How nematode sperm crawl

RNAi-dependent expression of sperm genes in ADL chemosensory neurons is required for olfactory responses in Caenorhabditis elegans

Environmental conditions experienced early in the life of an animal can result in gene expression changes later in its life history. We have previously shown that C. elegans animals that experienced the developmentally arrested and stress resistant dauer stage (postdauers) retain a cellular memory of early-life stress that manifests during adulthood as genome-wide changes in gene expression, chromatin states, and altered life history traits. One consequence of developmental reprogramming in C. elegans postdauer adults is the downregulation of osm-9 TRPV channel gene expression in the ADL chemosensory neurons resulting in reduced avoidance to a pheromone component, ascr#3. This altered response to ascr#3 requires the principal effector of the somatic nuclear RNAi pathway, the Argonaute (AGO) NRDE-3. To investigate the role of the somatic nuclear RNAi pathway in regulating the developmental reprogramming of ADL due to early-life stress, we profiled the mRNA transcriptome of control and postdauer ADL in wild-type and nrde-3 mutant adults. We found 711 differentially expressed (DE) genes between control and postdauer ADL neurons, 90% of which are dependent upon NRDE-3. Additionally, we identified a conserved sequence that is enriched in the upstream regulatory sequences of the NRDE-3-dependent differentially expressed genes. Surprisingly, 214 of the ADL DE genes are considered "germline-expressed", including 21 genes encoding the Major Sperm Proteins and two genes encoding the sperm-specific PP1 phosphatases, GSP-3 and GSP-4. Loss of function mutations in gsp-3 resulted in both aberrant avoidance and attraction behaviors. We also show that an AGO pseudogene, Y49F6A.1 (wago-11), is expressed in ADL and is required for ascr#3 avoidance. Overall, our results suggest that small RNAs and reproductive genes program the ADL mRNA transcriptome during their developmental history and highlight a nexus between neuronal and reproductive networks in calibrating animal neuroplasticity.

Oogenesis in Caenorhabditis elegans

BACKGROUND

The nematode, Caenorhabditis elegans has proven itself as a valuable model for investigating metazoan biology. C. elegans have a transparent body, an invariant cell lineage, and a high level of genetic conservation which makes it a desirable model organism. Although used to elucidate many aspects of somatic biology, a distinct advantage of C. elegans is its well annotated germline which allows all aspects of oogenesis to be observed in real time within a single animal. C. elegans hermaphrodites have two U-shaped gonad arms which produce their own sperm that is later stored to fertilise their own oocytes. These two germlines take up much of the internal space of each animal and germ cells are therefore the most abundant cell present within each animal. This feature and the genetic phenotypes observed for mutant worm gonads have allowed many novel findings that established our early understanding of germ cell dynamics. The mutant phenotypes also allowed key features of meiosis and germ cell maturation to be unveiled.

SUMMARY

This review will focus on the key aspects that make C. elegans an outstanding model for exploring each feature of oogenesis. This will include the fundamental steps associated with germline function and germ cell maturation and will be of use for those interested in exploring reproductive metazoan biology.

KEY MESSAGES

Since germ cell biology is highly conserved in animals, much can be gained from study of a simple metazoan like C. elegans. Past findings have enhanced understanding on topics that would be more laborious or challenging in more complex animal models.

Programmed DNA elimination in the parasitic nematode Ascaris

In most organisms, the whole genome is maintained throughout the life span. However, exceptions occur in some species where the genome is reduced during development through a process known as programmed DNA elimination (PDE). In the human and pig parasite Ascaris, PDE occurs during the 4 to 16 cell stages of embryogenesis, when germline chromosomes are fragmented and specific DNA sequences are reproducibly lost in all somatic cells. PDE was identified in Ascaris over 120 years ago, but little was known about its molecular details until recently. Genome sequencing revealed that approximately 1,000 germline-expressed genes are eliminated in Ascaris, suggesting PDE is a gene silencing mechanism. All germline chromosome ends are removed and remodeled during PDE. In addition, PDE increases the number of chromosomes in the somatic genome by splitting many germline chromosomes. Comparative genomics indicates that these germline chromosomes arose from fusion events. PDE separates these chromosomes at the fusion sites. These observations indicate that PDE plays a role in chromosome karyotype and evolution. Furthermore, comparative analysis of PDE in other parasitic and free-living nematodes illustrates conserved features of PDE, suggesting it has important biological significance. We summarize what is known about PDE in Ascaris and its relatives. We also discuss other potential functions, mechanisms, and the evolution of PDE in these parasites of humans and animals of veterinary importance.

MIG-23 is involved in sperm migration by modulating extracellular ATP levels in Ascaris suum

In nematodes, spermiogenesis is a process of sperm activation in which nonmotile spermatids are transformed into crawling spermatozoa. Sperm motility acquisition during this process is essential for successful fertilization, but the underlying mechanisms remain to be clarified. Herein, we have found that extracellular adenosine-5′-triphosphate (ATP) level regulation by MIG-23, which is a homolog of human ecto-nucleoside triphosphate diphosphohydrolase (E-NTPDase), was required for major sperm protein (MSP) filament dynamics and sperm motility in the nematode Ascaris suum. During sperm activation, a large amount of ATP was produced in mitochondria and was stored in refringent granules (RGs). Some of the produced ATP was released to the extracellular space through innexin channels. MIG-23 was localized in the sperm plasma membrane and contributed to the ecto-ATPase activity of spermatozoa. Blocking MIG-23 activity resulted in a decrease in the ATP hydrolysis activity of spermatozoa and an increase in the depolymerization rate of MSP filaments in pseudopodia, which eventually affected sperm migration. Overall, our data suggest that MIG-23, which contributes to the ecto-ATPase activity of spermatozoa, regulates sperm migration by modulating extracellular ATP levels.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

