| To understand how information is processed in neocortical circuits, it is crucial to map out in detail the role played by the individual neurons in the functioning of these circuits. This involves understanding how synaptic responses are integrated within the dendritic trees, and converted into trains of action potentials transmitted over the axon. In this thesis, using both simple and detailed compartmental models, I have studied the integrative behavior of the principal cell type of the cerebral cortex, the pyramidal neuron (PN). The objective has been to determine the rules of "arithmetic" that PNs use to integrate the thousands of excitatory-inhibitory (E-I) influences impinging on their dendritic trees. Initially, I considered a specific computations that neurons must engage in, in order to effectively process the natural signals to which they are exposed. Recordings from cortical neurons indicate that their receptive fields are commonly subjected to multiplicative and divisive scaling operations. However, the synaptic, neuronal, and network-level mechanisms that underlie response scaling remain poorly understood. We used a detailed compartmental model of a neocortical pyramidal cell to study the "scaling competence" of NMDA channels, which seem ideally suited to contribute to response scaling, in both the subthreshold and suprathreshold (i.e. somatic spiking) regimes. We found that NMDA-dependent scaling could be both accurate and precise over a very limited range of output as well as scaling factors. However, based on a recent study showing location-dependent modulatory effects in PN thin dendrites (Behabadi et al., 2007), we found a novel configuration of excitatory and inhibitory inputs on thin NMDA-rich dendrites that leads to accurate and precise scaling over a wide range of output firing rates and scaling factors. As a follow-up, I pursued a key question raised in the initial study: how do inhibitory inputs to PN thin dendrites influence output firing rates of PNs depending on their location relative to activated excitatory inputs and to the soma? Although there are a large variety of inhibitory interneuron (IN) types in the cortex (Markram et al., 2004), one of the most well-established classification schemes for INs is the spatial distribution of their synaptic contacts on the dendrites (or soma or axon) of their PN targets. How do these different inhibitory "locations" affect a pyramidal neuron's integrative behavior? Using both simple and detailed compartmental models of layer 5 pyramidal neurons, I studied excitatory-inhibitory interactions as a function of this key variable---location (dendritic vs. somatic vs. axonal) of inhibition---specifically in the context of its effect on dendritic NMDA spikes in PNs. I found that somatic inhibition reduced the effective magnitude of NMDA spikes at the soma, but did not affect the threshold level of dendritic excitation needed to initiate them, while, surprisingly, dendritic inhibition did not reduce the magnitude of these spikes seen at the soma, but made it more difficult to initiate a spike in the dendrite. Our model predictions were confirmed in experiments in brain slices carried out in collaboration with the Schiler lab at the University of Haifa. Using compartmental model, I also set out to characterize how the findings about subthreshold E-I interactions would translate to the more biologically relevant spiking regime. It was clear that interactions between excitatory and inhibitory inputs in the spiking regime are governed by numerous factors interacting in complicated ways. I identified the need for a theoretical framework in which to place the different aspects of the excitation and inhibition as well as the intrinsic properties of the cell, so that existing data and models of how E-I interactions modulate the firing rates of a PN can be linked together. Towards this end, I propose a simple framework composed of three biophysically motivated functions that capture: (1) the input nonlinearities that can modulate the net excitatory conductance delivered to a neuron, (2) the subthreshold nonlinear interactions between excitatory and inhibitory conductances, and (3) the nonlinearities at the firing mechanism introduced by factors such as conductance noise as well as intrinsic properties of the neuron. I show that a mathematical composition of these functions, despite its remarkable simplicity, captures and links a wide variety of different E-I interactions, including several representative effects in the existing literature as well as novel E-I effects that I validated using compartmental models. Although the framework is currently limited in scope, its success so far at integrating disparate effects in the literature, and at predicting the outcomes of vastly more complicated models in novel situations, leads us to believe that the framework has strong potential to serve both as a tool for understanding single neuron computation at the conceptual level, as well as a predictive tool to guide the design of future experiments. |
