Low-dimensional, morphologically accurate models of subthreshold membrane potential.
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 (H(2) 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.
Kellems
Anthony R
AR
Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA. tkellems@rice.edu
Roos
Derrick
D
Xiao
Nan
N
Cox
Steven J
SJ
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D001369:Axons / Q000502:physiology; D002462:Cell Membrane / Q000502:physiology*; D002490:Central Nervous System / Q000502:physiology*; D003198:Computer Simulation; D003712:Dendrites / Q000502:physiology; D006801:Humans; D007473:Ion Channels / Q000502:physiology; D007700:Kinetics; D016014:Linear Models; D008564:Membrane Potentials / Q000502:physiology*; D009434:Neural Pathways / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D051381:Rats; D009435:Synaptic Transmission / Q000502:physiology*
D007473:Ion Channels