The role of the nucleus for cell mechanics: an elastic phase field approach.

The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.

Modelling cell shape in 3D structured environments: A quantitative comparison with experiments.

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.

The role of flow in the self-assembly of dragline spider silk proteins.

Hydrodynamic flow in the spider duct induces conformational changes in dragline spider silk proteins (spidroins) and drives their assembly, but the underlying physical mechanisms are still elusive. Here we address this challenging multiscale problem with a complementary strategy of atomistic and coarse-grained molecular dynamics simulations with uniform flow. The conformational changes at the molecular level were analyzed for single-tethered spider silk peptides. Uniform flow leads to coiled-to-stretch transitions and pushes alanine residues into ß sheet and poly-proline II conformations. Coarse-grained simulations of the assembly process of multiple semi-flexible block copolymers using multi-particle collision dynamics reveal that the spidroins aggregate faster but into low-order assemblies when they are less extended. At medium-to-large peptide extensions (50%-80%), assembly slows down and becomes reversible with frequent association and dissociation events, whereas spidroin alignment increases and alanine repeats form ordered regions. Our work highlights the role of flow in guiding silk self-assembly into tough fibers by enhancing alignment and kinetic reversibility, a mechanism likely relevant also for other proteins whose function depends on hydrodynamic flow.

Membrane Tension Inhibits Lipid Mixing by Increasing the Hemifusion Stalk Energy.

Fusion of biological membranes is fundamental in various physiological events. The fusion process involves several intermediate stages with energy barriers that are tightly dependent on the mechanical and physical properties of the system, one of which is membrane tension. As previously established, the late stages of fusion, including hemifusion diaphragm and pore expansions, are favored by membrane tension. However, a current understanding of how the energy barrier of earlier fusion stages is affected by membrane tension is lacking. Here, we apply a newly developed experimental approach combining micropipette-aspirated giant unilamellar vesicles and optically trapped membrane-coated beads, revealing that membrane tension inhibits lipid mixing. We show that lipid mixing is 6 times slower under a tension of 0.12 mN/m compared with tension-free membranes. Furthermore, using continuum elastic theory, we calculate the dependence of the hemifusion stalk formation energy on membrane tension and intermembrane distance and find the increase in the corresponding energy barrier to be 1.6 kBT in our setting, which can explain the increase in lipid mixing time delay. Finally, we show that tension can be a significant factor in the stalk energy if the pre-fusion intermembrane distance is on the order of several nanometers, while for membranes that are tightly docked, tension has a negligible effect.

Force propagation between epithelial cells depends on active coupling and mechano-structural polarization.

Cell-generated forces play a major role in coordinating the large-scale behavior of cell assemblies, in particular during development, wound healing, and cancer. Mechanical signals propagate faster than biochemical signals, but can have similar effects, especially in epithelial tissues with strong cell-cell adhesion. However, a quantitative description of the transmission chain from force generation in a sender cell, force propagation across cell-cell boundaries, and the concomitant response of receiver cells is missing. For a quantitative analysis of this important situation, here we propose a minimal model system of two epithelial cells on an H-pattern ('cell doublet'). After optogenetically activating RhoA, a major regulator of cell contractility, in the sender cell, we measure the mechanical response of the receiver cell by traction force and monolayer stress microscopies. In general, we find that the receiver cells show an active response so that the cell doublet forms a coherent unit. However, force propagation and response of the receiver cell also strongly depend on the mechano-structural polarization in the cell assembly, which is controlled by cell-matrix adhesion to the adhesive micropattern. We find that the response of the receiver cell is stronger when the mechano-structural polarization axis is oriented perpendicular to the direction of force propagation, reminiscent of the Poisson effect in passive materials. We finally show that the same effects are at work in small tissues. Our work demonstrates that cellular organization and active mechanical response of a tissue are key to maintain signal strength and lead to the emergence of elasticity, which means that signals are not dissipated like in a viscous system, but can propagate over large distances.

Force generation in human blood platelets by filamentous actomyosin structures.

