A detailed single cell model

We can expand on the single segment cell example to create a more complex single cell model, and go through the process in more detail.

Note

Concepts covered in this example:

  1. Building a morphology from a arbor.segment_tree.

  2. Building a morphology from an SWC file.

  3. Writing and visualizing region and locset expressions.

  4. Building a decor.

  5. Discretising the morphology.

  6. Setting and overriding model and cell parameters.

  7. Running a simulation and visualising the results using a arbor.single_cell_model.

The cell

We start by building the cell. This will be a cable cell with complex geometry and dynamics which is constructed from 3 components:

  1. A morphology defining the geometry of the cell.

  2. A label dictionary storing labelled expressions which define regions and locations of interest on the cell.

  3. A decor defining various properties and dynamics on these regions and locations. The decor also includes hints about how the cell is to be modelled under the hood, by splitting it into discrete control volumes (CV).

The morphology

We begin by constructing the following morphology:

../_images/tutorial_morph.svg

This can be done by manually building a segment tree:

import arbor
from arbor import mpoint
from arbor import mnpos

# Define the morphology by manually building a segment tree

tree = arbor.segment_tree()

# Start with segment 0: a cylindrical soma with tag 1
tree.append(mnpos, mpoint(0.0, 0.0, 0.0, 2.0), mpoint( 40.0, 0.0, 0.0, 2.0), tag=1)
# Construct the first section of the dendritic tree with tag 3,
# comprised of segments 1 and 2, attached to soma segment 0.
tree.append(0,     mpoint(40.0, 0.0, 0.0, 0.8), mpoint( 80.0,  0.0, 0.0, 0.8), tag=3)
tree.append(1,     mpoint(80.0, 0.0, 0.0, 0.8), mpoint(120.0, -5.0, 0.0, 0.8), tag=3)
# Construct the rest of the dendritic tree: segments 3, 4 and 5.
tree.append(2,     mpoint(120.0, -5.0, 0.0, 0.8), mpoint(200.0,  40.0, 0.0, 0.4), tag=3)
tree.append(3,     mpoint(200.0, 40.0, 0.0, 0.4), mpoint(260.0,  60.0, 0.0, 0.2), tag=3)
tree.append(2,     mpoint(120.0, -5.0, 0.0, 0.5), mpoint(190.0, -30.0, 0.0, 0.5), tag=3)
# Construct a special region of the tree made of segments 6, 7, and 8
# differentiated from the rest of the tree using tag 4.
tree.append(5,     mpoint(190.0, -30.0, 0.0, 0.5), mpoint(240.0, -70.0, 0.0, 0.2), tag=4)
tree.append(5,     mpoint(190.0, -30.0, 0.0, 0.5), mpoint(230.0, -10.0, 0.0, 0.2), tag=4)
tree.append(7,     mpoint(230.0, -10.0, 0.0, 0.2), mpoint(360.0, -20.0, 0.0, 0.2), tag=4)
# Construct segments 9 and 10 that make up the axon with tag 2.
# Segment 9 is at the root, where its proximal end will be connected to the
# proximal end of the soma segment.
tree.append(mnpos, mpoint( 0.0, 0.0, 0.0, 2.0), mpoint(  -70.0, 0.0, 0.0, 0.4), tag=2)
tree.append(9,     mpoint(-70.0, 0.0, 0.0, 0.4), mpoint(-100.0, 0.0, 0.0, 0.4), tag=2)

morph = arbor.morphology(tree);

The same morphology can be represented using an SWC file (interpreted according to Arbor’s specifications). We can save the following in single_cell_detailed.swc.

# id,  tag,      x,      y,      z,      r,    parent
    1     1     0.0     0.0     0.0     2.0        -1  # seg0 prox / seg9 prox
    2     1    40.0     0.0     0.0     2.0         1  # seg0 dist
    3     3    40.0     0.0     0.0     0.8         2  # seg1 prox
    4     3    80.0     0.0     0.0     0.8         3  # seg1 dist / seg2 prox
    5     3   120.0    -5.0     0.0     0.8         4  # seg2 dist / seg3 prox
    6     3   200.0    40.0     0.0     0.4         5  # seg3 dist / seg4 prox
    7     3   260.0    60.0     0.0     0.2         6  # seg4 dist
    8     3   120.0    -5.0     0.0     0.5         5  # seg5 prox
    9     3   190.0   -30.0     0.0     0.5         8  # seg5 dist / seg6 prox / seg7 prox
   10     4   240.0   -70.0     0.0     0.2         9  # seg6 dist
   11     4   230.0   -10.0     0.0     0.2         9  # seg7 dist / seg8 prox
   12     4   360.0   -20.0     0.0     0.2        11  # seg8 dist
   13     2   -70.0     0.0     0.0     0.4         1  # seg9 dist / seg10 prox
   14     2  -100.0     0.0     0.0     0.4        13  # seg10 dist

