Rapid tool for cell nanoarchitecture integrity assessment.

With the rapid increase and accessibility of high-resolution imaging technologies of cells, the interpretation of results relies more and more on the assumption that the three-dimensional integrity of the surrounding cellular landscape is not compromised by the experimental setup. However, the only available technology for directly probing the structural integrity of whole-cell preparations at the nanoscale is electron cryo-tomography, which is time-consuming, costly, and complex. We devised an accessible, inexpensive and reliable screening assay to quickly report on the compatibility of experimental protocols with preserving the structural integrity of whole-cell preparations at the nanoscale. Our Rapid Cell Integrity Assessment (RCIA) assay is executed at room temperature and relies solely on light microscopy imaging. Using cellular electron cryo-tomography as a benchmark, we verify that RCIA accurately unveils the adverse impact of reagents and/or protocols such as those used for virus inactivation or to arrest dynamic processes on the cellular nanoarchitecture.

MicroScale Thermophoresis (MST) for studying actin polymerization kinetics.

Here, we present a MicroScale Thermophoresis (MST)-based assay for in vitro assessment of actin polymerization. By monitoring the thermophoretic behavior of ATTO488-labeled actin in a temperature gradient over time, we could follow polymerization in real time and resolve its three characteristic phases: nucleation, elongation, and steady-state equilibration. Titration experiments allowed us to evaluate the effects of actin-binding proteins (ABPs) on polymerization, including DNase I-induced inhibition and mDia2FH1FH2 (mDia2)-assisted acceleration of nucleation. The corresponding rates of actin filament elongation were quantitatively determined, yielding values in good agreement with those obtained using the pyrene-actin polymerization assay. Finally, we measured the effect of myosin on actin polymerization, circumventing the problems of fluorescence quenching and signal disturbance that occur with other techniques. MST is a simple and valuable research tool for investigating actin kinetics covering a wide range of molecular interactions, with low protein consumption.

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation.

Tubular protrusions are a common feature of living cells, arising from polymerization of stiff protein filaments against a comparably soft membrane. Although this process involves many accessory proteins in cells, in vitro experiments indicate that similar tube-like structures can emerge without them, through spontaneous bundling of filaments mediated by the membrane. Using theory and simulation of physical models, we have elaborated how nonequilibrium fluctuations in growth kinetics and membrane shape can yield such protrusions. Enabled by a new grand canonical Monte Carlo method for membrane simulation, our work reveals a cascade of dynamical transitions from individually polymerizing filaments to highly cooperatively growing bundles as a dynamical bottleneck to tube formation. Filament network organization as well as adhesion points to the membrane, which bias filament bending and constrain membrane height fluctuations, screen the effective attractive interactions between filaments, significantly delaying bundling and tube formation.

Experimental and computational assessment of F-actin influence in regulating cellular stiffness and relaxation behaviour of fibroblasts.

In biomechanics, a complete understanding of the structures and mechanisms that regulate cellular stiffness at a molecular level remain elusive. In this paper, we have elucidated the role of filamentous actin (F-actin) in regulating elastic and viscous properties of the cytoplasm and the nucleus. Specifically, we performed colloidal-probe atomic force microscopy (AFM) on BjhTERT fibroblast cells incubated with Latrunculin B (LatB), which results in depolymerisation of F-actin, or DMSO control. We found that the treatment with LatB not only reduced cellular stiffness, but also greatly increased the relaxation rate for the cytoplasm in the peripheral region and in the vicinity of the nucleus. We thus conclude that F-actin is a major determinant in not only providing elastic stiffness to the cell, but also in regulating its viscous behaviour. To further investigate the interdependence of different cytoskeletal networks and cell shape, we provided a computational model in a finite element framework. The computational model is based on a split strain energy function of separate cellular constituents, here assumed to be cytoskeletal components, for which a composite strain energy function was defined. We found a significant influence of cell geometry on the predicted mechanical response. Importantly, the relaxation behaviour of the cell can be characterised by a material model with two time constants that have previously been found to predict mechanical behaviour of actin and intermediate filament networks. By merely tuning two effective stiffness parameters, the model predicts experimental results in cells with a partly depolymerised actin cytoskeleton as well as in untreated control. This indicates that actin and intermediate filament networks are instrumental in providing elastic stiffness in response to applied forces, as well as governing the relaxation behaviour over shorter and longer time-scales, respectively.

Trains, tails and loops of partially adsorbed semi-flexible filaments.

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials.

Membrane sorting via the extracellular matrix.

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.

Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors.

Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle. The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths. Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface-adsorbed myosin motor fragments in the in vitro motility assay. Our results suggest that the persistence length of heavy meromyosin propelled actin filaments can be estimated with high accuracy and reproducibility using this approach provided that: (1) the in vitro motility assay experiments are designed to prevent bias in filament sliding directions, (2) at least 200 independent filament paths are studied, (3) the ratio between the sliding distance between measurements and the camera pixel-size is between 4 and 12, (4) the sliding distances between measurements is less than 50% of the expected persistence length, and (5) an appropriate cut-off value is chosen to exclude abrupt large angular changes in sliding direction that are complications, e.g., due to the presence of rigor heads. If the above precautions are taken the described method should be a useful routine part of in vitro motility assays thus expanding the amount of information to be gained from these.

Self-organization of motor-propelled cytoskeletal filaments at topographically defined borders.

Self-organization phenomena are of critical importance in living organisms and of great interest to exploit in nanotechnology. Here we describe in vitro self-organization of molecular motor-propelled actin filaments, manifested as a tendency of the filaments to accumulate in high density close to topographically defined edges on nano- and microstructured surfaces. We hypothesized that this "edge-tracing" effect either (1) results from increased motor density along the guiding edges or (2) is a direct consequence of the asymmetric constraints on stochastic changes in filament sliding direction imposed by the edges. The latter hypothesis is well captured by a model explicitly defining the constraints of motility on structured surfaces in combination with Monte-Carlo simulations [cf. Nitta et al. (2006)] of filament sliding. In support of hypothesis 2 we found that the model reproduced the edge tracing effect without the need to assume increased motor density at the edges. We then used model simulations to elucidate mechanistic details. The results are discussed in relation to nanotechnological applications and future experiments to test model predictions.

Actin filament curvature biases branching direction.

Mechanical cues affect many important biological processes in metazoan cells, such as migration, proliferation, and differentiation. Such cues are thought to be detected by specialized mechanosensing molecules linked to the cytoskeleton, an intracellular network of protein filaments that provide mechanical rigidity to the cell and drive cellular shape change. The most abundant such filament, actin, forms branched networks nucleated by the actin-related protein (Arp) 2/3 complex that support or induce membrane protrusions and display adaptive behavior in response to compressive forces. Here we show that filamentous actin serves in a mechanosensitive capacity itself, by biasing the location of actin branch nucleation in response to filament bending. Using an in vitro assay to measure branching from curved sections of immobilized actin filaments, we observed preferential branch formation by the Arp2/3 complex on the convex face of the curved filament. To explain this behavior, we propose a fluctuation gating model in which filament binding or branch nucleation by Arp2/3 occur only when a sufficiently large, transient, local curvature fluctuation causes a favorable conformational change in the filament, and we show with Monte Carlo simulations that this model can quantitatively account for our experimental data. We also show how the branching bias can reinforce actin networks in response to compressive forces. These results demonstrate how filament curvature can alter the interaction of cytoskeletal filaments with regulatory proteins, suggesting that direct mechanotransduction by actin may serve as a general mechanism for organizing the cytoskeleton in response to force.

From branched networks of actin filaments to bundles.

Cross-linking proteins can mediate the emergence of rigid bundles from a dense branched network of actin filaments. To enable their binding, the filaments must first bend towards each other. We derive an explicit criterion for the onset of bundling, in terms of the initial length of filaments L, their spacing b, and cross-linker concentration f, reflecting the balance between bending and binding energies. Our model system contains actin, the branching complex Arp2/3 and the bundling protein fascin. In the first distinct stage, during which only actin and Arp2/3 are active, an entangled aster-like mesh of actin filaments is formed. Tens of seconds later, when filaments at the aster periphery are long and barely branched, a sharp transition takes place into a star-like structure, marking the onset of bundling. Now fascin and actin govern bundle growth; Arp2/3 plays no role. Using kinetic Monte Carlo simulations we calculate the temporal evolution of b and L, and predict the onset of bundling as a function of f. Our predictions are in good qualitative agreement with several new experiments that are reported herein and demonstrate how f controls the aster-star transition and bundle length. We also present two models for aster growth corresponding to different experimental realizations. The first treats filament and bundle association as an irreversible sequence of elongation-association steps. The second, applicable for low f, treats bundling as a reversible self-assembly process, where the optimal bundle size is dictated by the balance between surface and bending energies. Finally, we discuss the relevance of our conclusions for the lamellipodium to filopodia transition in living cells, noting that bundles are more likely nucleated by "tip complex" cross-linkers (e.g. mDia2 or Ena/VASP), whereas fascin is mainly involved in bundle maintenance.

A mathematical analysis of obstructed diffusion within skeletal muscle.

