How nematode sperm crawl

Extending the aerolysin family: from bacteria to vertebrates

A number of bacterial virulence factors have been observed to adopt structures similar to that of aerolysin, the principal toxin of Aeromonas species. However, a comprehensive description of architecture and structure of the aerolysin-like superfamily has not been determined. In this study, we define a more compact aerolysin-like domain--or aerolysin fold--and show that this domain is far more widely spread than anticipated since it can be found throughout kingdoms. The aerolysin-fold could be found in very diverse domain and functional contexts, although a toxic function could often be assigned. Due to this diversity, the borders of the superfamily could not be set on a sequence level. As a border-defining member, we therefore chose pXO2-60--a protein from the pathogenic pXO2 plasmid of Bacillus anthracis. This fascinating protein, which harbors a unique ubiquitin-like fold domain at the C-terminus of the aerolysin-domain, nicely illustrates the diversity of the superfamily. Its putative role in the virulence of B. anthracis and its three dimensional model are discussed.

The flux model of the movement of tumor cells and healthy cells using a system of nonlinear heat equations

The interaction model is deduced from the concept of the flux motion of heat transfer, and the movement is constrained by space limitation. Furthermore, we analyze the model to obtain the behavior of two-cell populations at time close to initial state and far into the future.

The physiological acquisition of amoeboid motility in nematode sperm: is the tail the only thing the sperm lost?

Nematode spermatozoa are highly specialized amoeboid cells that must acquire motility through the extension of a single pseudopod. Despite morphological and molecular differences with flagellated spermatozoa (including a non-actin-based cytoskeleton), nematode sperm must also respond to cues present in the female reproductive tract that render them motile, thereby allowing them to locate and fertilize the egg. The factors that trigger pseudopod extension in vivo are unknown, although current models suggest the activation through proteases acting on the sperm surface resulting in a myriad of biochemical, physiological, and morphological changes. Compelling evidence shows that pseudopod extension is under the regulation of physiological events also observed in other eukaryotic cells (including flagellated sperm) that involve membrane rearrangements in response to extracellular cues that initiate various signal transduction pathways. An integrative approach to the study of nonflagellated spermatozoa will shed light on the identification of unique and conserved processes during fertilization among different taxa.

Modeling human diseases in Caenorhabditis elegans

Genes linked to human diseases often function in evolutionarily conserved pathways, which can be readily dissected in simple model organisms. Because of its short lifespan and well-known biology, coupled with a completely sequenced genome that shares extensive homology with that of mammals, Caenorhabditis elegans is one of the most versatile and powerful model organisms. Research in C. elegans has been instrumental for the elucidation of molecular pathways implicated in many human diseases. In this review, we introduce C. elegans as a model organism for biomedical research and we survey recent relevant findings that shed light on the basic molecular determinants of human disease pathophysiology. The nematode holds promise of providing clear leads towards the identification of potential targets for the development of new therapeutic interventions against human diseases.

The role of cell contraction and adhesion in dictyostelium motility

The crawling motion of Dictyostelium discoideum on substrata involves a number of coordinated events including cell contractions and cell protrusions. The mechanical forces exerted on the substratum during these contractions have recently been quantified using traction force experiments. Based on the results from these experiments, we present a biomechanical model of the contraction phase of Dictyostelium discoideum motility with an emphasis on the adhesive properties of the cell-substratum contact. Our model assumes that the cell contracts at a constant rate and is bound to the substratum by adhesive bridges that are modeled as elastic springs. These bridges are established at a spatially uniform rate while detachment occurs at a spatially varying, load-dependent rate. Using Monte Carlo simulations and assuming a rigid substratum, we find that the cell speed depends only weakly on the detachment kinetics of the cell-substratum interface, in agreement with experimental data. By varying the parameters that control the adhesive and contractile properties of the cell, we are able to make testable predictions. We also extend our model to include a flexible substrate and show that our model is able to produce substratum deformations and force patterns that are quantitatively and qualitatively in agreement with experimental data.