Note

SWC samples always form a segment with their parent sample. For example, sample 3 and sample 2 form a segment which has length = 0. We use these zero-length segments to represent an abrupt radius change in the morphology, like we see between segment 0 and segment 1 in the above morphology diagram.

More information on SWC loaders can be found here.

The morphology can then be loaded from single_cell_detailed.swc in the following way:

import arbor

# (1) Read the morphology from an SWC file

morph = arbor.load_swc_arbor("single_cell_detailed.swc")

The label dictionary

Next, we can define region and location expressions and give them labels. The regions and locations are defined using an Arbor-specific DSL, and the labels can be stored in a arbor.label_dict.

Note

The expressions in the label dictionary don’t actually refer to any concrete regions or locations of the morphology at this point. They are merely descriptions that can be applied to any morphology, and depending on its geometry, they will generate different regions and locations. However, we will show some figures illustrating the effect of applying these expressions to the above morphology, in order to better visualize the final cell.

More information on region and location expressions is available here.

First, we can define some regions, These are continuous parts of the morphology, They can correspond to full segments or parts of segments. Our morphology already has some pre-established regions determined by the tag parameter of the segments. They are defined as follows:

# (2) Create and populate the label dictionary.

labels = arbor.label_dict()

# Regions:

# Add labels for tag 1, 2, 3, 4
labels['soma'] = '(tag 1)'
labels['axon'] = '(tag 2)'
labels['dend'] = '(tag 3)'
labels['last'] = '(tag 4)'

This will generate the following regions when applied to the previously defined morphology:

../_images/tutorial_tag.svg

From left to right: regions “soma”, “axon”, “dend” and “last”

We can also define a region that represents the whole cell; and to make things a bit more interesting, a region that includes the parts of the morphology that have a radius greater than 1.5 μm. This is done in the following way:

# Add a label for a region that includes the whole morphology
labels['all'] = '(all)'
# Add a label for the parts of the morphology with radius greater than 1.5 μm.
labels['gt_1.5'] = '(radius-ge (region "all") 1.5)'

This will generate the following regions when applied to the previously defined morphology:

../_images/tutorial_all_gt.svg

Left: region “all”; right: region “gt_1.5”

By comparing to the original morphology, we can see region “gt_1.5” includes all of segment 0 and part of segment 9.

Finally, let’s define a region that includes two already defined regions: “last” and “gt_1.5”. This can be done as follows:

# Join regions "last" and "gt_1.5"
labels['custom'] = '(join (region "last") (region "gt_1.5"))'

This will generate the following region when applied to the previously defined morphology:

../_images/tutorial_custom.svg

Our label dictionary so far only contains regions. We can also add some locations. Let’s start with a location that is the root of the morphology, and the set of locations that represent all the terminal points of the morphology.

# Add a labels for the root of the morphology and all the terminal points
labels['root']     = '(root)'
labels['terminal'] = '(terminal)'

This will generate the following locsets (sets of one or more locations) when applied to the previously defined morphology:

../_images/tutorial_root_term.svg

Left: locset “root”; right: locset “terminal”

To make things more interesting, let’s select only the terminal points which belong to the previously defined “custom” region; and, separately, the terminal points which belong to the “axon” region:

# Add a label for the terminal locations in the "custom" region:
labels['custom_terminal'] = '(restrict (locset "terminal") (region "custom"))'
# Add a label for the terminal locations in the "axon" region:
labels['axon_terminal'] = '(restrict (locset "terminal") (region "axon"))'

This will generate the following 2 locsets when applied to the previously defined morphology:

../_images/tutorial_custom_axon_term.svg

Left: locset “custom_terminal”; right: locset “axon_terminal”

The decorations

With the key regions and location expressions identified and labelled, we can start to define certain features, properties and dynamics on the cell. This is done through a arbor.decor object, which stores a mapping of these “decorations” to certain region or location expressions.

