1. THE PURKINJE CELL
The cerebellar Purkinje cell is the only output neuron from the cerebellar
cortex. It is also among the largest and most complex neurons in the
mammalian brain. The about 200,000 synaptic inputs received by each Purkinje
cell constitute the most massive synaptic convergence found on any neuron
in the brain. Purkinje cells are also distinguished by high densities of
calcium channels on their dendrite which cause them to easily fire
dendritic calcium spikes.
The synaptic input to Purkinje cells comes from multiple sources, four of
which are explicitly represented in this model:
- excitatory input from cerebellar granule cells over their parallel fiber
axon. A Purkinje cell receives more than 150,000 such parallel fiber
inputs onto the spiny dendrite (thin dendrites). Both 'background'
(i.e. continuous random) and synchronous parallel fiber inputs can
- excitatory input from the inferior olive by the climbing fiber input.
Each Purkinje cell receives only ONE climbing fiber input, which is
only rarely activated. The single climbing fiber makes multiple
synapses on the smooth dendrite (i.e. the thicker parts of the
dendrite). Only synchronous activation is possible.
- inhibitory input from the cerebellar stellate cells onto most of the
dendrite. Only 'background' stellate cell inputs can be simulated.
- inhibitory input from the cerebellar basket cells onto the proximal smooth
dendrite and soma. Only synchronous activation is possible.
2. MODELING A PURKINJE CELL
A good general introduction of the model can be found at
http://www.bbf.uia.ac.be/publications/TNB_pub9.shtml, and many other of our
publications about this model are also available. A general overview of
the model scripts can be found at http://www.bbf.uia.ac.be/models/PM9.shtml
This is a compartmental model. The detailed dendritic geometry of the cell
is based on morphological data provided by Rapp, Yarom and Segev which
is replicated by 1600 electrically distinct compartments. These are
divided in three functional zones: the soma, the main dendrite and the
rest of the dendrite.
Ten different types of voltage dependent channels are modelled, 8021
channels in total, using Hodgkin Huxley-like equations based on
Purkinje cell specific voltage clamp data or, when necessary, on data from
other vertebrate neurons. The soma possesses fast (NaF) and persistent (NaP)
sodium channels, low threshold (CaT) calcium channels, and delayed
rectifier (Kdr), A-current (KA) and non-inactivating (KM) potassium
channels, and an anomalous rectifier (h1 and h2). The dendritic membrane
includes P-type (CaP) and T-type (CaT) calcium channels, two different
calcium-activated potassium channels (BK and K2) and a non-inactivating
potassium channel. The P-type calcium channel is a high-threshold, very
slowly inactivating channel, first described in the Purkinje cell and
responsible for the dendritic calcium spikes.
The changes in calcium concentration caused by voltage-activated calcium
influx is computed in a submembrane shell.
3. THE INTERFACE
When the simulation is first run, two windows pop up : the first
window contains a picture of a typical Purkinje cell with on the right
buttons for options on the graphical output. Beneath the window with the
Purkinje cell is a control panel to do several types of experiments.
a. Buttons in the control panel
The buttons in the Simulation control panel fall apart in three categories :
1. Buttons for Simulation control: standard GENESIS simulation control
Resets the simulation and clears the graphical output
(unless in overlay mode, see below).
Initiates the simulation and performs a simulation run for the
time as given in the time dialog.
Stops the current simulation (if any)
Quits the simulation (and GENESIS).
Time (default : 500 msec)
Sets the total time in milliseconds to be simulated during one
run (after clicking the 'RUN' button).
Output rate (default : 10)
Sets the output rate for the graphical output relative to the
simulation time step (which is 0.020 millisec). The default
rate of 10 means that only once every 10 steps the Purkinje
cell picture is updated.
Toggle Simulation time (default : off)
Allows you to display the simulation time in seconds as the
simulation progresses. This usually slows down the simulation.
2. Buttons for Simulation mode: Purkinje cell simulation experiments
Toggle In vivo - In vitro (default : In vitro)
This toggle switches between In vitro mode (where there is no
background input from stellate cells or parallel fibers) and
In vivo mode. The Settings window let you set the mean firing
frequency for stellate (inhibitory) cells and parallel (excitatory)
fibers. The Settings are only available for the 'In vivo' mode.
Current injection (default : on, constant current of 0.5 nA)
This is a toggle which switches between simulated current injection
directly into the soma or not. In the Settings window the current
level (in nanoAmperes) can be set and a choice must be made between
constant or current pulses. For the current pulses the pulse
amplitude (nA), width (msec) and period (msec, this is the period
between onset of two consecutive pulses) can be set in the
Activate parallel fibers
Hitting this button activates excitatory synaptic input from a
specified number of parallel fibers. In the Settings window you
can choose the number of parallel fibers that will be activated
and the relative synaptic strength of each. You can also toggle
between activating parallel fibers uniformly distributed over the
whole dendritic tree (default) or activating parallel fibers locally
on one specific branch of the tree. In the latter case the number of
synchronous activated parallel fibers synapses is preset to 20,
for distributed activation the number of activated synapses is cut
to a multiple of 25 with a maximum of 475. You can choose the branch
that will receive local activation by clicking the button
'Change area from xcell'. Then click anywhere on the spiny dendrite
of the Purkinje cell, the name of the selected branch will be updated.