Blood platelets are central elements of the blood clotting response after wounding. Upon vessel damage, they bind to the surrounding matrix and contract the forming thrombus, thus helping to restore normal blood circulation. The hemostatic function of platelets is directly connected to their mechanics and cytoskeletal organization. The reorganization of the platelet cytoskeleton during spreading occurs within minutes and leads to the formation of contractile actomyosin bundles, but it is not known if there is a direct correlation between the emerging actin structures and the force field that is exerted to the environment. In this study, we combine fluorescence imaging of the actin structures with simultaneous traction force measurements in a time-resolved manner. In addition, we image the final states with superresolution microscopy. We find that both the force fields and the cell shapes have clear geometrical patterns defined by stress fibers. Force generation is localized in a few hotspots, which appear early during spreading, and, in the mature state, anchor stress fibers in focal adhesions. Moreover, we show that, for a gel stiffness in the physiological range, force generation is a very robust mechanism and we observe no systematic dependence on the amount of added thrombin in solution or fibrinogen coverage on the substrate, suggesting that force generation after platelet activation is a threshold phenomenon that ensures reliable thrombus contraction in diverse environments.

IFITM3 blocks influenza virus entry by sorting lipids and stabilizing hemifusion.

Interferon-induced transmembrane protein 3 (IFITM3) inhibits the entry of numerous viruses through undefined molecular mechanisms. IFITM3 localizes in the endosomal-lysosomal system and specifically affects virus fusion with target cell membranes. We found that IFITM3 induces local lipid sorting, resulting in an increased concentration of lipids disfavoring viral fusion at the hemifusion site. This increases the energy barrier for fusion pore formation and the hemifusion dwell time, promoting viral degradation in lysosomes. In situ cryo-electron tomography captured IFITM3-mediated arrest of influenza A virus membrane fusion. Observation of hemifusion diaphragms between viral particles and late endosomal membranes confirmed hemifusion stabilization as a molecular mechanism of IFITM3. The presence of the influenza fusion protein hemagglutinin in post-fusion conformation close to hemifusion sites further indicated that IFITM3 does not interfere with the viral fusion machinery. Collectively, these findings show that IFITM3 induces lipid sorting to stabilize hemifusion and prevent virus entry into target cells.

The Ebola virus VP40 matrix layer undergoes endosomal disassembly essential for membrane fusion.

Ebola viruses (EBOVs) assemble into filamentous virions, whose shape and stability are determined by the matrix viral protein 40 (VP40). Virus entry into host cells occurs via membrane fusion in late endosomes; however, the mechanism of how the remarkably long virions undergo uncoating, including virion disassembly and nucleocapsid release into the cytosol, remains unknown. Here, we investigate the structural architecture of EBOVs entering host cells and discover that the VP40 matrix disassembles prior to membrane fusion. We reveal that VP40 disassembly is caused by the weakening of VP40-lipid interactions driven by low endosomal pH that equilibrates passively across the viral envelope without a dedicated ion channel. We further show that viral membrane fusion depends on VP40 matrix integrity, and its disassembly reduces the energy barrier for fusion stalk formation. Thus, pH-driven structural remodeling of the VP40 matrix acts as a molecular switch coupling viral matrix uncoating to membrane fusion during EBOV entry.

High curvature promotes fusion of lipid membranes: Predictions from continuum elastic theory.

The fusion of lipid membranes progresses through a series of hemifusion intermediates with two significant energy barriers related to the formation of stalk and fusion pore, respectively. These energy barriers determine the speed and success rate of many critical biological processes, including the fusion of highly curved membranes, for example synaptic vesicles and enveloped viruses. Here we use continuum elastic theory of lipid monolayers to determine the relationship between membrane shape and energy barriers to fusion. We find that the stalk formation energy decreases with curvature by up to 31 kBT in a 20-nm-radius vesicle compared with planar membranes and by up to 8 kBT in the fusion of highly curved, long, tubular membranes. In contrast, the fusion pore formation energy barrier shows a more complicated behavior. Immediately after stalk expansion to the hemifusion diaphragm, the fusion pore formation energy barrier is low (15-25 kBT) due to lipid stretching in the distal monolayers and increased tension in highly curved vesicles. Therefore, the opening of the fusion pore is faster. However, these stresses relax over time due to lipid flip-flop from the proximal monolayer, resulting in a larger hemifusion diaphragm and a higher fusion pore formation energy barrier, up to 35 kBT. Therefore, if the fusion pore fails to open before significant lipid flip-flop takes place, the reaction proceeds to an extended hemifusion diaphragm state, which is a dead-end configuration in the fusion process and can be used to prevent viral infections. In contrast, in the fusion of long tubular compartments, the surface tension does not accumulate due to the formation of the diaphragm, and the energy barrier for pore expansion increases with curvature by up to 11 kBT. This suggests that inhibition of polymorphic virus infection could particularly target this feature of the second barrier.