Note

Similar to the label dictionary, the decor object is merely a description of how an abstract cell should behave, which can then be applied to any morphology, and have a different effect depending on the geometry and region/locset expressions.

More information on decors can be found here.

The decor object can have default values for properties, which can then be overridden on specific regions. It is in general better to explicitly set all the default properties of your cell, to avoid the confusion to having simulator-specific default values. This will therefore be our first step:

# (3) Create and populate the decor.

decor = arbor.decor()

# Set the default properties of the cell (this overrides the model defaults).
decor.set_property(Vm =-55)
decor.set_ion('na', int_con=10,   ext_con=140, rev_pot=50, method='nernst/na')
decor.set_ion('k',  int_con=54.4, ext_con=2.5, rev_pot=-77)

We have set the default initial membrane voltage to -55 mV; the default initial temperature to 300 K; the default axial resistivity to 35.4 Ω·cm; and the default membrane capacitance to 0.01 F/m².

We also set the initial properties of the na and k ions because they will be utilized by the density mechanisms that we will be adding shortly. For both ions we set the default initial concentration and external concentration measures in mM; and we set the default initial reversal potential in mV. For the na ion, we additionally indicate the the progression on the reversal potential during the simulation will be dictated by the Nernst equation.

It happens, however, that we want the temperature of the “custom” region defined in the label dictionary earlier to be colder, and the initial voltage of the “soma” region to be higher. We can override the default properties by painting new values on the relevant regions using arbor.decor.paint().

# Override the cell defaults.
decor.paint('"custom"', tempK=270)
decor.paint('"soma"',   Vm=-50)

With the default and initial values taken care of, we now add some density mechanisms. Let’s paint a pas mechanism everywhere on the cell using the previously defined “all” region; an hh mechanism on the “custom” region; and an Ih mechanism on the “dend” region. The Ih mechanism is explicitly constructed in order to change the default values of its ‘gbar’ parameter.

from arbor import mechanism as mech

# Paint density mechanisms.
decor.paint('"all"', 'pas')
decor.paint('"custom"', 'hh')
decor.paint('"dend"',  mech('Ih', {'gbar': 0.001}))

The decor object is also used to place stimuli and spike detectors on the cell using arbor.decor.place(). We place 3 current clamps of 2 nA on the “root” locset defined earlier, starting at time = 10, 30, 50 ms and lasting 1ms each. As well as spike detectors on the “axon_terminal” locset for voltages above -10 mV. Every placement gets a label. The labels of detectors and synapses are used to form connection from and to them in the recipe.

# Place stimuli and spike detectors.
decor.place('"root"', arbor.iclamp(10, 1, current=2), 'iclamp0')
decor.place('"root"', arbor.iclamp(30, 1, current=2), 'iclamp1')
decor.place('"root"', arbor.iclamp(50, 1, current=2), 'iclamp2')
decor.place('"axon_terminal"', arbor.spike_detector(-10), 'detector')

Note

The number of individual locations in the 'axon_terminal' locset depends on the underlying morphology and the number of axon branches in the morphology. The number of detectors that get added on the cell is equal to the number of locations in the locset, and the label 'detector' refers to all of them. If we want to refer to a single detector from the group (to form a network connection for example), we need a arbor.selection_policy.

Finally, there’s one last property that impacts the behavior of a model: the discretisation. Cells in Arbor are simulated as discrete components called control volumes (CV). The size of a CV has an impact on the accuracy of the results of the simulation. Usually, smaller CVs are more accurate because they simulate the continuous nature of a neuron more closely.

The user controls the discretisation using a arbor.cv_policy. There are a few different policies to choose from, and they can be composed with one another. In this example, we would like the “soma” region to be a single CV, and the rest of the morphology to be comprised of CVs with a maximum length of 1 μm:

# Single CV for the "soma" region
soma_policy = arbor.cv_policy_single('"soma"')
# Single CV for the "soma" region
dflt_policy = arbor.cv_policy_max_extent(1.0)
# default policy everywhere except the soma
policy = dflt_policy | soma_policy
# Set cv_policy
decor.discretization(policy)

Finally, we create the cell.

# (4) Create the cell.

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

The model

Having created the cell, we construct an arbor.single_cell_model.

