A theoretical model of cytokinesis implicates feedback between membrane curvature and cytoskeletal organization in asymmetric cytokinetic furrowing

During cytokinesis, the cell undergoes a dramatic shape change as it divides into two daughter cells. Cell shape changes in cytokinesis are driven by a cortical ring rich in actin filaments and nonmuscle myosin II. The ring closes via actomyosin contraction coupled with actin depolymerization. Of interest, ring closure and hence the furrow ingression are nonconcentric (asymmetric) within the division plane across Metazoa. This nonconcentricity can occur and persist even without preexisting asymmetric cues, such as spindle placement or cellular adhesions. Cell-autonomous asymmetry is not explained by current models. We combined quantitative high-resolution live-cell microscopy with theoretical modeling to explore the mechanistic basis for asymmetric cytokinesis in the Caenorhabditis elegans zygote, with the goal of uncovering basic principles of ring closure. Our theoretical model suggests that feedback among membrane curvature, cytoskeletal alignment, and contractility is responsible for asymmetric cytokinetic furrowing. It also accurately predicts experimental perturbations of conserved ring proteins. The model further suggests that curvature-mediated filament alignment speeds up furrow closure while promoting energy efficiency. Collectively our work underscores the importance of membrane–cytoskeletal anchoring and suggests conserved molecular mechanisms for this activity

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

Mechanics of the cellular actin cortex: from signalling to shape change

The actin cortex is a thin layer of actin, myosin, and actin binding proteins that underlies the membrane of most animal cells. It is highly dynamic and can undergo remodelling on time-scales of tens of seconds thanks to protein turnover and myosin-mediated contractions. The cortex enables cells to resist external mechanical stresses, controls cell shape, and allows cells to exert forces on their neighbours. Thus, its mechanical properties are key to its physiological function. Here, we give an overview of how cortex composition, structure, and dynamics control cortex mechanics and cell shape. We use mitosis as an example to illustrate how global and local regulation of cortex mechanics give rise to a complex series of cell shape changes.Comment: Revie

Myo2 Motor Function in the Contractile Ring and the Regulation of Fission Yeast Cytokinesis

Animals, fungi, and amoebas require an actomyosin contractile ring at the division site to perform cytokinesis. The contractile ring initiates and guides the invagination of the plasma membrane as it forms new barriers between the nuclei at the cell equator. Defects in the contractile ring can result in misdirected, delayed, or premature cytokinesis, which leads to abnormal chromosome numbers. Aneuploidies resulting from failed cytokinesis sometimes lead to aggressive forms of cancer. This dissertation was motivated by the goal of better understanding the properties of the contractile ring and how it drives cytokinesis. Actomyosin is initially recruited to the cell equator through the coordination of scaffolding factors, actin-binding proteins, and signaling cascades. Subsequently, the sliding of actin filaments by myosin reshapes the resulting meshwork into a compact ring. Once fully assembled, the contractile ring establishes tension, which leads the plasma membrane inward. The primary motor proteins in the contractile ring of animal cells are class-II nonmuscle myosins, which typically function as bipolar filaments. Filament assembly is activated by phosphorylation and plays a central role in myosin function during cytokinesis. However, many underlying processes that regulate contractile ring function are poorly understood. Current models of cytokinesis have been based on mechanistic insights provided by two decades of work in the fission yeast system Schizosaccharomyces pombe. In fission yeast, the class-II myosin Myo2 provides the major source of motor activity in the contractile ring. Myo2 is two-headed and has a rod-like tail, which is consistent with other class-II myosins. Yet, it was unknown whether Myo2 assembles into filaments, or how phosphorylation affects its activity. To investigate these features, recombinant Myo2 was purified from the baculovirus/Sf9 insect cell expression system. Hydrodynamic measurements were used to examine whether Myo2 forms filaments. These sedimentation velocity data gave no indication that Myo2 self-assembles under the typical physiological salt concentrations, which suggests that Myo2 is unlike any class-II myosin known to date. Myo2 was also treated in vitro with its native kinase Pak1. Phosphorylation of Myo2 molecules had no effect on self-assembly, however it reduced actin-binding in motility assays and increased steady-state ATPase rates by two fold. Our results imply that the function and regulation of fission yeast Myo2 during cytokinesis depends on a specific scaffolding scheme at the plasma membrane, which has not been observed in other eukaryotes. Another interest of this dissertation was how the contractile ring is regulated during cytokinesis. We examined one cytokinesis protein, Cyk3, believed to mediate between the ring and extracellular processes. Genetics and live cell imaging analyses indicated that Cyk3 functions through a catalytically-inactive enzyme domain, which implicated Cyk3\u27s involvement in one of the primary cytokinesis signaling pathways. This dissertation sheds new light on core aspects of how fission yeast undergo cytokinesis, especially with respect to the mechanism of Myo2 activity in the contractile ring. Characterizing the physical and enzymatic properties of an essential myosin in a simple organism should provide insights into cytokinesis in higher organisms

