Hamiltonian Dynamics and Structural States of Two-Dimensional Active Particles

Shoham, Yuval; Oppenheimer, Naomi

doi:10.1103/physrevlett.131.178301

Cited by 4 publications

(2 citation statements)

References 41 publications

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“…First, the force dipole, which could be divided to the rotlet, 5,21–24 and the stresslet. 25–28 Closer still, the quadrupolar term is significant, then the octopole, and so forth. 29,30 Thus, by first finding the effect of a single point-force, the so-called Green's function of the problem, we can derive the general flow response.…”

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Hydrodynamically induced aggregation of two dimensional oriented active particles

Bashan,

Oppenheimer

2024

Soft Matter

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“…Such a Hamiltonian description has been useful for point vortices in an ideal fluid 32,33 and also, more recently, in viscous systems. 26,34–37 However, this formalism only holds when ψ is an even function of r . An odd component of ψ will cancel out in the (symmetric) summation, and H would be identically zero.…”

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Hydrodynamically induced aggregation of two dimensional oriented active particles

Bashan,

Oppenheimer

2024

Soft Matter

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A first-principles geometric model for dynamics of motor-driven centrosomal asters

Young,

Gomez Herrera,

Huan

et al. 2024

Preprint

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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 a first-principles model of aster dynamics, the S-model (S for stoichiometry), 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 non-platonic 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.

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