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The centrosomal aster is a mobile and adaptable cellular organelle that exerts and transmits forces necessary for tasks such as nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortically anchored force generators are dominant during such processes. Here, we present a comprehensive investigation of the S-model (S for stoichiometry) of aster dynamics based solely on such forces. The model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the stability of centering of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in single-cell nematode embryos, we use highly accurate simulations to examine the nonlinear structures of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. We find a generally rich dynamical landscape, dependent upon cell shape, such as internal constant-velocity equatorial orbits of asters that can be seen as traveling wave solutions. Finally, we study the interactions of multiple asters which we demonstrate an effective mutual repulsion due to their competition for surface force generators. We find, amazingly, that centrosomes can relax onto the vertices of platonic and nonplatonic solids, very closely mirroring the results of the classical Thomson problem for energy-minimizing configurations of electrons constrained to a sphere and interacting via repulsive Coulomb potentials. Our findings both explain experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics, and show the possibility of new nonlinear phenomena in cell biology. Published by the American Physical Society2025 

Nucleocytoplasmic transport is essential for cellular function, presenting a canonical example of rapid molecular sorting inside cells. It consists of a coordinated interplay between import/export of molecules in/out the cell nucleus. Here, we investigate the role of spatiotemporal dynamics of the nucleocytoplasmic transport and its regulation. We develop a biophysical model that captures the main features of the nucleocytoplasmic transport, in particular, its regulation through the Ran cycle. Our model yields steady-state profiles for the molecular components of the Ran cycle, their relaxation times, as well as the nuclear-to-cytoplasmic molecule ratio. We show that these quantities are affected by their spatial dynamics and heterogeneity within the nucleus. Specifically, we find that the spatial nonuniformity of Ran guanine exchange factor (RanGEF)—particularly its proximity to the nuclear envelope—increases the Ran content in the nucleus. We further show that RanGEF's accumulation near the nuclear envelope results from its intrinsic dynamics as a nuclear cargo, transported by the Ran cycle itself. Overall, our work highlights the critical role of molecular spatial dynamics in cellular processes and proposes new avenues for theoretical and experimental inquiries into the nucleocytoplasmic transport. Published by the American Physical Society2024 

Vorticity, a measure of the local rate of rotation of a fluid element, is the driver of incompressible flow. In viscous fluids, powering bulk flows requires the continuous injection of vorticity from boundaries to counteract the diffusive effects of viscosity. Here we power a flow from within by suspending approximately cylindrical particles and magnetically driving them to rotate at Reynolds numbers in the intermediate range. We find that a single particle generates a localized three-dimensional region of vorticity around it—which we call a vortlet—that drives a number of remarkable behaviours. Slight asymmetries in the particle shape can deform the vortlet and cause the particle to self-propel. Interactions between vortlets are similarly rich, generating bound dynamical states. When a large number of vortlets interact, they spontaneously form collectively moving flocks. These flocks remain coherent while propelling, splitting and merging. If enough particles are added so as to saturate the flow chamber, a homogeneous three-dimensional active chiral fluid of vortlets is formed, which can be manipulated with gravity or flow chamber boundaries, leading to lively collective dynamics. Our findings demonstrate an inertial regime for synthetic active matter, provide a controlled physical system for the quantitative study of three-dimensional flocking in non-sentient systems and establish a platform for the study of three-dimensional active chiral fluids. 

We provide a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, relying on principles of the kinematics of line elements. 

We re-examine the model proposed by Alexanderet al.(Phys. Fluids, vol. 18, 2006, 062103) for the closing of a circular hole in a molecularly thin incompressible Langmuir film situated on a Stokesian subfluid. For simplicity their model assumes that the surface phase is inviscid which leads to the result that the cavity area decreases at a constant rate determined by the ratio of edge tension to subfluid viscosity. We reformulate the problem, allowing for a regularising monolayer viscosity. The viscosity-dependent corrections to the hole dynamics are analysed and found to be non-trivial, even when the monolayer viscosity is small; these corrections may explain the departure of experimental data from the theoretical prediction when the hole radius becomes comparable to the Saffman–Delbrück length. Through fitting, under these relaxed assumptions, we find the edge tension could be as much as six times larger ($$\sim$$4.0 pN) than reported previously.