To use concentration-dependent conductances, you also must compute concentrations. This has been implemented in Nodus 3.2 as the pool subdefinition, which uses a wide range of modeling features, including diffusion, buffers and Nernst potentials. For more information and a description of the equations involved see the chapter by Yamada et al. in ‘Methods in Neuronal Modeling’ by Koch and Segev (1989).
Pools are defined as any other subdefinition with the new Pools command (Neuron menu). Like other subdefinitions, they must be tied to a compartment to become functional, see Nodus 3.1 manual p. 33-35 for a description of subdefinitions. However, pool subdefinitions can be linked to each other into groups, which makes them more complex than other subdefinitions. Imagine an onion shell type of model for diffusion, with ten shells. You wouldn’t want to tie all ten shells individually to each compartment. Therefore you can group these shells together, by linking them, and tie the first one of the group to the compartment.
The pool subdefinition dialog window has at the top left a Type popup menu. Pool subdefinitions are either a pool, which is a volume of unspecified shape, or a shell. For shells you have to specify the position relative to the membrane of the compartment. Each group can contain one supramembrane shell (i.e. the volume just outside of the membrane) and one submembrane shell (i.e. the volume just inside the membrane), you need both if you want to use Nernst potentials. If you want to model diffusion, you can define additional shells, 'inside shells' if you want to model diffusion into the cell, outside
shells if you want diffusion away from the cell. You can use as many inside or outside
shells as you like, up to a maximum of 16 shells in one group. If you use 'inside shells, you probably also want to use the core which is the remaining volume in the center of the compartment.
Pool subdefinitions can be linked together in groups. Use the Link to popup menu (top right) to link a ‘child’ pool subdefinition to a ‘parent’ (note that this is relation is opposite to the way you link compartments in the compartment definition). Each ‘child’ can have only one ‘parent’ and vice versa. They are all linked together in a group, named for the first parent (as shown in the Group name at the top right of the dialog window), which can be tied to a compartment. Diffusion is possible only to a ‘parent’ and to a ‘child’.
Each pool has a Size (the thickness of the shell or the volume of the pool) and a
Minimum concentration (which is also the initial concentration in µM).
Each pool can have several Actions. If no actions are defined, concentration is constant (this can be useful for a Nernst potential). You select an action with a popup menu, up to 10 different actions can be defined for each pool subdefinition. Most action cause the concentration in the pool to change, except for conductance (in)activation. Each action type needs 1 to 3 parameters. Because different types of actions are all listed together, it was impossible to show proper titles for all the action parameters. The titles shown reflect the last action type that was selected. To show the proper parameter titles for any action, press it’s popup menu or any of it's parameters.
The decay by tau action causes concentration to decay exponentially to the minimum concentration. The decay rate is determined by a time constant (in ms). This simple method of modeling changes in concentration is often used when detailed simulation of calcium is not deemed necessary. See for example the Traub82 Hippocampal Neuron. However, it can also be used to implement a simple model of an ion pump. Only one decay by tau action can be specified for a pool subdefinition.
The diffusion action causes diffusion to a neighboring shell or pool. Diffusion is only possible to linked pool subdefinitions (i.e. the ‘parent’ or ‘child’) and is always bidirectional. You have to specify the pool subdefinition to diffuse to, and the diffusion constant (in
µm2/ms). For pools a coupling factor must also be supplied, for shells Nodus computes the coupling factor based on the size of the compartment and the shell thickness.
The ionic current flow action causes the flow through the specified ionic channel to change the concentration. You have to specify the channel (with a popup menu). Parameters are the fraction of the current that contributes to the concentration (default is 1) and the ionic valency (e.g. +2 for calcium, +1 for potassium).
The nernst + ionic current action affects the concentration pool in the same way as the
ionic current flow action, but the ionic current is computed differently. It's reversal
potential is no longer constant (as specified with the Ionic Currents command, Nodus 3.1 manual, p. 92), but determined by the Nernst potential. To compute the Nernst potential, both a supramembrane and a submembrane shell must be tied to the compartment (they may belong to the same group of pool subdefinitions or not), and at least one of them must have the nernst + ionic current action.
The GHK + ionic current action affects the concentration pool in the same way as the
ionic current flow action, but the ionic current is computed differently. Ionic current is no
longer a linear function of voltage, but is instead computed by the Goldman-Hodgkin-Katz equation. To use the GHK equation , both a supramembrane and a submembrane shell must be tied to the compartment (they may belong to the same group of pool subdefinitions or not), and at least one of them must have the GHK + ionic current action. Not implemented in Nodus 3.2.1.
The synaptic current flow action causes the flow through the specified synaptic channel to change the concentration. You have to specify the channel (with a popup menu). Parameters are the fraction of the current that contributes to the concentration (default is 1) and the ionic valency (e.g. +2 for calcium, +1 for potassium).
The nernst + synaptic current action affects the concentration pool in the same way as the synaptic current flow action, but the synaptic current is computed differently. It’s reversal potential is no longer constant (as specified with the Synaptic Currents command, Nodus 3.1 manual, p. 96), but determined by the Nernst potential. To compute the Nernst potential, both a supramembrane and a submembrane shell must be tied to the compartment (they may belong to the same group of pool subdefinitions or not), and at least one of them must have the nernst + synaptic current action.
The GHK + synaptic current action affects the concentration pool in the same way as the synaptic current flow action, but the synaptic current is computed differently. Synaptic current is no longer a linear function of voltage, but is instead computed by the Goldman-Hodgkin-Katz equation. To use the GHK equation , both a supramembrane and a submembrane shell must be tied to the compartment (they may belong to the same group of pool subdefinitions or not), and at least one of them must have the GHK + synaptic
current action. Not implemented in Nodus 3.2.1.
The buffer #1, buffer #2 and buffer #3 actions are identical. They have been named this way to allow output of the free buffer concentrations. In the Configure Plots ( Nodus 3.1 manual, p. 70) and Text Output (Nodus 3.1 manual, p. 72) commands, the Value popup menu includes options to select free buffer #1, etc. These actions implement first order buffering of the concentration in the active pool subdefinition. Parameters are the total buffer concentration (in µM), the forward rate of buffer binding (in (1/µM•ms) and the backward rate of buffer binding (in 1/ms). Each of these actions can be used only once in a pool subdefinition.
The pump action implements an ion pump. Three parameters are necessary: a Kmax (in 1/ms), a Kd (in µM) and a density (in µmol/µm2). See Zador et al., PNAS 87, 6718-6722, 1990 for the equation.
The conductance (in)activation action is shown in italic to emphasize that it is different. It means that the active pool subdefinition will be used for the concentration- dependent (in)activation of the selected conductance. The conductance (in)activation action is available only in pools and submembrane shells. You have to specify the conductance equation with a popup menu (all voltage-dependent conductances are disabled) and the maximum range for the equation table (see Nodus 3.1 manual, p. 20, the table will contain conductance variables in the range 0 µM to the maximum you specified for the first
conductance (in)activation action encountered during simulation database compilation).
Subdefinition management: is similar to that for other subdefinitions. Additionally, there is a Smart duplicate & link button. This button is useful for duplicating shells if you want to create an onion model. The duplicated shell will be linked to the original one and have the same actions (if appropriate).