Cytopede: a three-dimensional tool for modeling cell motility on a flat surface

When cultured on flat surfaces, fibroblasts and many other cells spread to form thin lamellar sheets. Motion then occurs by extension of the sheet at the leading edge and retraction at the trailing edge. Comprehensive quantitative models of these phenomena have so far been lacking and to address this need, we have designed a three-dimensional code called Cytopede specialized for the simulation of the mechanical and signaling behavior of plated cells. Under assumptions by which the cytosol and the cytoskeleton are treated from a continuum mechanical perspective, Cytopede uses the finite element method to solve mass and momentum equations for each phase, and thus determine the time evolution of cellular models. We present the physical concepts that underlie Cytopede together with the algorithms used for their implementation. We then validate the approach by a computation of the spread of a viscous sessile droplet. Finally, to exemplify how Cytopede enables the testing of ideas about cell mechanics, we simulate a simple fibroblast model. We show how Cytopede allows computation, not only of basic characteristics of shape and velocity, but also of maps of cell thickness, cytoskeletal density, cytoskeletal flow, and substratum tractions that are readily compared with experimental data.

Cell physician: reading cell motion: a mathematical diagnostic technique through analysis of single cell motion

Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, is of paramount importance. The mathematical model developed in this paper determines some physical features and material properties of the cells locally through analysis of live cell image sequences and uses this information to make further inferences about the molecular structures, dynamics, and processes within the cells, such as the actin network, microdomains, chemotaxis, adhesion, and retrograde flow. The generality of the principals used in formation of the model ensures its wide applicability to different phenomena at various levels. Based on the model outcomes, we hypothesize a novel biological model for collective biomechanical and molecular mechanism of cell motion.

The Moving Boundary Node Method: A level set-based, finite volume algorithm with applications to cell motility

Eukaryotic cell crawling is a highly complex biophysical and biochemical process, where deformation and motion of a cell are driven by internal, biochemical regulation of a poroelastic cytoskeleton. One challenge to building quantitative models that describe crawling cells is solving the reaction-diffusion-advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry. Here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell. Our method preserves Cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry. Derivatives approximated using a Taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements. A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves. An implicit time-stepping algorithm is used to maintain stability. We use the algoirthm to simulate two simple models for cellular crawling. The first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate. In the second model, we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal.

Sperm and oocyte communication mechanisms controlling C. elegans fertility

During sexual reproduction in many species, sperm and oocyte secrete diffusible signaling molecules to help orchestrate the biological symphony of fertilization. In the Caenorhabditis elegans gonad, bidirectional signaling between sperm and oocyte is important for guiding sperm to the fertilization site and inducing oocyte maturation. The molecular mechanisms that regulate sperm guidance and oocyte maturation are being delineated. Unexpectedly, these mechanisms are providing insight into human diseases, such as amyotrophic lateral sclerosis, spinal muscular atrophy, and cancer. Here we review sperm and oocyte communication in C. elegans and discuss relationships to human disorders.

A sub-cellular viscoelastic model for cell population mechanics

Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and 'in silico' (computational) models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue.

The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement

We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.

A model of fibroblast motility on substrates with different rigidities

To function efficiently in the body, the biological cells must have the ability to sense the external environment. Mechanosensitivity toward the extracellular matrix was identified as one of the sensing mechanisms affecting cell behavior. It was shown experimentally that a fibroblast cell prefers locomoting over the stiffer substrate when given a choice between a softer and a stiffer substrate. In this article, we develop a discrete model of fibroblast motility with substrate-rigidity sensing. Our model allows us to understand the interplay between the cell-substrate sensing and the cell biomechanics. The model cell exhibits experimentally observed substrate rigidity sensing, which allows us to gain additional insights into the cell mechanosensitivity.

MSP hormonal control of the oocyte MAP kinase cascade and reactive oxygen species signaling

