The Physiology and Computation of Pyramidal Neurons

A variety of neural signals have been measured as correlates to consciousness. In particular, late current sinks in layer 1, distributed activity across the cortex, and feedback processing have all been implicated. What are the physiological underpinnings of these signals? What computational role do they play in the brain? Why do they correlate to consciousness? This thesis begins to answer these questions by focusing on the pyramidal neuron. As the primary communicator of long-range feedforward and feedback signals in the cortex, the pyramidal neuron is set up to play an important role in establishing distributed representations. Additionally, the dendritic extent, reaching layer 1, is well situated to receive feedback inputs and contribute to current sinks in the upper layers. An investigation of pyramidal neuron physiology is therefore necessary to understand how the brain creates, and potentially uses, the neural correlates of consciousness. An important part of this thesis will be in establishing the computational role that dendritic physiology plays. In order to do this, a combined experimental and modeling approach is used.

This thesis beings with single-cell experiments in layer 5 and layer 2/3 pyramidal neurons. In both cases, dendritic nonlinearities are characterized and found to be integral regulators of neural output. Particular attention is paid to calcium spikes and NMDA spikes, which both exist in the apical dendrites, considerable distances from the spike initiation zone. These experiments are then used to create detailed multicompartmental models. These models are used to test hypothesis regarding spatial distribution of membrane channels, to quantify the effects of certain experimental manipulations, and to establish the computational properties of the single cell. We find that the pyramidal neuron physiology can carry out a coincidence detection mechanism. Further abstraction of these models reveals potential mechanisms for spike time control, frequency modulation, and tuning. Finally, a set of experiments are carried out to establish the effect of long-range feedback inputs onto the pyramidal neuron. A final discussion then explores a potential way in which the physiology of pyramidal neurons can establish distributed representations, and contribute to consciousness.

Formal languages, part theory, and change

A general definition of interpreted formal language is presented. The notion “is a part of" is formally developed and models of the resulting part theory are used as universes of discourse of the formal languages. It is shown that certain Boolean algebras are models of part theory.

With this development, the structure imposed upon the universe of discourse by a formal language is characterized by a group of automorphisms of the model of part theory. If the model of part theory is thought of as a static world, the automorphisms become the changes which take place in the world. Using this formalism, we discuss a notion of abstraction and the concept of definability. A Galois connection between the groups characterizing formal languages and a language-like closure over the groups is determined.

It is shown that a set theory can be developed within models of part theory such that certain strong formal languages can be said to determine their own set theory. This development is such that for a given formal language whose universe of discourse is a model of part theory, a set theory can be imbedded as a submodel of part theory so that the formal language has parts which are sets as its discursive entities.

Functional, clustered, feedforward, and mesoscale brain networks

The brain is a network spanning multiple scales from subcellular to macroscopic. In this thesis I present four projects studying brain networks at different levels of abstraction. The first involves determining a functional connectivity network based on neural spike trains and using a graph theoretical method to cluster groups of neurons into putative cell assemblies. In the second project I model neural networks at a microscopic level. Using diferent clustered wiring schemes, I show that almost identical spatiotemporal activity patterns can be observed, demonstrating that there is a broad neuro-architectural basis to attain structured spatiotemporal dynamics. Remarkably, irrespective of the precise topological mechanism, this behavior can be predicted by examining the spectral properties of the synaptic weight matrix. The third project introduces, via two circuit architectures, a new paradigm for feedforward processing in which inhibitory neurons have the complex and pivotal role in governing information flow in cortical network models. Finally, I analyze axonal projections in sleep deprived mice using data collected as part of the Allen Institute's Mesoscopic Connectivity Atlas. After normalizing for experimental variability, the results indicate there is no single explanatory difference in the mesoscale network between control and sleep deprived mice. Using machine learning techniques, however, animal classification could be done at levels significantly above chance. This reveals that intricate changes in connectivity do occur due to chronic sleep deprivation.