Studying the bending of a cell sheet in vivo, like invagination in embryos, can be complex due to a multitude of cellular processes and properties that interact with each other. Computer simulations can help to unravel this process. 2D computer simulations, however, lack the ability to take into account the effect three-dimensional properties, like endodermal plate shape and cell number, have on the shape of an embryo. Therefore, we developed a 3D cell-based model, that is able to simulate cells as separate deformable entities with a conserved cell volume. A blastula is formed by adhering the cells together as a sphere. The simulation results showed that changing individual mechanical properties, like cell stiffness, cell-cell adhesion, and the apical constriction factor, had a direct effect on the cell’s behavior and future shape. These properties influenced the ability of a cell sheet to bend and eventually change the global shape of the embryo. The observed shape transitions the endodermal region goes through during the inward bending of the cell sheet in the simulation, can give an insight into the mechanisms involved, and timing of events in biological model organisms. Changing geometrical properties (endodermal plate shape, endodermal cell number and the start position of constriction), which is not possible in 2D models, showed that the inwards bending is more dependent on the number of cells involved than on the shape of the endodermal region, and thus that the invagination process is very robust to irregularities. When qualitatively comparing our simulation results to biological data from literature, we saw that our simulations did not exactly reproduce the shapes observed in nature. This might indicate that additional mechanisms are playing a role during invagination.

Optical trapping of (sub)micron-sized particles is broadly employed in nanoscience and engineering. The materials commonly employed for these particles, however, have physical properties that limit the transfer of linear or angular momentum (or both). This reduces the magnitude of forces and torques, and the spatiotemporal resolution, achievable in linear and angular traps. Here, we overcome these limitations through the use of single-crystal rutile TiO ₂ , which has an exceptionally large optical birefringence, a high index of refraction, good chemical stability, and is amenable to geometric control at the nanoscale. We show that rutile TiO ₂ nanocylinders form powerful joint force and torque transducers in aqueous environments by using only moderate laser powers to apply nN·nm torques at kHz rotational frequencies to tightly trapped particles. In doing so, we demonstrate how rutile TiO ₂ nanocylinders outperform other materials and offer unprecedented opportunities to expand the control of optical force and torque at the nanoscale.