Alex Mogilner

Actin and |[alpha]|-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner

Using two-colour imaging and high resolution TIRF microscopy, we investigated the assembly and maturation of nascent adhesions in migrating cells. We show that nascent adhesions assemble and are stable within the lamellipodium. The assembly is independent of myosin II but its rate is proportional to the protrusion rate and requires actin polymerization. At the lamellipodium back, the nascent adhesions either disassemble or mature through growth and elongation. Maturation occurs along an α-actinin–actin template that elongates centripetally from nascent adhesions. α-Actinin mediates the formation of the template and organization of adhesions associated with actin filaments, suggesting that actin crosslinking has a major role in this process. Adhesion maturation also requires myosin II. Rescue of a myosin IIA knockdown with an actin-bound but motor-inhibited mutant of myosin IIA shows that the actin crosslinking function of myosin II mediates initial adhesion maturation. From these studies, we have developed a model for adhesion assembly that clarifies the relative contributions of myosin II and actin polymerization and organization.

Mechanism of shape determination in motile cells

The shape of motile cells is determined by many dynamic processes spanning several orders of magnitude in space and time, from local polymerization of actin monomers at subsecond timescales to global, cell-scale geometry that may persist for hours. Understanding the mechanism of shape determination in cells has proved to be extremely challenging due to the numerous components involved and the complexity of their interactions. Here we harness the natural phenotypic variability in a large population of motile epithelial keratocytes from fish (Hypsophrys nicaraguensis) to reveal mechanisms of shape determination. We find that the cells inhabit a low-dimensional, highly correlated spectrum of possible functional states. We further show that a model of actin network treadmilling in an inextensible membrane bag can quantitatively recapitulate this spectrum and predict both cell shape and speed. Our model provides a simple biochemical and biophysical basis for the observed morphology and behaviour of motile cells.

Direct measurement of the lamellipodial protrusive force in a migrating cell

There has been a great deal of interest in the mechanism of lamellipodial protrusion (Pollard, T., and G. Borisy. 2003. Cell. 112:453–465). However, one of this mechanisms endpoints, the force of protrusion, has never been directly measured. We place an atomic force microscopy cantilever in the path of a migrating keratocyte. The deflection of the cantilever, which occurs over a period of ∼10 s, provides a direct measure of the force exerted by the lamellipodial leading edge. Stall forces are consistent with ∼100 polymerizing actin filaments per micrometer of the leading edge, each working as an elastic Brownian ratchet and generating a force of several piconewtons. However, the force-velocity curves obtained from this measurement, in which velocity drops sharply under very small loads, is not sensitive to low loading forces, and finally stalls rapidly at large loads, are not consistent with current theoretical models for the actin polymerization force. Rather, the curves indicate that the protrusive force generation is a complex multiphase process involving actin and adhesion dynamics.

Regulation of actin dynamics in rapidly moving cells: a quantitative analysis.

We develop a mathematical model that describes key details of actin dynamics in protrusion associated with cell motility. The model is based on the dendritic-nucleation hypothesis for lamellipodial protrusion in nonmuscle cells such as keratocytes. We consider a set of partial differential equations for diffusion and reactions of sequestered actin complexes, nucleation, and growth by polymerization of barbed ends of actin filaments, as well as capping and depolymerization of the filaments. The mechanical aspect of protrusion is based on an elastic polymerization ratchet mechanism. An output of the model is a relationship between the protrusion velocity and the number of filament barbed ends pushing the membrane. Significantly, this relationship has a local maximum: too many barbed ends deplete the available monomer pool, too few are insufficient to generate protrusive force, so motility is stalled at either extreme. Our results suggest that to achieve rapid motility, some tuning of parameters affecting actin dynamics must be operating in the cell.

The Shape of Motile Cells

Motile cells - fan-like keratocytes, hand-shaped nerve growth cones, polygonal fibroblasts, to name but a few - come in different shapes and sizes. We discuss the origins of this diversity as well as what shape tells us about the physics and biochemistry underlying cell movement. We start with geometric rules describing cell-edge kinetics that govern cell shape, followed by a discussion of the underlying biophysics; we consider actin treadmilling, actin-myosin contraction, cell-membrane deformations, adhesion, and the complex interactions between these modules, as well as their regulation by microtubules and Rho GTPases. Focusing on several different cell types, including keratocytes and fibroblasts, we discuss how dynamic cell morphology emerges from the interplay between the different motility modules and the environment.

Mathematics of cell motility: have we got its number?