The MSP domain is a conserved immunoglobulin-like structure that is important for C. elegans reproduction and human motor neuron survival. C. elegans MSPs are the most abundant proteins in sperm, where they function as intracellular cytoskeletal proteins and secreted hormones. Secreted MSPs bind to multiple receptors on oocyte and ovarian sheath cell surfaces to induce oocyte maturation and sheath contraction. MSP binding stimulates oocyte MPK-1 ERK MAP Kinase (MAPK) phosphorylation, but the function and mechanism are not well understood. Here we show that the Shp class protein-tyrosine phosphatase PTP-2 acts in oocytes downstream of sheath/oocyte gap junctions to promote MSP-induced MPK-1 phosphorylation. PTP-2 functions in the oocyte cytoplasm, not at the cell surface to inhibit multiple RasGAPs, resulting in sustained Ras activation. We also provide evidence that MSP promotes production of reactive oxygen species (ROS), which act as second messengers to augment MPK-1 phosphorylation. The Cu/Zn superoxide dismutase SOD-1, an enzyme that catalyzes ROS breakdown in the cytoplasm, inhibits MPK-1 phosphorylation downstream of or in parallel to ptp-2. Our results support the model that MSP triggers PTP-2/Ras activation and ROS production to stimulate MPK-1 activity essential for oocyte maturation. We propose that secreted MSP domains and Cu/Zn superoxide dismutases function antagonistically to control ROS and MAPK signaling.

Chemical basis for minimal cognition

We have developed a simple chemical system capable of self-movement in order to study the physicochemical origins of movement. We propose how this system may be useful in the study of minimal perception and cognition. The system consists simply of an oil droplet in an aqueous environment. A chemical reaction within the oil droplet induces an instability, the symmetry of the oil droplet breaks, and the droplet begins to move through the aqueous phase. The complement of physical phenomena that is then generated indicates the presence of feedback cycles that, as will be argued, form the basis for self-regulation, homeostasis, and perhaps an extended form of autopoiesis. We discuss the result that simple chemical systems are capable of sensory-motor coupling and possess a homeodynamic state from which cognitive processes may emerge.

Biochemical mechanisms for regulating protrusion by nematode major sperm protein

Crawling motion is ubiquitous in eukaryotic cells and contributes to important processes such as immune response and tumor growth. To crawl, a cell must adhere to the substrate, while protruding at the front and retracting at the rear. In most crawling cells protrusion is driven by highly regulated polymerization of the actin cytoskeleton, and much of the biochemical network for this process is known. Nematode sperm utilize a cytoskeleton composed of Major Sperm Protein (MSP), which is considered to form a simpler, yet similar, crawling motility apparatus. Key components involved in the polymerization of MSP have been identified; however, little is known about the chemical kinetics for this system. Here we develop a model for MSP polymerization that takes into account the effects of several of the experimentally identified cytosolic and membrane-bound proteins. To account for some of the data, the model requires force-dependent polymerization, as is predicted by Brownian ratchet mechanisms. Using the tethered polymerization ratchet model with our biochemical kinetic model for MSP polymerization, we find good agreement with experimental data on MSP-driven protrusion. In addition, our model predicts the force-velocity relation that is expected for in vitro protrusion assays.

The stochastic search dynamics of interneuron migration

Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment.

Tipping the balance: robustness of tip cell selection, migration and fusion in angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, 'stabilised' tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer.

How a cell crawls and the role of cortical myosin II

The movements of Dictyostelium discoideum amoebae translocating on a glass surface in the absence of chemoattractant have been reconstructed at 5-second intervals and motion analyzed by employing 3D-DIAS software. A morphometric analysis of pseudopods, the main cell body, and the uropod provides a comprehensive description of the basic motile behavior of a cell in four dimensions (4D), resulting in a list of 18 characteristics. A similar analysis of the myosin II phosphorylation mutant 3XASP reveals a role for the cortical localization of myosin II in the suppression of lateral pseudopods, formation of the uropod, cytoplasmic distribution of cytoplasm in the main cell body, and efficient motility. The results of the morphometric analysis suggest that pseudopods, the main cell body, and the uropod represent three motility compartments that are coordinated for efficient translocation. It provides a contextual framework for interpreting the effects of mutations, inhibitors, and chemoattractants on the basic motile behavior of D. discoideum. The generality of the characteristics of the basic motile behavior of D. discoideum must now be tested by similar 4D analyses of the motility of amoeboid cells of higher eukaryotic cells, in particular human polymorphonuclear leukocytes.