Genomics of the Parasitic Nematode Ascaris and Its Relatives

Nematodes of the genus Ascaris are important parasites of humans and swine, and the phylogenetically related genera (Parascaris, Toxocara, and Baylisascaris) infect mammals of veterinary interest. Over the last decade, considerable genomic resources have been established for Ascaris, including complete germline and somatic genomes, comprehensive mRNA and small RNA transcriptomes, as well as genome-wide histone and chromatin data. These datasets provide a major resource for studies on the basic biology of these parasites and the host-parasite relationship. Ascaris and its relatives undergo programmed DNA elimination, a highly regulated process where chromosomes are fragmented and portions of the genome are lost in embryonic cells destined to adopt a somatic fate, whereas the genome remains intact in germ cells. Unlike many model organisms, Ascaris transcription drives early development beginning prior to pronuclear fusion. Studies on Ascaris demonstrated a complex small RNA network even in the absence of a piRNA pathway. Comparative genomics of these ascarids has provided perspectives on nematode sex chromosome evolution, programmed DNA elimination, and host-parasite coevolution. The genomic resources enable comparison of proteins across diverse species, revealing many new potential drug targets that could be used to control these parasitic nematodes.

Mutant VAPB: Culprit or Innocent Bystander of Amyotrophic Lateral Sclerosis?

Nearly twenty years ago a mutation in the VAPB gene, resulting in a proline to serine substitution (p.P56S), was identified as the cause of a rare, slowly progressing, familial form of the motor neuron degenerative disease Amyotrophic Lateral Sclerosis (ALS). Since then, progress in unravelling the mechanistic basis of this mutation has proceeded in parallel with research on the VAP proteins and on their role in establishing membrane contact sites between the ER and other organelles. Analysis of the literature on cellular and animal models reviewed here supports the conclusion that P56S-VAPB, which is aggregation-prone, non-functional and unstable, is expressed at levels that are insufficient to support toxic gain-of-function or dominant negative effects within motor neurons. Instead, insufficient levels of the product of the single wild-type allele appear to be required for pathological effects, and may be the main driver of the disease. In light of the multiple interactions of the VAP proteins, we address the consequences of specific VAPB depletion and highlight various affected processes that could contribute to motor neuron degeneration. In the future, distinction of specific roles of each of the two VAP paralogues should help to further elucidate the basis of p.P56S familial ALS, as well as of other more common forms of the disease.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.

Taxon-specific expansion and loss of tektins inform metazoan ciliary diversity

Background

Cilia and flagella are complex cellular structures thought to have first evolved in a last ciliated eukaryotic ancestor due to the conserved 9 + 2 microtubule doublet structure of the axoneme and associated proteins. The Tektin family of coiled-coil domain containing proteins was previously identified in cilia of organisms as diverse as green algae and sea urchin. While studies have shown that some Tektins are necessary for ciliary function, there has been no comprehensive phylogenetic survey of tektin genes. To fill this gap, we sampled tektin sequences broadly among metazoan and unicellular lineages in order to determine how the tektin gene complements evolved in over 100 different extant species.

Results

Using Bayesian and Maximum Likelihood analyses, we have ascertained with high confidence that all metazoan tektins arose from a single ancestral tektin gene in the last common ancestor of metazoans and choanoflagellates. Gene duplications gave rise to two tektin genes in the metazoan ancestor, and a subsequent expansion to three and four tektin genes in early bilaterian ancestors. While all four tektin genes remained highly conserved in most deuterostome and spiralian species surveyed, most tektin genes in ecdysozoans are highly derived with extensive gene loss in several lineages including nematodes and some crustaceans. In addition, while tektin-1, − 2, and − 4 have remained as single copy genes in most lineages, tektin-3/5 has been duplicated independently several times, notably at the base of the spiralian, vertebrate and hymenopteran (Ecdysozoa) clades.

Conclusions

We provide a solid description of tektin evolution supporting one, two, three, and four ancestral tektin genes in a holozoan, metazoan, bilaterian, and nephrozoan ancestor, respectively. The isolated presence of tektin in a cryptophyte and a chlorophyte branch invokes events of horizontal gene transfer, and that the last common ciliated eukaryotic ancestor lacked a tektin gene. Reconstructing the evolutionary history of the tektin complement in each extant metazoan species enabled us to pinpoint lineage specific expansions and losses. Our analysis will help to direct future studies on Tektin function, and how gain and loss of tektin genes might have contributed to the evolution of various types of cilia and flagella.

Electronic supplementary material

The online version of this article (10.1186/s12862-019-1360-0) contains supplementary material, which is available to authorized users.

Soma-germ line interactions and a role for muscle in the regulation of C. elegans sperm motility

The development of highly differentiated sperm cells that are specialized for navigating to and fusing with an oocyte is essential for sexual reproduction. As a major part of differentiation, sperm undergo extensive post-meiotic maturation en route to the oocyte. This is regulated largely by soma-derived cues. In Caenorhabditis elegans, this process is called sperm activation, and it transforms immotile spermatids into migratory fertilization-competent cells. Here, we show that the negative regulator of sperm activation, SWM-1, is produced in an unexpected cell type: body wall muscle. SWM-1 is secreted into the body cavity and enters the gonad; there, it is present with its likely target, TRY-5, a spermiogenesis activator. We show that, in addition to SWM-1, the somatic gonad and body fluid can exchange other factors, suggesting that soma-germ line transfer could affect other reproductive processes. In addition, we show that SWM-1 may have a separate role in the sperm migratory environment, to which it is contributed by both males and hermaphrodites. These findings reveal that late stages in gamete differentiation can be regulated at the whole-organism level by broadly secreted factors.This article has an associated 'The people behind the papers' interview.