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface.

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

Clathrin coats partially preassemble and subsequently bend during endocytosis.

Eukaryotic cells use clathrin-mediated endocytosis to take up a large range of extracellular cargo. During endocytosis, a clathrin coat forms on the plasma membrane, but it remains controversial when and how it is remodeled into a spherical vesicle. Here, we use 3D superresolution microscopy to determine the precise geometry of the clathrin coat at large numbers of endocytic sites. Through pseudo-temporal sorting, we determine the average trajectory of clathrin remodeling during endocytosis. We find that clathrin coats assemble first on flat membranes to 50% of the coat area before they become rapidly and continuously bent, and this mechanism is confirmed in three cell lines. We introduce the cooperative curvature model, which is based on positive feedback for curvature generation. It accurately describes the measured shapes and dynamics of the clathrin coat and could represent a general mechanism for clathrin coat remodeling on the plasma membrane.

Simulating 3D Cell Shape with the Cellular Potts Model.

Computer simulations have become a widely used method for the field of mechanobiology. An important question is whether one can predict the shape and forces of cells as a function of the extracellular environment. Different types of models have been described before to simulate cell and tissue shapes in structured environments. In this chapter, we give a brief overview of commonly used models and then describe the Cellular Potts Model, a lattice-based modelling framework, in more detail. We provide a hands-on guide on how to build a model that simulates the shape of a single cell on a micropattern in three dimensions in different open source software packages using the Cellular Potts framework. A simulation is set up with an initial configuration of generalized cells that change shape and position due to an energy function that incorporates cellular volume and surface area constraints as well as interaction energies between the generalized cells.

An Improved Method for Assessing Antigen Presentation on the Surface of Plasmodium falciparum-Infected Erythrocytes by Immuno-Electron Microscopy.

Immuno-electron microscopy can detect and localize antigens in cells or tissues at a resolution of several nanometers. In the case of P. falciparum-infected erythrocytes, immuno-EM studies are frequently hampered by the electron-dense nature of the hemoglobin and access of antibodies to antigenic sites, particularly if the targeted protein is presented on the host cell surface or lies in proximity to the host cell cytoskeleton. Here, we describe an improved immuno-EM protocol that overcomes these problems. The improved signal to noise ratio and the enhanced access to antigenic sites now allows one to obtain information regarding target density and distribution and, hence, additional insights into the architecture and function of parasite-induced, or -affected, structures.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections.

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Asynchronous nuclear cycles in multinucleated Plasmodium falciparum facilitate rapid proliferation.

Malaria-causing parasites proliferate within erythrocytes through schizogony, forming multinucleated stages before cellularization. Nuclear multiplication does not follow a strict geometric 2n progression, and each proliferative cycle produces a variable number of progeny. Here, by tracking nuclei and DNA replication, we show that individual nuclei replicate their DNA at different times, despite residing in a shared cytoplasm. Extrapolating from experimental data using mathematical modeling, we provide strong indication that a limiting factor exists, which slows down the nuclear multiplication rate. Consistent with this prediction, our data show that temporally overlapping DNA replication events were significantly slower than partially overlapping or nonoverlapping events. Our findings suggest the existence of evolutionary pressure that selects for asynchronous DNA replication, balancing available resources with rapid pathogen proliferation.

