Mechanochemical Crosstalk Produces Cell-Intrinsic Patterning of the Cortex to Orient the Mitotic Spindle.

Proliferating animal cells are able to orient their mitotic spindles along their interphase cell axis, setting up the axis of cell division, despite rounding up as they enter mitosis. This has previously been attributed to molecular memory and, more specifically, to the maintenance of adhesions and retraction fibers in mitosis [1-6], which are thought to act as local cues that pattern cortical Gαi, LGN, and nuclear mitotic apparatus protein (NuMA) [3, 7-18]. This cortical machinery then recruits and activates Dynein motors, which pull on astral microtubules to position the mitotic spindle. Here, we reveal a dynamic two-way crosstalk between the spindle and cortical motor complexes that depends on a Ran-guanosine triphosphate (GTP) signal [12], which is sufficient to drive continuous monopolar spindle motion independently of adhesive cues in flattened human cells in culture. Building on previous work [1, 12, 19-23], we implemented a physical model of the system that recapitulates the observed spindle-cortex interactions. Strikingly, when this model was used to study spindle dynamics in cells entering mitosis, the chromatin-based signal was found to preferentially clear force generators from the short cell axis, so that cortical motors pulling on astral microtubules align bipolar spindles with the interphase long cell axis, without requiring a fixed cue or a physical memory of interphase shape. Thus, our analysis shows that the ability of chromatin to pattern the cortex during the process of mitotic rounding is sufficient to translate interphase shape into a cortical pattern that can be read by the spindle, which then guides the axis of cell division.

Bond breaking dynamics in semiflexible networks under load.

We examine the bond-breaking dynamics of transiently cross-linked semiflexible networks using a single filament model in which that filament is peeled from an array of cross-linkers. We examine the effect of quenched disorder in the placement of the linkers along the filament and the effect of stochastic bond-breaking (assuming Bell model unbinding kinetics) on the dynamics of filament cross-linker dissociation and the statistics of ripping events. We find that bond forces decay exponentially away from the point of loading and that bond breaking proceeds sequentially down the linker array from the point of loading in a series of stochastic ripping events. We compare these theoretical predictions to the observed trajectories of large beads in a cross-linked microtubule network and identify the observed jumps of the bead with the linker rupture events predicted by the single filament model.

Microemulsions, modulated phases and macroscopic phase separation: a unified picture of rafts.

We consider two mechanisms that can lead to an inhomogeneous distribution of components in a multicomponent lipid bilayer: macroscopic phase separation and the formation of modulated phases. A simple model that encompasses both mechanisms displays a phase diagram that also includes a structured fluid, a microemulsion. Identifying rafts with the inhomogeneities of this structured fluid, we see how rafts are related to the occurrence of macroscopic phase separation or the formation of modulated phases in other systems, and focus our attention on specific differences between them.

Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation.

The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells-the hair cells-are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes-sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.

Macroscopic phase separation, modulated phases, and microemulsions: a unified picture of rafts.

We simulate a simple phenomenological model describing phase behavior in a multicomponent membrane, a model capable of producing macroscopic phase separation, modulated phases, and microemulsions, all of which have been discussed in terms of raft phenomena. We show that one effect of thermal fluctuations on the mean-field phase diagram is that it permits a direct transition between either one of the coexisting liquid phases to a microemulsion. This implies that one system exhibiting phase separation can be related to a similar system exhibiting the heterogeneities characteristic of a microemulsion. The two systems could differ in their average membrane composition or in the relative compositions of their exoplasmic and cytoplasmic leaves. The model provides a unified description of these raft-associated phenomena.

Seeing the Forest in Lieu of the Trees: Continuum Simulations of Cell Membranes at Large Length Scales.

Biological membranes exhibit long-range spatial structure in both chemical composition and geometric shape, which gives rise to remarkable physical phenomena and important biological functions. Continuum models that describe these effects play an important role in our understanding of membrane biophysics at large length scales. We review the mathematical framework used to describe both composition and shape degrees of freedom, and present best practices to implement such models in a computer simulation. We discuss in detail two applications of continuum models of cell membranes: the formation of microemulsion and modulated phases, and the effect of membrane-mediated interactions on the assembly of membrane proteins.

Model of a raft in both leaves of an asymmetric lipid bilayer.

We present a theory of inhomogeneities in the plasma membrane, or rafts, that can exist in both leaves of the plasma membrane. We note that although neither of the major phospholipid components of the outer leaf, sphingomyelin (SM) nor phosphatidylcholine (PC), evinces a tendency to form phases characterized by nonzero curvature, one of the major components of the inner leaf, phosphatidylethanolamine (PE), displays a strong tendency to do so whereas the other, phosphatidylserine (PS), does not. Therefore, we posit that the concentration difference of PS and PE couples to height fluctuations of the plasma membrane bilayer. This brings about a microemulsion in the inner leaf. Coupling of the concentration difference between PS and PE in the inner leaf and SM and PC in the outer leaf propagates the microemulsion to that leaf as well. The characteristic size of the inhomogeneities is equal to the square-root of the ratio of the bending modulus of the bilayer to its surface tension, a size which is ~100 nm for the plasma membrane. If the coupling between leaves were to be provided by the interchange of cholesterol, then our model raft would consist of SM and cholesterol in the outer leaf and PS and cholesterol in the inner leaf floating in a sea of PC and PE in both leaves.

Patterning of polar active filaments on a tense cylindrical membrane.

