The overall goal of this project is to develop a mathematical model to determine the dynamics of the semi circular canal cupula and endolymph in the toadfish, Opsanus tau. The model will incorporate detailed physiological and morphological data. We will apply the model to determine the micromechanical response of the cupula including the mechanical strain acting on sensory hair cell cilia resulting from rotation of the head and mechanical indentation of the membranous labyrinth. This will provide a means to describe the relationship between the mechanical response and presynaptic events associated with the afferent response. The work is motivated by recent evidence suggesting a causal relationship between the micromechanics, dendritic morphology and afferent dynamic response. Afferent response in the toadfish has been categorized in three broad classes -- low gain, high gain and acceleration. The type of dynamic response correlates well with the location and geometry of the afferent dendritic processes within the crista. Consistent with this data, theoretical work by Rabbitt and Damiano predicts a frequency dependent deflected shape of the cupula that reflects the increase in gain present in the afferent dynamic response. We will build upon this previous work to include the micromechanics of the cupula. The endolymph will be modeled as a viscous Newtonian fluid coupled to the deformable cupula. Mechanical behavior of the cupula, the crista and the hair cell cilia will be modeled as a combination of elastic and visco-elastic materials reflecting the geometry and constituents of the tissue ultrastructures. The micromechanical response will include the distribution of strain acting on individual hair cell cilia. Mechanical deformation will provide the input to a hair cell transduction model describing the nonlinear relationship between the mechanical strain and the receptor potential. This will be utilized to drive a stochastic model of the hair cell synaptic response, dendritic field transmission and spike generation. The complete model will allow us to address the afferent response dynamics from first principles and to describe the influence of the morphology on the response of individual afferents. Model predictions will be compared to collaborative experimental data at several stages in the transduction process. Collaborative experimental measurements of the cupula deflection, excitatory Post-synaptic potential and afferent response will drive the evolution of the model. Results are expected to help to distinguish the influence of adaptation and hair cell diversity from the influence of cupular micromechanics, synaptic response and passive dendritic summation. In addition to these fundamental results, we will also be able to address the influence of numerous end-organ related conditions such as genetic and acquired malformations of the labyrinth, metabolic disorders, and the response in microgravity.
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