Analytical and numerical investigation of the flow past the lateral antennular flagellum of the crayfish Procambarus clarkii.

Analytical and numerical methodologies are combined to investigate the flow fields that approach and pass around the lateral flagellum of the crayfish Procambarus clarkii. Two cases are considered, the first being that of a free-flicking flagellum and the second corresponding to a flagellum fixed inside a small bore tube. The first case is the natural one while the second corresponds to the experimental configuration investigated by Mellon and Humphrey in the accompanying paper. In that study the authors observed a hydrodynamic-dependent asymmetry in the spiking responses recorded from single, bimodally sensitive local interneurons (Type I) in the crayfish deutocerebrum, whereby the direction of an abruptly initiated flow of freshwater (or odorant) past the flagellum resulted in consistently larger numbers of spikes in response to the hydrodynamic stimulation when the flow direction was proximal-to-distal. In this communication we show that the proximal-to-distal and the distal-to-proximal flows produced in the flagellum-in-tube experiment correspond closely to the flows associated with the downward and upward flicks, respectively, of a free-flicking flagellum. We also show from calculations of the drag forces acting on the putative mechanoreceptor sensilla circumferentially distributed around a free-flicking flagellum that there are at least three sources of hydrodynamic asymmetry possibly related to the electrophysiological asymmetry observed: (i) the sense of the drag forces acting on medial and lateral mechanoreceptors changes in the same way for both with change in flick direction; (ii) during a downward (an upward) flick, a ventral (dorsal) mechanoreceptor experiences a larger drag force magnitude than a dorsal (ventral) mechanoreceptor; (iii) because of the difference in speeds between downward and upward flicks, the magnitudes of the drag forces acting on medial, lateral and ventral mechanoreceptors during a downward flick are about two times larger relative to the forces acting on medial, lateral and dorsal mechanoreceptors during an upward flick. All three of these naturally occurring hydrodynamic asymmetries are correctly reproduced in the flagellum-in-tube experiment.