network_ring.rst

A ring network

In this example, a small network of cells, arranged in a ring, will be created and the simulation distributed over multiple threads or GPUs if available.

Note

Concepts covered in this example:

1. Building a basic :py:class:`arbor.cell` with a synapse site and spike generator.
2. Building a :py:class:`arbor.recipe` with a network of interconnected cells.
3. Running the simulation and extract the results.

The cell

Step (1) shows how a simple cell with a dendrite is created. We construct the following :term:`morphology` and label the soma and dendrite:

A 4-segment cell with a soma (pink) and a branched dendrite (light blue).

# (1) Build a segment tree
tree = arbor.segment_tree()

# Soma (tag=1) with radius 6 μm, modelled as cylinder of length 2*radius
s = tree.append(arbor.mnpos, arbor.mpoint(-12, 0, 0, 6), arbor.mpoint(0, 0, 0, 6), tag=1)

# Single dendrite (tag=3) of length 50 μm and radius 2 μm attached to soma.
b0 = tree.append(s, arbor.mpoint(0, 0, 0, 2), arbor.mpoint(50, 0, 0, 2), tag=3)

# Attach two dendrites (tag=3) of length 50 μm to the end of the first dendrite.
# Radius tapers from 2 to 0.5 μm over the length of the dendrite.
b1 = tree.append(b0, arbor.mpoint(50, 0, 0, 2), arbor.mpoint(50+50/sqrt(2), 50/sqrt(2), 0, 0.5), tag=3)
# Constant radius of 1 μm over the length of the dendrite.
b2 = tree.append(b0, arbor.mpoint(50, 0, 0, 1), arbor.mpoint(50+50/sqrt(2), -50/sqrt(2), 0, 1), tag=3)

# Associate labels to tags
labels = arbor.label_dict()
labels['soma'] = '(tag 1)'
labels['dend'] = '(tag 3)'

In step (2) we create a :term:`label` for both the root and the site of the synapse. These locations will form the endpoints of the connections between the cells.

We'll create labels for the root (red) and a synapse_site (black).

# (2) Mark location for synapse at the midpoint of branch 1 (the first dendrite).
labels['synapse_site'] = '(location 1 0.5)'
# Mark the root of the tree.
labels['root'] = '(root)'

After we've created a basic :py:class:`arbor.decor`, step (3) places a synapse with an exponential decay ('expsyn') is on the 'synapse_site'. Note that mechanisms can be initialized with their name; 'expsyn' is short for arbor.mechanism('expsyn').

Step (4) places a spike detector at the 'root'. :py:class:`spike_detectors <spike_detector>` will send spikes into an :class:`arbor.connection`, whereas the :ref:`expsyn mechanism <mechanisms_builtins>` can receive spikes from an :class:`arbor.connection`.

decor = arbor.decor()

# Put hh dynamics on soma, and passive properties on the dendrites.
decor.paint('"soma"', 'hh')
decor.paint('"dend"', 'pas')

# (3) Attach a single synapse.
decor.place('"synapse_site"', 'expsyn')

# (4) Attach a spike detector with threshold of -10 mV.
decor.place('"root"', arbor.spike_detector(-10))

cell = arbor.cable_cell(tree, labels, decor)

The recipe

To create a model with multiple connected cells, we need to use a :py:class:`recipe <arbor.recipe>`. The recipe is where the different cells and the :ref:`connections <interconnectivity>` between them are defined.

Step (5) shows a class definition for a recipe with multiple cells. Instantiating the class requires the desired number of cells as input. Compared to the :ref:`simple cell recipe <tutorialsinglecellrecipe>`, the main differences are connecting the cells (8), returning a configurable number of cells (6) and returning a new cell per gid (7) (make_cable_cell() returns the cell above).

Step (8) creates an :py:class:`arbor.connection` between consecutive cells. If a cell has gid gid, the previous cell has a gid (gid-1)%self.ncells. The connection has a weight of 0.1 μS and a delay of 5 ms. The first two arguments to :py:class:`arbor.connection` are the source and target of the connection, and these are defined by the cell index gid and the source or target index. (:term:`Remember <connection>` that sources and targets are separately indexed.)

The two endpoints are of type :class:`arbor.cell_member`, and can be initialized with a (gid,index) tuple. The cells have one synapse (step 3), so the target endpoint has the 0th index. The cell has one spike generator (step 4), so its source index is also 0.

Lastly, we must inform the recipe how many sources and targets we have on each cell (gid). :func:`arbor.cable_cell.num_targets` and :func:`arbor.cable_cell.num_sources` must be set to 1: each cell has one source and one target endpoint.

Step (9) attaches an :py:class:`arbor.event_generator` on the 0th target (synapse) on the 0th cell; this means it is connected to the "synapse_site" on cell 0. This initiates the signal cascade through the network. The :class:`arbor.explicit_schedule` in instantiated with a list of times in milliseconds, so here a single event at the 1 ms mark is emitted. Note that this synapse is connected twice, once to the event generator, and once to another cell.