Mathematical and computational modeling is rapidly becoming an essential research technique complementing traditional experimental biological methods. However, lack of standard modeling methods, difficulties of translating biological phenomena into mathematical language, and differences in biological and mathematical mentalities continue to hinder the scientific progress. Here we focus on one area—cell motility—characterized by an unusually high modeling activity, largely due to a vast amount of quantitative, biophysical data, ‘modular’ character of motility, and pioneering vision of the area’s experimental leaders. In this review, after brief introduction to biology of cell movements, we discuss quantitative models of actin dynamics, protrusion, adhesion, contraction, and cell shape and movement that made an impact on the process of biological discovery. We also comment on modeling approaches and open questions.

The Spatial Arrangement of Chromosomes during Prometaphase Facilitates Spindle Assembly

Error-free chromosome segregation requires stable attachment of sister kinetochores to the opposite spindle poles (amphitelic attachment). Exactly how amphitelic attachments are achieved during spindle assembly remains elusive. We employed photoactivatable GFP and high-resolution live-cell confocal microscopy to visualize complete 3D movements of individual kinetochores throughout mitosis in nontransformed human cells. Combined with electron microscopy, molecular perturbations, and immunofluorescence analyses, this approach reveals unexpected details of chromosome behavior. Our data demonstrate that unstable lateral interactions between kinetochores and microtubules dominate during early prometaphase. These transient interactions lead to the reproducible arrangement of chromosomes in an equatorial ring on the surface of the nascent spindle. A computational model predicts that this toroidal distribution of chromosomes exposes kinetochores to a high density of microtubules which facilitates subsequent formation of amphitelic attachments. Thus, spindle formation involves a previously overlooked stage of chromosome prepositioning which promotes formation of amphitelic attachments.

An Adhesion-Dependent Switch between Mechanisms That Determine Motile Cell Shape

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.

Emergence of Large-Scale Cell Morphology and Movement from Local Actin Filament Growth Dynamics

Variations in cell migration and morphology are consequences of changes in underlying cytoskeletal organization and dynamics. We investigated how these large-scale cellular events emerge as direct consequences of small-scale cytoskeletal molecular activities. Because the properties of the actin cytoskeleton can be modulated by actin-remodeling proteins, we quantitatively examined how one such family of proteins, enabled/vasodilator-stimulated phosphoprotein (Ena/VASP), affects the migration and morphology of epithelial fish keratocytes. Keratocytes generally migrate persistently while exhibiting a characteristic smooth-edged “canoe” shape, but may also exhibit less regular morphologies and less persistent movement. When we observed that the smooth-edged canoe keratocyte morphology correlated with enrichment of Ena/VASP at the leading edge, we mislocalized and overexpressed Ena/VASP proteins and found that this led to changes in the morphology and movement persistence of cells within a population. Thus, local changes in actin filament dynamics due to Ena/VASP activity directly caused changes in cell morphology, which is coupled to the motile behavior of keratocytes. We also characterized the range of natural cell-to-cell variation within a population by using measurable morphological and behavioral features—cell shape, leading-edge shape, filamentous actin (F-actin) distribution, cell speed, and directional persistence—that we have found to correlate with each other to describe a spectrum of coordinated phenotypes based on Ena/VASP enrichment at the leading edge. This spectrum stretched from smooth-edged, canoe-shaped keratocytes—which had VASP highly enriched at their leading edges and migrated fast with straight trajectories—to more irregular, rounder cells migrating slower with less directional persistence and low levels of VASP at their leading edges. We developed a mathematical model that accounts for these coordinated cell-shape and behavior phenotypes as large-scale consequences of kinetic contributions of VASP to actin filament growth and protection from capping at the leading edge. This work shows that the local effects of actin-remodeling proteins on cytoskeletal dynamics and organization can manifest as global modifications of the shape and behavior of migrating cells and that mathematical modeling can elucidate these large-scale cell behaviors from knowledge of detailed multiscale protein interactions.

Mechanism of transport of IFT particles in C. elegans cilia by the concerted action of kinesin-II and OSM-3 motors.

The assembly and function of cilia on Caenorhabditis elegans neurons depends on the action of two kinesin-2 motors, heterotrimeric kinesin-II and homodimeric OSM-3–kinesin, which cooperate to move the same intraflagellar transport (IFT) particles along microtubule (MT) doublets. Using competitive in vitro MT gliding assays, we show that purified kinesin-II and OSM-3 cooperate to generate movement similar to that seen along the cilium in the absence of any additional regulatory factors. Quantitative modeling suggests that this could reflect an alternating action mechanism, in which the motors take turns to move along MTs, or a mechanical competition, in which the motors function in a concerted fashion to move along MTs with the slow motor exerting drag on the fast motor and vice versa. In vivo transport assays performed in Bardet-Biedl syndrome (BBS) protein and IFT motor mutants favor a mechanical competition model for motor coordination in which the IFT motors exert a BBS protein–dependent tension on IFT particles, which controls the IFT pathway that builds the cilium foundation.