BRIAN Simulator

1. BRIAN Simulator 11/4/11

2. 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?

3. 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.html

4. Make sure it works! frombrianimport * brian_sample_run()

5. 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

6. 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) : volt dge/dt = -ge/(5*ms) : volt dgi/dt = -gi/(10*ms) : volt ''' P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-60*mV) P.v = -60*mV Pe = 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()

7. 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) : volt dge/dt = -ge/(5*ms) : volt dgi/dt = -gi/(10*ms) : volt ''' P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-60*mV) P.v = -60*mV Pe = 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()

8. 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) : volt dge/dt = -ge/(5*ms) : volt dgi/dt = -gi/(10*ms) : volt ''' P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-60*mV) P.v = -60*mV Pe = 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()

9. 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) : volt dge/dt = -ge/(5*ms) : volt dgi/dt = -gi/(10*ms) : volt ''' P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-60*mV) P.v = -60*mV Pe = 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()

10. My First BRIAN Model from brian import * eqs = ''' dv/dt = (ge+gi-(v+49*mV))/(20*ms) : volt dge/dt = -ge/(5*ms) : volt dgi/dt = -gi/(10*ms) : volt ''' P = NeuronGroup(4000, eqs, threshold=-50*mV, reset=-60*mV) P.v = -60*mV Pe = 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()

11. 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

12. Exercise: Can you make HW 4’s networks in BRIAN? Feedforward Inhibition Feedback Inhibition

13. Spike timing dependent plasticity

14. stdp1.py • 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 Firing rate (Hz) time Final weight Synapse number Count Final weight

15. 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) Firing rate (Hz) time Final weight Synapse number Count Final weight