Characterizing cortical myosin mini-filament regulation, length and its macroscopic implications in cytokinetic dynamics

Au cours de la cytokinèse, le génome dédoublé est compartimentalisé en deux cellules filles. L’anneau contractile, une structure dynamique, est constitué d’actine, myosine (NMY-II) et d’autres protéines accessoires. NMY-2 est le seul moteur protéique impliqué dans la contraction de l’anneau durant la cytokinèse. Depuis longtemps, il a été considéré que celle-ci glissait le long des filaments d’actine grâce à sa capacité de traction. Récemment, plusieurs études ont découvert que son activité réticulante joue un rôle en cytokinèse et il est connu que la NMY-2 peut s’assembler en filaments bipolaires à partir de dimères. Ainsi, nous postulons que leur dimension (nombre de moteurs ATPasiques) pourrait dicter leur contribution en activité motrice et réticulante. Afin de déterminer la composition des filaments corticaux de NMY-2, nous avons utilisé une technique d'imagerie de molécules individuelles à l’aide de la microscopie TIRF. J’ai trouvé à travers l’analyse statistique de la distribution des NMY-2 mesurés que les filaments sont assemblés à deux dimensions constantes: Des filaments composés de 20 dimères et 30 dimères. La kinase Rho est une activatrice de NMY-2 nécessaire pour les niveaux physiologiques de NMY-2 sur l’anneau contractile, pour des cinétiques et fermeture concentrique de l’anneau. La déplétion de RhoK augmente l’abondance relative des filaments de 20 dimères. Ainsi, RhoK pourrait réguler le recrutement de la NMY et aussi l’assemblage des filaments corticaux de NMY-2. De plus, à l’aide de la microscopie confocale à temps réel, j’ai trouvé que lors de la déplétion de RhoK, il se produit une réduction du recrutement et du délai d’initiation du sillon, une fermeture lente et une augmentation significative de la concentricité de l’anneau. De plus, j’ai mesuré des défauts dans l’organisation corticale de l’anneau contractile en patch. La déplétion de MRCK-1 n’affecte pas l’initiation du sillon, les cinétiques de fermeture, ou la fermeture concentrique de l’anneau. Paradoxalement, la déplétion de MRCK-1 augmente le recrutement cortical de NMY-2, mais quand depleté simultanément avec Rho-K il diminue NMY-2 à l’équateur comparé à la déplétion seule de Rho-K. De plus, la double déplétion, conduit à un phénotype de concentricité de l’anneau, suivie d’un recentrage.Non-muscle myosin II (myosin) is important for many cellular processes, including cytokinesis. Myosin is a major component of the contractile ring, which constricts to close the connection between the two daughter cells. It was long accepted that actomyosin contractile filament sliding closes the cytokinetic ring. However, several recent papers conclude that myosin’s actin crosslinking activity is more important than its motor activity. These two functions likely relate to the number of actin-binding heads per bipolar myosin mini-filament. I then measured the size of cortical bipolar myosin mini-filaments and tested how mini-filament size and abundance influences cytokinesis. To measure the composition of individual myosin-containing cortical features, I developed a TIRF microscopy-based assay to calculate the number of NMY-2 dimers per feature from a ratio of endogenous/functional NMY-2-GFP. Interestingly control cells possess 2 populations: mini-filaments with an average of 20 dimers and with 30 dimers that are built to consistent specifications. Depletion of the NMY-2 activator Rho-Kinase or Anillin, a contractile ring scaffold protein, significantly alters the relative abundance of small and larger NMY-2 filament populations. I then tested the macroscopic implications of perturbations that alter cortical NMY-2 assembly. I measured NMY-2 regulators depleted cells and measured NMY-2 cortical recruitment, organization, and the kinetics (speed and concentricity) of cytokinesis. Rho-K depletion decreases NMY-II cortical recruitment and organization, slows ring closure and makes it more concentric. Depletion of MRCK-1, a less well-understood conserved myosin kinase, increased myosin cortical recruitment but had little effect on furrowing kinetics. Following simultaneous depletion of MRCK and RhoK, cortical myosin organization and recruitment were drastically reduced and, as expected for a much weaker cortex, a unique concentric phenotype emerged. Thus, while Rho-kinase is the more important kinase for myosin activation, MRCK-1 contributes to myosin organization and contractile ring dynamics. We conclude that myosin is recruited to the cortex as multi-headed mini-filaments whose assembly is tightly regulated and which impacts several aspects of contractile ring function

