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1. Active spiralling of microtubules driven by kinesin motors

   https://doi.org/10.1038/s41598-025-03384-y  

   Ng’ang’a, Douglas Kagoiya; Kang’iri, Samuel Macharia; Hess, Henry; Nitta, Takahiro (December 2025, Scientific Reports)

   Cytoskeletal filaments propelled by surface-bound motor proteins can be viewed as active polymers, a class of active matter. When constraints are imposed on their movements, the propelled cytoskeletal filaments show dynamic patterns distinct from equilibrium conformations. Pinned at their leading ends, propelled microtubules or actin filaments form rotating spirals, whose shape is determined by the interplay between motor forces and the mechanics of the cytoskeletal filaments. We simulated the spiral formations of microtubules propelled by kinesin motors in an overdamped dynamics framework, which in addition to the mechanics of the spiralling microtubule explicitly includes the mechanics of kinesin motors. The simulation revealed that spiral formation was initiated by localized buckling of microtubules near the pinned ends, and the conditions for occurrence of spiral formation were summarized in a phase diagram. The radius of the formed spirals scaled with the surface motor density with an exponent of approximately − 1/4, distinct from previous theoretical and simulation studies based on implicit modelling of motor proteins. This result can be understood as a consequence of the contributions of kinesin motors to the total elastic deformation energy, highlighting the importance of mechanics of motor proteins in the behaviour of the active polymers. These findings can be useful in accurate modelling of active polymers and in designing active polymer-based applications such as molecular shuttles driven by motor proteins. 

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2. Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors

   https://doi.org/https://doi.org/10.1140/epje/s10189-021-00042-9  

   Lamson, A; Moore, J; Fang, F; Glaser, M; Shelley, M; Betterton, M (January 2021, The European physical journal)

   null (Ed.)

   In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor–filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor–filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by 103–106 compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor–filament networks on micrometer to millimeter length scales. 

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3. A design framework for actively crosslinked filament networks

   https://doi.org/https://doi.org/10.1088/1367-2630/abd2e4  

   Fuerthauer, S; Needleman, D; Shelley, M (January 2021, New journal of physics)

   null (Ed.)

   Living matter moves, deforms, and organizes itself. In cells this is made possible by networks of polymer filaments and crosslinking molecules that connect filaments to each other and that act as motors to do mechanical work on the network. For the case of highly cross-linked filament networks, we discuss how the material properties of assemblies emerge from the forces exerted by microscopic agents. First, we introduce a phenomenological model that characterizes the forces that crosslink populations exert between filaments. Second, we derive a theory that predicts the material properties of highly crosslinked filament networks, given the crosslinks present. Third, we discuss which properties of crosslinks set the material properties and behavior of highly crosslinked cytoskeletal networks. The work presented here, will enable the better understanding of cytoskeletal mechanics and its molecular underpinnings. This theory is also a first step toward a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab. 

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4. Active Condensation of Filaments Under Spatial Confinement

   https://doi.org/10.3389/fphy.2022.897255  

   Ansari, Saad; Yan, Wen; Lamson, Adam Ray; Shelley, Michael J.; Glaser, Matthew A.; Betterton, Meredith D. (June 2022, Frontiers in Physics)

   Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles. 

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5. How Cross-Link Numbers Shape the Large-Scale Physics of Cytoskeletal Materials

   https://doi.org/10.1146/annurev-conmatphys-052521-093943  

   Fürthauer, Sebastian; Shelley, Michael J. (March 2022, Annual Review of Condensed Matter Physics)

   Cytoskeletal networks are the main actuators of cellular mechanics, and a foundational example for active matter physics. In cytoskeletal networks, motion is generated on small scales by filaments that push and pull on each other via molecular-scale motors. These local actuations give rise to large-scale stresses and motion. To understand how microscopic processes can give rise to self-organized behavior on larger scales it is important to consider what mechanisms mediate long-ranged mechanical interactions in the systems. Two scenarios have been considered in the recent literature. The first scenario is systems that are relatively sparse, in which most of the large-scale momentum transfer is mediated by the solvent in which cytoskeletal filaments are suspended. The second scenario is systems in which filaments are coupled via cross-link molecules throughout. Here, we review the differences and commonalities between the physics of these two regimes. We also survey the literature for the numbers that allow us to place a material within either of these two classes. 

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