2012/07/26 by Daniel Soudry, Soudry, Daniel, Ron Meir +1
Biochemistry, Genetics and Molecular Biology · Neuroscience · Physics and Astronomy · #FOS: Biological sciences #Gene Regulatory Network Analysis #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1207.6251
Soudry D and Meir R (2014) The neuronal response at extended timescales: a linearized spiking input--output relation. Front. Comput. Neurosci. 8:29. doi: 10.3389/fncom.2014.00029. This version of the paper is now obsolete. For the the updated and published version - see comments
openalex publication_date 2012/07/26 · arxiv created 2014/04/29 · arxiv updated 2014/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new processes are constantly being discovered, biophysical neuron models increasingly become "too complex to be useful" yet "too simple to be realistic". A fundamental open question in theoretical neuroscience pertains to how this deadlock may be resolved. In order to tackle this problem, we first define the notion of a "excitable neuron model". Then we analytically derive the input-output relation of such neuronal models, relating input spike trains to output spikes based on known biophysical properties. Thus we obtain closed-form expressions for the mean firing rates, all second order statistics (input-state-output correlation and spectra) and construct optimal linear estimators for the neuronal response and internal state. These results are guaranteed to hold, given a few generic assumptions, for any stochastic biophysical neuron model (with an arbitrary number of slow kinetic processes) under general sparse stimulation. This solution suggests that the common simplifying approach that ignores much of the complexity of the neuron might actually be unnecessary and even deleterious in some cases. Specifically, the stochasticity of ion channels and the temporal sparseness of inputs is exactly what rendered our analysis tractable, allowing us to incorporate slow kinetics.