Cell biology. Shrinking gels pull cells

Actin-myosin spatial patterns from a simplified isotropic viscoelastic model

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.

Extending the molecular clutch beyond actin-based cell motility

Many cell movements occur via polymerization of the actin cytoskeleton beneath the plasma membrane at the front of the cell, forming a protrusion called a lamellipodium, while myosin contraction squeezes forward the back of the cell. In what is known as the "molecular clutch" description of cell motility, forward movement results from the engagement of the acto-myosin motor with cell-matrix adhesions, thus transmitting force to the substrate and producing movement. However during cell translocation, clutch engagement is not perfect, and as a result, the cytoskeleton slips with respect to the substrate, undergoing backward (retrograde) flow in the direction of the cell body. Retrograde flow is therefore inversely proportional to cell speed and depends on adhesion and acto-myosin dynamics. Here we asked whether the molecular clutch was a general mechanism by measuring motility and retrograde flow for the Caenorhabditis elegans sperm cell in different adhesive conditions. These cells move by adhering to the substrate and emitting a dynamic lamellipodium, but the sperm cell does not contain an acto-myosin cytoskeleton. Instead the lamellipodium is formed by the assembly of Major Sperm Protein (MSP), which has no biochemical or structural similarity to actin. We find that these cells display the same molecular clutch characteristics as acto-myosin containing cells. We further show that retrograde flow is produced both by cytoskeletal assembly and contractility in these cells. Overall this study shows that the molecular clutch hypothesis of how polymerization is transduced into motility via adhesions is a general description of cell movement regardless of the composition of the cytoskeleton.

Role of posttranslational modifications in C. elegans and ascaris spermatogenesis and sperm function

Generally, spermatogenesis and sperm function involve widespread posttranslational modification of regulatory proteins in many different species. Nematode spermatogenesis has been studied in detail, mostly by genetic/molecular genetic techniques in the free-living Caenorhabditis elegans and by biochemistry/cell biology in the pig parasite Ascaris suum. Like other nematodes, both of these species produce sperm that use a form of amoeboid motility termed crawling, and many aspects of spermatogenesis are likely to be similar in both species. Consequently, work in these two nematode species has been largely complementary. Work in C. elegans has identified a number of spermatogenesis-defective genes and, so far, 12 encode enzymes that are implicated as catalysts of posttranslational protein modification. Crawling motility involves extension of a single pseudopod and this process is powered by a unique cytoskeleton composed of Major Sperm Protein (MSP) and accessory proteins, instead of the more widely observed actin. In Ascaris, pseudopod extension and crawling motility can be reconstituted in vitro, and biochemical studies have begun to reveal how posttranslational protein modifications, including phosphorylation, dephosphorylation and proteolysis, participate in these processes.

Transformation: how do nematode sperm become activated and crawl?

Nematode sperm undergo a drastic physiological change during spermiogenesis (sperm activation). Unlike mammalian flagellated sperm, nematode sperm are amoeboid cells and their motility is driven by the dynamics of a cytoskeleton composed of major sperm protein (MSP) rather than actin found in other crawling cells. This review focuses on sperm from Caenorhabditis elegans and Ascaris suum to address the roles of external and internal factors that trigger sperm activation and power sperm motility. Nematode sperm can be activated in vitro by several factors, including Pronase and ionophores, and in vivo through the TRY-5 and SPE-8 pathways. Moreover, protease and protease inhibitors are crucial regulators of sperm maturation. MSP-based sperm motility involves a coupled process of protrusion and retraction, both of which have been reconstituted in vitro. Sperm motility is mediated by phosphorylation signals, as illustrated by identification of several key components (MPOP, MFPs and MPAK) in Ascaris and the characterization of GSP-3/4 in C. elegans.

Myosin concentration underlies cell size-dependent scalability of actomyosin ring constriction

The rate of actomyosin ring constriction in cells of different sizes correlates with myosin motor concentration in Neurospora crassa cells, leading to increased division rates in larger cells during cytokinesis.

