A quantitative understanding of the cerebral cortex is a major challenge of science in the 21st century. Mathematical and computational models are useful tools in developing this understanding since they allow scientists to test theories about which neural connectivity patterns give rise to which neural activity patterns. However, the cortex is too complex to represent every detail in a model. For example, the human cortex contains billions of neurons arranged in hundreds of interconnected subregions. Instead, mathematical studies rely on identifying fundamental organizing principles of the cortex and using them to build and study simplified models. One such principle is the widely reported balance between the activity of excitatory neurons (which promote activity in other neurons) and inhibitory neurons (which suppress activity). Most previous studies of excitatory-inhibitory balance do not account for the spatial connectivity structure of cortical neuronal networks. This project studies the implications of excitatory-inhibitory balance when the spatial structure cortical neuronal connectivity is taken into account. Prior work has shown that this combination of balance and spatial structure produces similar neural activity patterns as those observed in experimental recordings. The project will use this foundation to construct mathematical models that link anatomical features of the cortex to functional properties such as the neural coding of visual information and the neural basis of motor learning. As such, the project will contribute to the understanding of the cortex and its function. A deeper understanding of cortex can improve disease treatment, brain machine interfaces and the capabilities of intelligent machines.
The project comprises three sub-projects that use spatially extended balanced network models to provide new insights into the following three features of cortical networks: (1) Correlations between the activity of neurons. Correlated neural activity plays a role in neural coding and disease. Previous balanced network models produce small correlations in contrast to larger correlations observed in many cortical recordings. This project explores how spatial network structure introduces new network states with larger correlations. (2) Intrinsic dynamics. Previous balanced network models produce simple macroscopic dynamics, but the computations required to learn new motor sequences rely on more complicated network dynamics. This project explores the rich dynamics exhibited by spatially extended balanced networks and their ability to support motor learning. (3) Sensory coding. This project explores the impact of balance on sensory coding in a model of the primary visual cortex that accounts for the intricate spatial structure of orientation tuning maps. The mathematical techniques developed in this project represent novel approaches to studying spatially extended neuronal networks, which typically involve nonlinear integral equations. In the proposed work, excitation-inhibition balance is exploited to show that these equations become linear at large system size, facilitating the analysis of networks with realistic neuron models and connectivity structure. The novel mathematical approaches contribute to the general study of complex systems and dynamics on large networks.