Mechanical modes of 'amoeboid' cell migration

The morphological term 'amoeboid' migration subsumes a number of rather distinct biophysical modes of cellular locomotion that range from blebbing motility to entirely actin-polymerization-based gliding. Here, we discuss the diverse principles of force generation and force transduction that lead to the distinct amoeboid phenotypes. We argue that shifting the balance between actin protrusion, actomyosin contraction, and adhesion to the extracellular substrate can explain the different modes of amoeboid movement and that blebbing and gliding are barely extreme variants of one common migration strategy. Depending on the cell type, physiological conditions or experimental manipulation, amoeboid cells can adopt the distinct mechanical modes of amoeboid migration.

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.

Shapes and self-movement in protocell systems

The effect of shapes on self-movement has been studied with an extended model of autopoiesis. Autopoiesis is known as a theory of self-boundary maintenance. In this study, not only the autopoietic generation of the self-boundary, but also the emergence of self-motility, has been examined. As a result of computer simulations, it has been found that different membrane shapes cause different types of self-movement A kind of chemotaxis has been observed for some shapes. The mechanism of chemotaxis is discussed by studying the internal chemical processes within the shape boundaries.

Growth based morphogenesis of vertebrate limb bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea "growth-based morphogenesis." We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs.

The amyotrophic lateral sclerosis 8 protein VAPB is cleaved, secreted, and acts as a ligand for Eph receptors

VAP proteins (human VAPB/ALS8, Drosophila VAP33, and C. elegans VPR-1) are homologous proteins with an amino-terminal major sperm protein (MSP) domain and a transmembrane domain. The MSP domain is named for its similarity to the C. elegans MSP protein, a sperm-derived hormone that binds to the Eph receptor and induces oocyte maturation. A point mutation (P56S) in the MSP domain of human VAPB is associated with Amyotrophic lateral sclerosis (ALS), but the mechanisms underlying the pathogenesis are poorly understood. Here we show that the MSP domains of VAP proteins are cleaved and secreted ligands for Eph receptors. The P58S mutation in VAP33 leads to a failure to secrete the MSP domain as well as ubiquitination, accumulation of inclusions in the endoplasmic reticulum, and an unfolded protein response. We propose that VAP MSP domains are secreted and act as diffusible hormones for Eph receptors. This work provides insight into mechanisms that may impact the pathogenesis of ALS.

Large P body-like RNPs form in C. elegans oocytes in response to arrested ovulation, heat shock, osmotic stress, and anoxia and are regulated by the major sperm protein pathway

As Caenorhabditis elegans hermaphrodites age, sperm become depleted, ovulation arrests, and oocytes accumulate in the gonad arm. Large ribonucleoprotein (RNP) foci form in these arrested oocytes that contain RNA-binding proteins and translationally masked maternal mRNAs. Within 65 min of mating, the RNP foci dissociate and fertilization proceeds. The majority of arrested oocytes with foci result in viable embryos upon fertilization, suggesting that foci are not deleterious to oocyte function. We have determined that foci formation is not strictly a function of aging, and the somatic, ceh-18, branch of the major sperm protein pathway regulates the formation and dissociation of oocyte foci. Our hypothesis for the function of oocyte RNP foci is similar to the RNA-related functions of processing bodies (P bodies) and stress granules; here, we show three orthologs of P body proteins, DCP-2, CAR-1 and CGH-1, and two markers of stress granules, poly (A) binding protein (PABP) and TIA-1, appear to be present in the oocyte RNP foci. Our results are the first in vivo demonstration linking components of P bodies and stress granules in the germ line of a metazoan. Furthermore, our data demonstrate that formation of oocyte RNP foci is inducible in non-arrested oocytes by heat shock, osmotic stress, or anoxia, similar to the induction of stress granules in mammalian cells and P bodies in yeast. These data suggest commonalities between oocytes undergoing delayed fertilization and cells that are stressed environmentally, as to how they modulate mRNAs and regulate translation.

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.

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.

