Cortical Spikes use Analog Sparse Coding

Quantifying the message communicated by neurons in the cortex by averaging action potentials over repeated trials of a given stimulus can reveal neuronal tuning features. For example, simple cells in the visual cortex have been characterized by reverse correlation based on the detailed structure of their oriented receptive fields. This structure, in turn, has been modeled using large libraries of such receptive fields to allow the simultaneous coding of visual stimuli with small numbers of appropriate combinations of cells selected from the library. This strategy, known as sparse coding, has been shown to produce excellent approximations for natural visual inputs. In concert with this mathematical development has been the discovery of cells use of oscillations in the gamma frequency range for general coding tasks, such as a mechanism for synchronizing distal networks of neurons. More recently, spikes timed with oscillations have been shown to exhibit local phase delays within a single gamma cycle, but such delays have resisted a behavioral functional interpretation. We show here that a specific coordinate system for the gamma cycle allows resultant phase delays to be interpreted quantitatively in classical terms. Specifically, extracted phase delays from mice viewing oriented sinusoidal grating images are shown to have the same distributions as those from a computer sparse coding model using natural images, suggesting for the first time a direct link between experimentally measured phase delays and model receptive fields. Significance StatementNetworks of pyramidal cells in the cortex exhibit action potentials (spikes) that are characterized by randomness and low firing rates. Spike averaging methods have been ordinarily useful in dealing with these features to reveal behavioral task structure, but the randomness and slowness so far prevented the specification of a satisfactory generative spike model. We show that a spike can be analyzed using the context of a specific phase of the gamma component of its membrane potential. The result is each spike can be can be assigned a scalar, which makes it immediately useful for network models.