Mechanical Regulation in Cell Division and in Neurotransmitter Release

During their lifecycle, cells must produce forces which play important roles in several subcellular processes. Force-producing components are organized into macromolecular assemblies of proteins that are often dynamic, and are constructed or disassembled in response to various signals. The forces themselves may directly be involved in subcellular mechanics, or they may influence mechanosensing proteins either within or outside these structures. These proteins play different roles: they may ensure the stability of the force-producing structure, or they may send signals to a coupled process. The generation and sensing of subcellular forces is an active research topic, and this thesis focusses on the roles of these forces in two key areas: cell division and neurotransmitter release. The first part of the thesis deals with the effect of force on cell wall growth regulation during division in the fission yeast Schizosaccharomyces pombe, a cigar-shaped, unicellular organism. During cytokinesis, the last stage of cell division in which the cell physically divides into two, a tense cytokinetic ring anchored to the cellular membrane assembles and constricts, accompanied by the inward centripetal growth of new cell wall, called septum, in the wake of the inward-moving membrane. The contour of the septum hole maintains its circularity as it reduces in size—an indication of regulated growth. To characterize the cell wall growth process, we performed image analysis on contours of the leading edge of the septum obtained via fluorescence microscopy in the labs of our collaborators. We quantified the deviations from circularity using the edge roughness. The roughness was spatially correlated, suggestive of regulated growth. We hypothesized that the cell wall growers are mechanosensitive and respond to the force exerted by the ring. A mathematical model based on this hypothesis then showed that this leads to corrections of roughness in a curvature-dependent fashion. Thus, one of the roles of ring tension is to communicate with the mechanosensitive septum growth processes and coordinate growth to ensure the daughter cells have a functional cell wall. The second part of the thesis deals with how ring tension is produced and sustained, using experimentally measured ultrastructure of the cytokinetic ring itself. Recent super-resolution experiments have revealed that several key proteins of the fission yeast constricting ring are organized into membrane-anchored complexes called nodes. The force producing protein myosin-II in these nodes exerts pulling forces on polymeric actin filaments that are synthesized from polymerizers residing in the nodes. How these forces are marshalled to generate ring tension, and how such an organization maintains its stability is unclear. Using a mathematical model with coarse-grained representations of actin and myosin, we showed that such a node-based organization reproduces previously measured ring tension values. The model explains the origin of experimentally observed bidirectional motion of the nodes in the ring, and showed that turnover of the nodes rescues the ring from inherent contractile instabilities that would be expected when a force-producing structure is made up of small object that effectively attract one another. Finally, the third part of the thesis deals with the role of forces produced by SNARE proteins at synapses between two neurons during neurotransmission. A key step here is synaptic release, where inside a neuron, membrane-bound compartments called vesicles filled with neurotransmitter fuse with the membrane of the neuron forming a transient fusion pore, and release their contents to the outside of the cell. These neurotransmitter molecules are sensed by another neuron that is physically separate from the neuron in question and this neuron propagates the signal henceforth. Thus, regulation of neurotransmitter release is a key step in neurotransmission. A fusion machinery consisting of several proteins facilitates membrane fusion, and pore nucleation requires the formation of a SNARE protein complex in this machinery, whose role during pore dilation is unclear. Using electrophysiological measurements, our collaborators experimentally measured the statistics of the size of single fusion pores in vitro, and observed that average pore sizes increased with the number of SNARE proteins. Using mathematical modeling, we showed that this effect was due to an entropic crowding force that expands the pore and increases with the number of SNAREs, and counteracts the energy barrier to fusion pore expansion