Binding of intercellular adhesion molecule 1 to β2-integrin regulates distinct cell adhesion processes on hepatic and cerebral endothelium

Flowing polymorphonuclear neutrophils (PMNs) are forced to recruit toward inflamed tissue and adhere to vascular endothelial cells, which is primarily mediated by the binding of β₂-integrins to ICAM-1. This process is distinct among different organs such as liver and brain; however, the underlying kinetic and mechanical mechanisms regulating tissue-specific recruitment of PMNs remain unclear. Here, binding kinetics measurement showed that ICAM-1 on murine hepatic sinusoidal endothelial cells (LSECs) bound to lymphocyte function-associated antigen-1 (LFA-1) with higher on- and off-rates but lower effective affinity compared with macrophage-1 antigen (Mac-1), whereas ICAM-1 on cerebral endothelial cells (BMECs or bEnd.3 cells) bound to LFA-1 with higher on-rates, similar off-rates, and higher effective affinity compared with Mac-1. Physiologically, free crawling tests of PMN onto LSEC, BMEC, or bEnd.3 monolayers were consistent with those kinetics differences between two β₂-integrins interacting with hepatic sinusoid or cerebral endothelium. Numerical calculations and Monte Carlo simulations validated tissue-specific contributions of β₂-integrin-ICAM-1 kinetics to PMN crawling on hepatic sinusoid or cerebral endothelium. Thus, this work first quantified the biophysical regulation of PMN adhesion in hepatic sinusoids compared with cerebral endothelium.

Proteomic and evolutionary analyses of sperm activation identify uncharacterized genes in Caenorhabditis nematodes

BACKGROUND

Nematode sperm have unique and highly diverged morphology and molecular biology. In particular, nematode sperm contain subcellular vesicles known as membranous organelles that are necessary for male fertility, yet play a still unknown role in overall sperm function. Here we take a novel proteomic approach to characterize the functional protein complement of membranous organelles in two Caenorhabditis species: C. elegans and C. remanei.

RESULTS

We identify distinct protein compositions between membranous organelles and the activated sperm body. Two particularly interesting and undescribed gene families-the Nematode-Specific Peptide family, group D and the here designated Nematode-Specific Peptide family, group F-localize to the membranous organelle. Both multigene families are nematode-specific and exhibit patterns of conserved evolution specific to the Caenorhabditis clade. These data suggest gene family dynamics may be a more prevalent mode of evolution than sequence divergence within sperm. Using a CRISPR-based knock-out of the NSPF gene family, we find no evidence of a male fertility effect of these genes, despite their high protein abundance within the membranous organelles.

CONCLUSIONS

Our study identifies key components of this unique subcellular sperm component and establishes a path toward revealing their underlying role in reproduction.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Rapid Gene Family Evolution of a Nematode Sperm Protein Despite Sequence Hyper-conservation

Reproductive proteins are often observed to be the most rapidly evolving elements within eukaryotic genomes. The major sperm protein (MSP) is unique to the phylum Nematoda and is required for proper sperm locomotion and fertilization. Here, we annotate the MSP gene family and analyze their molecular evolution in 10 representative species across Nematoda. We show that MSPs are hyper-conserved across the phylum, having maintained an amino acid sequence identity of 83.5–97.7% for over 500 million years. This extremely slow rate of evolution makes MSPs some of the most highly conserved genes yet identified. However, at the gene family level, we show hyper-variability in both gene copy number and genomic position within species, suggesting rapid, lineage-specific gene family evolution. Additionally, we find evidence that extensive gene conversion contributes to the maintenance of sequence identity within chromosome-level clusters of MSP genes. Thus, while not conforming to the standard expectation for the evolution of reproductive proteins, our analysis of the molecular evolution of the MSP gene family is nonetheless consistent with the widely repeatable observation that reproductive proteins evolve rapidly, in this case in terms of the genomic properties of gene structure, copy number, and genomic organization. This unusual evolutionary pattern is likely generated by strong pleiotropic constraints acting on these genes at the sequence level, balanced against expansion at the level of the whole gene family.

The secreted MSP domain of C. elegans VAPB homolog VPR-1 patterns the adult striated muscle mitochondrial reticulum via SMN-1

The major sperm protein domain (MSPd) has an extracellular signaling function implicated in amyotrophic lateral sclerosis. Secreted MSPds derived from the C. elegans VAPB homolog VPR-1 promote mitochondrial localization to actin-rich I-bands in body wall muscle. Here we show that the nervous system and germ line are key MSPd secretion tissues. MSPd signals are transduced through the CLR-1 Lar-like tyrosine phosphatase receptor. We show that CLR-1 is expressed throughout the muscle plasma membrane, where it is accessible to MSPd within the pseudocoelomic fluid. MSPd signaling is sufficient to remodel the muscle mitochondrial reticulum during adulthood. An RNAi suppressor screen identified survival of motor neuron 1 (SMN-1) as a downstream effector. SMN-1 acts in muscle, where it colocalizes at myofilaments with ARX-2, a component of the Arp2/3 actin-nucleation complex. Genetic studies suggest that SMN-1 promotes Arp2/3 activity important for localizing mitochondria to I-bands. Our results support the model that VAPB homologs are circulating hormones that pattern the striated muscle mitochondrial reticulum. This function is crucial in adults and requires SMN-1 in muscle, likely independent of its role in pre-mRNA splicing.

