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INNOVATIVE METHODOLOGY

Structure and Visualization of High-Dimensional Conductance Spaces

¹Volen Center, ²Biology Department, and ³Computer Science Department, Brandeis University, Waltham, Massachusetts; and ⁴Biology Department, Emory University, Atlanta, Georgia

Submitted 7 April 2006; accepted in final form 26 April 2006

Neurons, and realistic models of neurons, typically express several different types of voltage-gated conductances. These conductances are subject to continual regulation. Therefore it is essential to understand how changes in the conductances of a neuron affect its intrinsic properties, such as burst period or delay to firing after inhibition of a particular duration and magnitude. Even in model neurons, it can be difficult to visualize how the intrinsic properties vary as a function of their underlying maximal conductances. We used a technique, called clutter-based dimension reordering (CBDR), which enabled us to visualize intrinsic properties in high-dimensional conductance spaces. We applied CBDR to a family of models with eight different types of voltage- and calcium-dependent channels. CBDR yields images that reveal structure in the underlying conductance space. CBDR can also be used to visualize the results of other types of analysis. As examples, we use CBDR to visualize the results of a connected-components analysis, and to visually evaluate the results of a separating-hyperplane (i.e., linear classifier) analysis. We believe that CBDR will be a useful tool for visualizing the conductance spaces of neuronal models in many systems.

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