Exploring the control circuit of cell migration by mathematical modeling

We have developed a top-down, rule-based mathematical model to explore the basic principles that coordinate mechanochemical events during animal cell migration, particularly the local-stimulation-global-inhibition model suggested originally for chemotaxis. Cells were modeled as a shape machine that protrudes or retracts in response to a combination of local protrusion and global retraction signals. Using an optimization algorithm to identify parameters that generate specific shapes and migration patterns, we show that the mechanism of local stimulation global inhibition can readily account for the behavior of Dictyostelium under a large collection of conditions. Within this collection, some parameters showed strong correlation, indicating that a normal phenotype may be maintained by complementation among functional modules. In addition, comparison of parameters for control and nocodazole-treated Dictyostelium identified the most prominent effect of microtubules as regulating the rates of retraction and protrusion signal decay, and the extent of global inhibition. Other changes in parameters can lead to profound transformations from amoeboid cells into cells mimicking keratocytes, neurons, or fibroblasts. Thus, a simple circuit of local stimulation-global inhibition can account for a wide range of cell behaviors. A similar top-down approach may be applied to other complex problems and combined with molecular manipulations to define specific protein functions.

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.

Intelligent behaviors of amoeboid movement based on complex dynamics of soft matter

We review how soft matter is self-organized to perform information processing at the cell level by examining the model organism Physarum plasmodium. The amoeboid organism, Physarum polycephalum, in the class of true slime molds, exhibits the intelligent behavior of foraging in complex situations. When placed in a maze with food sources at two exits, the organism develops tubular structures with its body which connect the food sources along the shortest path so that the rates of nutrient absorption and intracellular communication are maximized. This intelligent behavior results from the organism's control of a dynamic network through which mechanical and chemical information is transmitted. We review experimental studies that explore the development and adaptation of structures that make up the network. Recently a model of the dynamic network has been developed, and we review the formulation of this model and present some key results. The model captures the dynamics of existing networks, but it does not answer the question of how such networks form initially. To address the development of cell shape, we review existing mechanochemical models of the protoplasm of Physarum, present more general models of motile cells, and discuss how to adapt existing models to explore the development of intelligent networks in Physarum.

Mathematical Models of Cell Motility

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Teaching hydrogels how to move like an earthworm

Breaking of symmetry is an important principle employed in nature to achieve directional movement in systems of various dimensional scales. The same principle can be utilized in engineered devices. Here we highlight recent work on directed motion and transport capacity of environmentally sensitive polymer gels. The directional motion of cylindrical hydrogels is driven by spatially and temporally controlled propagation of volume phase transitions along their length. This system could potentially be used in a wide variety of areas including biochemical test systems, targeted drug delivery and "soft" medical tools.

Oesophagostomum dentatum: potential as a model for genomic studies of strongylid nematodes, with biotechnological prospects

There are substantial gaps in the knowledge of the molecular processes of development and reproduction in parasitic nematodes, despite the fact that understanding such processes could lead to novel ways of treating and controlling parasitic diseases, through blocking or disrupting key biological pathways. Biotechnological advances through large-scale sequencing projects, approaches for the analysis of differential gene and protein expression and functional genomics (e.g., double-stranded RNA interference) now provide opportunities to investigate the molecular basis of developmental processes in some parasitic nematodes. The porcine nodule worm, Oesophagostomum dentatum (order Strongylida), may provide a platform for testing the function of genes from this and related nematodes, given that this species can be grown and maintained in culture in vitro for periods longer than other nematodes of the same order. In this article, we review relevant biological, biochemical and molecular biological and genomic information about O. dentatum and propose that the O. dentatum - pig system provides an attractive model for exploring molecular developmental and reproductive processes in strongylid nematodes, leading toward new intervention methods and biotechnological outcomes.

Ameboid cell motility: A model and inverse problem, with an application to live cell imaging data

In this article a mathematical model for ameboid cell movement is developed using a spring-dashpot system with Newtonian dynamics. The model is based on the facts that the cytoskeleton plays a primary role for cell motility and that the cytoplasm is viscoelastic. Based on the model, the inverse problem can be posed: if a structure like a spring-dashpot system is embedded into the living cell, what kind of characteristic properties must the structure have in order to reproduce a given movement of the cell? This inverse problem is the primary topic of this paper. On one side the model mimics some features of the movement, and on the other side, the solution to the inverse problem provides model parameters that give some insight, principally into the mechanical aspect, but also, through qualitative reasoning, into chemical and biophysical aspects of the cell. Moreover, this analysis can be done locally or globally and in different media by using the simplest possible information: positions of the cell and nuclear membranes. It is shown that the model and solution to the inverse problem for simulated data sets are highly accurate. An application to a set of live cell imaging data obtained from random movements of a human brain tumor cell (U87-MG human glioblastoma cell line) then provides an example of the efficiency of the model, through the solution of its inverse problem, as a way of understanding experimental data.