In eukaryotes, cytokinesis is accomplished by an actomyosin-based contractile ring. Although in Caenorhabditis elegans embryos larger cells divide at a faster rate than smaller cells, it remains unknown whether a similar mode of scalability operates in other cells. We investigated cytokinesis in the filamentous fungus Neurospora crassa, which exhibits a wide range of hyphal circumferences. We found that N. crassa cells divide using an actomyosin ring and larger rings constricted faster than smaller rings. However, unlike in C. elegans, the total amount of myosin remained constant throughout constriction, and there was a size-dependent increase in the starting concentration of myosin in the ring. We predict that the increased number of ring-associated myosin motors in larger rings leads to the increased constriction rate. Accordingly, reduction or inhibition of ring-associated myosin slows down the rate of constriction. Because the mechanical characteristics of contractile rings are conserved, we predict that these findings will be relevant to actomyosin ring constriction in other cell types.

Measuring forces between two single actin filaments during bundle formation

Bundles of filamentous actin are dominant cytoskeletal structures, which play a crucial role in various cellular processes. As yet quantifying the fundamental interaction between two individual actin filaments forming the smallest possible bundle has not been realized. Applying holographic optical tweezers integrated with a microfluidic platform, we were able to measure the forces between two actin filaments during bundle formation. Quantitative analysis yields forces up to 0.2 pN depending on the concentration of bundling agents.

Mechanisms of Cell Propulsion by Active Stresses

The mechanisms by which cytoskeletal flows and cell-substrate interactions interact to generate cell motion are explored using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell-substrate friction. It is found that 1) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, 2) gradients in cell-substrate friction can induce motion even when the active stresses are symmetrically distributed, 3) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell, and 4) the cell velocity depends biphasically on the cell-substrate adhesion strength if active stress is enhanced by adhesion. Specific experimental tests of the calculated dependences are proposed.

Treadmilling of actin filaments via Brownian dynamics simulations

Actin polymerization is coupled to the hydrolysis of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (P(i)). Therefore, each protomer within an actin filament can attain three different nucleotide states corresponding to bound ATP, ADP/P(i), and ADP. These protomer states form spatial patterns on the growing (or shrinking) filaments. Using Brownian dynamics simulations, the growth behavior of long filaments is studied, together with the associated protomer patterns, as a function of ATP-actin monomer concentration, C(T), within the surrounding solution. For concentrations close to the critical concentration C(T)=C(T,cr), the filaments undergo treadmilling, i.e., they grow at the barbed and shrink at the pointed end, which leads to directed translational motion of the whole filament. The corresponding nonequilibrium states are characterized by several global fluxes and by spatial density and flux profiles along the filaments. We focus on a certain set of transition rates as deduced from in vitro experiments and find that the associated treadmilling (or turnover) rate is about 0.08 monomers per second.

Cell crawling assisted by contractile stress induced retraction

Cell locomotion is a result of a series of synchronized chemo-mechanical processes. Crawling-type cell locomotion consists of three steps: protrusion, translocation, and retraction. Previous works have shown that both protrusion and retraction can produce cell movement. For the latter, a cell derives its propulsive force from retraction induced protrusion mechanism, which was experimentally verified by Chen (1979, "Induction of Spreading During Fibroblast Movement," J. Cell Biol., 81, pp. 684-691). In this paper, using finite element method, we take a computational biomimetic approach to study cell crawling assisted by contractile stress induced de-adhesion at the rear of the focal adhesion zone (FAZ). We assume the formation of the FAZ is driven by receptor-ligand bonds and nonspecific interactions. The contractile stress is generated due to the molecular activation of the intracellular actin-myosin machinery. The exerted contractile stress and its time dependency are modeled in a phenomenological manner as a two-spring mechanosensor proposed by Schwarz (2006, "Focal Adhesions as Mechanosensors: The Two-Spring Model," BioSystems, 83(2-3), pp. 225-232). Through coupling the kinetics of receptor-ligand bonds with contractile stress, de-adhesion can be achieved when the stall value of the contractile stress is larger than a critical one. De-adhesion at the rear end of the FAZ causes a redistribution of elastic energy and induces cell locomotion. Parametric studies were conducted to investigate the connection between the cell locomotion speed and stall stress, and receptor-ligand kinetics. Finally, we provide a scaling relationship that can be used to estimate the cell locomotion speed.