Maternal MEMI Promotes Female Meiosis II in Response to Fertilization in Caenorhabditis elegans

In most animals, female meiosis completes only after fertilization. Sperm entry has been implicated in providing a signal for the initiation of the final meiotic processes; however, a maternal component required for this process has not been previously identified. We report the characterization of a novel family of three highly similar paralogs (memi-1, memi-2, memi-3) that encode oocyte-specific proteins. A hyper-morphic mutation memi-1(sb41) results in failure to exit female meiosis II properly; however, loss of all three paralogs results in a "skipped meiosis II" phenotype. Mutations that prevent fertilization, such as fer-1(hc1), also cause a skipped meiosis II phenotype, suggesting that the MEMI proteins represent a maternal component of a postfertilization signal that specifies the meiosis II program. MEMI proteins are degraded before mitosis and sensitive to ZYG-11, a substrate-specific adapter for cullin-based ubiquitin ligase activity, and the memi-1(sb41) mutation results in inappropriate persistence of the MEMI-1 protein into mitosis. Using an RNAi screen for suppressors of memi-1(sb41), we identified a sperm-specific PP1 phosphatase, GSP-3/4, as a putative sperm component of the MEMI pathway. We also found that MEMI and GSP-3/4 proteins can physically interact via co-immunoprecipitation. These results suggest that sperm-specific PP1 and maternal MEMI proteins act in the same pathway after fertilization to facilitate proper meiosis II and the transition into embryonic mitosis.

Comparison of cell migration mechanical strategies in three-dimensional matrices: a computational study

Cell migration on a two-dimensional flat surface has been extensively studied and is generally characterized by a front-protrusion-rear-contraction process. In a three-dimensional (3D) environment, on the other hand, cells adopt multiple migration strategies depending on the cell type and the properties of the extracellular matrix (ECM). By using computer simulations, we find that these migration strategies can be classified by various spatial-temporal dynamics of actin protrusion, actin-myosin contraction and actin-ECM adhesion. We demonstrate that if we include or exclude proteolysis of ECM, and vary adhesion dynamics and spatial distributions of protrusion, contraction and adhesion, our model can reproduce six experimentally observed motility modes: mesenchymal, chimneying, amoeboid, blebbing, finger-like protrusion and rear-squeezing cell locomotory behaviours. We further find that the mode of the cell motility evolves in response to the ECM density and adhesion detachment rate. The model makes non-trivial predictions about cell speed as a function of the adhesion strength, and ECM elasticity and mesh size.

Modelling of Yeast Mating Reveals Robustness Strategies for Cell-Cell Interactions

Mating of budding yeast cells is a model system for studying cell-cell interactions. Haploid yeast cells secrete mating pheromones that are sensed by the partner which responds by growing a mating projection toward the source. The two projections meet and fuse to form the diploid. Successful mating relies on precise coordination of dynamic extracellular signals, signaling pathways, and cell shape changes in a noisy background. It remains elusive how cells mate accurately and efficiently in a natural multi-cell environment. Here we present the first stochastic model of multiple mating cells whose morphologies are driven by pheromone gradients and intracellular signals. Our novel computational framework encompassed a moving boundary method for modeling both a-cells and α-cells and their cell shape changes, the extracellular diffusion of mating pheromones dynamically coupled with cell polarization, and both external and internal noise. Quantification of mating efficiency was developed and tested for different model parameters. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the α-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In addition, we investigated mating discrimination, the ability of an a-cell to distinguish between α-cells either making or not making α-factor, and mating competition, in which multiple a-cells compete to mate with one α-cell. Our simulations were consistent with previous experimental results. Moreover, we performed a combination of simulations and experiments to estimate the diffusion rate of the pheromone a-factor. In summary, we constructed a framework for simulating yeast mating with multiple cells in a noisy environment, and used this framework to reproduce mating behaviors and to identify strategies for robust cell-cell interactions.

One of the riddles of Nature is how cells interact with one another to create complex cellular networks such as the neural networks in the brain. Forming precise connections between irregularly shaped cells is a challenge for biology. We developed computational methods for simulating these complex cell-cell interactions. We applied these methods to investigate yeast mating in which two yeast cells grow projections that meet and fuse guided by pheromone attractants. The simulations described molecules both inside and outside of the cell, and represented the continually changing shapes of the cells. We found that positioning the secretion and sensing of pheromones at the same location on the cell surface was important. Other key factors for robust mating included secreting a protein that removed excess pheromone from outside of the cell so that the signal would not be too strong. An important advance was being able to simulate as many as five cells in complex mating arrangements. Taken together we used our novel computational methods to describe in greater detail the yeast mating process, and more generally, interactions among cells changing their shapes in response to their neighbors.

An integrative toy model of cell flattening, spreading, and ruffling

BACKGROUND

The processes of cell spreading and crawling are frequently associated with mysterious waves and ruffling cycles of the leading edge.

OBJECTIVE

To develop a physical model that can account for these phenomena based on a few simple and plausible rules governing adhesion, contractility, polymerization of cytoskeleton, and membrane tension.

METHODS

Extension of a continuum mechanical model of phagocytosis [J Cell Sci. (2006);119(Pt 9):1903-13] adding a simple coupling between membrane curvature and cytoskeletal polymerization.

RESULTS

We show that our generalized model has just the right nonlinearity needed for triggering of stochastic/chaotic cycles of ruffling similar to those that are observed in real cells.

CONCLUSIONS

The cycles are caused by a branching instability at the leading edge that leads to bifurcations of protrusion into forward moving lamellipodium and upward and rearward folding ruffles. The amplitude of the instability is modulated by the surface tension, with higher tension stabilizing against ruffling (but inhibiting protrusion) and lower tension promoting ruffling and protrusion.

COMP-1 promotes competitive advantage of nematode sperm

Competition among sperm to fertilize oocytes is a ubiquitous feature of sexual reproduction as well as a profoundly important aspect of sexual selection. However, little is known about the cellular mechanisms sperm use to gain competitive advantage or how these mechanisms are regulated genetically. In this study, we utilize a forward genetic screen in Caenorhabditis elegans to identify a gene, comp-1, whose function is specifically required in competitive contexts. We show that comp-1 functions in sperm to modulate their migration through and localization within the reproductive tract, thereby promoting their access to oocytes. Contrary to previously described models, comp-1 mutant sperm show no defects in size or velocity, thereby defining a novel pathway for preferential usage. Our results indicate not only that sperm functional traits can influence the outcome of sperm competition, but also that these traits can be modulated in a context-dependent manner depending on the presence of competing sperm.