Signaling through the phosphatidylinositol 3-kinase regulates mechanotaxis induced by local low magnetic forces in Entamoeba histolytica

In micro-organisms, as well as in metazoan cells, cellular polarization and directed migration are finely regulated by external stimuli, including mechanical stresses. The mechanisms sustaining the transduction of such external stresses into intracellular biochemical signals remain mainly unknown. Using an external magnetic tip, we generated a magnetic field gradient that allows migration analysis of cells submitted to local low-intensity magnetic forces (50 pN). We applied our system to the amoeba Entamoeba histolytica. Indeed, motility and chemotaxis are key activities that allow this parasite to invade and destroy the human tissues during amoebiasis. The magnetic force was applied either inside the cytoplasm or externally at the rear pole of the amoeba. We observed that the application of an intracellular force did not affect cell polarization and migration, whereas the application of the force at the rear pole of the cell induced a persistent polarization and strongly directional motion, almost directly opposed to the magnetic force. This phenomenon was completely abolished when phosphatidylinositol 3-kinase activity was inhibited by wortmanin. This result demonstrated that the applied mechanical stimulus was transduced and amplified into an intracellular biochemical signal, a process that allows such low-intensity force to strongly modify the migration behavior of the cell.

Transgenic soybeans expressing siRNAs specific to a major sperm protein gene suppress Heterodera glycines reproduction

The soybean cyst nematode (SCN), Heterodera glycines, is the major disease-causing agent limiting soybean production in the USA. The current management strategy to reduce yield loss by SCN involves the deployment of resistant soybean cultivars and rotation to non-host crops. Although this management scheme has shown some success, continued yearly yield loss estimates demonstrate the limitations of these techniques. As a result, new control strategies are needed to complement the existing methods. Reported here is a novel method of SCN control that utilises RNA interference (RNAi). Transgenic soybeans were generated following transformation with an RNAi expression vector containing inverted repeats of a cDNA clone of the major sperm protein (MSP) gene from H. glycines. The accumulation of MSP-specific short interfering RNA (siRNA) molecules were detected by northern blot analysis of transgenic soybeans. T₀ plants displaying MSP siRNA accumulation were deployed in a bioassay to evaluate the effects of MSP interfering molecules on H. glycines reproduction. Bioassay data has shown up to a 68% reduction in eggs g^-1 root tissue, demonstrating that MSPi transgenic plants significantly reduced the reproductive potential of H. glycines. An additional bioassay evaluating progeny nematodes for maintenance of reproductive suppression indicated that progeny were also impaired in their ability to successfully reproduce, as demonstrated by a 75% reduction in eggs g^-1 root tissue. The results of this study demonstrate the efficacy of an RNAi-based strategy for control of the soybean cyst nematode. In addition, these results may have important implications for the control of other plant parasitic nematodes.

Nematode sperm motility: nonpolar filament polymerization mediated by end-tracking motors

In nematode sperm cell motility, major sperm protein (MSP) filament assembly results in dynamic membrane protrusions in a manner that closely resembles actin-based motility in other eukaryotic cells. Paradoxically, whereas actin-based motility is driven by addition of ATP-bound actin subunits onto actin filament plus-ends located at the cell membrane, MSP dimers assemble from solution into nonpolar filaments that lack a nucleotide binding site. Thus, filament polarity and on-filament ATP hydrolysis, although essential for actin-based motility, appear to be unnecessary for membrane protrusions by MSP. As a potential resolution to this paradox, we propose a model for MSP filament assembly and force generation by MSP filament end-tracking proteins. In this model, ATP hydrolysis drives affinity-modulated, processive interactions between membrane-associated proteins and elongating filament ends. However, in contrast to the "actoclampin" model for actin filament end-tracking motors, ATP activates the tracking protein (or a soluble cofactor) rather than the MSP subunits themselves (in contrast to activation of actin subunits by ATP binding). The MSP end-tracking model predicts properties that are consistent with several key observations of MSP-based motility, including persistent membrane attachment, polymerization of filament ends at the membrane with depolymerization of free-filament ends away from the membrane, as well as a saturating dependence of polymerization rate on the concentration of non-MSP soluble cytoplasmic components.