Nonmuscle myosin IIA dynamically guides regulatory light chain phosphorylation and assembly of nonmuscle myosin IIB.

Nonmuscle myosin II minifilaments have emerged as central elements for force generation and mechanosensing by mammalian cells. Each minifilament can have a different composition and activity due to the existence of the three nonmuscle myosin II paralogs A, B and C and their respective phosphorylation pattern. We have used CRISPR/Cas9-based knockout cells, quantitative image analysis and mathematical modeling to dissect the dynamic processes that control the formation and activity of heterotypic minifilaments and found a strong asymmetry between paralogs A and B. Loss of NM IIA completely abrogates regulatory light chain phosphorylation and reduces the level of assembled NM IIB. Activated NM IIB preferentially co-localizes with pre-formed NM IIA minifilaments and stabilizes the filament in a force-dependent mechanism. NM IIC is only weakly coupled to these processes. We conclude that NM IIA and B play clearly defined complementary roles during assembly of functional minifilaments. NM IIA is responsible for the formation of nascent pioneer minifilaments. NM IIB incorporates into these and acts as a clutch that limits the force output to prevent excessive NM IIA activity. Together these two paralogs form a balanced system for regulated force generation.

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy.

Traction force microscopy (TFM) is the main method used in mechanobiology to measure cell forces. Commonly this is being used for cells adhering to flat soft substrates that deform under cell traction (2D-TFM). TFM relies on the use of linear elastic materials, such as polydimethylsiloxane (PDMS) or polyacrylamide (PA). For 2D-TFM on PA, the difficulty in achieving high throughput results mainly from the large variability of cell shapes and tractions, calling for standardization. We present a protocol to rapidly and efficiently fabricate micropatterned PA hydrogels for 2D-TFM studies. The micropatterns are first created by maskless photolithography using near-UV light where extracellular matrix proteins bind only to the micropatterned regions, while the rest of the surface remains non-adhesive for cells. The micropatterning of extracellular matrix proteins is due to the presence of active aldehyde groups, resulting in adhesive regions of different shapes to accommodate either single cells or groups of cells. For TFM measurements, we use PA hydrogels of different elasticity by varying the amounts of acrylamide and bis-acrylamide and tracking the displacement of embedded fluorescent beads to reconstruct cell traction fields with regularized Fourier Transform Traction Cytometry (FTTC). To further achieve precise recording of cell forces, we describe the use of a controlled dose of patterned light to release cell tractions in defined regions for single cells or groups of cells. We call this method local UV illumination traction force microscopy (LUVI-TFM). With enzymatic treatment, all cells are detached from the sample simultaneously, whereas with LUVI-TFM traction forces of cells in different regions of the sample can be recorded in sequence. We demonstrate the applicability of this protocol (i) to study cell traction forces as a function of controlled adhesion to the substrate, and (ii) to achieve a greater number of experimental observations from the same sample.

Comparison of direct and inverse methods for 2.5D traction force microscopy.

Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green's functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method.

Quantifying force transmission through fibroblasts: changes of traction forces under external shearing.

Mammalian cells have evolved complex mechanical connections to their microenvironment, including focal adhesion clusters that physically connect the cytoskeleton and the extracellular matrix. This mechanical link is also part of the cellular machinery to transduce, sense and respond to external forces. Although methods to measure cell attachment and cellular traction forces are well established, these are not capable of quantifying force transmission through the cell body to adhesion sites. We here present a novel approach to quantify intracellular force transmission by combining microneedle shearing at the apical cell surface with traction force microscopy at the basal cell surface. The change of traction forces exerted by fibroblasts to underlying polyacrylamide substrates as a response to a known shear force exerted with a calibrated microneedle reveals that cells redistribute forces dynamically under external shearing and during sequential rupture of their adhesion sites. Our quantitative results demonstrate a transition from dipolar to monopolar traction patterns, an inhomogeneous distribution of the external shear force to the adhesion sites as well as dynamical changes in force loading prior to and after the rupture of single adhesion sites. Our strategy of combining traction force microscopy with external force application opens new perspectives for future studies of force transmission and mechanotransduction in cells.