Chiral flows can induce neck formation in viscoelastic surfaces

During division in animal cells, the actomyosin cortex has been found to exhibit counter-rotating cortical flows, also known as chiral flows, along the axis of division. Furthermore, such chiral surface flows were shown to influence cellular rearrangements and drive the left-right symmetry breaking in developing organisms. In spite of this prospective biological importance, at the current state, no numerical simulations have been done to study the influence of chiral flows on the cell cortex shape. To deepen the insight on that matter, we present here a numerical study of an axi-symmetric viscoelastic surface embedded in a viscous fluid. To investigate the influence of a chiral flow field on the surface shape and material transport, we impose a generic counter-rotating force field on this surface which induces a chiral flow field. Notably, we find that the building of a neck, as is observed during cell division, occurs if there is a strong shear elastic component. Furthermore we find that a large areal relaxation time results in flows towards the equator of the surface. These flows assist the transport of a surface concentration during the forming of a contractile ring. Accordingly, we show that chiral forces by themselves can drive pattern formation and stabilise contractile rings at the equator.Comment: 13 pages, 5 pages for appendix, 6 figure

Shaping plant microtubule networks via overlap formation

Microtubules are long filaments made up from protein building blocks and ubiquitously employed by eukaryotic cells for a wide range of often essential cellular processes. To perform these functions, microtubules are virtually always organized into higher order networks. Microtubule networks in cells of land plants are fundamental for guiding growth processes and for bringing about their unique mode of cell division. The latter is facilitated by the so‑called phragmoplast network, consisting of two opposing sets of microtubules that foster in their centre the formation and radial outgrowth of a disc-shaped membrane compartment (termed the cell plate) that ultimately divides the two daughter cells. The mechanisms driving the spatial organisation of such networks are of outstanding interest because plant cells do not rely on major microtubule organizers as in most other organisms. Instead, plant cells use a wide range of dispersed interactions among individual microtubules to shape functional microtubule networks. Chapter 1 introduces encounters between microtubules of opposite polarity and consequent bundling as potentially powerful handles to organize microtubules into networks. These encounters generate an area of antiparallel microtubule overlap and such overlaps are a striking feature of the phragmoplast microtubule network. For long it is recognized that the short overlaps formed among the two opposing sets of phragmoplast microtubules and the membranous structures of the cell plate fall within the same plane. In chapter 2 we hypothesize that the limited length of these overlaps is required for the confined accumulation of cell plate membranes. To investigate this, we start out by co-visualizing overlaps and cell-plate membrane material in living cells of the moss Physcomitrella patens, an emerging model plant system with a convenient genetic toolset and tissues readily observable through microscopy. We reaffirm an early association between overlaps and membranes and further explored this association by experimentally altering overlap length. Incited by length control mechanisms of overlaps in animal cells, we identify two kinesin-4 motor proteins that jointly limit the length of phragmoplast microtubule overlaps in moss. Using cells lacking these kinesin-4s we then show that over-elongation of microtubule overlaps leads to a broadening of initial cell plate membrane depositions and a delayed progression of radial cell plate outgrowth. The cross walls ultimately formed by the wider membrane depositions were found to be thick and irregularly shaped. We thus demonstrate that kinesin-4-dependent overlap shortening in the phragmoplast defines the site of cell plate synthesis for the proper scaffolding of a new cell wall segment separating two daughter cells. In chapter 3 we further investigate molecular mechanisms that could explain how linkage between a microtubule overlap and membrane assembly activity is realized. We focus on the exocyst tethering complex, one of the membrane tethering complexes involved