Modulation of the reaction rate of regulating protein induces large morphological and motional change of amoebic cell

Morphologies of moving amoebae are categorized into two types. One is the "neutrophil" type in which the long axis of cell roughly coincides with its moving direction. This type of cell extends a leading edge at the front and retracts a narrow tail at the rear, whose shape has been often drawn as a typical amoeba in textbooks. The other one is the "keratocyte" type with widespread lamellipodia along the front side arc. Short axis of cell in this type roughly coincides with its moving direction. In order to understand what kind of molecular feature causes conversion between two types of morphologies, and how two typical morphologies are maintained, a mathematical model of amoebic cells is developed. This model describes movement of cell and intracellular reactions of activator, inhibitor and actin filaments in a unified way. It is found that the producing rate of activator is a key factor of conversion between two types. This model also explains the observed data that the keratocyte type cells tend to rapidly move along a straight line. The neutrophil type cells move along a straight line when the moving velocity is small, but they show fluctuated motions deviating from a line when they move as fast as the keratocyte type cells. Efficient energy consumption in the neutrophil type cells is predicted.

Galphao/i and Galphas signaling function in parallel with the MSP/Eph receptor to control meiotic diapause in C. elegans

BACKGROUND

A conserved biological feature of sexual reproduction in animals is that oocytes arrest in meiotic prophase and resume meiosis in response to extraovarian signals. In C. elegans, sperm trigger meiotic resumption by means of the major sperm protein (MSP) signal. MSP promotes meiotic resumption by functioning as an ephrin-signaling antagonist and by counteracting inhibitory inputs from the somatic gonadal sheath cells.

RESULTS

By using a genome-wide RNAi screen in a female-sterile genetic background, we identified 17 conserved genes that maintain meiotic arrest in the absence of the MSP signal. In vitro binding experiments show that MSP promotes oocyte mitogen-activated protein kinase activation and meiotic maturation in part through direct interaction with the VAB-1 Eph receptor. Four conserved proteins, including a disabled protein (DAB-1), a vav family GEF (VAV-1), a protein kinase C (PKC-1), and a STAM homolog (PQN-19), function with the VAB-1 Eph/MSP receptor in oocytes. We show that antagonistic Galphao/i and Galphas signaling pathways function in the soma to regulate meiotic maturation in parallel to the VAB-1 pathway. Galphas activity is necessary and sufficient to promote meiotic maturation, which it does in part by antagonizing inhibitory sheath/oocyte gap-junctional communication.

CONCLUSIONS

Our findings show that oocyte Eph receptor and somatic cell G protein signaling pathways control meiotic diapause in C. elegans, highlighting contrasts and parallels between MSP signaling in C. elegans and luteinizing hormone signaling in mammals.

The role of gap junctions in Caenorhabditis elegans oocyte maturation and fertilization

We have investigated the role of gap junctions in Caenorhabditis elegans oocyte maturation and fertilization. Gap junctions are observed between oocytes and the surrounding ovarian sheath cells in wild-type gonads. The sheath transcription factor CEH-18 is required to negatively regulate oocyte maturation, mitogen-activated protein kinase (MAPK) activation, and ovulation. Transmission electron microscopy (TEM) indicates that sheath/oocyte gap junctions are rare or absent in ceh-18(mg57) null mutant gonads. To test the hypothesis that gap junctions negatively regulate oocyte maturation, we performed an RNAi screen of innexin genes, which encode channel-forming proteins. Here we show that INX-14 and INX-22 are required in the female germ line to inhibit oocyte maturation, MAPK activation, and ovulation. Genetic analysis and TEM are consistent with INX-14 and INX-22 being components of sheath/oocyte gap junctions. Our results support the hypothesis that gap junctions maintain oocytes in meiotic prophase I when sperm are absent. We also implicate these channels in regulating sheath cell contractile activity and sperm recruitment to the spermatheca, the site of sperm storage and fertilization. Together with previous studies, our results help establish the C. elegans gonad as a model system for investigating the molecular mechanism(s) by which gap junctions regulate meiosis and fertilization.

