Please use this identifier to cite or link to this item:
For citation please use:
Main Title: Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach
Author(s): Schwalger, Tilo
Type: Article
Abstract: Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.
Subject(s): colored noise
escape noise
first-passage-time density
hazard rate
integrate-and-fire neuron
interspike interval density
neuronal population dynamics
threshold-crossing statistics
Issue Date: 19-Oct-2021
Date Available: 15-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2021
Journal Title: Biological Cybernetics
Publisher: Springer Nature
Volume: 115
Issue: 5
Publisher DOI: 10.1007/s00422-021-00899-1
Page Start: 539
Page End: 562
EISSN: 1432-0770
ISSN: 0340-1200
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Daten-Assimilation in den Neurowissenschaften
Appears in Collections:Technische Universität Berlin » Publications

Files in This Item:
Format: Adobe PDF | Size: 1.25 MB
DownloadShow Preview

Item Export Bar

This item is licensed under a Creative Commons License Creative Commons