Resumen de Correlations in spontaneous activity states in the brain
Studying neural activity correlations is essential for understanding how information is processed in the brain. Traditionally, it was believed that the activities of neighboring neurons were necessarily correlated, due to the large amount of common afferents (Shadlen et al. 1998). However, recent studies have found that this is not always the case (Renart et al. 2010, Ecker et al. 2010).
The main topic of this thesis is the study of decorrelation in balanced recurrent networks of densely connected neurons with strong interactions. Our main contribution is the development of a theory that generalizes and extends the previously found results in binary neurons (Renart et al. 2010) to different kinds of neuron models, with special emphasis on biologically realistic ones.
We show that most of the features of the asynchronous state, if it exists, do not depend on the neuron model. Asynchronous states are equivalent to a dynamical phenomenon that consists in the precise tracking of excitatory fluctuations by inhibition. In such states, balance equations that relate spike train auto- and cross-covariance functions necessarily have to be accomplished. Although both spike train and total current cross-covariance functions are small, the asynchronous state is characterized by finite values of cross-covariances between the current components, i.e., the part of the incoming current that arrives from a given population (Excitatory, Inhibitory, External) in agreement with experimental data (Renart et al. 2010, Graupner et al. 2013).
We analytically show that the asynchronous state in networks of leaky-integrate-and-fire (LIF) neurons exists. Two approximations are employed. We use the linear response (Brunel et al. 1999 , Lindner et al. 2001) and the adiabatic approximations (Moreno-Bote et al. 2004) that account for the effect of incoming currents on the activity of the neuron and allow one to find self-consistent equations for spike train cross-covariance functions. Analytical and numerical results are in agreement for networks whose sizes are biologically relevant. We also show how the balance equations for spike train cross-covariance functions allow one to calculate auto-covariance functions of macroscopic magnitudes, such as the multi-unit activity (MUA).
In the last chapter of this thesis we study the generation of slow oscillations using a model where adaptation and slow inhibition (GABA_B) are present (Parga et al. 2007). The model reproduces experimental data in slices of ferrets and explains the role of the slow inhibition in the durations of the Up/Down cycles and their variability. We find that the degree by which the tracking of excitation by inhibition is accomplished also has an impact on these magitudes.
