**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.