The bipolar organization of the microtubule-based mitotic spindle is essential for the faithful segregation of chromosomes in cell division. Despite our extensive knowledge of genes and proteins, the physical mechanism of how the ensemble of microtubules can assemble into a proper bipolar shape remains elusive. Here, we study the pathways of spindle self-organization using cell-free Xenopus egg extracts and computer-based automated shape analysis. Our microscopy assay allows us to simultaneously record the growth of hundreds of spindles in the bulk cytoplasm and systematically analyze the shape of each structure over the course of self-organization. We find that spindles that are maturing into a bipolar shape take a route that is distinct from those ending up with faulty structures, such as those of a tripolar shape. Moreover, matured structures are highly stable with little occasions of transformation between different shape phenotypes. Visualizing the movement of microtubules further reveals a fraction of microtubules that assemble between extra poles and push the poles apart, suggesting the presence of active extensile force that prevents pole coalescence. Together, we propose that a proper control over the magnitude and location of the extensile, pole-pushing force is crucial for establishing spindle bipolarity while preventing multipolarity.
We present a physical mechanism that can cause the mitotic spindle to oscillate. The driving force for this mechanism emerges from the polymerization of astral microtubules interacting with the cell cortex. We show that Brownian ratchet model for growing microtubules reaching the cell cortex, mediate an effective mass to the spindle body and therefore force it to oscillate. We compare the predictions of this mechanism with the previous mechanisms which were based on the effects of motor proteins. Finally we combine the effects of microtubules polymerization and motor proteins, and present the …
In the mitotic spindle microtubules attach to kinetochores via catch bonds during metaphase, and microtubule depolymerization forces give rise to stochastic chromosome oscillations. We investigate the cooperative stochastic microtubule dynamics in spindle models consisting of ensembles of parallel microtubules, which attach to a kinetochore via elastic linkers. We include the dynamic instability of microtubules and forces on microtubules and kinetochores from elastic linkers. A one-sided model, where an external force acts on the kinetochore is solved analytically employing a mean-field approa…
The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. …
Faithful segregation of genetic material during cell division requires alignment of chromosomes between two spindle poles and attachment of their kinetochores to each of the poles. Failure of these complex dynamical processes leads to chromosomal instability (CIN), a characteristic feature of several diseases including cancer. While a multitude of biological factors regulating chromosome congression and bi-orientation have been identified, it is still unclear how they are integrated so that coherent chromosome motion emerges from a large collection of random and deterministic processes. Here w…
The mitotic spindle lies at the heart of the spatio-temporal control over cellular components during cell division. The spindle consists of microtubules, which are not only crosslinked by motor proteins but also by passive binding proteins. These passive crosslinkers stabilize the highly dynamic mitotic spindle by generating friction forces between sliding filaments. However, it remains unclear how the friction coefficient depends on the number of crosslinkers and the size of the overlap between the microtubules. Here, we use theory and computer simulations to study the friction between two fi…
The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work towards the formation of the spindle, one of which is the `capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis wit…
Successful cell division requires a tight regulation of chromosome motion via the activity of molecular motors. Many of the key players at the origin of the forces generating the movement have been identified, but their spatial and temporal organization remains elusive. The protein complex Kinetochore on the chromosome associates with microtubules emanating from one of the spindle poles and drives the chromosome toward the pole. Chromokinesin motors on the chromosome arms also interact with microtubules, ejecting the chromosome away from the pole. In animal cells, a monooriented chromosome (as…
Assembly and stability of mitotic spindle is governed by the interplay of various intra-cellular forces, e.g. the forces generated by motor proteins by sliding overlapping anti-parallel microtubules (MTs) polymerized from the opposite centrosomes, the interaction of kinetochores with MTs, and the interaction of MTs with the chromosomes arms. We study the mechanical behavior and stability of spindle assembly within the framework of a minimal model which includes all these effects. For this model, we derive a closed--form analytical expression for the force acting between the centrosomes as a fu…
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and heavily crosslinked. Relating their large-scale dynamics to properties of their constituents remains an unsolved problem. Here we study an in vitro system made from microtubules and XCTK2 kinesin motors, which forms an aligned and active gel. Using photobleaching we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local polarity. This phenomenon is also obse…
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 anti-parallel crosslinkers, microtubule pattern goes through transition from fan-like structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To accomplish these organizations, we use polymer crowding agents. Here we study how altering the properties of the crowders, such as size, concentration, and molecular weight, a…
During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al. 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to for…
Building on the striking similarity between the structure of the spindle during mitosis in living cells and nematic textures in confined liquid crystals, we use a continuum model of two-dimensional nematic liquid crystal droplets, to examine the physical aspects of cell division. The model investigates the interplay between bulk elasticity of the microtubule assembly, described as a nematic liquid crystal, and surface elasticity of the cell cortex, modelled as a bounding flexible membrane, in controlling cell shape and division. The centrosomes at the spindle poles correspond to the cores of t…
The microtubule (MT) motor Kip3p is very processive kinesin that promotes catastrophes and pausing in particular on cortical contact. These properties explain the role of Kip3p in positioning the mitotic spindle in budding yeast and potentially other processes controlled by kinesin-8 family members. We present a theoretical approach to positioning of a MT network in a cell. In order to explore the underlying mechanism we introduce an idealized system of two MTs connected by a microtubule organizing center (MTOC). The dynamics of Kip3p is modeled by interacting stochastic particles, which allow…
Microtubules (MTs) are cytoplasmic protein polymers that are essential for fundamental cellular processes including the maintenance of cell shape, organelle transport and formation of the mitotic spindle. Microtubule dynamic instability is critical for these processes, but it remains poorly understood, in part because the relationship between the structure of the MT tip and the growth/depolymerization transitions is enigmatic. What are the functionally significant aspects of a tip structure that is capable of promoting MT growth, and how do changes in these characteristics cause the transition…
The proper positioning of the mitotic spindle is crucial for asymmetric cell division and generating cell diversity during development. Proper position in the single-cell embryo of Caenorhabditis elegans is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated centrosomal arrays of microtubules (MTs). We present here the first systematic theoretical study of how these $O(1000)$ centrosomal microtubules (MTs) interact through the immersing cytoplasm, the cell periphery and PNC, and with each other, to achieve proper position. This study is made …
In eukaryotic cells, motor proteins (MP) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules (MT) form whose stability and dynamics under the influence of MPs has been studied extensively. Although passive cross linkers (PCL) were known to provide structural stability to filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on MT overlap remains largely unexplored. Here, we formulate and cha…