Step (10) places a :term:`probe` at the "root" of each cell.

Step (11) instantiates the recipe with 4 cells.

# (5) Create a recipe that generates a network of connected cells.
class ring_recipe (arbor.recipe):
   def __init__(self, ncells):
      # The base C++ class constructor must be called first, to ensure that
      # all memory in the C++ class is initialized correctly.
      arbor.recipe.__init__(self)
      self.ncells = ncells
      self.props = arbor.neuron_cable_properties()
      self.cat = arbor.default_catalogue()
      self.props.register(self.cat)

   # (6) The num_cells method that returns the total number of cells in the model
   # must be implemented.
   def num_cells(self):
      return self.ncells

   # (7) The cell_description method returns a cell
   def cell_description(self, gid):
      return make_cable_cell(gid)

   # The kind method returns the type of cell with gid.
   # Note: this must agree with the type returned by cell_description.
   def cell_kind(self, gid):
      return arbor.cell_kind.cable

   # (8) Make a ring network. For each gid, provide a list of incoming connections.
   def connections_on(self, gid):
      src = (gid-1)%self.ncells
      w = 0.01
      d = 5
      return [arbor.connection((src,0), (gid,0), w, d)]

   def num_targets(self, gid):
      return 1

   def num_sources(self, gid):
      return 1

   # (9) Attach a generator to the first cell in the ring.
   def event_generators(self, gid):
      if gid==0:
            sched = arbor.explicit_schedule([1])
            return [arbor.event_generator((0,0), 0.1, sched)]
      return []

   # (10) Place a probe at the root of each cell.
   def probes(self, gid):
      return [arbor.cable_probe_membrane_voltage('"root"')]

   def global_properties(self, kind):
      return self.props

# (11) Instantiate recipe
ncells = 4
recipe = ring_recipe(ncells)

The execution

To create a simulation, we must create an :class:`arbor.context` and :py:class:`arbor.domain_decomposition`.

Step (12) creates a default execution context, and uses the :func:`arbor.partition_load_balance` to create a default domain decomposition. You can print the objects to see what defaults they produce on your system.

Step (13) sets all spike generators to record using the :py:class:`arbor.spike_recording.all` policy. This means the timestamps of the generated events will be kept in memory. Be default, these are discarded.

In addition to having the timestamps of spikes, we want to extract the voltage as a function of time.

Step (14) sets the probes (step 10) to measure at a certain schedule. This is sometimes described as attaching a :term:`sampler` to a :term:`probe`. :py:func:`arbor.simulation.sample` expects a :term:`probe id` and the desired schedule (here: a recording frequency of 10 kHz). Note that the probe id is a separate index from those of :term:`connection` endpoints; probe ids correspond to the index of the list produced by :py:func:`arbor.recipe. probes` on cell gid.

:py:func:`arbor.simulation.sample` returns a handle to the :term:`samples <sample>` that will be recorded. We store these handles for later use.

Step (15) executes the simulation for a duration of 100 ms.

# (12) Create a default execution context, domain decomposition and simulation
context = arbor.context()
decomp = arbor.partition_load_balance(recipe, context)
sim = arbor.simulation(recipe, decomp, context)

# (13) Set spike generators to record
sim.record(arbor.spike_recording.all)

# (14) Attach a sampler to the voltage probe on cell 0. Sample rate of 10 sample every ms.
handles = [sim.sample((gid, 0), arbor.regular_schedule(0.1)) for gid in range(ncells)]

# (15) Run simulation
sim.run(100)
print('Simulation finished')

The results

Step (16) prints the timestamps of the spikes:

# Print spike times
print('spikes:')
for sp in sim.spikes():
   print(' ', sp)

Step (17) generates a plot of the sampling data. :py:func:`arbor.simulation.samples` takes a handle of the probe we wish to examine. It returns a list of (data, meta) terms: data being the time and value series of the probed quantity; and meta being the location of the probe. The size of the returned list depends on the number of discrete locations pointed to by the handle, which in this case is 1, so we can take the first element. (Recall that in step (10) we attached a probe to the "root", which describes one location. It could have described a :term:`locset`.)

# Plot the recorded voltages over time.
print("Plotting results ...")
df_list = []
for gid in range(ncells):
   samples, meta = sim.samples(handles[gid])[0]
   df_list.append(pandas.DataFrame({'t/ms': samples[:, 0], 'U/mV': samples[:, 1], 'Cell': f"cell {gid}"}))

df = pandas.concat(df_list)
seaborn.relplot(data=df, kind="line", x="t/ms", y="U/mV",hue="Cell",ci=None).savefig('network_ring_result.svg')

Since we have created ncells cells, we have ncells traces. We should be seeing phase shifted traces, as the action potential propagated through the network.

We plot the results using pandas and seaborn:

The full code

You can find the full code of the example at python/examples/network_ring.py.