\alpha[T](1-g)-\beta g\]

where \(\alpha [T]\) denotes the transition probability from state \((1-g)\) to state \((g)\); and \(\beta\) represents the transition probability of the other direction. \(\alpha\) is the binding constant. \(\beta\) is the unbinding constant. \([T]\) is the neurotransmitter concentration, and has the duration of 0.5 ms.

Moreover, the post-synaptic current on the post-synaptic neuron is formulated as

\[I_{syn} = g_{max} g (V-E)\]

where \(g_{max}\) is the maximum conductance, and E is the reverse potential.

Model Examples

Model Parameters

Parameter

Init Value

Unit

Explanation

delay

0

ms

The decay length of the pre-synaptic spikes.

g_max

.42

µmho(µS)

Maximum conductance.

E

0

mV

The reversal potential for the synaptic current.

alpha

.98

Binding constant.

beta

.18

Unbinding constant.

T

.5

mM

Neurotransmitter concentration.

T_duration

.5

ms

Duration of the neurotransmitter concentration.

Model Variables

Member name

Initial values

Explanation

g

0

Synapse gating variable.

pre_spike

False

The history of pre-synaptic neuron spikes.

spike_arrival_time

-1e7

The arrival time of the pre-synaptic neuron spike.

References

1

Vijayan S, Kopell N J. Thalamic model of awake alpha oscillations and implications for stimulus processing[J]. Proceedings of the National Academy of Sciences, 2012, 109(45): 18553-18558.

__init__(pre, post, conn, delay=0.0, g_max=0.42, E=0.0, alpha=0.98, beta=0.18, T=0.5, T_duration=0.5, method='exponential_euler', **kwargs)[source]

Methods

__init__(pre, post, conn[, delay, g_max, E, ...])

build_inputs([inputs, show_code])

build_monitors([show_code])

cpu()

cuda()

derivative(g, t, TT)

ints([method])

Collect all integrators in this node and the children nodes.

jax_update(_t, _dt)

load_states(filename[, verbose, check])

Load the model states.

nodes([method, _paths])

Collect all children nodes.

numpy_update(_t, _dt)

register_constant_delay(key, size, delay[, ...])

Register a constant delay.

run(duration[, dt, report, inputs, extra_func])

The running function.

save_states(filename[, all_vars])

Save the model states.

step(t_and_dt, **kwargs)

to(devices)

tpu()

train_vars([method])

The shortcut for retrieving all trainable variables.

unique_name([name, type])

Get the unique name for this object.

update(*args, **kwargs)

The function to specify the updating rule.

vars([method])

Collect all variables in this node and the children nodes.

Attributes

implicit_nodes

Used to wrap the implicit children nodes which cannot be accessed by self.xxx

implicit_vars

Used to wrap the implicit variables which cannot be accessed by self.xxx

target_backend

Used to specify the target backend which the model to run.