Low-dimensional, morphologically accurate models of subthreshold membrane
Publication Date: 2009 Jan 27 PMID: 19172386
Authors: Kellems, A. R. - Roos, D. - Xiao, N. - Cox, S. J.
Journal: J Comput Neurosci
The accurate simulation of a neuron's ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a single spine, i.e., 1 mum. We argue here that one can retain this highly detailed input structure while dramatically reducing the overall system dimension if one is content to accurately reproduce the associated membrane potential at a small number of places, e.g., at the site of action potential initiation, under subthreshold stimulation. The latter hypothesis permits us to approximate the active cell model with an associated quasi-active model, which in turn we reduce by both time-domain (Balanced Truncation) and frequency-domain ([Formula: see text] approximation of the transfer function) methods. We apply and contrast these methods on a suite of typical cells, achieving up to four orders of magnitude in dimension reduction and an associated speed-up in the simulation of dendritic democratization and resonance. We also append a threshold mechanism and indicate that this reduction has the potential to deliver an accurate quasi-integrate and fire model.
On staying with the theme of subthreshold membrane voltages (see my previous shares if you missed them) - This is the type of work that needs to be done if we're to make anything out of the almost infinite complexity of the analog world.... Comp neuro is a wonderful thing.