A computational investigation of the relationships between single-neuron and network dynamics in the cerebral cortex

The brain in complex animals is organized in different areas, such as visual areas, motor areas etc., which are believed to be responsible for specific functions. Each area can have in turn its own organization, but for all areas it is believed that their functions rely on the dynamics of networks of neurons rather than on single neurons. On the other hand, the network dynamics reflect and arise from the integration and coordination of the activity of populations of single neurons. Understanding how single-neurons and neural-circuits dynamics complement each other to produce brain functions is thus of paramount importance. LFPs and EEGs are good indicators of the dynamics of mesoscopic and macroscopic populations of neurons, while microscopic-level activities can be documented by measuring the membrane potential, the synaptic currents or the spiking activity of individual neurons. How can we combine the information coming from microscopic, mesoscopic and macroscopic levels to get better insights about the relationships between single-neuron activity and the state of neural circuits? How can we model the relationship between these two levels? How can we optimally analyze concurrent recordings at multiple scales to gain insights on the relationship between macroscopic/mesoscopic and microscopic brain dynamics? In this thesis we develop mathematical modelling and mathematical analysis tools that can help the interpretation of joint measures of neural activity at microscopic and mesoscopic or macroscopic scales. In particular, we develop network models of recurrent cortical circuits that can clarify the impact of several aspects of single-neuron dynamics (that depend on the details of synaptic dynamics) on the activity of the whole neural population (i.e., at the mesoscopic level). We then develop statistical tools to characterize the relationship between the action potential firing of single neurons and mass signals. We apply these latter analysis techniques to joint recordings of the firing activity of individual cell-type identified neurons and mesoscopic (i.e., LFP) and macroscopic (i.e., EEG) signals in the mouse neocortex. We identified several general aspects of the relationship between cell-specific neural firing and mass circuit activity, providing for example general and robust mathematical rules which infer single-neuron firing activity from mass measures such as the LFP and the EEG.