We study the dynamics and patterning of polar contractile filaments on the surface of a cylindrical cell using active hydrodynamic equations that incorporate couplings between curvature and filament orientation. Cables and rings spontaneously emerge as steady state configurations on the cylinder, and can be stationary or moving, helical or tilted segments moving along helical trajectories. We observe phase transitions in the steady state patterns upon changing cell diameter or motor-driven activity and make several testable predictions. Our results are relevant to the dynamics and patterning of a variety of active biopolymers in cylindrical cells.

Measurement of monolayer viscosity using noncontact microrheology.

Microrheological studies of phospholipid monolayers, bilayers, and other Langmuir monolayer systems are traditionally performed by observing the thermal fluctuations of tracers attached to the membrane or interface. Measurements of this type obtain surface moduli that are orders of magnitude different from those obtained using macroscopic or active techniques. These large discrepancies can result from uncertainties in the tracer's coupling to the monolayer or the local disruption of the monolayer by the tracer. To avoid such problems, we perform a microrheological experiment with the tracer particle placed at a known depth beneath the monolayer; this avoids the issues mentioned at the cost of generating a weaker, purely hydrodynamic coupling between the tracer and the monolayer. We calculate the appropriate response functions for this submerged particle microrheology and demonstrate the technique on three model monolayer systems.

Low frequency entrainment of oscillatory bursts in hair cells.

Sensitivity of mechanical detection by the inner ear is dependent upon a highly nonlinear response to the applied stimulus. Here we show that a system of differential equations that support a subcritical Hopf bifurcation, with a feedback mechanism that tunes an internal control parameter, captures a wide range of experimental results. The proposed model reproduces the regime in which spontaneous hair bundle oscillations are bistable, with sporadic transitions between the oscillatory and the quiescent state. Furthermore, it is shown, both experimentally and theoretically, that the application of a high-amplitude stimulus to the bistable system can temporarily render it quiescent before recovery of the limit cycle oscillations. Finally, we demonstrate that the application of low-amplitude stimuli can entrain bundle motility either by mode-locking to the spontaneous oscillation or by mode-locking the transition between the quiescent and oscillatory states.

Phase slips in oscillatory hair bundles.

Hair cells of the inner ear contain an active amplifier that allows them to detect extremely weak signals. As one of the manifestations of an active process, spontaneous oscillations arise in fluid immersed hair bundles of in vitro preparations of selected auditory and vestibular organs. We measure the phase-locking dynamics of oscillatory bundles exposed to low-amplitude sinusoidal signals, a transition that can be described by a saddle-node bifurcation on an invariant circle. The transition is characterized by the occurrence of phase slips, at a rate that is dependent on the amplitude and detuning of the applied drive. The resultant staircase structure in the phase of the oscillation can be described by the stochastic Adler equation, which reproduces the statistics of phase slip production.

Cylindrical cellular geometry ensures fidelity of division site placement in fission yeast.

Successful cytokinesis requires proper assembly of the contractile actomyosin ring, its stable positioning on the cell surface and proper constriction. Over the years, many of the key molecular components and regulators of the assembly and positioning of the actomyosin ring have been elucidated. Here we show that cell geometry and mechanics play a crucial role in the stable positioning and uniform constriction of the contractile ring. Contractile rings that assemble in locally spherical regions of cells are unstable and slip towards the poles. By contrast, actomyosin rings that assemble on locally cylindrical portions of the cell under the same conditions do not slip, but uniformly constrict the cell surface. The stability of the rings and the dynamics of ring slippage can be described by a simple mechanical model. Using fluorescence imaging, we verify some of the quantitative predictions of the model. Our study reveals an intimate interplay between geometry and actomyosin dynamics, which are likely to apply in a variety of cellular contexts.

Theoretical model for cellular shapes driven by protrusive and adhesive forces.

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix.

Curling and local shape changes of red blood cell membranes driven by cytoskeletal reorganization.

Human red blood cells (RBCs) lack the actin-myosin-microtubule cytoskeleton that is responsible for shape changes in other cells. Nevertheless, they can display highly dynamic local deformations in response to external perturbations, such as those that occur during the process of apical alignment preceding merozoite invasion in malaria. Moreover, after lysis in divalent cation-free media, the isolated membranes of ruptured ghosts show spontaneous inside-out curling motions at the free edges of the lytic hole, leading to inside-out vesiculation. The molecular mechanisms that drive these rapid shape changes are unknown. Here, we propose a molecular model in which the spectrin filaments of the RBC cortical cytoskeleton control the sign and dynamics of membrane curvature depending on whether the ends of the filaments are free or anchored to the bilayer. Computer simulations of the model reveal that curling, as experimentally observed, can be obtained either by an overall excess of weakly-bound filaments throughout the cell, or by the flux of such filaments toward the curling edges. Divalent cations have been shown to arrest the curling process, and Ca2+ ions have also been implicated in local membrane deformations during merozoite invasion. These effects can be replicated in our model by attributing the divalent cation effects to increased filament-membrane binding. This process converts the curl-inducing loose filaments into fully bound filaments that arrest curling. The same basic mechanism can be shown to account for Ca2+-induced local and dynamic membrane deformations in intact RBCs. The implications of these results in terms of RBC membrane dynamics under physiological, pathological, and experimental conditions is discussed.

Physical model of the dynamic instability in an expanding cell culture.

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.

Physical model of contractile ring initiation in dividing cells.

We present a physical mechanism to describe initiation of the contractile ring during cell division. The model couples the membrane curvature with the contractile forces produced by protein clusters attached to the membrane. These protein clusters are mobile on the membrane and possess either an isotropic or an anisotropic spontaneous curvature. Our results show that under these conditions the contraction force gives rise to an instability that corresponds in a closed cellular system to the initiation of the contractile ring. We find a quantization of this process at distinct length-scales, which we compare to available data for different types of eukaryote cells.