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Mammalian cell migration in open spaces requires F-actin polymerization and myosin contraction. While many studies have focused on myosin’s coupling to focal adhesion and stress fibers, the indirect effect of myosin contraction on cell migration through actin depolymerization is not well studied. In this work, we quantified how cell velocity and effective power output are influenced by the rate of actin depolymerization, which is affected by myosin contraction. In addition, we derived scaling laws to provide physical insights into cell migration. Model analysis shows that the cell migration velocity displays a biphasic dependence on the rate of actin depolymerization and myosin contraction. Our model further predicts that the effective cell energy output depends not only on the cell velocity but also on myosin contractility. The work has implications on in vivo processes such as immune response and cancer metastasis, where cells overcome barriers imposed by the physical environment. 

The cross-sectional area of myelinated axons increases greatly during postnatal development in mammals and is an important influence on axonal conduction velocity. This radial growth is driven primarily by an accumulation of neurofilaments, which are cytoskeletal polymers that serve a space-filling function in axons. Neurofilaments are assembled in the neuronal cell body and transported into axons along microtubule tracks. The maturation of myelinated axons is accompanied by an increase in neurofilament gene expression and a decrease in neurofilament transport velocity, but the relative contributions of these processes to the radial growth are not known. Here, we address this question by computational modeling of the radial growth of myelinated motor axons during postnatal development in rats. We show that a single model can explain the radial growth of these axons in a manner consistent with published data on axon caliber, neurofilament and microtubule densities, and neurofilament transport kinetics in vivo. We find that the increase in the cross-sectional area of these axons is driven primarily by an increase in the influx of neurofilaments at early times and by a slowing of neurofilament transport at later times. We show that the slowing can be explained by a decline in the microtubule density. 

A comparative study ( Sun et al., 2019 ) showed that the abundance of proteins at sites of endocytosis in fission and budding yeast is more similar in the two species than previously thought, yet membrane invaginations in fission yeast elongate twofold faster and are nearly twice as long as in budding yeast. Here we use a three-dimensional model of a motile endocytic invagination ( Nickaeen et al., 2019 ) to investigate factors affecting elongation of the invaginations. We found that differences in turgor pressure in the two yeast species can largely explain the paradoxical differences observed experimentally in endocytic motility. 

Neurofilaments are abundant space-filling cytoskeletal polymers in axons that are transported along microtubule tracks. Neurofilament transport is accelerated at nodes of Ranvier, where axons are locally constricted. Strikingly, these constrictions are accompanied by sharp decreases in neurofilament number, no decreases in microtubule number, and increases in the packing density of these polymers, which collectively bring nodal neurofilaments closer to their microtubule tracks. We hypothesize that this leads to an increase in the proportion of time that the filaments spend moving and that this can explain the local acceleration. To test this, we developed a stochastic model of neurofilament transport that tracks their number, kinetic state, and proximity to nearby microtubules in space and time. The model assumes that the probability of a neurofilament moving is dependent on its distance from the nearest available microtubule track. Taking into account experimentally reported numbers and densities for neurofilaments and microtubules in nodes and internodes, we show that the model is sufficient to explain the local acceleration of neurofilaments within nodes of Ranvier. This suggests that proximity to microtubule tracks may be a key regulator of neurofilament transport in axons, which has implications for the mechanism of neurofilament accumulation in development and disease.