Collaborative Research: The Ever-Changing Network: How Changes in Architecture Shape Neural Computations

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Our brains are constantly changing. Experiences and memories leave their imprints on connections between neurons. Understanding this process is fundamental to understanding how the brain works. While this question has been of central importance to neuroscience for decades, at this moment researchers are well positioned to make significant progress -- new recording devices and imaging techniques are revealing the activity and changes within the networks of the brain at unprecedented scale and resolution. Sound mathematical models are essential to keep up with the mounting avalanche of data. The goal of this project is to develop mathematical tools to assist with improving understanding how networks of neurons are shaped by experiences. Developing this theory is crucial for understanding learning, as well as associated disorders. The project will focus on how learning improves the brain's ability to make decisions and store memories. Graduate students and postdocs joining this project will be part of an established, interdisciplinary mathematics research community. Trainees will gain a wide perspective of mathematical neuroscience through integrated research at three institutions, including extensive visits among them. This research project builds on earlier results of this team to address a central challenge in the mathematical analysis of biophysically realistic neuronal networks: How brain activity changes brain structure over time. Understanding neural computation demands a description of how network dynamics co-evolves with network architecture. The research team will address this challenge by answering specific questions about the interplay between spatiotemporal patterns of neural activity, the attendant changes in network architectures, and the resulting neural computations. This project focuses on two main questions. First, what mathematical techniques can describe the co-evolution of network dynamics and network connectivity toward stable assemblies of neurons? To address this question this project will build a theory describing how global network structure evolves under the dynamics of biophysically realistic plasticity rules that operate on the scale of individual spikes and synapses. Analysis of these models requires novel multiscale and averaging methods. The resulting equations allow analysis of the stability of network architectures and their dependence on stimulus drive. With these results, the second question can be addressed: How does network plasticity create spatiotemporal dynamics that support the basic building blocks of neural computation? Models to understand how plasticity forms networks whose dynamics underlie specific operations on incoming stimuli will be developed to address this question. The mechanism by which long-term plasticity can reshape the connectivity of a network to encode a precise temporal sequence of events will also be investigated.