Temporal uncertainty in reading the neural code (proportional noise).

It is widely accepted that neural information is encoded in the timing of action potentials. However, such information can only be transmitted if the receiver (soma, muscle fibre) can measure time precisely. We argue that such timing is inevitably imprecise due to biological fluctuations in receiver function. We show that this leads to a receiver output, where the standard deviation of receiver output noise is proportional to the mean level of the receiver output. Proportional noise is fundamentally distinct from the common assumption of square-root relationship seen in renewal processes (e.g. Poisson noise), which is usually assumed in neural firing patterns. We show that proportional noise may be the limiting constraint in receiver function, and that it could account for such diverse perceptual and motor behaviours encompassed by Weber's and Fitt's laws, as well as the dynamic trajectories of rapid feed-forward motor behaviours such as arm reaching and saccades. We conclude that temporal uncertainty should be potentially a fundamental stochastic constraint on network function and behaviour.