AMPA

class brainpy.state.AMPA(in_size, name=None, alpha=Quantity(0.98, "1 / (mM * ms)"), beta=Quantity(0.18, "kHz"), T=Quantity(0.5, "mM"), T_dur=Quantity(0.5, "ms"), g_initializer=Constant(value=0. mS))

AMPA receptor synapse model.

This class implements a kinetic model of AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptor-mediated synaptic transmission. AMPA receptors are ionotropic glutamate receptors that mediate fast excitatory synaptic transmission in the central nervous system.

The model uses a Markov process approach to describe the state transitions of AMPA receptors between closed and open states, governed by neurotransmitter binding:

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

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

where:

• \(g\) represents the fraction of receptors in the open state

• \(\alpha\) is the binding rate constant [ms^-1 mM^-1]

• \(\beta\) is the unbinding rate constant [ms^-1]

• \([T]\) is the neurotransmitter concentration [mM]

• \(I_{syn}\) is the resulting synaptic current

• \(g_{max}\) is the maximum conductance

• \(V\) is the membrane potential

• \(E\) is the reversal potential

The neurotransmitter concentration \([T]\) follows a square pulse of amplitude T and duration T_dur after each presynaptic spike.

Parameters:

• in_size (Size) – Size of the input.

• name (str, optional) – Name of the synapse instance.

• alpha (ArrayLike, default 0.98/(u.ms*u.mM)) – Binding rate constant [ms^-1 mM^-1].

• beta (ArrayLike, default 0.18/u.ms) – Unbinding rate constant [ms^-1].

• T (ArrayLike, default 0.5*u.mM) – Peak neurotransmitter concentration when released [mM].

• T_dur (ArrayLike, default 0.5*u.ms) – Duration of neurotransmitter presence in the synaptic cleft [ms].

• g_initializer (ArrayLike or Callable, default init.Constant(0. * u.mS)) – Initial value or initializer for the synaptic conductance.

g

Fraction of receptors in the open state.

Type:

HiddenState

spike_arrival_time

Time of the most recent presynaptic spike.

Type:

ShortTermState

See also

GABAa

Inhibitory GABAa receptor synapse model.

BioNMDA

NMDA receptor synapse model with Mg2+ block.

Expon

Simpler exponential decay synapse.

Notes

• The model captures the fast-rising and relatively fast-decaying excitatory currents characteristic of AMPA receptor-mediated transmission [1].

• The time course of the synaptic conductance is determined by both the binding and unbinding rate constants and the duration of transmitter presence.

• This implementation uses an exponential Euler integration method.

• For thalamic oscillation applications, see [2].

References

[1]

Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1994). Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. Journal of computational neuroscience, 1(3), 195-230.

[2]

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

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an AMPA synapse
>>> ampa = brainpy.state.AMPA(100)
>>> ampa.init_state(batch_size=1)

init_state(batch_size=None, **kwargs)

State initialization function.

reset_state(batch_size=None, **kwargs)

State resetting function.