Sean X. Sun

MinC Spatially Controls Bacterial Cytokinesis by Antagonizing the Scaffolding Function of FtsZ

BACKGROUND Cytokinesis in bacteria is mediated by a cytokinetic ring, termed the Z ring, which forms a scaffold for recruitment of other cell-division proteins. The Z ring is composed of FtsZ filaments, but their organization in the Z ring is poorly understood. In Escherichia coli, the Min system contributes to the spatial regulation of cytokinesis by preventing the assembly of the Z ring away from midcell. The effector of the Min system, MinC, inhibits Z ring assembly by a mechanism that is not clear. RESULTS Here, we report that MinC controls the scaffolding function of FtsZ by antagonizing the mechanical integrity of FtsZ structures. Specifically, MinC antagonizes the ability of FtsZ filaments to be in a solid-like gel state. MinC is a modular protein whose two domains (MinC(C) and MinC(N)) synergize to inhibit FtsZ function. MinC(C) interacts directly with FtsZ polymers to target MinC to Z rings. MinC(C) also prevents lateral interactions between FtsZ filaments, an activity that seems to be unique among cytoskeletal proteins. Because MinC(C) is inhibitory in vivo, it suggests that lateral interactions between FtsZ filaments are important for the structural integrity of the Z ring. MinC(N) contributes to MinC activity by weakening the longitudinal bonds between FtsZ molecules in a filament leading to a loss of polymer rigidity and consequent polymer shortening. On the basis of our results, we develop the first computational model of the Z ring and study the effects of MinC. CONCLUSIONS Control over the scaffolding activity of FtsZ probably represents a universal regulatory mechanism of bacterial cytokinesis.

A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells

Tissue cells sense and respond to the stiffness of the surface on which they adhere. Precisely how cells sense surface stiffness remains an open question, though various biochemical pathways are critical for a proper stiffness response. Here, based on a simple mechanochemical model of biological friction, we propose a model for cell mechanosensation as opposed to previous more biochemically based models. Our model of adhesion complexes predicts that these cell-surface interactions provide a viscous drag that increases with the elastic modulus of the surface. The force-velocity relation of myosin II implies that myosin generates greater force when the adhesion complexes slide slowly. Then, using a simple cytoskeleton model, we show that an external force applied to the cytoskeleton causes actin filaments to aggregate and orient parallel to the direction of force application. The greater the external force, the faster this aggregation occurs. As the steady-state probability of forming these bundles reflects a balance between the time scale of bundle formation and destruction (because of actin turnover), more bundles are formed when the cytoskeleton time-scale is small (i.e., on stiff surfaces), in agreement with experiment. As these large bundles of actin, called stress fibers, appear preferentially on stiff surfaces, our mechanical model provides a mechanism for stress fiber formation and stiffness sensing in cells adhered to a compliant surface.

Condensation of FtsZ filaments can drive bacterial cell division

Forces are important in biological systems for accomplishing key cell functions, such as motility, organelle transport, and cell division. Currently, known force generation mechanisms typically involve motor proteins. In bacterial cells, no known motor proteins are involved in cell division. Instead, a division ring (Z-ring) consists of mostly FtsZ, FtsA, and ZipA is used to exerting a contractile force. The mechanism of force generation in bacterial cell division is unknown. Using computational modeling, we show that Z-ring formation results from the colocalization of FtsZ and FtsA mediated by the favorable alignment of FtsZ polymers. The model predicts that the Z-ring undergoes a condensation transition from a low-density state to a high-density state and generates a sufficient contractile force to achieve division. FtsZ GTP hydrolysis facilitates monomer turnover during the condensation transition, but does not directly generate forces. In vivo fluorescence measurements show that FtsZ density increases during division, in accord with model results. The mechanism is akin to van der Waals picture of gas-liquid condensation, and shows that organisms can exploit microphase transitions to generate mechanical forces.

Mapping Local Matrix Remodeling Induced by a Migrating Tumor Cell Using Three-Dimensional Multiple-Particle Tracking

Mesenchymal cell migration through a three-dimensional (3D) matrix typically involves major matrix remodeling. The direction of matrix deformation occurs locally in all three dimensions, which cannot be measured by current techniques. To probe the local, 3D, real-time deformation of a collagen matrix during tumor cell migration, we developed an assay whereby matrix-embedded beads are tracked simultaneously in all three directions with high resolution. To establish a proof of principle, we investigated patterns of collagen I matrix deformation near fibrosarcoma cells in the absence and presence of inhibitors of matrix metalloproteinases and acto-myosin contractility. Our results indicate that migrating cells show patterns of local matrix deformation toward the cell that are symmetric in magnitude with respect to the axis of cell movement. In contrast, patterns of matrix release from the cell are asymmetric: the matrix is typically relaxed first at the back of the cell, allowing forward motion, and then at the cells leading edge. Matrix deformation in regions of the matrix near the cells leading edge is elastic and mostly reversible, but induces irreversible matrix rupture events near the trailing edge. Our results also indicate that matrix remodeling spatially correlates with protrusive activity. This correlation is mediated by myosin II and Rac1, and eliminated after inhibition of pericellular proteolysis or ROCK. We have developed an assay based on high-resolution 3D multiple-particle tracking that allows us to probe local matrix remodeling during mesenchymal cell migration through a 3D matrix and simultaneously monitor protrusion dynamics.

