BRIAN Simulator

11/4/11

NEURON is cool, but…

• …it’s not suited particularly well for large network simulations

• What if you want to look at properties of thousands of neurons interacting with one another?

• What about changing properties of synapses through time?

BRIAN Simulator

• BRIAN allows for efficient simulations of large neural networks

• Includes nice routines for setting up random connectivity, recording spike times, changing synaptic weights as a function of activity

• www.briansimulator.org– Should be able to run from the unzipped brian

directory– http://www.briansimulator.org/docs/installation.ht

ml

Make sure it works!from brian import * brian_sample_run()

Building blocks of BRIAN

• Model consists of:– Equations– NeuronGroup – a group of neurons which obeys

those equations– Connection – a way to define connection matrices

between neurons– SpikeMonitor (and others) – a way to measure

properties of the simulated network

My First BRIAN Model

• To start, let’s walk through the example code on briansimulator.org homepage

• Copy this text into IDLE (or whichever .py editor you’re using)

• Make sure it runs first!

from brian import *eqs = '''dv/dt = (ge+gi-(v+49*mV))/(20*ms) :

voltdge/dt = -ge/(5*ms) : voltdgi/dt = -gi/(10*ms) : volt'''P = NeuronGroup(4000, eqs, threshold=-

50*mV, reset=-60*mV)P.v = -60*mVPe = P.subgroup(3200)Pi = P.subgroup(800)Ce = Connection(Pe, P, 'ge',

weight=1.62*mV, sparseness=0.02)Ci = Connection(Pi, P, 'gi', weight=-

9*mV, sparseness=0.02)M = SpikeMonitor(P)run(1*second)raster_plot(M)show()

My First BRIAN Model• First – we set up the model• Notice the units! These are important

in BRIAN, they help ensure everything you’re modeling makes sense

• Equations are written as strings, these are executed by the differential equation solver in BRIAN– Unit names/abbreviations are

reserved keywords in BRIAN• Create our NeuronGroup using this

model– Define number of neurons, model

used, threshold & reversal potentials• Questions:

– What is the reversal potential here?– How does this model differ from HH?

from brian import *eqs = '''dv/dt = (ge+gi-(v+49*mV))/(20*ms) :

voltdge/dt = -ge/(5*ms) : voltdgi/dt = -gi/(10*ms) : volt'''P = NeuronGroup(4000, eqs, threshold=-

50*mV, reset=-60*mV)P.v = -60*mVPe = P.subgroup(3200)Pi = P.subgroup(800)Ce = Connection(Pe, P, 'ge',

weight=1.62*mV, sparseness=0.02)Ci = Connection(Pi, P, 'gi', weight=-

9*mV, sparseness=0.02)M = SpikeMonitor(P)run(1*second)raster_plot(M)show()

My First BRIAN Model• Initialize the neurons to

starting potentials• Connect them

– Here, constant weight, random connectivity from each subpopulation (excitatory & inhibitory) to all neurons

• Which state variable to propagate to in “target” neuron: ‘ge’ for excitatory synapses, ‘gi’ for inhibitory

from brian import *eqs = '''dv/dt = (ge+gi-(v+49*mV))/(20*ms) :

voltdge/dt = -ge/(5*ms) : voltdgi/dt = -gi/(10*ms) : volt'''P = NeuronGroup(4000, eqs, threshold=-

50*mV, reset=-60*mV)P.v = -60*mVPe = P.subgroup(3200)Pi = P.subgroup(800)Ce = Connection(Pe, P, 'ge',

weight=1.62*mV, sparseness=0.02)Ci = Connection(Pi, P, 'gi', weight=-

9*mV, sparseness=0.02)M = SpikeMonitor(P)run(1*second)raster_plot(M)show()

My First BRIAN Model• Hook up your

electrophysiology equipment (here, measure spike times)– Can also record population

rate, ISI – search documentation for Monitor

– Only this info is saved from the simulation

• Run the simulation!• Plot

– Other plotting tools (hist_plot, Autocorrelograms, pylab, etc)

from brian import *eqs = '''dv/dt = (ge+gi-(v+49*mV))/(20*ms) :

voltdge/dt = -ge/(5*ms) : voltdgi/dt = -gi/(10*ms) : volt'''P = NeuronGroup(4000, eqs, threshold=-

50*mV, reset=-60*mV)P.v = -60*mVPe = P.subgroup(3200)Pi = P.subgroup(800)Ce = Connection(Pe, P, 'ge',

weight=1.62*mV, sparseness=0.02)Ci = Connection(Pi, P, 'gi', weight=-

9*mV, sparseness=0.02)M = SpikeMonitor(P)run(1*second)raster_plot(M)show()

My First BRIAN Model

from brian import *eqs = '''dv/dt = (ge+gi-(v+49*mV))/(20*ms) : voltdge/dt = -ge/(5*ms) : voltdgi/dt = -gi/(10*ms) : volt'''P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-

60*mV)P.v = -60*mVPe = P.subgroup(3200)Pi = P.subgroup(800)Ce = Connection(Pe, P, 'ge', weight=1.62*mV,

sparseness=0.02)Ci = Connection(Pi, P, 'gi', weight=-9*mV,

sparseness=0.02)M = SpikeMonitor(P)R = PopulationRateMonitor(P,.01*second)H = ISIHistogramMonitor(P,bins =

[0*ms,5*ms,10*ms,15*ms,20*ms,25*ms,30*ms,35*ms,40*ms])

run(1*second)raster_plot(M)hist_plot(H)plt.figure()plt.plot(R.times,R.rate)plt.xlabel(‘time (s)’)plt.ylabel(‘firing rate (Hz)’)show()

Exercise: Can you make HW 4’s networks in BRIAN?

• Try with both HH-style and integrate and fire models

• Use documentation at briansimulator.org for help (especially Connection and Equations)– Hint: search HodgkinHuxley

and Library Models• Let’s use simplified

exponential synapses– Time constant tau = 3 ms for

excitatory, 6 ms for inhibitory

Feedforward Inhibition

Feedback Inhibition

Exercise: Can you make HW 4’s networks in BRIAN?

Feedforward Inhibition

Feedback Inhibition

Spike timing dependent plasticity

• Sets up network of Poisson spiking neurons, all projecting to a single neuron

• Each synapse implements an STDP rule

• By end of simulation, synapses become either strong or weak

stdp1.py

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Final weight

Synapse numberCo

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stdp2.py

• Only difference is that we’ve changed how pre-before-post and post-before-pre synapses are weighted (and, in model code, stdp2 uses ExponentialSTDP, to make things easier)

timeFirin

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Final weight

Synapse number

Coun

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