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How sensory stimuli are encoded in neuronal activity is a major challenge for understanding perception. A prominent effect of sensory stimulation is to elicit oscillations in the Local Field Potential (LFP) recordings over a broad range of frequencies. The mechanism underlying the emergence of oscillations and their role in encoding sensory information is still not clear. Recent work suggested the idea that different stimulus features could be encoded in the neural activity at different timescales. Belitski et al. [1] recorded LFPs and spiking activity in the primary visual cortex of anesthetized macaques presented with naturalistic movies and found that the power of the gamma and low-frequency bands of LFP carried largely independent information about visual stimuli, while the information carried by the spiking activity was redundant with that carried by the gamma-band LFPs. To better understand these findings, Mazzoni et al. [2] simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population. They demonstrated that an increase in external inputs leads both to an increase in spiking activity, and an increase in gamma-range LFP oscillations that are generated by the excitatory-inhibitory interactions, while the low-frequency band of the LFP encodes the dynamics at slow time scales of the input. Furthermore, it was shown that low and high frequencies bands work are essentially independent channels for encoding information, in agreement with the experimental findings [1].
In this work we reconsider the dynamics of a model of excitatory and inhibitory integrate-and-fire neurons in the presence of time-dependent inputs and compute analytically average firing rate and LFP spectra, together with the information that they convey about the stimulus. We used two different type of inputs: (1) stimuli that are constant during temporal intervals of fixed duration, but then change abruptly to a new value from an interval to the next (2) a dynamic stimulus which evolves according to an Ornstein-Uhlenbeck (OU) process. We then used the derived analytical formulas to fit the data recorded in anesthetized monkeys. We first fitted parameters characterizing the network model using spontaneous activity (i.e. before the movie starts). We then fit parameters characterizing the input to the network during the movie. In all cases, we find that the analytical formulas provide excellent fits to the data. This analytical approach can be used to identify the key parameters underlying input-dependent changes in the LFP spectral dynamics.