Actin cap associated focal adhesions and their distinct role in cellular mechanosensing

The ability for cells to sense and adapt to different physical microenvironments plays a critical role in development, immune responses, and cancer metastasis. Here we identify a small subset of focal adhesions that terminate fibers in the actin cap, a highly ordered filamentous actin structure that is anchored to the top of the nucleus by the LINC complexes; these differ from conventional focal adhesions in morphology, subcellular organization, movements, turnover dynamics, and response to biochemical stimuli. Actin cap associated focal adhesions (ACAFAs) dominate cell mechanosensing over a wide range of matrix stiffness, an ACAFA-specific function regulated by actomyosin contractility in the actin cap, while conventional focal adhesions are restrictively involved in mechanosensing for extremely soft substrates. These results establish the perinuclear actin cap and associated ACAFAs as major mediators of cellular mechanosensing and a critical element of the physical pathway that transduce mechanical cues all the way to the nucleus.

Magnetic tweezers measurement of single molecule torque.

Torsional stress in linear biopolymers such as DNA and chromatin has important consequences for nanoscale biological processes. We have developed a new method to directly measure torque on single molecules. Using a cylindrical magnet, we manipulate a novel probe consisting of a nanorod with a 0.1 microm ferromagnetic segment coupled to a magnetic bead. We achieve controlled introduction of turns into the molecule and precise measurement of torque and molecule extension as a function of the number of turns at low pulling force. We show torque measurement of single DNA molecules and demonstrate for the first time measurements of single chromatin fibers.

The distinct roles of the nucleus and nucleus-cytoskeleton connections in three-dimensional cell migration

Cells often migrate in vivo in an extracellular matrix that is intrinsically three-dimensional (3D) and the role of actin filament architecture in 3D cell migration is less well understood. Here we show that, while recently identified linkers of nucleoskeleton to cytoskeleton (LINC) complexes play a minimal role in conventional 2D migration, they play a critical role in regulating the organization of a subset of actin filament bundles – the perinuclear actin cap - connected to the nucleus through Nesprin2giant and Nesprin3 in cells in 3D collagen I matrix. Actin cap fibers prolong the nucleus and mediate the formation of pseudopodial protrusions, which drive matrix traction and 3D cell migration. Disruption of LINC complexes disorganizes the actin cap, which impairs 3D cell migration. A simple mechanical model explains why LINC complexes and the perinuclear actin cap are essential in 3D migration by providing mechanical support to the formation of pseudopodial protrusions.

Z-ring force and cell shape during division in rod-like bacteria

The life cycle of bacterial cells consists of repeated elongation, septum formation, and division. Before septum formation, a division ring called the Z-ring, which is made of a filamentous tubulin analog, FtsZ, is seen at the mid cell. Together with several other proteins, FtsZ is essential for cell division. Visualization of strains with GFP-labeled FtsZ shows that the Z-ring contracts before septum formation and pinches the cell into two equal halves. Thus, the Z-ring has been postulated to act as a force generator, although the magnitude of the contraction force is unknown. In this article, we develop a mathematical model to describe the process of growth and Z-ring contraction in rod-like bacteria. The elasticity and growth of the cell wall is incorporated in the model to predict the contraction speed, the cell shape, and the contraction force. With reasonable parameters, the model shows that a small force from the Z-ring (8 pN in Escherichia coli) is sufficient to accomplish division.

Three-dimensional cell migration does not follow a random walk.

Significance The motility of cells in the absence of gradients has long been described in terms of random walks. Most of what we know about eukaryotic cell migration has stemmed from well-controlled studies of cell migration on flat dishes. However, cells in vivo often move through 3D environments. Despite this difference, cell speed and persistence are typically extracted from fits using the same persistence random walk (PRW) model. This paper shows that the assumptions of the PRW model are erroneous for 3D cell migration. We introduce and validate a new model of 3D cell migration that takes into account cell heterogeneity and the anisotropic movements induced by local remodeling of the 3D matrix. Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cell-to-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and self-correlation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.

Equilibrium free energies from path sampling of nonequilibrium trajectories

Jarzynski’s relation between equilibrium free energy and nonequilibrium work is rewritten as an average of work with respect to a work weighted ensemble. The present form is more appropriate for computer application of Jarzynski’s relation where the dissipative work is frequently much greater than kBT. Monte Carlo sampling of very short nonequilibrium trajectories yields good estimates of the equilibrium free energy change. The procedure can be thought of as a generalization of thermodynamic integration in ordinary free energy calculations. Very short trajectories can be used to compute the free energy difference. In the infinitely short trajectory limit, we recover the thermodynamic integration scheme. We also show that free energy estimate can be obtained from moments of the work distribution. The last result is most useful for experimental measurements of the free energy.