# (5) Construct the model

model = arbor.single_cell_model(cell)

The global properties

The global properties of a single cell model include:

  1. The mechanism catalogue: A mechanism catalogue is a collection of density and point mechanisms. Arbor has 3 built in mechanism catalogues: default, allen and bbp. The mechanism catalogue in the global properties of the model must include the catalogues of all the mechanisms painted on the cell decor.

  2. The default parameters: The initial membrane voltage; the initial temperature; the axial resistivity; the membrane capacitance; the ion parameters; and the discretisation policy.

Note

You may notice that the same parameters can be set both at the cell level and at the model level. This is intentional. The model parameters apply to all the cells in a model, whereas the cell parameters apply only to that specific cell.

The idea is that the user is able to define a set of global properties for all cells in a model which can then be overridden for individual cells, and overridden yet again on certain regions of the cells.

You may now be wondering why this is needed for the single cell model where there is only one cell by design. You can use this feature to ease moving from simulating a set of single cell models to simulating a network of these cells. For example, a user may choose to individually test several single cell models before simulating their interactions. By using the same global properties for each model, and customizing the cell global properties, it becomes possible to use the cell descriptions of each cell, unchanged, in a larger network model.

Earlier in the example we mentioned that it is better to explicitly set all the default properties of your cell, while that is true, it is better yet to set the default properties of the entire model:

# (6) Set the model default properties

model.properties.set_property(Vm =-65, tempK=300, rL=35.4, cm=0.01)
model.properties.set_ion('na', int_con=10,   ext_con=140, rev_pot=50, method='nernst/na')
model.properties.set_ion('k',  int_con=54.4, ext_con=2.5, rev_pot=-77)

We set the same properties as we did earlier when we were creating the decor of the cell, except for the initial membrane voltage, which is -65 mV as opposed to -55 mV.

During the decoration step, we also made use of 3 mechanisms: pas, hh and Ih. As it happens, the pas and hh mechanisms are in the default Arbor catalogue, whereas the Ih mechanism is in the “allen” catalogue. We can extend the default catalogue as follow:

# Extend the default catalogue with the Allen catalogue.
# The function takes a second string parameter that can prefix
# the name of the mechanisms to avoid collisions between catalogues
# in this case we have no collisions so we use an empty prefix string.
model.catalogue.extend(arbor.allen_catalogue(), "")

Now all three mechanisms in the decor object have been made available to the model.

The probes

The model is almost ready for simulation. Except that the only output we would be able to measure at this point is the spikes from the spike detectors placed in the decor.

The arbor.single_cell_model can also measure the voltage on specific locations of the cell. We can indicate the location we would like to probe using labels from the label_dict:

# (7) Add probes.

# Add voltage probes on the "custom_terminal" locset
# which sample the voltage at 50 kHz
model.probe('voltage', where='"custom_terminal"',  frequency=50)

The simulation

The cell and model descriptions are now complete and we can run the simulation:

# (8) Run the simulation for 100 ms, with a dt of 0.025 ms

model.run(tfinal=100, dt=0.025)

The results

Finally we move on to the data collection segment of the example. We have added a spike detector on the “axon_terminal” locset. The arbor.single_cell_model automatically registers all spikes on the cell from all spike detectors on the cell and saves the times at which they occurred.

# (9) Print the spikes.

print(len(model.spikes), 'spikes recorded:')
for s in model.spikes:
    print(s)

A more interesting result of the simulation is perhaps the output of the voltage probe previously placed on the “custom_terminal” locset. The model saves the output of the probes as [time, value] pairs which can then be plotted. We use pandas and seaborn for the plotting, but the user can choose the any other library:

import pandas
import seaborn

# (10) Plot the voltages

df_list = []
for t in model.traces:
    df_list.append(pandas.DataFrame({'t/ms': t.time, 'U/mV': t.value, 'Location': str(t.location), 'Variable': t.variable}))
df = pandas.concat(df_list,ignore_index=True)
seaborn.relplot(data=df, kind="line", x="t/ms", y="U/mV",hue="Location",col="Variable",ci=None).savefig('single_cell_detailed_result.svg')

The following plot is generated. The orange line is slightly delayed from the blue line, which is what we’d expect because branch 4 is longer than branch 3 of the morphology. We also see 3 spikes, corresponding to each of the current clamps placed on the cell.

../_images/single_cell_detailed_result.svg

The full code

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