Curvature sensing as an emergent property of multiscale assembly of septins.

The ability of cells to sense and communicate their shape is central to many of their functions. Much is known about how cells generate complex shapes, yet how they sense and respond to geometric cues remains poorly understood. Septins are GTP-binding proteins that localize to sites of micrometer-scale membrane curvature. Assembly of septins is a multistep and multiscale process, but it is unknown how these discrete steps lead to curvature sensing. Here, we experimentally examine the time-dependent binding of septins at different curvatures and septin bulk concentrations. These experiments unexpectedly indicated that septins' curvature preference is not absolute but rather is sensitive to the combinations of membrane curvatures present in a reaction, suggesting that there is competition between different curvatures for septin binding. To understand the physical underpinning of this result, we developed a kinetic model that connects septins' self-assembly and curvature-sensing properties. Our experimental and modeling results are consistent with curvature-sensitive assembly being driven by cooperative associations of septin oligomers in solution with the bound septins. When combined, the work indicates that septin curvature sensing is an emergent property of the multistep, multiscale assembly of membrane-bound septins. As a result, curvature preference is not absolute and can be modulated by changing the physicochemical and geometric parameters involved in septin assembly, including bulk concentration, and the available membrane curvatures. While much geometry-sensitive assembly in biology is thought to be guided by intrinsic material properties of molecules, this is an important example of how curvature sensing can arise from multiscale assembly of polymers.

Phase behavior and surface tension of soft active Brownian particles.

We study quasi two-dimensional, monodisperse systems of active Brownian particles (ABPs) for a range of activities, stiffnesses, and densities. We develop a microscopic, analytical method for predicting the dense phase structure formed after motility-induced phase separation (MIPS) has occurred, including the dense cluster's area fraction, interparticle pressure, and radius. Our predictions are in good agreement with our Brownian dynamics simulations. We, then, derive a continuum model to investigate the relationship between the predicted interparticle pressure, the swim pressure, and the macroscopic pressure in the momentum equation. We find that formulating the point-wise macroscopic pressure as the interparticle pressure and modeling the particle activity through a spatially variant body force - as opposed to a volume-averaged swim pressure - results in consistent predictions of pressure in both the continuum model and the microscopic theory. This formulation of pressure also results in nearly zero surface tension for the phase separated domains, irrespective of activity, stiffness, and area fraction. Furthermore, using Brownian dynamics simulations and our continuum model, we showed that both the interface width and surface tension, are intrinsic characteristics of the system. On the other hand, if we were to exclude the body force induced by activity, we find that the resulting surface tension values are linearly dependent on the size of the simulation, in contrast to the statistical mechanical definition of surface tension.

Cell nucleus as a microrheological probe to study the rheology of the cytoskeleton.

Mechanical properties of the cell are important biomarkers for probing its architectural changes caused by cellular processes and/or pathologies. The development of microfluidic technologies has enabled measuring the cell's mechanical properties at high throughput so that mechanical phenotyping can be applied to large samples in reasonable timescales. These studies typically measure the stiffness of the cell as the only mechanical biomarker and do not disentangle the rheological contributions of different structural components of the cell, including the cell cortex, the interior cytoplasm and its immersed cytoskeletal structures, and the nucleus. Recent advancements in high-speed fluorescent imaging have enabled probing the deformations of the cell cortex while also tracking different intracellular components in rates applicable to microfluidic platforms. We present a, to our knowledge, novel method to decouple the mechanics of the cell cortex and the cytoplasm by analyzing the correlation between the cortical deformations that are induced by external microfluidic flows and the nucleus displacements, induced by those cortical deformations, i.e., we use the nucleus as a high-throughput microrheological probe to study the rheology of the cytoplasm, independent of the cell cortex mechanics. To demonstrate the applicability of this method, we consider a proof-of-concept model consisting of a rigid spherical nucleus centered in a spherical cell. We obtain analytical expressions for the time-dependent nucleus velocity as a function of the cell deformations when the interior cytoplasm is modeled as a viscous, viscoelastic, porous, and poroelastic material and demonstrate how the nucleus velocity can be used to characterize the linear rheology of the cytoplasm over a wide range of forces and timescales/frequencies.

Mechanics of the spindle apparatus.

During mitosis microtubules self-organize to form a bipolar mitotic spindle structure, which positions the sister chromatids on the spindle mid-plane and separates them afterwards. Previous studies have identified many spindle associated proteins. Yet, we do not fully understand how these nanoscopic proteins lead to force generation through interactions of individual microtubules, motor proteins and chromosomes, and how a large number of these local interactions ultimately determine the structure and mechanics of the spindle in micron scale. Here we review the current understanding and open questions related to the structure and mechanics of the mitotic spindle. We then discuss how a combination of electron microscopy and computational modeling can be used to tackle some of these open questions.

Hydrodynamic interactions of filaments polymerizing against obstacles.

Polymerization and depolymerization of cytoskeletal filaments against cellular structures can generate forces that are key to many cellular processes, such as cell motility and chromosomes movements during cell division. Motions generated by these forces induce global cytoplasmic flows and couple the dynamics of the polymerizing filaments and other bodies immersed in the fluid through their long-range hydrodynamic interactions (HIs). Previous theoretical and computational studies have largely ignored HIs. We use three dimensional discrete simulations to study the relationship between polymerization forces and their resulting flows and HIs. As a model system, we choose a filament that is polymerizing against an obstacle, and is embedded in a cylindrical array of parallel filaments of the same length. We consider three distinct mechanical scenarios for the filaments within the array: (a) all of the filaments are polymerizing with the same velocity; (b) they are all fixed in space, and (c) they are freely suspended. We show that each of these conditions produce their unique cytoplasmic flows and each result in differentiable polymerization forces and velocities. We also study the effect of buckling of filaments on polymerization forces and velocities and discuss the effect of HIs on the onset of buckling transition. Finally, we show that HIs result in the bundling of the buckled filaments within the array.

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network.

The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

Cytoplasmic flows as signatures for the mechanics of mitotic positioning.

The proper positioning of mitotic spindle in the single-cell Caenorhabditis elegans embryo is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated astral microtubules (MTs). Pronuclear migration produces global cytoplasmic flows that couple the mechanics of all MTs, the PNC, and the cell periphery with each other through their hydrodynamic interactions (HIs). We present the first computational study that explicitly accounts for detailed HIs between the cytoskeletal components and demonstrate the key consequences of HIs for the mechanics of pronuclear migration. First, we show that, because of HIs between the MTs, the cytoplasm-filled astral MTs behave like a porous medium, with its permeability decreasing with increasing the number of MTs. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex and the pulling of MTs by cytoplasmically bound force generators. Although achieving proper position and orientation on reasonable time scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow. We suggest that cytoplasmic flows can be used to differentiate between mechanisms.

Forces positioning the mitotic spindle: Theories, and now experiments.

The position of the spindle determines the position of the cleavage plane, and is thus crucial for cell division. Although spindle positioning has been extensively studied, the underlying forces ultimately responsible for moving the spindle remain poorly understood. A recent pioneering study by Garzon-Coral et al. uses magnetic tweezers to perform the first direct measurements of the forces involved in positioning the mitotic spindle. Combining this with molecular perturbations and geometrical effects, they use their data to argue that the forces that keep the spindle in its proper position for cell division arise from astral microtubules growing and pushing against the cell's cortex. Here, we review these ground-breaking experiments, the various biomechanical models for spindle positioning that they seek to differentiate, and discuss new questions raised by these measurements.