An Idealized Model of Extrusome Ejection Through the Collapse of a Capsule

Extrusomes are extrusive organelles found in a variety of organisms, including cnidarians, dinoflagellates, and protists. These organelles typically contain a fluid-filled capsule that houses a structure, such as a coiled tubule or barb, which is rapidly ejected toward a target. Although the ejection mechanisms and morphology vary widely, a common feature is the rapid acceleration of the ejected structure through a fluid. In this paper, we develop an idealized model to simulate the collapse of an extrusome capsule, which enables the ejection of a barb or other internal structure. Specifically, we used the immersed boundary method to numerically simulate the collapse of a simplified capsule, modeled as the two sides of an elliptical shell with a flat plate along the bottom. As the capsule collapses, the elliptical sides straighten, ejecting both the internal fluid and the enclosed structure towards either free fluid or a flexible target. We investigate the effects of key model parameters, such as the size of the capsule opening. We also explore the role of the Reynolds number (Re), to consider the fluid dynamics across a range of regimes, from inertial-dominated flows relevant to some extrusome firings to viscous-dominated flows characteristic of cellular-scale processes. Our results demonstrate that decreasing the capsule opening gap size leads to increased firing velocity and shorter ejection times. Similarly, increasing the capsule's minor axis reduces the time it takes the barb to reach the target as a larger volume of fluid is moved. The relationship between Re and the time to contact is nonmonotonic, but higher Re values generally result in faster target contact, even at longer initial distances. Furthermore, we observe that higher Re values enhance the robustness of the target contact in different configurations. Finally, we quantify how the stiffness of the barb affects its ability to reach the target. We find that the large deformations of the flexible barbs slow their trajectories and that the stiffer barbs hit their targets sooner. These findings provide a foundational understanding of the biomechanics and fluid dynamics of extrusome ejection through the collapse of a capsule. The insights gained may contribute to the development of microinjectors in drug delivery, where precise and rapid mechanical movements are critical.