Activate basket axon
Hitting this button activates inhibitory input from the basket
axons that are wrapped around the main dendrite (the thicker
dendrite directly attached to the soma) and the soma. The Settings
window let you set the relative synaptic strength of all contacts.
Activate climbing fiber
Hitting this button activates excitatory synaptic input from the
climbing fiber that makes strong synapses on the main and thick
dendrites. The Settings window let you set the relative synaptic
strength and the delay between consequent climbing fiber synapses
(so it defines the actual speed of signal transmission within the
climbing fiber axon).
3. Buttons for Simulation information
Shows you this information
Shows authors and contributors
b. Output windows
There are two output windows : the window with the picture of
a Purkinje cell (the cell output window) and a graph window that is not
visible when the simulation is started (the graph output window, to open it
click 'graph' button in the cell output window).
1. The cell output window
The cell output window displays the value of a calculated variable
by changing the (rainbow) color of the compartment the variable
belongs to. Red means a high value, blue means a low value. Default
is to display compartmental voltage. It is possible to display the
calcium concentration or the conductance or current for all the types
of channels implemented in this Purkinje cell model. If a channel or
value is not present in a compartment, a default of zero is used.
You select the output type by clicking one of the buttons to the
upper right of the cell output window. The simulation will stop
(simulation time is reset to zero) and GENESIS will take some
time to change all the display messaged. The name of the selected
variable will appear above the cell and the range of values
displayed is shown below the cell (Color maximum or minimum). The
tutorial automatically selects an appropriate range for each
variable, but you can change this if desired.
For the channels (the synaptic Exc. chan. or Inh. chan, or the
voltage-gated CaP, CaT, K2 and so on), an additional choice can
be made between channel conductance (Gk button, the default),
channel current (Ik button) and for the CaP or CaT channels the
reversal potential (Ek button; for the other channels this is
constant). Channel conductance and current can be shown as
Normalized values (default) or Absolute values.
For the other possible outputs (compartmental voltage, concentration)
there are no further options.
Besides the colorfull output of variables, the tutorial lets
you follow the change of a particular variable in the graph window.
To make the graph window visible, click the 'Graph' button once in the
cell window. To follow a particular variable you are interested in
(e.g. calcium concentration in the main dendrite) set the cell output
window into the mode that colorizes the Purkinje cell to follow the
variable you are interested in (i.e. click to 'Comp. Ca' button to
visualize calcium concentration in the compartments). Now click
the add plot button in the graph window and click then on the main
dendrite in the cell window, the graph will respond with an output
of the form 'main_7_Ca' (the number could be different). If
you now run a simulation, the graph window will show the compartmental
calcium concentration in the main dendrite. When several plots are
made in the same simulation, the color of the plots can be used
to differentiate between them and to associate every plot with an
electrode in the cell window (the electrodes are made visible by
clicking the 'Electrodes' button in the cell window). When you
change the cell output mode to one that uses the same units the
current selected graphs will remain active (e.g. changing the cell
output from CaP conductance to CaT conductance), otherwise they
will be cleared (e.g. from CaP conductance Comp. Ca).
Output compartmental voltage (in volts).
Output compartmental calcium concentration (in milliMolar).
Output excitatory synaptic channels.
Output inhibitory synaptic channels.
CaP, CaT, ... h1, h2
Output different channel types. h1 and h2 are two components
of the same anomalous rectifier current.
Ik, Gk, Ek
Output current (in Amperes or aribitrary units), conductance
(in Siemens or aribitrary units) or reversal potential (in
volts) of a channel. These buttons are only available if the
main output for the cell is a channel type.
Output mode : Normalized / Absolute
Toggle between Normalized (default) or Absolute values. For
channel types only. In the Normalized output mode the
conductance or current is normalized relative to the surface
area of the compartment, this allows you to compare relative
activation levels between different compartments (the units are
aribitrary). In the Absolute output mode the real values are
shown in Amperes (current) or Siemens (conductance); these
are typically much larger for large compartments so that
changes in smaller ones might not be discernible.
Graph / No Graph
Toggle between hide (default) / show the graph output window.
Electrodes / No Electrodes
Toggle between hide (default) / show the recording electrodes
in the cell window.
Color maximum and Color minimum
Set the color scales for the cell display. Updated
automatically when a different output is selected.
2. The graph output window
The graph output window lets you follow the change of a particular
variable during a simulation. For more explanation on how to choose
that variable, see the paragraphs about the cell output window above.
Clear the graph and remove all recording sites. If the recording
electrodes were visible in the cell output window, the cell output
window will be refreshed.
Use this button to add plot(s) to the graph. This must be done
as no plots are preselected. You can either click on the cell
to select or type a name in the dialog box.
Overlay off / on
When a reset is performed, normally all plots are cleared.
When overlay is on they are saved so that you can compare plots
from different runs.
Allows to set the range of the axes of the graph. The graph is
automatically scaled for the type of the first recording site
Resets the axes to their default values.