The geometry and motion of nematode sperm cells

The nematode sperm cell crawls by recycling major sperm protein (MSP) from dimers into subfilaments, filaments, and filament complexes, as a result of thermal writhing in the presence of hydrophobic patches. Polymerization near leading edges of the cell intercolates MSP dimers onto the tips of growing filament complexes, forcing them against the cell boundary, and extending the cytoskeleton in the direction of motion. Strong adhesive forces attach the cell to the substrate in the forward part of the lamellipod, while depolymerization in the rearward part of the cell breaks down the cytoskeleton, contracting the lamellipod and pulling the cell body forward. The movement of these cells, then, is caused by coordinated protrusive, adhesive and contractile forces, spatially separated across the lamellipod. This paper considers a phenomenological model that tracks discrete elements of the cytoskeleton in curvilinear coordinates. The pseudo-two dimensional model primarily considers protrusion and rotation of the cell, along with the evolution of the cell boundary. General assumptions are that pH levels within the lamellipod regulate protrusion, contraction and adhesion, and that growth of the cytoskeleton, over time, is perpendicular to the evolving cell boundary. The model follows the growth and contraction of a discrete number of MSP fiber complexes, since they appear to be the principle contributors for force generation in cell boundary protrusion and contraction, and the backbone for the dynamic geometry and motion.

The role of filament-packing dynamics in powering amoeboid cell motility

Although several models have been proposed to account for how cytoskeleton polymerization drives protrusion in cell motility, the precise mechanism remains controversial. Here, we show that, in addition to force exerted directly against the membrane by growing filaments, the way elongating filaments pack also contributes to protrusion by generating an expansion of the cytoskeleton gel. Tomography shows that filament packing in the major sperm protein (MSP) -based nematode sperm-motility machinery resembles that observed with rigid rods. Maximum rod-packing density decreases dramatically as the rods lengthen. Therefore, as filaments elongate, the cytoskeleton gel expands to accommodate their packing less densely. This volume expansion combines with polymerization to drive protrusion. Consistent with this hypothesis, an engineered MSP mutant that generates shorter filaments shows higher filament-packing density and slower movement.

Depolymerization-driven flow in nematode spermatozoa relates crawling speed to size and shape

Cell crawling is an inherently physical process that includes protrusion of the leading edge, adhesion to the substrate, and advance of the trailing cell body. Research into advance of the cell body has focused on actomyosin contraction, with cytoskeletal disassembly regarded as incidental, rather than causative; however, extracts from nematode spermatozoa, which use Major Sperm Protein rather than actin, provide at least one example where cytoskeletal disassembly apparently generates force in the absence of molecular motors. To test whether depolymerization can explain force production during nematode sperm crawling, we constructed a mathematical model that simultaneously describes the dynamics of both the cytoskeleton and the cytosol. We also performed corresponding experiments using motile Caenorhabditis elegans spermatozoa. Our experiments reveal that crawling speed is an increasing function of both cell size and anterior-posterior elongation. The quantitative, depolymerization-driven model robustly predicts that cell speed should increase with cell size and yields a cytoskeletal disassembly rate that is consistent with previous measurements. Notably, the model requires anisotropic elasticity, with the cell being stiffer along the direction of motion, to accurately reproduce the dependence of speed on elongation. Our simulations also predict that speed should increase with cytoskeletal anisotropy and disassembly rate.

Mathematical modeling of cell migration

Mathematical modeling has become increasingly important in many areas of biology during the past two decades, and the area of cell migration and motility has seen significant contributions from a wide range of modeling approaches. In this chapter, we cover examples from the broad range of work in this area, emphasizing the models' biological significance and the relationships between them. We focus on three specific areas: cell protrusion, cell adhesion, and retraction/whole-cell models. At the end of this chapter, we provide our perspective on issues that future models and experiments should consider in order to advance the boundaries of this field.

Nonequilibrium-driven motion in actin networks: comet tails and moving beads

We present 3D dynamic Monte-Carlo simulations of the growth of an actin network close to an obstacle coated with Wiskott-Aldrich syndrome protein (WASP), an inducer of actin branching. Our simulations incorporate both elasticity and relaxation of the actin tail, thus allowing for local network compression. Whilst steady state motility derives mainly from polymerization at the leading edge, nonthermal stored elastic energy and retrograde flow are observed in a thin slab of material close to the obstacle. We observe a crossover from steady to hopping bead motion as the branching rate is decreased.

