Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization

Effects of microtubule length and crowding on active microtubule network organization

Active filament networks can organize into various dynamic architectures driven by cross-linking motors. Densities and kinetic properties of motors and microtubules have been shown previously to determine active microtubule network self-organization, but the effects of other control parameters are less understood. Using computer simulations, we study here how microtubule lengths and crowding effects determine active network architecture and dynamics. We find that attractive interactions mimicking crowding effects or long microtubules both promote the formation of extensile nematic networks instead of asters. When microtubules are very long and the network is highly connected, a new isotropically motile network state resembling a "gliding mesh" is predicted. Using in vitro reconstitutions, we confirm the existence of this gliding mesh experimentally. These results provide a better understanding of how active microtubule network organization can be controlled, with implications for cell biology and active materials in general.

Length Regulation Drives Self-Organization in Filament-Motor Mixtures

Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.

Cross-linker design determines microtubule network organization by opposing motors

Inheritance of genetic material following chromosome duplication in eukaryotic cell division is coordinated by the spindle apparatus. The spindle is a highly interconnected network of microtubule filaments that are cross-linked by different types of molecular motors. How the different motors cooperate to organize the spindle network is not understood. Here, we show that an asymmetric cross-linker design can confer bifunctionality to a mitotic motor in the presence of other motors. The asymmetric motor supports both extensile and contractile microtubule network behaviors as observed in different parts of the spindle. These findings define rules controlling the generation of active microtubule networks and allow us to better understand how motors cooperate to organize the correct spindle architecture when a cell divides.

During cell division, cross-linking motors determine the architecture of the spindle, a dynamic microtubule network that segregates the chromosomes in eukaryotes. It is unclear how motors with opposite directionality coordinate to drive both contractile and extensile behaviors in the spindle. Particularly, the impact of different cross-linker designs on network self-organization is not understood, limiting our understanding of self-organizing structures in cells but also our ability to engineer new active materials. Here, we use experiment and theory to examine active microtubule networks driven by mixtures of motors with opposite directionality and different cross-linker design. We find that although the kinesin-14 HSET causes network contraction when dominant, it can also assist the opposing kinesin-5 KIF11 to generate extensile networks. This bifunctionality results from HSET’s asymmetric design, distinct from symmetric KIF11. These findings expand the set of rules underlying patterning of active microtubule assemblies and allow a better understanding of motor cooperation in the spindle.

Actin network architecture can ensure robust centering or sensitive decentering of the centrosome

The orientation of cell polarity depends on the position of the centrosome, the main microtubule-organizing center (MTOC). Microtubules (MTs) transmit pushing forces to the MTOC as they grow against the cell periphery. How the actin network regulates these forces remains unclear. Here, in a cell-free assay, we used purified proteins to reconstitute the interaction of a microtubule aster with actin networks of various architectures in cell-sized microwells. In the absence of actin filaments, MTOC positioning was highly sensitive to variations in microtubule length. The presence of a bulk actin network limited microtubule displacement, and MTOCs were held in place. In contrast, the assembly of a branched actin network along the well edges centered the MTOCs by maintaining an isotropic balance of pushing forces. An anisotropic peripheral actin network caused the MTOC to decenter by focusing the pushing forces. Overall, our results show that actin networks can limit the sensitivity of MTOC positioning to microtubule length and enforce robust MTOC centering or decentering depending on the isotropy of its architecture.

Crowder and surface effects on self-organization of microtubules

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

Micron-scale geometrical features of microtubules as regulators of microtubule organization

The organization of micron-sized, multi-microtubule arrays from individual microtubules is essential for diverse cellular functions. The microtubule polymer is largely viewed as a passive building block during the organization process. An exception is the 'tubulin code' where alterations to tubulin at the amino acid level can influence the activity of microtubule-associated proteins. Recent studies reveal that micron-scale geometrical features of individual microtubules and polymer networks, such as microtubule length, overlap length, contact angle, and lattice defects, can also regulate the activity of microtubule-associated proteins and modulate polymer dynamics. We discuss how the interplay between such geometrical properties of the microtubule lattice and the activity of associated proteins direct multiple aspects of array organization, from microtubule nucleation and coalignment to specification of array dimensions and remodeling of dynamic networks. The mechanisms reviewed here highlight micron-sized features of microtubules as critical parameters to be routinely investigated in the study of microtubule self-organization.

