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.
Highlights
The coding and representation of signals using sequences of action potentials or spikes is an energy intensive process (Attwell and Laughlin, 2001)
For a given spike-rate, the internal decoder provides a reconstruction which has a higher fidelity than other reconstructions. These predictions will be compared to spike-timing data obtained from peripheral sensory neurons in the electrosensory system of weakly electric fish and from cortical pyramidal neurons in the somatosensory system of the rat. They will be compared to spike trains predicted by a classical leaky-integrate and fire (LIF) neuron and a Leaky Integrate-and-fire (LIF) neuron with a dynamic threshold (LIF-DT)
The motivation for this work rests on the following assumptions: (1) A neuron is subject to an energy constraint in the form of a limit on the average spike rate
Summary
The coding and representation of signals using sequences of action potentials or spikes is an energy intensive process (Attwell and Laughlin, 2001). An optimum neural coder for a given mean spike-rate the optimum trade-off is achieved by timing the spikes to produce the best possible reconstruction of the input signal. This would require a reconstruction mechanism (a decoder) to reside within the neuron so that an internal error signal can be generated by comparing the reconstruction with the input signal. This is similar to certain forms of digital coding where the decoder is built into the coder so that an internal copy of the error is available (Jayant and Noll, 1984)
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