Characterization of the encoding properties of intraspinal mechanosensory neurons in the lamprey.

Proprioceptive sensory inputs are an integral part of the closed-loop system of locomotion. In the lamprey, a model organism for vertebrate locomotion, such sensory inputs come from intraspinal mechanosensory cells called "edge cells". These edge cells synapse directly onto interneurons in the spinal central pattern generator (CPG) circuit and allow the CPG to adjust the motor output according to how the body is bending. However, the encoding properties of the edge cells have never been fully characterized. To identify these properties and better understand edge cells' role in locomotion, we isolated spinal cords of silver lampreys (Ichthyomyzon unicuspis) and recorded extracellularly from the lateral tracts where edge cell axons are located. We identified cells that responded to mechanical stimuli and used standard spike sorting algorithms to identify separate units, then examined how the cells respond to bending rate and bending angle. Although some cells respond to the bending angle, as was previously known, the strongest and most common responses were to bending velocity. These encoding properties will help us better understand how lampreys and other basal vertebrates adapt their locomotor rhythms to different water flow patterns, perturbations, or other unexpected changes in their environments.

Effect of parity on productivity and sustainability of Lotka-Volterra food chains: bounded orbits in food chains.

Hairston, Slobodkin, and Smith conjectured that top down forces act on food chains, which opposed the previously accepted theory that bottom up forces exclusively dictate the dynamics of populations. We model food chains using the Lotka-Volterra predation model and derive sustainability constants which determine which species will persist or go extinct. Further, we show that the productivity of a sustainable food chain with even trophic levels is predator regulated, or top down, while a sustainable food chain with odd trophic levels is resource limited, which is bottom up, which is consistent with current ecological theory.

Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment.