Structure and dynamics of human vimentin intermediate filament dimer and tetramer in explicit and implicit solvent models

Intermediate filaments, in addition to microtubules and microfilaments, are one of the three major components of the cytoskeleton in eukaryotic cells, and play an important role in mechanotransduction as well as in providing mechanical stability to cells at large stretch. The molecular structures, mechanical and dynamical properties of the intermediate filament basic building blocks, the dimer and the tetramer, however, have remained elusive due to persistent experimental challenges owing to the large size and fibrillar geometry of this protein. We have recently reported an atomistic-level model of the human vimentin dimer and tetramer, obtained through a bottom-up approach based on structural optimization via molecular simulation based on an implicit solvent model (Qin et al. in PLoS ONE 2009 4(10):e7294, 9). Here we present extensive simulations and structural analyses of the model based on ultra large-scale atomistic-level simulations in an explicit solvent model, with system sizes exceeding 500,000 atoms and simulations carried out at 20 ns time-scales. We report a detailed comparison of the structural and dynamical behavior of this large biomolecular model with implicit and explicit solvent models. Our simulations confirm the stability of the molecular model and provide insight into the dynamical properties of the dimer and tetramer. Specifically, our simulations reveal a heterogeneous distribution of the bending stiffness along the molecular axis with the formation of rather soft and highly flexible hinge-like regions defined by non-alpha-helical linker domains. We report a comparison of Ramachandran maps and the solvent accessible surface area between implicit and explicit solvent models, and compute the persistence length of the dimer and tetramer structure of vimentin intermediate filaments for various subdomains of the protein. Our simulations provide detailed insight into the dynamical properties of the vimentin dimer and tetramer intermediate filament building blocks, which may guide the development of novel coarse-grained models of intermediate filaments, and could also help in understanding assembly mechanisms.     

Ommatidial development in Drosophila eye disc fragments

We have tested the hypothesis that the leading edge of the growing Drosophila compound eye acts as a template that organizes unpatterned cells of the retinal epithelium into the accurate cellular mosaic of the eye. Unpatterned fragments of the epithelium, not containing the leading edge of the growing field, were transplanted into larval hosts. After hosts pupated, the implants were recovered; most contained ommatidia, demonstrating that the leading edge of the growing eye pattern is not required for its propagation. In a second set of experiments, implants were recovered before hosts pupated and examined for ommatidia using a monoclonal antibody. These implants likewise differentiated ommatidia and the temporal progress of retinal development in the implants mirrored that of normal development. A schedule of ommatidial development thus appears to be mapped onto the retinal epithelium in advance of the leading edge.     

Fine filaments observed within the cytoplasm surrounding the leading edge of the septum in telophase cells of Spirogyra (Zygnematales, Chlorophyta)

Electron microscope observation revealed the presence of many fine filaments within the cytoplasm surrounding the leading edge of the septum in telophase cells of Spirogyra verruculosa Jao. These filaments, about 7 nm each in diameter, ran parallel to one another along the leading edge of the septum and, sometimes, they appeared to be gathered into at least two bundles. These filament distribution patterns coincided well with those of the fluorescence of rhodamine-labeled phalloidin in the vicinity of the septum in telophase cells. The present results suggest that the fine filaments observed within the cytoplasm surrounding the leading edge of the septum may be actin filaments.     

Distribution of junction- and differentiation-related proteins in urothelial cells at the leading edge of primary explant outgrowths

Leading edge cells, which are located at the forefront of a wound margin, play a significant role in coordinating the wound healing process. In this study, leading edge cells of the urothelial explant outgrowth, resembling leading edge cells during urothelial full-thickness wound healing in vivo, were analyzed for expression and distribution of junction and differentiation-related proteins. Ultrastructural and immunofluorescence studies revealed that urothelial cells at the leading edge expressed ZO-1, claudin-4, occludin, E-cadherin, cytokeratin 7 and cytokeratin 20, while no expression of claudin-8 was noted. ZO-1, claudin-4, occludin and E-cadherin were localized along the cell membranes where neighbouring leading edge cells were in contact. Cytokeratin 7 was detected as filaments and cytokeratin 20 as small dots and sparse filaments. In conclusion, we detected early expression of ZO-1, claudin-4 and occludin at the urothelial leading edge, predicating the later formation of tight junctions as a necessary stage for the differentiation process that subsequently begins. The expression of occludin and cytokeratin 20 in urothelial cells at the leading edge suggests that leading edge cells may develop into fully differentiated superficial cells.     

Dynamic Network Morphology and Tension Buildup in a 3D Model of Cytokinetic Ring Assembly

During fission yeast cytokinesis, actin filaments nucleated by cortical formin Cdc12 are captured by myosin motors bound to a band of cortical nodes and bundled by cross-linking proteins. The myosin motors exert forces on the actin filaments, resulting in a net pulling of the nodes into a contractile ring, while cross-linking interactions help align actin filaments and nodes into a single bundle. We used these mechanisms in a three-dimensional computational model of contractile ring assembly, with semiflexible actin filaments growing from formins at cortical nodes, capturing of filaments by neighboring nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin filament density at the cell cortex, morphologies of condensing node-filament networks, and regimes of cortical tension by varying the node pulling force and strength of cross-linking among actin filaments. Results show that cross-linking interactions can lead to confinement of actin filaments at the simulated cortical boundary. We show that the ring-formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars, and meshworks can appear in the process of ring assembly. These results are consistent with prior experiments with mutations in actin-filament turnover regulators, myosin motor activity, and changes in the concentration of cross-linkers that alter the morphology of the condensing network. Transient star shapes appear in some simulations, and these morphologies offer an explanation for star structures observed in prior experimental images. Finally, we quantify tension along actin filaments and forces on nodes during ring assembly and show that the mechanisms describing ring assembly can also drive ring constriction once the ring is formed.     

Leading edge movement and ultrastructure in mouse macrophages

The first event in the process of translocation of a cell over a substrate is the forward protrusion of a thin layer of cytoplasm, sometimes referred to as the leading edge. To gain more direct information on structural reorganizations associated with protrusion we have documented the ultrastructure of the actin cytoskeleton of mouse macrophages whose history of locomotion prior to fixation for electron microscopy had been recorded by video microscopy. It is shown that rapid protrusion is associated with the formation of a dense, diagonal network of actin filaments, lacking organized bundles. In cell edges that showed minor fluctuations back and forth over a period of 30 sec or more no dense meshworks were found: instead, a loose peripheral bundle of actin filaments was commonly observed. Cell edges that first protruded and then retracted showed a similar ultrastructure to those that exhibited only forward movement, but the width of the leading edge meshwork was, by comparison, reduced. Measurements showed that there was an approximate correlation between the leading edge mesh width and the net forward translocation observed during the terminal 30 sec, up to fixation. The results are discussed in relation to present concepts of the protrusion mechanism.     

Interplay between Brownian motion and cross-linking controls bundling dynamics in actin networks

Morphology changes in cross-linked actin networks are important in cell motility, division, and cargo transport. Here, we study the transition from a weakly cross-linked network of actin filaments to a heavily cross-linked network of actin bundles through microscopic Brownian dynamics simulations. We show that this transition occurs in two stages: first, a composite bundle network of small and highly aligned bundles evolves from cross-linking of individual filaments and, second, small bundles coalesce into the clustered bundle state. We demonstrate that Brownian motion speeds up the first stage of this process at a faster rate than the second. We quantify the time to reach the composite bundle state and show that it strongly increases as the mesh size increases only when the concentration of cross-links is small and that it remains roughly constant if we decrease the relative ratio of cross-linkers as we increase the actin concentration. Finally, we examine the dependence of the bundling timescale on filament length, finding that shorter filaments bundle faster because they diffuse faster.     

Filament arrangements in negatively stained cultured cells: the organization of actin

Treatment of spread, cultured cells with Triton X-100 followed by negative staining reveals the organization of the unextracted intracellular filamentous elements: actin, microtubules and the 100 angstrom filaments. The present report describes the organization of the actin-like filaments in human skin fibroblasts and mouse 3 T 3 cells. As shown in earlier studies, the cytoplasmic stress fibres were seen to be composed of bundles of colinear actin-like filaments. In addition to these large stress fibres much smaller bundles of thin filaments as well as randomly oriented thin filaments were also observed. A thick bundle of thin filaments, 0.2 microm to 0.5 microm in diameter, was found to delimit the concave cell edges most prominent in well-spread stationary cells. The leading edge and ruffled border of human skin fibroblasts appeared as a broad web, of meshwork of diagonally oriented thin filaments interconnecting radiating, linear bundles of thin filaments about 0.1 microm in diameter. These bundles corresponding to the microspikes described earlier ranged from about 1.5 microm in length and were separated by 1 microm to 3 microm laterally. The leading edge of 3 T 3 cells showed a similar organization but with fewer radiating thin filament bundles. Both the filaments in the bundles and in the meshwork formed arrowhead complexes with smooth muscle myosin subfragment - 1 which were unipolar and directed towards the main body of the cell. The findings are discussed in relation to the mechanisms of non-muscle cell motility.     

Modeling of the actin-cytoskeleton in symmetric lamellipodial fragments

The pushing structures of cells include laminar sheets, termed lamellipodia, made up of a meshwork of actin filaments that grow at the front and depolymerise at the rear, in a treadmilling mode. We here develop a mathematical model to describe the turnover and the mechanical properties of this network.Our basic modeling assumptions are that the lamellipodium is idealised as a two-dimensional structure, and that the actin network consists of two families of possibly bent, but locally parallel filaments. Instead of dealing with individual polymers, the filaments are assumed to be continuously distributed.The model includes (de)polymerization, of the mechanical effects of cross-linking, cell-substrate adhesion, as well as of the leading edge of the membrane.In the first version presented here, the total amount of F-actin is prescribed by assuming a constant polymerisation speed at the leading edge and a fixed total number and length distribution of filaments. We assume that cross-links at filament crossing points as well as integrin linkages with the matrix break and reform in response to incremental changes in network organization. In this first treatment, the model successfully simulates the persistence of the treadmilling network in radially spread cells.Key words: modelling, cell movement, actin-network     

Reorganization of the actin cytoskeleton in the protruding lamellae of human fibroblasts.

To investigate the mechanisms of protrusion in vertebrate cells, the primary event in cell motility, human fibroblasts were treated with neomycin, an inhibitor of the phosphatidylinositol cycle, to induce protrusion. Changes in cell motility and the cytoskeleton were examined by video, fluorescence, scanning electron, and confocal microscopy and by cytofluorometry. Protrusion in neomycin-treated human fibroblasts is correlated with a transient overall decrease in F-actin followed by an increase in F-actin at the leading edge of the protruding lamella. In growing lamellae, F-actin is organized in a marginal band at the leading edge. Although actin is present in the lamella behind the leading edge, very little of it is F-actin. Scanning electron microscopy of detergent-extracted cells reveals a band of dense filaments at the leading edge, corresponding to the marginal band of F-actin seen in fluorescently labeled cells, and a sparse population of short, fragmented filaments, in the rest of the lamella. Gelsolin is colocalized with F-actin in the marginal band and is also present in the lamella where F-actin is largely absent. The data support the hypothesis that the protrusion is initiated by the breakdown of cortical actin filaments, possibly mediated by gelsolin, whereas expansion of the protrusion requires de novo polymerization of actin filaments at the leading edge.     

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model’s ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Simulation of biological evolution under attack,but not really: a response to Meester

The leading Intelligent Design theorist William Dembski (Rowman & Littlefield, Lanham MD, 2002) argued that the first No Free Lunch theorem, first formulated by Wolpert and Macready (IEEE Trans Evol Comput 1: 67–82, 1997), renders Darwinian evolution impossible. In response, Dembski’s critics pointed out that the theorem is irrelevant to biological evolution. Meester (Biol Phil 24: 461–472, 2009) agrees with this conclusion, but still thinks that the theorem does apply to simulations of evolutionary processes. According to Meester, the theorem shows that simulations of Darwinian evolution, as these are typically set in advance by the programmer, are teleological and therefore non-Darwinian. Therefore, Meester argues, they are useless in showing how complex adaptations arise in the universe. Meester uses the term “teleological” inconsistently, however, and we argue that, no matter how we interpret the term, a Darwinian algorithm does not become non-Darwinian by simulation. We show that the NFL theorem is entirely irrelevant to this argument, and conclude that it does not pose a threat to the relevance of simulations of biological evolution.     

Factors affecting seed germination and seedling establishment of a long-lived desert shrub (<Emphasis Type="Italic">Coleogyne ramosissima</Emphasis>: Rosaceae)

Long-lived desert shrubs exhibit infrequent, episodic recruitment from seed. In spite of this long time scale, selection on life history attributes that affect seedling recruitment should be strong. We studied factors affecting germination phenology and seedling establishment for Coleogyne ramosissima, a dominant shrub species in the ecotone between warm and cold deserts in western North America. We also examined ecotypic differentiation in establishment strategy in response to selection regimes in two contrasting habitats. We followed patterns of dormancy loss, germination, emergence, and survival in reciprocal field experiments at warm winter Mojave Desert and cold winter Colorado Plateau study sites. Seed germination took place in late winter, under winter rain conditions at the warm desert site and under snow at the cold desert site. Distinctive germination phenologies for the two seed populations at contrasting field sites followed predictions based on laboratory germination experiments. There was no seed bank carryover across years. Seedling survival at the end of three growing seasons was remarkably high (mean survival 54%). Most seedling mortality was due to sprout predation by rodents early the first spring in unprotected caches. Emergence and establishment at each site were significantly higher for seeds from the local population, supporting the idea of ecotypic differentiation in establishment strategy. Establishment success was an order of magnitude greater overall at the Colorado Plateau site, which represents the leading edge of an upward elevational shift in distribution for this species under the current climatic regime. The Mojave Desert site is on the trailing edge of this shift, and recruitment there is apparently a much less frequent occurrence.     

