Source code for brainmodels.synapses.AMPA

# -*- coding: utf-8 -*-

import brainpy as bp
import brainpy.math as bm

from .base import Synapse

__all__ = [
  'AMPA',
]


[docs]class AMPA(Synapse): r"""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 :math:`g` represents the probability of channel opening, :math:`1-g` represents the probability of ion channel closing, and :math:`\alpha` and :math:`\beta` are the transition probability. Because neurotransmitters can open ion channels, the transfer probability from :math:`1-g` to :math:`g` is affected by the concentration of neurotransmitters. We denote the concentration of neurotransmitters as :math:`[T]` and get the following Markov process. .. image:: ../../images/synapse_markov.png :align: center We obtained the following formula when describing the process by a differential equation. .. math:: \frac{dg}{dt} =\alpha[T](1-g)-\beta g where :math:`\alpha [T]` denotes the transition probability from state :math:`(1-g)` to state :math:`(g)`; and :math:`\beta` represents the transition probability of the other direction. :math:`\alpha` is the binding constant. :math:`\beta` is the unbinding constant. :math:`[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 .. math:: I_{syn} = g_{max} g (V-E) where :math:`g_{max}` is the maximum conductance, and `E` is the reverse potential. **Model Examples** .. plot:: :include-source: True >>> import brainpy as bp >>> import brainmodels >>> import matplotlib.pyplot as plt >>> >>> neu1 = brainmodels.neurons.HH(1) >>> neu2 = brainmodels.neurons.HH(1) >>> syn1 = brainmodels.synapses.AMPA(neu1, neu2, bp.connect.All2All()) >>> net = bp.Network(pre=neu1, syn=syn1, post=neu2) >>> >>> runner = bp.StructRunner(net, inputs=[('pre.input', 5.)], monitors=['pre.V', 'post.V', 'syn.g']) >>> runner.run(150.) >>> >>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8) >>> fig.add_subplot(gs[0, 0]) >>> plt.plot(runner.mon.ts, runner.mon['pre.V'], label='pre-V') >>> plt.plot(runner.mon.ts, runner.mon['post.V'], label='post-V') >>> plt.legend() >>> >>> fig.add_subplot(gs[1, 0]) >>> plt.plot(runner.mon.ts, runner.mon['syn.g'], label='g') >>> plt.legend() >>> plt.show() **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. """
[docs] def __init__(self, pre, post, conn, delay=0., g_max=0.42, E=0., alpha=0.98, beta=0.18, T=0.5, T_duration=0.5, method='exp_auto', name=None): super(AMPA, self).__init__(pre=pre, post=post, conn=conn, method=method, name=name) self.check_pre_attrs('t_last_spike') self.check_post_attrs('input', 'V') # parameters self.delay = delay self.g_max = g_max self.E = E self.alpha = alpha self.beta = beta self.T = T self.T_duration = T_duration # connections self.pre_ids, self.post_ids = self.conn.require('pre_ids', 'post_ids') # variables self.g = bm.Variable(bm.zeros(len(self.pre_ids))) self.pre_spike = bp.ConstantDelay(self.pre.num, delay, dtype=pre.spike.dtype) self.spike_arrival_time = bm.Variable(bm.ones(self.pre.num) * -1e7)
def derivative(self, g, t, TT): dg = self.alpha * TT * (1 - g) - self.beta * g return dg
[docs] def update(self, _t, _dt): self.pre_spike.push(self.pre.spike) self.spike_arrival_time.value = bm.where(self.pre_spike.pull(), _t, self.spike_arrival_time) syn_st = bm.pre2syn(self.spike_arrival_time, self.pre_ids) TT = ((_t - syn_st) < self.T_duration) * self.T self.g.value = self.integral(self.g, _t, TT, dt=_dt) g_post = bm.syn2post(self.g, self.post_ids, self.post.num) self.post.input -= self.g_max * g_post * (self.post.V - self.E)