2021-11-18 • Prototype new sim
Contents
2021-11-18 • Prototype new sim¶
One numba-optimised function doing synaptic integration and izhikevich sim.
To allow simulations with many neurons / input spike trains to fit in memory, we do not save all signals, only “recorded” ones (as the simulators like Brian do).
Prelude¶
from voltage_to_wiring_sim.notebook_init import *
Preloading: numpy, numba, matplotlib.pyplot, seaborn.
Importing from submodules … ✔
Imported `np`, `mpl`, `plt`, `sns`, `pd`
Imported codebase (`voltage_to_wiring_sim`) as `v`
Imported `*` from `v.support.units`
Setup autoreload
v.print_reproducibility_info()
This cell was last run by tfiers on yoga on Mon 03 Jan 2022, at 16:18 (UTC+0100).
Last git commit (Thu 09 Dec 2021, 11:06).
Uncommited changes to 3 files.
Parameters¶
dt = 0.1 * ms
duration = 10 * second
N = 4 # number of neurons
τ_syn = 7 * ms
injected_noise_σ = 3 * mV
v_r = -60 * mV
v_t = -40 * mV
v_peak = 35 * mV
c = -50 * mV # aka v_reset
C = 100 * pF
k = 0.7 * (nS/mV)
b = -2 * nS
a = 0.03 / ms
d = 100 * pA;
v_syn = np.array([0*mV, 0*mV, 0*mV, -65*mV]);
# This is the postsynaptic reversal potential for all this neuron's output connections
ge = 4 * nS
gi = 16 * nS
Δg = np.array([
[0, ge, 0, 0],
[0, 0, 0, 0],
[0, ge, 0, 0],
[0, 0, 0, 0],
]); # [from, to]
recorded_neurons = [0, 2];
Sim¶
num_timesteps = v.sim.izhikevich_neuron.to_num_timesteps(duration, dt)
100000
from numpy import zeros, ones, newaxis
from numpy.random import randn
v_record = np.empty((num_timesteps, len(recorded_neurons)))
recorded_neurons = np.array(recorded_neurons)
# The type of this iterable may not be `tuple`. (Because we want to use it to select multiple elements.
# See the last example here: https://numpy.org/doc/stable/user/basics.indexing.html)
v_syn.shape = (N, 1)
# Transform into column vector, to make the subtraction (v_syn - v) below
# generate a matrix, via broadcasting.
v = ones(N) * v_r
u = zeros(N)
g = zeros((N, N))
spikes = tuple([[] * N])
for i in range(num_timesteps):
# Synaptic conductance & current
g -= g / τ_syn * dt
I_syn = g * (v_syn - v)
I_syn_total = np.sum(I_syn, axis=0)
# todo: make stochastic differential,
# https://brian2.readthedocs.io/en/stable/resources/tutorials/1-intro-to-brian-neurons.html#stochastic-neurons
I_noise = randn(N) * injected_noise_σ
# Izhikevich neuron
v += (k * (v - v_r) * (v - v_t) - u + I_syn_total + I_noise) / C * dt
u += a * (b * (v - v_r) - u) * dt
has_spiked = v >= v_peak
v[has_spiked] = c
u[has_spiked] += d
# Conductance bumps. The non-spiking rows are zeroed by the multiplication.
# (Hence the transformation of `has_spiked` into a column vector: for broadcasting).
g += Δg * has_spiked[:, newaxis]
# Record spike times
for j in v.indices_where(has_spiked):
spikes[j].append(i)
# Record selected signals
v_record[i, :] = v[recorded_neurons]
# For spikers, retroactively set previous timestep's v to v_peak.
# Goal: consistent spike height.
v_record[i-1, has_spiked[recorded_neurons]] = v_peak
Current direction is how positive charges move. Ergo positive current = \(v_m\) increase (depolarisation).
On discretizing the voltage reset¶
“We’re basically choosing between a slightly too sharp and early peak, and a slightly too late and flat-topped one.”
from voltage_to_wiring_sim.experiments.N_to_1_IE import Params, simulate_and_test_connections
from dataclasses import replace
base_params = Params()
sim_and_test = v.cache_to_disk(simulate_and_test_connections)
d, td, ts = sim_and_test(base_params)
________________________________________________________________________________
[Memory] Calling voltage_to_wiring_sim.experiments.N_to_1_IE.simulate_and_test_connections...
simulate_and_test_connections(Params(sim_duration=600, timestep=0.0001, τ_syn=0.007, neuron_params=IzhikevichParams(C=1e-10, k=7e-07, v_r=-0.06, v_t=-0.04, v_peak=0.035, a=30.0, b=-2e-09, c=-0.05, d=1e-10), imaging_spike_SNR=20, window_duration=0.1, num_spike_trains=30, p_inhibitory=0.2, p_connected=0.7, spike_rate=20.0, Δg_syn_exc=4.0000000000000007e-10, Δg_syn_inh=1.6000000000000003e-09, v_syn_exc=0.0, v_syn_inh=-0.065, rng_seed=0))
30/30
___________________________________simulate_and_test_connections - 26.4s, 0.4min
ax = v.plot_signal(d.izh_output.V_m.slice(4.75, 0.2) / mV, time_units=ms)
zoom_start = 4865 * ms
zoom_duration = 7 * ms
ax.axvspan(zoom_start / ms, (zoom_start + zoom_duration) / ms, alpha=0.3);
ax.set(xlabel="Time (ms)", ylabel="$V_m$ (mV)");
v.plot_signal(d.izh_output.V_m.slice(zoom_start, zoom_duration) / mV, time_units=ms, marker="o", ms=3);
Reproducibility¶
v.print_reproducibility_info(verbose=True)
This cell was last run by lpxtf3 on DUIP74576
on Thu 18 Nov 2021, at 23:21 (UTC+0000).
Last git commit (Thu 18 Nov 2021, 17:05).
Uncommited changes to:
M codebase/voltage_to_wiring_sim/experiments/N_to_1_IE.py
M notebooks/2021-11-11__vary_both_inh_strength_and_proportion.ipynb
?? notebooks/2021-11-18__constant_input_spikes-Copy1.ipynb
?? notebooks/2021-11-18__constant_input_spikes.ipynb
Platform:
Windows-10
CPython 3.9.6 (C:\miniforge3\python.exe)
Intel(R) Xeon(R) W-2123 CPU @ 3.60GHz
Dependencies of voltage_to_wiring_sim and their installed versions:
numpy 1.21.1
matplotlib 3.4.2
numba 0.53.1
joblib 1.0.1
seaborn 0.11.1
scipy 1.7.0
preload 2.2
nptyping 1.4.2
Full conda list:
# packages in environment at C:\miniforge3:
#
# Name Version Build Channel
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ca-certificates 2021.10.8 h5b45459_0 conda-forge
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chardet 4.0.0 py39hcbf5309_1 conda-forge
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