Topological bridges between circuits, models, and behavior

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Project summary The plight of the neuroscientist trying to understand the brain using linear analysis methods is akin to studying the makeup of the ocean using the bits you find with a metal detector. Everything we know about the neural basis of decision making, from biology to computation to behavior, makes it clear that the relationship between neurons and behavior is profoundly nonlinear. However, for good mathematical reasons, our attempts to understand that relationship typically rely only on linear measures. These measures have an especially hard time dealing with the reality that neural networks are far from static. Indeed, the flexibility of interactions between neurons, while adding an additional nonlinearity, is a critically important clue about underlying mechanisms and computations. The goal of the proposed project is to test the hypothesis that nonlinear measures of correlated variability in a population of neurons will 1) establish a strong link between neurons and perceptual decisions, 2) constrain models of the circuit mechanisms by which cognition affects perception, and 3) predict the effects of causally manipulating different subtypes of inhibitory interneurons on population activity. We will use and develop methods from algebraic topology to characterize the activity of neuronal populations in a holistic, nonlinear way. Our project leverages the complementary strengths between three highly interactive approaches: primate neurophysiology and psychophysics, modeling neuronal circuits, and two photon imaging and optogenetic manipulation of subtypes of inhibitory interneurons in mice. In Aim 1, we will test the hypothesis that sensory and cognitive processes including contrast, adaptation, attention, and motivation affect performance on visual tasks exactly when they change the topological signatures of the correlated variability in visual or parietal cortex. In Aim 2, we will use a biophysically realistic model to understand which changes in a cortical circuit would or would not change the topological signatures of neuronal population activity. In Aim 3, we will test the predictions of our model to understand how manipulating the activity of different subtypes of inhibitory interneurons affects topological summaries of neuronal activity and information processing in the network. This work uses novel mathematical ideas to bridge different levels of the study of cortical circuits. It will have implications for our understanding of the relationship between neuronal circuits and behavior across species, systems, and theoretical approaches.