Exogenous environmental changes are known to affect the intrinsic characteristics of biological organizms. For instance, the synthesis rate of the morphogen decapentaplegic (Dpp) in a Drosophila wing imaginal disc has been found to double with an increase of 5.9°C in ambient temprerature. If not compensated, such a change would alter the signaling Dpp gradient significantly and thereby the development of thewing imaginal disc. To learn how flies continue to develop "normally" under such an exogenous change, we formulate in this paper a spatially two-dimensional reaction-diffusion system of partial differential equations (PDE) that accounts for the biological processes at work in the Drosophila wing disc essential for the formation of signaling Dpp gradient. By way of this PDE model, we investigate the effect of the apical-basal thickness and antero-posterior span of the wing on the shape of signaling gradients and the robustness of wing development in an altered environment (including an enhanced morphogen synthesis rate). Our principal result is a delineation of the role of wing disc size change in maintaining the magnitude and shape of the signaling Dpp gradient. The result provides a theoretical basis for the observed robustness of wing development, preserving relative but not absolute tissue pattern, when the morphogen synthesis rate is significantly altered. A similar robustness considerqation for simultaneous changes of multiple intrinsic system characteristics is also discussed briefly.

In our previous work, the basilar membrane velocity V(BM) for a gerbil cochlea was calculated and compared with physiological measurements. The calculated V(BM) showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the V(BM) for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase.

The organ of Corti is the sensory epithelium in the cochlea of the inner ear. It is modeled as a shell-of-revolution structure with continuous and discrete components. Our recent work has been on the inclusion of the viscous fluid. Measurements from various laboratories provide the opportunity to refocus on the elastic properties. The current detailed model for the organ of Corti is reasonably consistent with diverse measurements. Most components have little stiffness in the propagation direction. However, the isotropic stiffness of the pillar heads is found to offer an explanation for the difference in point load and pressure measurements. The individual rows of inner hair cell stereocilia with tip links and the Hensen stripe are included, since these details are important for the determination of the neural excitation. The results for low frequency show a phase of tip link tension similar to auditory nerve measurements. The nonlinearity of fluid in the small gaps is considered. A result is that as amplitude increases, because of the near contact with the Hensen stripe, the excitation changes polarity, similar to the peak-splitting neural behavior sometimes observed.

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.