Molecules are transported through the myofilament lattice of skeletal muscle fibers during muscle activation. The myofilaments, along with the myosin heads, sarcoplasmic reticulum, t-tubules, and mitochondria, obstruct the diffusion of molecules through the muscle fiber. In this work, we studied the process of obstructed diffusion within the myofilament lattice using Monte Carlo simulation, level-set and homogenization theory. We found that these intracellular obstacles significantly reduce the diffusion of material through skeletal muscle and generate diffusion anisotropy that is consistent with experimentally observed slower diffusion in the radial than the longitudinal direction. Our model also predicts that protein size has a significant effect on the diffusion of material through muscle, which is consistent with experimental measurements. Protein diffusion on the myofilament lattice is also anomalous (i.e., it does not obey Brownian motion) for proteins that are close in size to the myofilament spacing. The obstructed transport of Ca2+ and ATP-bound Ca2+ through the myofilament lattice also generates smaller Ca2+ transients. In addition, we used homogenization theory to discover that the nonhomogeneous distribution in the troponin binding sites has no effect on the macroscopic Ca2+ dynamics. The nonuniform sarcoplasmic reticulum Ca2+-ATPase pump distribution also introduces small asymmetries in the myoplasmic Ca2+ transients.

Nonequilibrium self-assembly of a filament coupled to ATP/GTP hydrolysis.

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: two phases of unbounded growth: a rapidly growing phase and an intermediate phase, and one bounded growth phase. We analyze all these phases, with an emphasis on the bounded growth phase. We also discuss how hydrolysis affects force-velocity curves. The bounded growth phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero (i.e., to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations.

An integrative simulation model linking major biochemical reactions of actin-polymerization to structural properties of actin filaments.

We report on an advanced universal Monte Carlo simulation model of actin polymerization processes offering a broad application panel. The model integrates major actin-related reactions, such as assembly of actin nuclei, association/dissociation of monomers to filament ends, ATP-hydrolysis via ADP-Pi formation and ADP-ATP exchange, filament branching, fragmentation and annealing or the effects of regulatory proteins. Importantly, these reactions are linked to information on the nucleotide state of actin subunits in filaments (ATP hydrolysis) and the distribution of actin filament lengths. The developed stochastic simulation modelling schemes were validated on: i) synthetic theoretical data generated by a deterministic model and ii) sets of our and published experimental data obtained from fluorescence pyrene-actin experiments. Build on an open-architecture principle, the designed model can be extended for predictive evaluation of the activities of other actin-interacting proteins and can be applied for the analysis of experimental pyrene actin-based or fluorescence microscopy data. We provide a user-friendly, free software package ActinSimChem that integrates the implemented simulation algorithms and that is made available to the scientific community for modelling in silico any specific actin-polymerization system.

Actin bundling: initiation mechanisms and kinetics.

Bundling of rapidly polymerizing actin filaments underlies the dynamics of filopodial protrusions that play an important role in cell migration and cell-cell interaction. Recently, the formation of actin bundles has been reconstituted in vitro, and two scenarios of bundle initiation, involving binding of two filament tips and, alternatively, linking of the tip of one filament to the side of the other, have been discussed. A first theoretical analysis is presented indicating that the two mechanisms can be distinguished experimentally. While both of them result counterintuitively in comparable numbers of bundles, these numbers scale differently with the average bundle length. We propose an experiment for determining which of the two mechanisms is involved in the in vitro bundle formation.

[Assessment of the mechanical activity of cardiac isomyosins V1 and V3 by an in vitro motility assay with regulated thin filaments].

A series of experiments in an in vitro motility assay with reconstructed thin filaments has been performed to determine the dependence of the velocity of thin filament movement on the concentration of calcium in solution (in the pCa range from 5 to 8) for rabbit cardiac isomyosins V1 and V3. The "pCa-velocity" curves had the sigmoid form. It was found for each isoform that sliding velocities of regulated thin filaments (at the saturating calcium concentration (pCa 5)) and actin filaments did not differ from each other. The Hill coefficient was 1.04 and 0.75 for isomyosins V1 and V3, respectively. The calcium sensitivity of V3 was found to be higher than that of V1. In the framework of the same method, the relationship between the velocity of thin filament sliding and the concentration of the actin-binding protein a-actinin (analog of the "force-velocity" relationship) has been estimated for each isoform V1 and V3 at the saturating calcium concentration. The results obtained suggest that the calcium regulation of the contractile activity of isomyosins V1 and V3 occurs by different mechanisms.

Mechanics and dynamics of actin-driven thin membrane protrusions.

Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.

Discontinuous unbinding transitions of filament bundles.

Bundles of semiflexible polymers such as actin filaments are studied theoretically. The bundle formation is governed by attractive filament interactions mediated by cross-linking sticker molecules. Using a combination of analytical arguments and Monte Carlo simulations, it is shown that the formation of bundles of parallel filaments requires a threshold concentration of linkers which becomes independent of the filament number for large bundles. The unbinding of bundles happens in a single, discontinuous transition. We discuss the behavior of the bundle thickness at and below the transition. In the bound phase, large bundles tend to segregate into sub-bundles due to slow kinetics. Our results are in qualitative agreement with experiments on F-actin in the presence of the cross-linking protein alpha-actinin.