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.

A conservative algorithm for parabolic problems in domains with moving boundaries

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. Numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward.

A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell's cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell's boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.

Motility efficiency and spatiotemporal synchronization in non-metastatic vs. metastatic breast cancer cells

Metastatic breast cancer cells move not only more rapidly and persistently than their non-metastatic variants but in doing so use the mechanical work of the cytoskeleton more efficiently. The efficiency of the cell motions is defined for entire cells (rather than parts of the cell membrane) and is related to the work expended in forming membrane protrusions and retractions. This work, in turn, is estimated by integrating the protruded and retracted areas along the entire cell perimeter and is standardized with respect to the net translocation of the cell. A combination of cross-correlation, Granger causality, and morphodynamic profiling analyses is then used to relate the efficiency to the cell membrane dynamics. In metastatic cells, the protrusions and retractions are highly "synchronized" both in space and in time and these cells move efficiently. In contrast, protrusions and retractions formed by non-metastatic cells are not "synchronized" corresponding to low motility efficiencies. Our work provides a link between the kinematics of cell motions and their energetics. It also suggests that spatiotemporal synchronization might be one of the hallmarks of invasiveness of cancerous cells.

Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions

The molecular requirements and morphology of migrating cells can vary depending on matrix geometry; therefore, predicting the optimal migration strategy or the effect of experimental perturbation is difficult. We present a model of cell motility that encompasses actin-polymerization-based protrusions, actomyosin contractility, variable actin-plasma membrane linkage leading to membrane blebbing, cell-extracellular-matrix adhesion and varying extracellular matrix geometries. This is used to explore the theoretical requirements for rapid migration in different matrix geometries. Confined matrix geometries cause profound shifts in the relationship of adhesion and contractility to cell velocity; indeed, cell-matrix adhesion is dispensable for migration in discontinuous confined environments. The model is challenged to predict the effect of different combinations of kinase inhibitors and integrin depletion in vivo, and in confined matrices based on in vitro two-dimensional measurements. Intravital imaging is used to verify bleb-driven migration at tumour margins, and the predicted response to single and combinatorial manipulations.

Mathematical modeling of the impact of actin and keratin filaments on keratinocyte cell spreading

Keratin intermediate filaments (IFs) form cross-linked arrays to fulfill their structural support function in epithelial cells and tissues subjected to external stress. How the cross-linking of keratin IFs impacts the morphology and differentiation of keratinocytes in the epidermis and related surface epithelia remains an open question. Experimental measurements have established that keratinocyte spreading area is inversely correlated to the extent of keratin IF bundling in two-dimensional culture. In an effort to quantitatively explain this relationship, we developed a mathematical model in which isotropic cell spreading is considered as a first approximation. Relevant physical properties such as actin protrusion, adhesion events, and the corresponding response of lamellum formation at the cell periphery are included in this model. Through optimization with experimental data that relate time-dependent changes in keratinocyte surface area during spreading, our simulation results confirm the notion that the organization and mechanical properties of cross-linked keratin filaments affect cell spreading; in addition, our results provide details of the kinetics of this effect. These in silico findings provide further support for the notion that differentiation-related changes in the density and intracellular organization of keratin IFs affect tissue architecture in epidermis and related stratified epithelia.

Crawling of a driven adherent membrane

We discuss motions of an elastic N × M membrane model whose constituents can bind reversibly with strength ε to adhesive sites of a flat substrate. One of the edges of the membrane ("front") is driven in one direction at rate constant p by N stochastically treadmilling short parallel lines ("cortex"). The main conclusions derived from Monte Carlo studies of this model are the following: (a) Since the polymerizing cortex pushes only the leading edge of the membrane, the major part of the membranes is dragged behind. Therefore, the locomotion of the membrane can be described by frictional sliding processes which are asymmetrically distributed between front and rear of the membrane. A signature of this asymmetry is the difference between the life times of adhesion bonds at front and rear, τ(1) and τ(M), respectively, where τ(1) ≫ τ(M). (b) There are four characteristic times for the membrane motion: The first time, T(0) ~ τ(M) ~ e(aε), is the resting time where the displacement of the membrane is practically zero. The second time, T(p) ~ τ(1) ~ M, is the friction time which characterizes the time between two consecutive ruptures of adhesion bonds at the front, and which signalizes the onset of drift ("protrusion") at the leading edge. The third time, T(r) ~ M(γ(ε)) (γ > 1), characterizes the "retraction" of the trailing edge, which is the retarded response to the pulling leading edge. The fourth time, T(L) ~ M(2), is the growth time for fluctuation of the end-to-end distance. (c) The separation of time scales, T(r)/T(p) ~ M(γ(ε) - 1), leads to stretched fluctuations of the end-to-end distance, which are considered as stochastic cycles of protrusion and retraction on the time scale of T(L). (d) The drift velocity v obeys anomalous scaling, v/p~f(p(1/γ(ε))M), where f(z) ~ const. for small drag pM ≪ 1, and f(z) ~ z(-γ(ε)) for pM ≫ 1, which implies v~M(-γ(ε)). These results may also turn out to be useful for the (more difficult) problem of understanding the protrusion-retraction cycle of crawling biological cells. We compare our model and our results to previous two-particle theories for membrane protrusion and to known stochastic friction models.

Asymmetry between pushing and pulling for crawling cells

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.

