On generation of statoconia in gravireceptors of mollusks.

Two models of development of statoconia in the statocyst of mollusks, based on the experimental data [Hearing Res. 49 (1990) 63; Hearing Res. 109 (1997) 125; Hearing Res. 109 (1997) 109;] are proposed. The purpose of the present work is to apply mathematical modeling to the analysis of mechanisms of statoconia formation and generation by supporting cells at the stage of their accumulation in the cyst lumen. In the case of Aplysia californica, it is not clear whether there is a temporal change of statoconia due to their growth in the cyst lumen similar to that in Biomphalaria, or whether the growth of statoconia occurs in supporting cells before they get into the cyst lumen. This question has to do with a more general and insufficiently investigated problem of the mechanisms of statoconia evolution during their stage of accumulation. This is related to A. californica as well as to the initial phase of development of Biomphalaria glabrata. This problem is of practical importance because the majority of experiments related to the study of the effects of altered gravity on the development of gravireceptors in the two mollusks A. californica and B. glabrata deals with the initial phase of statoconia development. It is assumed that two main processes determine the evolution of statoconia in developing mollusks: generation of new statoconia by growing supporting cells and growth of statoconia sizes in the cyst lumen. Analysis of experimental data related to the generation of statoconia in Aplysia and comparison of these data with the results of modeling of accumulation of statoconia suggest that the basic mechanism of evolution of size distribution of statoconia in Aplysia is growth of embryonic statoconia in supporting cells, that follows the growth of animal size. Thus, the large sizes of statoconia are determined by their development within supporting cells rather than by their growth in the cyst lumen. Analysis of the data concerning Biomphalaria allows us to assume that distribution of supporting cells which generate statoconia also varies. The results of modeling of evolution of statoconia specify necessary additional experiments, which are required to refine and test the model.

Qualitative model of otolith-ocular asymmetry in vertical eccentric rotation experiments.

Today, investigation of the vestibulo-ocular reactions is a mainstream method of studying the vestibular asymmetry. Analysis of experimental data requires a model of otolith-ocular interaction. The proposed model is based on the literary data concerning measurements of ocular counter-rotation (OCR) and luminous line rotation (LLR) in experiments with eccentric rotation carried out by Wetzig et al. [Acta Astronaut. 21 (1990) 519-525]. The method utilizes a number of simplifications and suppositions, the basic of which is linearity of all stages of transformation of mechanical stimulus with the exception of the proportionality of neural response to acceleration. It was demonstrated that the model qualitatively imitates the behavior of OCR and LLR in response to centrifugal acceleration of utricular otoliths and permits analysis of the role of various parameters of the otolith-ocular interaction. Comparison of modeling and experimental dependences of OCR and LLR on acceleration can help understand otolithic asymmetry.

Models of the mechanical sensitivity and growth of otoliths in fish.

It has been suggested that, in the fish, the change of otolith mass during development under altered gravity conditions and the growth of otoliths in normal conditions, are determined by feedback between otolith dynamics and the processes that regulate otolith growth. The hypothesis originates from an oscillator model of the otolith in which otolith mass is one of the parameters. However, the validity of this hypothesis is not obvious and has not been experimentally verified. We tested this hypothesis by comparing the oscillator model with a simplified spatially distributed model of the otolith. It was shown that in the case of a spatially distributed fixation of the otolith plate (otoconial layer) to the macular surface, the mechanical sensitivity of the otolith does not depend on the total otolith mass nor on its longitudinal size. It is determined by otolith thickness, the Young's modulus and viscosity of gel layer of the growing otolith. These parameters may change in order to maintain otolith sensitivity under conditions (such as growth or altered gravity) that change the dynamics of otolith movement.

Models of otolithic membrane-hair cell bundle interaction.

Transformation of the mechanical input in the chain: acceleration of otolithic membrane (OM)-displacement of the OM gel layer-deflection of hair cell bundle (HCB)-formation of the temporal pattern of polarization was studied using simplified analytical models of these stages of conversion of mechanical stimulus into the HCB electrical response. The dynamic behavior of an OM was modeled by a homogeneous viscoelastic (Kelvin-Voight body) model of the OM. Two alternative models of an 'HCB-surrounding gel' interaction corresponding to different types of the HCB were considered: (1) a model of stereocilia tip-link deformation in the case when the HCBs passively follow the gel deformation and (2) a model in which the tip-link dynamics is determined by an 'HCB-viscous fluid' interaction. It was shown that in the first model the 'HCB-OM gel' system functions as an accelerometer while in the second model it measures the time derivative of external acceleration. A simplified model of the temporal formation of cell depolarization is proposed and analyzed. Results of the modeling suggest that formation of a temporal response of the HCB to external acceleration occurs mainly due to two mutually correlated factors: the spatial dependence of gel displacement on the distance from a macular plane and the spatial distribution of stereocilia heights in the HCB.