Flexible frequency control of cortical oscillations enables computations required for working memory
Working memory (WM) requires selective information gating, active information maintenance, and rapid active updating. Hence performing a WM task needs rapid and controlled transitions between neural persistent activity and the resting state. We propose that changes in correlations in neural activity provides a mechanism for the required WM operations. As a proof of principle, we implement sustained activity and WM in recurrently coupled spiking networks with neurons receiving excitatory random background activity where background correlations are induced by a common noise source. We first characterize how the level of background correlations controls the stability of the persistent state. With sufficiently high correlations, the sustained state becomes practically unstable, so it cannot be initiated by a transient stimulus. We exploit this in WM models implementing the delay match to sample task by modulating flexibly in time the correlation level at different phases of the task. The modulation sets the network in different working regimes: more prompt to gate in a signal or clear the memory. We examine how the correlations affect the ability of the network to perform the task when distractors are present. We show that in a winner-take-all version of the model, where two populations cross-inhibit, correlations make the distractor blocking robust. In a version of the mode where no cross inhibition is present, we show that appropriate modulation of correlation levels is sufficient to also block the distractor access while leaving the relevant memory trace in tact. The findings presented in this manuscript can form the basis for a new paradigm about how correlations are flexibly controlled by the cortical circuits to execute WM operations.
In this paper, we study the dynamics of a quadratic integrate-and-fire neuron, spiking in the gamma (30-100 Hz) range, coupled to a delta/theta frequency (1-8 Hz) neural oscillator. Using analytical and semianalytical methods, we were able to derive characteristic spiking times for the system in two distinct regimes (depending on parameter values): one regime where the gamma neuron is intrinsically oscillating in the absence of theta input, and a second one in which gamma spiking is directly gated by theta input, i.e., windows of gamma activity alternate with silence periods depending on the underlying theta phase. In the former case, we transform the equations such that the system becomes analogous to the Mathieu differential equation. By solving this equation, we can compute numerically the time to the first gamma spike, and then use singular perturbation theory to find successive spike times. On the other hand, in the excitable condition, we make direct use of singular perturbation theory to obtain an approximation of the time to first gamma spike, and then extend the result to calculate ensuing gamma spikes in a recursive fashion. We thereby give explicit formulas for the onset and offset of gamma spike burst during a theta cycle, and provide an estimation of the total number of spikes per theta cycle both for excitable and oscillator regimes.
Gamma oscillations are a prominent phenomenon related to a number of brain functions. Data show that individual pyramidal neurons can fire at rate below gamma with the population showing clear gamma oscillations and synchrony. In one kind of idealized model of such weak gamma, pyramidal neurons fire in clusters. Here we provide a theory for clustered gamma PING rhythms with strong inhibition and weaker excitation. Our simulations of biophysical models show that the adaptation of pyramidal neurons coupled with their low firing rate leads to cluster formation. A partially analytic study of a canonical model shows that the phase response curves with a near zero flat region, caused by the presence of the slow adaptive current, are the key to the formation of clusters. Furthermore we examine shunting inhibition and show that clusters become robust and generic.