Cell migration with multiple pseudopodia: temporal and spatial sensing models

Cell migration triggered by pseudopodia (or "false feet") is the most used method of locomotion. A 3D finite element model of a cell migrating over a 2D substrate is proposed, with a particular focus on the mechanical aspects of the biological phenomenon. The decomposition of the deformation gradient is used to reproduce the cyclic phases of protrusion and contraction of the cell, which are tightly synchronized with the adhesion forces at the back and at the front of the cell, respectively. First, a steady active deformation is considered to show the ability of the cell to simultaneously initiate multiple pseudopodia. Here, randomness is considered as a key aspect, which controls both the direction and the amplitude of the false feet. Second, the migration process is described through two different strategies: the temporal and the spatial sensing models. In the temporal model, the cell "sniffs" the surroundings by extending several pseudopodia and only the one that receives a positive input will become the new leading edge, while the others retract. In the spatial model instead, the cell senses the external sources at different spots of the membrane and only protrudes one pseudopod in the direction of the most attractive one.

Control of oocyte growth and meiotic maturation in Caenorhabditis elegans

In sexually reproducing animals, oocytes arrest at diplotene or diakinesis and resume meiosis (meiotic maturation) in response to hormones. Chromosome segregation errors in female meiosis I are the leading cause of human birth defects, and age-related changes in the hormonal environment of the ovary are a suggested cause. Caenorhabditis elegans is emerging as a genetic paradigm for studying hormonal control of meiotic maturation. The meiotic maturation processes in C. elegans and mammals share a number of biological and molecular similarities. Major sperm protein (MSP) and luteinizing hormone (LH), though unrelated in sequence, both trigger meiotic resumption using somatic Gα(s)-adenylate cyclase pathways and soma-germline gap-junctional communication. At a molecular level, the oocyte responses apparently involve the control of conserved protein kinase pathways and post-transcriptional gene regulation in the oocyte. At a cellular level, the responses include cortical cytoskeletal rearrangement, nuclear envelope breakdown, assembly of the acentriolar meiotic spindle, chromosome segregation, and likely changes important for fertilization and the oocyte-to-embryo transition. This chapter focuses on signaling mechanisms required for oocyte growth and meiotic maturation in C. elegans and discusses how these mechanisms coordinate the completion of meiosis and the oocyte-to-embryo transition.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

A comparison of computational models for eukaryotic cell shape and motility

Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction–diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a “free-boundary” problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.

Modeling of adhesion, protrusion, and contraction coordination for cell migration simulations

Cell migration is a highly complex, dynamical biological phenomenon that involves precise spatio-temporal coordination of distinctive sub-processes including adhesion, protrusion, and contraction of the cell. Observations of individual tumor cell migration reveal that cells generally exhibit either mesenchymal-type or amoeboid-type migration modes in native like environments. However, it has also been observed that some migrating cells are capable of morphologically adapting to their environment by modifying their type of migration. Recent studies suggest in fact that changes in biophysical and biomechanical properties of tumor cells can reversibly control their transition from one type of migration to the other. These changes may be caused by internal cell biomechanical mechanisms as well as mechanical and topological properties of the extracellular matrix. In order to understand the complex transition between the two modes and the role played by internal cellular mechanics during migration, we have developed a novel axisymmetric hyperviscoelastic cell model to simulate the dynamical behavior of a migrating cell. Numerical results from our study quantitatively demonstrate that the biomechanical properties of the cell may play an important role in the amoeboid-mesenchymal transition during migration. Our study will therefore not only help in creating a new platform for simulating cellular processes but will also provide insights into the role of sub-cellular mechanics in regulating various modes of migration during tumor invasion and metastasis.

A critical stress model for cell motility

A detailed theoretical model that combines the conventional viscoelastic continuum description of cell motion with a dynamic active stress is presented. The model describes the ameboid cells movement comprising of protrusion and adhesion of the front edge followed by detachment and movement of the tail. Unlike the previous viscoelastic descriptions in which the cell movement is steady, the presented model describes the “walking” of the cell in response to specific active stress components acting separately on the front and rear of the cell. In this locomotive model first the tail of the cell is attached to the substrate and active stress is applied to the front of the cell. Consequently, the stress in the tail increases. When the stress in the tail exceeds a critical value, namely critical stress, the conditions are updated so that the front is fixed and the tail of the cell is detached from the substrate and moves towards the front. Consequently, the stress in the tail decreases. When the stress goes to zero, the starting conditions become active and the process continues. At start the cell is stretched and its length is increased as the front of cell migrates more than the rear. However, after several steps the front and rear move equally and the cell length stays constant during the movement. In this manuscript we analyzed such cell dynamics including the length variation and moving velocity. Finally, by considering this fact that at the single-cell level, interactions with the extracellular environment occur on a nanometer length scale, the value of critical stress was estimated.

Self-organized cell motility from motor-filament interactions

Cell motility is driven primarily by the dynamics of the cell cytoskeleton, a system of filamentous proteins and molecular motors. It has been proposed that cell motility is a self-organized process, that is, local short-range interactions determine much of the dynamics that are required for the whole-cell organization that leads to polarization and directional motion. Here we present a mesoscopic mean-field description of filaments, motors, and cell boundaries. This description gives rise to a dynamical system that exhibits multiple self-organized states. We discuss several qualitative aspects of the asymptotic states and compare them with those of living cells.

Computational modelling of maternal interactions with spermatozoa: potentials and prospects

Understanding the complex interactions between gametes, embryos and the maternal tract is required knowledge for combating infertility and developing new methods of contraception. Here we present some main aspects of spermatozoa interactions with the mammalian oviduct before fertilisation and discuss how computational modelling can be used as an invaluable aid to experimental investigation in this field. A complete predictive computational model of gamete and embryo interactions with the female reproductive tract is a long way off. However, the enormity of this task should not discourage us from working towards it. Computational modelling allows us to investigate aspects of maternal communication with gametes and embryos, which are financially, ethically or practically difficult to look at experimentally. In silico models of maternal communication with gametes and embryos can be used as tools to complement in vivo experiments, in the same way as in vitro and in situ models.