in cell plate formation in flowering plants. We survey the localization of several moss exocyst subunits during cell division and find that one (Sec6) localizes to microtubule overlaps already before the onset of cell plate biogenesis. Experiments in which overlap length is altered and overlap formation is suppressed reveal that these structures play an important role in positioning Sec6 during cell division. The ability of moss Sec6 to interact with an evolutionary conserved factor in cell plate membrane fusion called KEULE is demonstrated, signifying a potential functional link between membrane tethering and fusion activities during cell plate formation. The precise role of Sec6 positioning by overlaps is as yet unclear, but in the light of the importance of overlaps for spatial control of cytokinesis will prove to be an intriguing direction for future research efforts. In chapter 4 we gain further mechanistic insight in kinesin-4 mediated overlap length control and governance of division apparatus length as a whole. We focus on microtubule growth in overlaps regulated by kinesin-4, the poleward transport of microtubule polymers (termed flux), and the interplay between these processes. First, a method based on localized photo-activation is established for the quantitative assessment of microtubule flux. We demonstrate that initially flux in the metaphase spindle occurs synchronized and at high rates, to be replaced by a heterogeneous and on average much slower microtubule flux in the phragmoplast. Since polymerisation of microtubules could provide direct fuel for flux, we postulate that the rate of microtubule growth at sites of overlap could determine flux rates. To test this, we experimentally enhance polymerisation rates through knock-out of kinesin-4 proteins. This approach is validated by experiments demonstrating that they can supress microtubule outgrowth at overlaps in an in vivo setting. Upon kinesin-4 removal, flux rates are enhanced signifying coupling to rates of polymerization. We also find that lack of kinesin-4s leads elongation of the entire division apparatus and that this length change is proportional to the temporal activity patterns of the two kinesin-4s. Based on these findings we propose a mechanism for length regulation through a balance of microtubule growth in the overlap zone, retrograde microtubule translocation and putatively microtubule breakdown at the poles. Microtubule turnover in this system is high in the metaphase spindle (~1.5 μm/min), which, partly through kinesin-4 action, is succeeded by a more slowly turning over system in the form of the phragmoplast. While in general the involvement of antiparallel microtubule overlaps in spatial organization of bipolar microtubule configurations is evident, how they could help shape other geometries is largely unknown. Chapter 5 starts out with the observation that within the unipolarized microtubule array of tip growing moss cells during interphase, there is occasional formation of overlaps at dispersed sites in the network. Tip growth is a mode of growth allowing rapid colonization of the environment and is achieved through highly polarized secretion, whereby the microtubule network reportedly steers the grows axis. We identify one kinesin-4 motor (Kin4-Ia) recruited to the observed overlaps within this network and use knock-out of Kin4-Ia to assess its role in tip growth. This reveals that absence of Kin4-Ia leads to a less adaptable axis of tip growth, prompting further investigation of Kin4-Ia behaviour at interphase overlaps. We find that this kinesin-4 is recruited with a slight delay to overlaps after their formation and inhibits plus end polymerization of overlap microtubules, thereby limiting overlap length. We then uncover that this activity helps to keep the network polarized towards the tip and prevent the overall organization from becoming hyperaligned with the cell axis. We propose that the latter observation might explain the decrease in growth axis adaptability. Overall, this thesis demonstrates that in plant microtubule networks of varying architecture, the formation of antiparallel overlaps provides a defined network feature for the recruitment of other microtubule-based process. Together, overlaps and activities coordinated from there, are potent organizers of functional plant microtubule arrays. The potential wider implications of these findings, their relationship to membrane-bound cytokinetic processes, and their evolutionary context are briefly discussed in Chapter 6.</p