Visualization and Structure of an Eight-Dimensional Conductance Space

Adam L. Taylor, Astrid A. Prinz, Timothy J. Hickey and Eve Marder

Email: altaylor@brandeis.edu

Neurons, and realistic models of neurons, typically express many
different types of voltage-gated channels. A family of model neurons
will exhibit different spontaneous behaviors (e.g. silence, tonic
firing, endogenous bursting) depending on the maximal conductances of
these different channel types. When there are more than three types of
channels, it can be difficult to visualize how the different behavior
types depend on the underlying maximal conductances. We encountered this
problem when trying to visualize spontaneous behavior types in a family
of models with eight different types of voltage- and calcium- dependent
channels. Previous work systematically raster-scanned the conductance
space by independently varying each conductance in six discrete
steps. This generated a database of 68 (=1,679,616) models. We now use
the dimensional stacking technique to visualize this conductance
space. This technique embeds an eight-dimensional plot in two dimensions
by plotting less "important" dimensions at a reduced scale. We used a
simple measure of the simplicity of the resulting plots to choose which
dimensions were important. This yielded plots which revealed significant
structure in the underlying conductance space. These plots could then be
used to compare a region in conductance space (e.g. the space occupied
by tonically firing neurons) to a putative description of it (e.g. a
half-space, all the models lying to one side of a hyperplane). This
allowed us to see when such a simple description was unlikely to be
adequate, and resort to a more complex description (e.g. the union of
two half-spaces). We believe dimensional stacking will be a useful
technique for visualizing the conductance spaces of neuron model
families in many systems.