A stimulus-dependent spike threshold is an optimal neural coder

Abstract

A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.

A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains

“…Thus with few exceptions (see below), adaptive threshold models have been qualitative. They demonstrate some features of experimentally observed ISI distributions, and at best correlations between adjacent ISIs In recent years deterministic adaptive threshold models with an exponential kernel have been used to predict spike-times from cortical and peripheral neurons [37,39,54] (see [38] for an early review) and predict peri-stimulus time histograms [39,41] with good accuracy. Capturing spike-times accurately is perhaps the first requirement in our analysis, and this gives confidence that the model may tell us something about ISI correlations.…”

“…outward potassium currents, including voltage gated potassium currents and calcium-dependent or AHP currents (e.g., [5,30,[32][33][34][35][36]). An adaptive threshold model is known to accurately predict spike-times in neurons ranging from cortical [37][38][39] to peripheral [39]. Further, we recently showed that a spike-timing code based on an adaptive threshold is an optimal neural code which minimizes coding error (estimation error) for a fixed long-term spike-rate (energy consumption) [39][40][41].…”

“…An adaptive threshold model is known to accurately predict spike-times in neurons ranging from cortical [37][38][39] to peripheral [39]. Further, we recently showed that a spike-timing code based on an adaptive threshold is an optimal neural code which minimizes coding error (estimation error) for a fixed long-term spike-rate (energy consumption) [39][40][41]. Thus, adaptation with its signature serial interval correlations, are likely tied to fundamental mechanisms responsible for a timing-based neural code.…”

“…An ion channel that may be a substantial contributor to adaptation currents is the non-inactivating M-current (KCNQ/Kv7 family) [60] which is a voltage-gated potassium channel with slow dynamics (relative to the mean ISI). This channel may be responsible for spike-timing precision, and hence a timing-based neural code (see [39] for a discussion). The possible role of the M-current and the specific sources of noise have been explored earlier (see [30] above in relation to types of SCCs, and [5]).…”

General neural mechanisms can account for rising slope preference in localization of ambiguous sounds

“…Our adaptation and onset models are similar or equivalent to membrane potential and synapse dynamics that are found throughout the nervous system (see Methods and Appendix). Adaptation allows neurons to minimize energy costs while encoding persistent stimuli (Jones et al, 2015) and to increase their sensitivity to new stimuli (Fairhall et al, 2001). At the population level, excitatory-inhibitory networks are often found in other sensory modalities, such as in orientation tuning in vision (Ben-Yishai et al, 1995) or in the detection of touch in the field of somatosensation (Mountcastle, 1959).…”