'Run-and-tumble' or 'look-and-run'? A mechanical model to explore the behavior of a migrating amoeboid cell

Single cell migration constitutes a fundamental phenomenon involved in many biological events. Amoeboid cells are single cell organisms that migrate in a cyclic manner like worms. In this paper, we propose a 3D finite element model of an amoeboid cell migrating over a 2D surface. In particular, we focus on the mechanical aspect of the problem. The cell is able to generate cyclic active deformations, such as protrusion and contraction, in any direction. The progression of the cell is governed by a tight synchronization between the adhesion forces, which are alternatively applied at the front and at the rear edges of the cell, and the protrusion-contraction phases of the cell body. Finally, two important aspects have been taken into account: (1) the external stimuli in response to which the cell migrates (e.g. need to feed, morphogenetic events, normal or abnormal environment cues), (2) the heterogeneity of the 2D substrate (e.g. obstacles, rugosity, slippy regions) for which two distinct approaches have been evaluated: the 'run-and-tumble' strategy and the 'look-and-run' strategy. Overall, the results show a good agreement with respect to the experimental observations and the data from the literature (e.g. velocity and strains). Therefore, the present model helps, on one hand, to better understand the intimate relationship between the deformation modes of a cell and the adhesion strength that is required by the cell to crawl over a substrate, and, on the other hand, to put in evidence the crucial role played by mechanics during the migration process.

How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility

To regulate shape changes, motility and chemotaxis in eukaryotic cells, signal transduction pathways channel extracellular stimuli to the reorganization of the actin cytoskeleton. The complexity of such networks makes it difficult to understand the roles of individual components, let alone their interactions and multiple feedbacks within a given layer and between layers of signalling. Even more challenging is the question of if and how the shape of the cell affects and is affected by this internal spatiotemporal reorganization. Here we build on our previous 2D cell motility model where signalling from the Rho family GTPases (Cdc42, Rac, and Rho) was shown to organize the cell polarization, actin reorganization, shape change, and motility in simple gradients. We extend this work in two ways: First, we investigate the effects of the feedback between the phosphoinositides (PIs) , and Rho family GTPases. We show how that feedback increases heights and breadths of zones of Cdc42 activity, facilitating global communication between competing cell “fronts”. This hastens the commitment to a single lamellipodium initiated in response to multiple, complex, or rapidly changing stimuli. Second, we show how cell shape feeds back on internal distribution of GTPases. Constraints on chemical isocline curvature imposed by boundary conditions results in the fact that dynamic cell shape leads to faster biochemical redistribution when the cell is repolarized. Cells with frozen cytoskeleton, and static shapes, consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes, the degree of the shape-induced effects being proportional to the extent of cell deformation. We explain these concepts in the context of several in silico experiments using our 2D computational cell model.

Single cells, such as amoeba and white blood cells, change shape and move in response to environmental stimuli. Their behaviour is a consequence of the intracellular properties balanced by external forces. The internal regulation is modulated by several proteins that interact with one another and with membrane lipids. We examine, through in silico experiments using a computational model of a moving cell, the interactions of an important class of such proteins (Rho GTPases) and lipids (phosphoinositides, PIs), their spatial redistribution, and how they affect and are affected by cell shape. Certain GTPases promote the assembly of the actin cytoskeleton. This then leads to the formation of a cell protrusion, the leading edge. The feedback between PIs and GTPases facilitates global communication across the cell, ensuring that multiple, complex, or rapidly changing stimuli can be resolved into a single decision for positioning the leading edge. Interestingly, the cell shape itself affects the intracellular biochemistry, resulting from interactions between the curvature of the chemical fronts and the cell edge. Cells with static shapes consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes. This potential to respond more rapidly to external stimuli depends on the degree of cellular shape deformation.

Secreted VAPB/ALS8 major sperm protein domains modulate mitochondrial localization and morphology via growth cone guidance receptors

VIDEO ABSTRACT

The VAPB/ALS8 major sperm protein domain (vMSP) is implicated in amyotrophic lateral sclerosis and spinal muscular atrophy, yet its function in the nervous system is not well understood. In Caenorhabditis elegans and Drosophila, the vMSP is cleaved from its transmembrane anchor and secreted in a cell type-specific fashion. We show that vMSPs secreted by neurons act on Lar-like protein-tyrosine phosphatase and Roundabout growth cone guidance receptors expressed in striated muscle. This signaling pathway promotes Arp2/3-dependent actin remodeling and mitochondrial localization to actin-rich muscle I-bands. C. elegans VAPB mutants have mitochondrial localization, morphology, mobility, and fission/fusion defects that are suppressed by Lar-like receptor or Arp2/3 inactivation. Hence, growth cone guidance receptor pathways that remodel the actin cytoskeleton have unanticipated effects on mitochondrial dynamics. We propose that neurons secrete vMSPs to promote striated muscle energy production and metabolism, in part through the regulation of mitochondrial localization and function.

Contractile network models for adherent cells

Cells sense the geometry and stiffness of their adhesive environment by active contractility. For strong adhesion to flat substrates, two-dimensional contractile network models can be used to understand how force is distributed throughout the cell. Here we compare the shape and force distribution for different variants of such network models. In contrast to Hookean networks, cable networks reflect the asymmetric response of biopolymers to tension versus compression. For passive networks, contractility is modeled by a reduced resting length of the mechanical links. In actively contracting networks, a constant force couple is introduced into each link in order to model contraction by molecular motors. If combined with fixed adhesion sites, all network models lead to invaginated cell shapes, but only actively contracting cable networks lead to the circular arc morphology typical for strongly adhering cells. In this case, shape and force distribution are determined by local rather than global determinants and thus are suited to endow the cell with a robust sense of its environment. We also discuss nonlinear and adaptive linker mechanics as well as the relation to tissue shape.