Major sperm protein signaling promotes oocyte microtubule reorganization prior to fertilization in Caenorhabditis elegans

In most animals, female meiotic spindles assemble in the absence of centrosomes; instead, microtubule nucleation by chromatin, motor activity, and microtubule dynamics drive the self-organization of a bipolar meiotic spindle. Meiotic spindle assembly commences when microtubules gain access to chromatin after nuclear envelope breakdown (NEBD) during meiotic maturation. Although many studies have addressed the chromatin-based mechanism of female meiotic spindle assembly, it is less clear how signaling influences microtubule localization and dynamics prior to NEBD. Here we analyze microtubule behavior in Caenorhabditis elegans oocytes at early stages of the meiotic maturation process using confocal microscopy and live-cell imaging. In C. elegans, sperm trigger oocyte meiotic maturation and ovulation using the major sperm protein (MSP) as an extracellular signaling molecule. We show that MSP signaling reorganizes oocyte microtubules prior to NEBD and fertilization by affecting their localization and dynamics. We present evidence that MSP signaling reorganizes oocyte microtubules through a signaling network involving antagonistic G alpha(o/i) and G alpha(s) pathways and gap-junctional communication with somatic cells of the gonad. We propose that MSP-dependent microtubule reorganization promotes meiotic spindle assembly by facilitating the search and capture of microtubules by meiotic chromatin following NEBD.

Polarization and Movement of Keratocytes: A Multiscale Modelling Approach

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3. In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte.

Blebbing of Dictyostelium cells in response to chemoattractant

Stimulation of Dictyostelium cells with a high uniform concentration of the chemoattractant cyclic-AMP induces a series of morphological changes, including cell rounding and subsequent extension of pseudopodia in random directions. Here we report that cyclic-AMP also elicits blebs and analyse their mechanism of formation. The surface area and volume of cells remain constant during blebbing indicating that blebs form by the redistribution of cytoplasm and plasma membrane rather than the exocytosis of internal membrane coupled to a swelling of the cell. Blebbing occurs immediately after a rapid rise and fall in submembraneous F-actin, but the blebs themselves contain little F-actin as they expand. A mutant with a partially inactivated Arp2/3 complex has a greatly reduced rise in F-actin content, yet shows a large increase in blebbing. This suggests that bleb formation is not enhanced by the preceding actin dynamics, but is actually inhibited by them. In contrast, cells that lack myosin-II completely fail to bleb. We conclude that bleb expansion is likely to be driven by hydrostatic pressure produced by cortical contraction involving myosin-II. As blebs are induced by chemoattractant, we speculate that hydrostatic pressure is one of the forces driving pseudopod extension during movement up a gradient of cyclic-AMP.

Start me up: Cell signaling and the journey from oocyte to embryo inC. elegans

Intercellular communication plays a pivotal role in regulating and coordinating oocyte meiosis and fertilization, key triggers for embryonic development. The nematode Caenorhabaditis elegans has emerged as an important experimental paradigm for exploring these fundamental reproductive processes and their regulation. The oocytes of most animal species arrest during meiotic prophase and complete meiosis in response to intercellular signaling in the process of meiotic maturation. Oocyte meiotic maturation is defined by the transition between diakinesis and metaphase of meiosis I and is accompanied by nuclear envelope breakdown and meiotic spindle assembly. As such, the meiotic maturation process is essential for completing meiosis and a prerequisite for successful fertilization. In C. elegans, the processes of meiotic maturation, ovulation, and fertilization are temporally coupled: sperm utilize the major sperm protein as a hormone to trigger oocyte meiotic maturation, and, in turn, the maturing oocyte signals its own ovulation, leading to fertilization. The powerful genetic screens possible in C. elegans have led to the identification of several sperm cell surface proteins that are required for the interaction and fusion of gametes at fertilization. The study of these proteins provides fundamental insights into fertilization mechanisms, their role in speciation, and their potential conservation across phyla. Signaling processes sparked by fertilization are required for meiotic chromosome segregation and initiating the embryonic program. Here we review recent advances in understanding how signaling mechanisms contribute to the oocyte-to-embryo transition in C. elegans.