The goal of this thesis is to investigate the biophysical basis underlying the nonlinear relationship between firing response and current stimulation in single motor neurons. After reviewing the relevant motoneuron physiology and theories that describe complex dendritic signaling properties, I hypothesize that at least five passive electrical properties must be considered to better understand the physiological input-output properties of motor neurons in vivo: input resistance, system time constant, and three signal propagation properties between the soma and dendrites that depend on the signal direction (i.e. soma to dendrites or vice versa) and type (i.e. direct (DC) or alternating (AC) current). To test my hypothesis, I begin with characterizing the signal propagation of the dendrites, by directly measuring voltage attenuations along the path of dendrites of the type-identified anatomical neuron models. Based on this characterization of dendritic signaling, I develop the novel realistic reduced modeling approach by which the complex geometry and passive electrical properties of anatomically reconstructed dendrites can be analytically mapped into simple two-compartment modeling domain without any restrictive assumptions. Combining mathematical analysis and computer simulations of my new reduced model, I show how individual biophysical properties (system input resistance, time constant and dendritic signaling) contribute to the local excitability of the dendrites, which plays an essential role in activating the plateau generating membrane mechanisms and subsequent nonlinear input-output relations in a single neuron. The biophysical theories and computer simulations in this thesis are primarily applied to motor neurons that compose the motor neuron pool for control of movement. However, the general features of the new reduced neuron modeling approach and important insights into neuronal computations are not limited to this area. My findings can be extended to other areas including artificial neural networks consisting of single compartment processors.
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