Non-monotonic accumulation of spike time variance during membrane potential oscillations

A spike-phase neural code has been proposed as a mechanism to encode stimuli based on the precise timing of spikes relative to the phase of membrane potential oscillations. This form of coding has been reported in both in vivo and in vitro experiments across several regions of the brain, yet there are concerns that such precise timing may be compromised by an effect referred to as variance accumulation, wherein spike timing variance increases over the phase of an oscillation. Here, we provide a straightforward explanation of this effect based on the theoretical spike time variance. The proposed theory is consistent with recordings of mitral neurons. It shows that spike time variance can increase in a nonlinear fashion with spike number, in a way that is dependent upon the frequency and amplitude of the oscillation. Further, non-monotonic accumulation of variance can arise from different combinations of oscillation parameters. Nonlinear accumulation sometimes leads to lower variance than that of a mean rate-matched homogeneous Poisson process, particularly for spikes that occur in later phases of oscillation. However, such an advantage is limited to a narrow range of oscillation amplitudes and frequencies. These results suggest fundamental constraints on spike-phase coding, and reveal how certain spikes in a sequence may exhibit increased firing time precision relative to their neighbors.