Collective and contractile filament motions in the myosin motility assay

Cells require mechanical forces for their physiological functions. The forces are generated mainly from molecular interactions between actin filaments, cross-linking proteins, and myosin motors in the actin cytoskeleton. To better understand the molecular interactions, many studies employed myosin motility assays with actin filaments propelled by myosin heads fixed on a surface. Various interesting behaviors of actin filaments have been observed in the motility assay experiments. Despite the popularity of the motility assays, there were only a few computational models designed for simulating the motility assay systems. Most of the previous models have limitations which precluded full understanding of molecular origins for behaviors of actin filaments. In this study, we used an agent-based computational model based on Brownian dynamics for simulating the motility assay system. Our model rigorously describes the mechanics, dynamics, and interactions of actin filaments, cross-linking proteins, and molecular motors. Using the model, we first investigated how properties of actin filaments and motors affect gliding motions of actin filaments without volume-exclusion effects as a base study. We found that actin filaments can continuously glide at relative fast speed only when they are sufficiently longer than the average spacing between neighboring motors and that the gliding speed of F-actins shows a biphasic dependence on processivity of motors. Then, we showed that volume-exclusion effects between actin filaments can induce diverse collective movements and alignment of actin filaments, thus creating thick bundles and ring-like structures in the absence of cross-linking proteins. Lastly, we demonstrated that cross-linking proteins can lead to distinct contractile behaviors of actin networks depending on the density and kinetics of the cross-linking proteins. Results from our study show the ability of our model to simulate the motility assay system under various conditions and provide insights into understanding of different behaviors of actin filaments.

Mimicking Sub-Structures Self-Organization in Microtubules

Microtubules (MTs) are highly dynamic polymers distributed in the cytoplasm of a biological cell. Alpha and beta globular proteins constituting the heterodimer building blocks combine to form these tubules through polymerization, controlled by the concentration of Guanosine-triphosphate (GTPs) and other Microtubule Associated Proteins (MAPs). MTs play a crucial role in many intracellular processes, predominantly in mitosis, organelle transport and cell locomotion. Current research in this area is focused on understanding the exclusive behaviors of self-organization and their association with different MAPs through organized laboratory experiments. However, the intriguing intelligence behind these tiny machines resulting in complex self-organizing structures is mostly unexplored. In this study, we propose a novel swarm engineering framework in modeling rules for these systems, by combining the principles of design with swarm intelligence. The proposed framework was simulated on a game engine and these simulations demonstrated self-organization of rings and protofilaments in MTs. Analytics from these simulations assisted in understanding the influence of GTPs on protofilament formation. Also, results showed that the population density of GTPs rather than their bonding probabilities played a crucial role in polymerization in forming microtubule substructures.

Remarkable structural transformations of actin bundles are driven by their initial polarity, motor activity, crosslinking, and filament treadmilling

Bundled actin structures play a key role in maintaining cellular shape, in aiding force transmission to and from extracellular substrates, and in affecting cellular motility. Recent studies have also brought to light new details on stress generation, force transmission and contractility of actin bundles. In this work, we are primarily interested in the question of what determines the stability of actin bundles and what network geometries do unstable bundles eventually transition to. To address this problem, we used the MEDYAN mechano-chemical force field, modeling several micron-long actin bundles in 3D, while accounting for a comprehensive set of chemical, mechanical and transport processes. We developed a hierarchical clustering algorithm for classification of the different long time scale morphologies in our study. Our main finding is that initially unipolar bundles are significantly more stable compared with an apolar initial configuration. Filaments within the latter bundles slide easily with respect to each other due to myosin activity, producing a loose network that can be subsequently severely distorted. At high myosin concentrations, a morphological transition to aster-like geometries was observed. We also investigated how actin treadmilling rates influence bundle dynamics, and found that enhanced treadmilling leads to network fragmentation and disintegration, while this process is opposed by myosin and crosslinking activities. Interestingly, treadmilling bundles with an initial apolar geometry eventually evolve to a whole gamut of network morphologies based on relative positions of filament ends, such as sarcomere-like organization. We found that apolar bundles show a remarkable sensitivity to environmental conditions, which may be important in enabling rapid cytoskeletal structural reorganization and adaptation in response to intracellular and extracellular cues.