A Cell-based Model of Endothelial Cell Migration,Proliferation and Maturation During Corneal Angiogenesis

The motivation of this work stems from two critical experimental observations associated with corneal angiogenesis: (1) angiogenesis will not succeed without endothelial cell proliferation, and (2) proliferation mainly occurs at the leading edge of developing sprouts (Sholley et al., Lab. Invest. 51:624–634, 1984). To discover the underlying mechanisms of these phenomena, we develop a cell-based mathematical model that integrates a mechanical model of elongation with a biochemical model of cell phenotype variation regulated by angiopoietins within a developing sprout. This model allows for a detailed study of the relative roles of endothelial cell migration, proliferation, and maturation. The model is validated by quantitatively comparing its predictions with data derived from corneal angiogenesis experiments. We conclude that cell elasticity and cell-to-cell adhesion allow only limited sprout extension in the absence of proliferation, and the maturation process combined with bioavailability of VEGF can explain the localization of proliferation to the leading edge. We also use this model to investigate the effects of X-ray irradiation, Ang-2 inhibition, and extracellular matrix anisotropy on sprout morphology and extension.     

The role of actin turnover in retrograde actin network flow in neuronal growth cones

The balance of actin filament polymerization and depolymerization maintains a steady state network treadmill in neuronal growth cones essential for motility and guidance. Here we have investigated the connection between depolymerization and treadmilling dynamics. We show that polymerization-competent barbed ends are concentrated at the leading edge and depolymerization is distributed throughout the peripheral domain. We found a high-to-low G-actin gradient between peripheral and central domains. Inhibiting turnover with jasplakinolide collapsed this gradient and lowered leading edge barbed end density. Ultrastructural analysis showed dramatic reduction of leading edge actin filament density and filament accumulation in central regions. Live cell imaging revealed that the leading edge retracted even as retrograde actin flow rate decreased exponentially. Inhibition of myosin II activity before jasplakinolide treatment lowered baseline retrograde flow rates and prevented leading edge retraction. Myosin II activity preferentially affected filopodial bundle disassembly distinct from the global effects of jasplakinolide on network turnover. We propose that growth cone retraction following turnover inhibition resulted from the persistence of myosin II contractility even as leading edge assembly rates decreased. The buildup of actin filaments in central regions combined with monomer depletion and reduced polymerization from barbed ends suggests a mechanism for the observed exponential decay in actin retrograde flow. Our results show that growth cone motility is critically dependent on continuous disassembly of the peripheral actin network.     

Actin cable distribution and dynamics arising from cross-linking,motor pulling,and filament turnover

The growth of fission yeast relies on the polymerization of actin filaments nucleated by formin For3p, which localizes at tip cortical sites. These actin filaments bundle to form actin cables that span the cell and guide the movement of vesicles toward the cell tips. A big challenge is to develop a quantitative understanding of these cellular actin structures. We used computer simulations to study the spatial and dynamical properties of actin cables. We simulated individual actin filaments as semiflexible polymers in three dimensions composed of beads connected with springs. Polymerization out of For3p cortical sites, bundling by cross-linkers, pulling by type V myosin, and severing by cofilin are simulated as growth, cross-linking, pulling, and turnover of the semiflexible polymers. With the foregoing mechanisms, the model generates actin cable structures and dynamics similar to those observed in live-cell experiments. Our simulations reproduce the particular actin cable structures in myoVΔ cells and predict the effect of increased myosin V pulling. Increasing cross-linking parameters generates thicker actin cables. It also leads to antiparallel and parallel phases with straight or curved cables, consistent with observations of cells overexpressing α-actinin. Finally, the model predicts that clustering of formins at cell tips promotes actin cable formation.     

Actin filament turnover regulated by cross-linking accounts for the size, shape, location, and number of actin bundles in Drosophila bristles

Drosophila bristle cells are shaped during growth by longitudinal bundles of cross-linked actin filaments attached to the plasma membrane. We used confocal and electron microscopy to examine actin bundle structure and found that during bristle elongation, snarls of uncross-linked actin filaments and small internal bundles also form in the shaft cytoplasm only to disappear within 4 min. Thus, formation and later removal of actin filaments are prominent features of growing bristles. These transient snarls and internal bundles can be stabilized by culturing elongating bristles with jasplakinolide, a membrane-permeant inhibitor of actin filament depolymerization, resulting in enormous numbers of internal bundles and uncross-linked filaments. Examination of bundle disassembly in mutant bristles shows that plasma membrane association and cross-bridging adjacent actin filaments together inhibits depolymerization. Thus, highly cross-bridged and membrane-bound actin filaments turn over slowly and persist, whereas poorly cross-linked filaments turnover more rapidly. We argue that the selection of stable bundles relative to poorly cross-bridged filaments can account for the size, shape, number, and location of the longitudinal actin bundles in bristles. As a result, filament turnover plays an important role in regulating cytoskeleton assembly and consequently cell shape.