Cytoskeleton dynamics powers nematode sperm motility

Nematode sperm provide a simple and specialized system for studying the molecular mechanism of amoeboid cell motility. Locomotion is generated by the assembly dynamics of their cytoskeleton, which is based on the major sperm protein (MSP). Protrusive force is generated at the leading edge of the lamellipod by MSP filament formation and bundling, whereas the contractile force that drags the rearward cell body forward is generated by cytoskeleton disassembly. The dynamics of the system can be reconstituted in vitro using cell-free extracts of Ascaris sperm, in which vesicles derived from the leading edge of the cell can be either pushed or pulled. The addition of ATP to the cell-free extract initiates MSP filament polymerization and bundling immediately behind the vesicle, and the expansion of the resulting gel pushes the vesicle at rates comparable to those seen in living cells. In contrast, the addition of Yersinia tyrosine phosphatase generates depolymerization and gel contraction that pulls the vesicles. Overall, nematode sperm motility illustrates that cell locomotion can be generated by cytoskeletal dynamics alone without the use of myosin-like motor proteins.

Merotelic kinetochores in mammalian tissue cells

Merotelic kinetochore attachment is a major source of aneuploidy in mammalian tissue cells in culture. Mammalian kinetochores typically have binding sites for about 20-25 kinetochore microtubules. In prometaphase, kinetochores become merotelic if they attach to microtubules from opposite poles rather than to just one pole as normally occurs. Merotelic attachments support chromosome bi-orientation and alignment near the metaphase plate and they are not detected by the mitotic spindle checkpoint. At anaphase onset, sister chromatids separate, but a chromatid with a merotelic kinetochore may not be segregated correctly, and may lag near the spindle equator because of pulling forces toward opposite poles, or move in the direction of the wrong pole. Correction mechanisms are important for preventing segregation errors. There are probably more than 100 times as many PtK1 tissue cells with merotelic kinetochores in early mitosis, and about 16 times as many entering anaphase as the 1% of cells with lagging chromosomes seen in late anaphase. The role of spindle mechanics and potential functions of the Ndc80/Nuf2 protein complex at the kinetochore/microtubule interface is discussed for two correction mechanisms: one that functions before anaphase to reduce the number of kinetochore microtubules to the wrong pole, and one that functions after anaphase onset to move merotelic kinetochores based on the ratio of kinetochore microtubules to the correct versus incorrect pole.

Structure of MFP2 and its function in enhancing MSP polymerization in Ascaris sperm amoeboid motility

The simplicity and specialization of the cell motility machinery of Ascaris sperm provides a powerful system in which to probe the basic molecular mechanism of amoeboid cell motility. Although Ascaris sperm locomotion closely resembles that seen in many other types of crawling cell, movement is generated by modulation of a cytoskeleton based on the major sperm protein (MSP) rather than the actin present in other cell types. The Ascaris motility machinery can be studied conveniently in a cell-free in vitro system based on the movement of plasma membrane vesicles by fibres constructed from bundles of MSP filaments. In addition to ATP, MSP and a plasma membrane protein, reconstitution of MSP motility in this cell-free extract requires cytosolic proteins to orchestrate the site-specific assembly and bundling of MSP filaments that generates locomotion. One of these proteins, MFP2, accelerates the rate of movement in this assay. Here, we describe crystal structures of two isoforms of MFP2 and show that both are constructed from two domains that have the same fold based on a novel, compact beta sheet arrangement. Patterns of conservation observed in a structure-based analysis of MFP2 sequences from different nematode species identified regions that may be putative functional interfaces involved both in interactions between MFP2 domains and also with other components of the sperm motility machinery. Analysis of the growth of fibres in vitro in the presence of added MFP2 indicated that MFP2 increases the rate of locomotion by enhancing the effective rate of MSP filament polymerization. This observation, together with the structural data, suggests that MFP2 may function in a manner analogous to formins in actin-based motility.

Clocks and patterns in myxobacteria: a remembrance of Art Winfree

At the beginning of their aggregation phase waves of cell density sweep across the surface of myxobacteria colonies. These waves are unlike any other in biology. Waves can be linear, concentric or spiral and when they collide, instead of annihilating one another they appear to pass through each other unchanged. Moreover, the wavelength determines the spacing and pattern of fruiting bodies that will rise up presaging sporulation. The explanation for these waves was suggested by the work of Art Winfree on cellular clocks, and confirmed by a mathematical model that explains all of the observed wave behavior. The story of how this model evolved illustrates the roles of chance and scientific networking in the search for the explanation of a new phenomenon.