Cell motility resulting from spontaneous polymerization waves

The crawling of cells on a substrate is in many cases driven by the actin cytoskeleton. How actin filaments and associated proteins are organized to generate directed motion is still poorly understood. Recent experimental observations suggest that spontaneous cytoskeletal waves might orchestrate the actin-filament network to produce directed motion. We investigate this possibility by studying a mean-field description of treadmilling filaments interacting with nucleating proteins, a system that is known to self-organize into waves. Confining the system by a boundary that shares essential features of membranes, we find that spontaneous waves can generate directional motion. We also find that it can produce lateral waves along the confining membrane as are observed in spreading cells.

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.

Fluid transport by active elastic membranes

A flexible membrane deforming its shape in time can self-propel in a viscous fluid. Alternatively, if the membrane is anchored, its deformation will lead to fluid transport. Past work in this area focused on situations where the deformation kinematics of the membrane were prescribed. Here we consider models where the deformation of the membrane is not prescribed, but instead the membrane is internally forced. Both the time-varying membrane shape and the resulting fluid motion result then from a balance between prescribed internal active stresses, internal passive resistance, and external viscous stresses. We introduce two specific models for such active internal forcing: one where a distribution of active bending moments is prescribed, and one where active inclusions exert normal stresses on the membrane by pumping fluid through it. In each case, we asymptotically calculate the membrane shape and the fluid transport velocities for small forcing amplitudes, and recover our results using scaling analysis.

The gap junctional protein INX-14 functions in oocyte precursors to promote C. elegans sperm guidance

Innexins are the subunits of invertebrate gap junctions. Here we show that the innexin INX-14 promotes sperm guidance to the fertilization site in the Caenorhabditis elegans hermaphrodite reproductive tract. inx-14 loss causes cell nonautonomous defects in sperm migration velocity and directional velocity. Results from genetic and immunocytochemical analyses provide strong evidence that INX-14 acts in transcriptionally active oocyte precursors in the distal gonad, not in transcriptionally inactive oocytes that synthesize prostaglandin sperm-attracting cues. Somatic gonadal sheath cell interaction is necessary for INX-14 function, likely via INX-8 and INX-9 expressed in sheath cells. However, electron microscopy has not identified gap junctions in oocyte precursors, suggesting that INX-14 acts in a channel-independent manner or INX-14 channels are difficult to document. INX-14 promotes prostaglandin signaling to sperm at a step after F-series prostaglandin synthesis in oocytes. Taken together, our results support the model that INX-14 functions in a somatic gonad/germ cell signaling mechanism essential for sperm function. We propose that this mechanism regulates the transcription of a factor(s) that modulates prostaglandin metabolism, transport, or activity in the reproductive tract.

Cell motility: the integrating role of the plasma membrane

The plasma membrane is of central importance in the motility process. It defines the boundary separating the intracellular and extracellular environments, and mediates the interactions between a motile cell and its environment. Furthermore, the membrane serves as a dynamic platform for localization of various components which actively participate in all aspects of the motility process, including force generation, adhesion, signaling, and regulation. Membrane transport between internal membranes and the plasma membrane, and in particular polarized membrane transport, facilitates continuous reorganization of the plasma membrane and is thought to be involved in maintaining polarity and recycling of essential components in some motile cell types. Beyond its biochemical composition, the mechanical characteristics of the plasma membrane and, in particular, membrane tension are of central importance in cell motility; membrane tension affects the rates of all the processes which involve membrane deformation including edge extension, endocytosis, and exocytosis. Most importantly, the mechanical characteristics of the membrane and its biochemical composition are tightly intertwined; membrane tension and local curvature are largely determined by the biochemical composition of the membrane and the biochemical reactions taking place; at the same time, curvature and tension affect the localization of components and reaction rates. This review focuses on this dynamic interplay and the feedbacks between the biochemical and biophysical characteristics of the membrane and their effects on cell movement. New insight on these will be crucial for understanding the motility process.

Viscoelastic gel-strip model for the simulation of migrating cells

Migrating tumor cells can exhibit both mesenchymal- and amoeboid-type behaviors. Recent studies have shown that both cellular and extracellular structural and mechanical variables control the transition of tumor cells from one mode to the other and provide them with morphological plasticity. The mesenchymal-mode migration is characterized by strong adhesion and proteolytic machinery to navigate through complex extracellular matrices. The amoeboid-mode migration is characterized by little or no adhesion and strong actomyosin contraction to squeeze through the matrices. While adhesion dependent migration has been computationally and experimentally studied in both 2D and 3D environments, quantitative models of amoeboid motion in native environments are lacking. In order to address this major gap in our understanding and to probe the mesenchymal to amoeboid transitions quantitatively and comprehensively, we have developed an axisymmetric viscoelastic gel-strip model of a single cell to investigate a cell migrating in native-like environments. In this model, cell migration and morphology are governed by internal stresses as well as external forces. The internal stresses are controlled by F-actin density distribution, protrusion strength, and contraction strength. The external forces are controlled by adhesion strength and steric resistance from the extracellular matrix. Our model predicts that the transition of the cell migration mode from mesenchymal- to amoeboid-type, and vice versa, is closely related to the loss of adhesion as well as increased contraction strength of the cells. Our results indicate that amoeboid migration is more suited for low-resistance environment while mesenchymal migration is preferred in high-resistance environment, which would explain the versatile behaviors of tumor cells in complex environments.