Coriolis and centrifugal forces drive haltere deformations and influence spike timing.

The halteres of flies are mechanosensory organs that serve a crucial role in the control of agile flight, providing sensory input for rapid course corrections to perturbations. Derived from hind wings, halteres are actively flapped and are thus subject to a variety of inertial forces as the fly undergoes complex flight trajectories. Previous analyses of halteres modelled them as a point mass, showing that Coriolis forces lead to subtle deflections orthogonal to the plane of flapping. By design, these models could not consider the effects of force gradients associated with a mass distribution, nor could they reveal three-dimensional spatio-temporal patterns of strain that result from those forces. In addition, diversity in the geometry of halteres, such as shape and asymmetries, could not be simply modelled with a point mass on a massless rod. To study the effects of mass distributions and asymmetries, we examine the haltere subject to both flapping and body rotations using three-dimensional finite-element simulations. We focus on a set of simplified geometries, in which we vary the stalk and bulb shape. We find that haltere mass distribution gives rise to two unreported deformation modes: (i) halteres twist with a magnitude that strongly depends on stalk and bulb geometry and (ii) halteres with an asymmetric mass distribution experience out-of-plane bending due to centrifugal forces, independent of body rotation. Since local strains at the base of the haltere drive deformations of mechanosensory neurons, we combined measured neural encoding mechanisms with our structural analyses to predict the spatial and temporal patterns of neural activity. This activity depends on both the flapping and rotation dynamics, and we show how the timing of neural activity is a viable mechanism for rotation-rate encoding. Our results provide new insights in haltere dynamics and show the viability for timing-based encoding of fly body rotations by halteres.