Mechanobiology by the numbers: a close relationship between biology and physics.

Studies of mechanobiology lie at the interface of various scientific disciplines from biology to physics. Accordingly, quantification and mathematical modelling have been instrumental in fuelling the progress in this rapidly developing research field, assisting experimental work on many levels.

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.

A geometrical theory of gliding motility based on cell shape and surface flow.

Gliding motility proceeds with little changes in cell shape and often results from actively driven surface flows of adhesins binding to the extracellular environment. It allows for fast movement over surfaces or through tissue, especially for the eukaryotic parasites from the phylum apicomplexa, which includes the causative agents of the widespread diseases malaria and toxoplasmosis. We have developed a fully three-dimensional active particle theory which connects the self-organized, actively driven surface flow over a fixed cell shape to the resulting global motility patterns. Our analytical solutions and numerical simulations show that straight motion without rotation is unstable for simple shapes and that straight cell shapes tend to lead to pure rotations. This suggests that the curved shapes of Plasmodium sporozoites and Toxoplasma tachyzoites are evolutionary adaptations to avoid rotations without translation. Gliding motility is also used by certain myxo- or flavobacteria, which predominantly move on flat external surfaces and with higher control of cell surface flow through internal tracks. We extend our theory for these cases. We again find a competition between rotation and translation and predict the effect of internal track geometry on overall forward speed. While specific mechanisms might vary across species, in general, our geometrical theory predicts and explains the rotational, circular, and helical trajectories which are commonly observed for microgliders. Our theory could also be used to design synthetic microgliders.

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.

Na2B6Si2: A Prototype Silico-boride with Closo (B6)2- Clusters.

The compound Na2B6Si2 was synthesized under high-pressure, high-temperature conditions at pressures ranging from 6 to 9.5 GPa and temperatures from 1070 to 1270 K before quenching to room temperature followed by slow decompression. The crystal structure was determined from microcrystals using precession-assisted electron diffraction tomography, validated by dynamical refinement and full-profile refinements using optimized coordinates from quantum chemical calculations (space group R3̅m, Pearson symbol hR30, a = 5.0735(1) Å and c = 16.0004(7) Å). The atomic arrangement consists of a unique framework formed by electron-precise octahedral closo (B6)2- clusters connected via ethane-like (Si2)0 dumbbells. The Na+ cations occupy cavities in the hierarchical variation of a Heusler-type framework. The balance (Na+)2([B6]2-)(Si0)2 reveals an electron precise Zintl-Wade phase, which is in line with electronic band structure calculations predicting semiconducting behavior.

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.

Zintl Phase versus Covalent Metal: Chemical Bonding in Silicon Dumbbells of Ca5Si3 and CaSi3.

Silicon dumbbells constitute identifiable anionic molecular species in Zintl phases and so-called covalent metals holding units with homopolar bonding inside a metallic framework. Based on electron-precise Ca5Si3 and metallic CaSi3, the chemical bonding in Si2 units is investigated by computational quantum chemical methods considering the dual nature of the wave function. This concerted wave-vector and real space study substantiates that the Si2 dumbbells in Ca5Si3 can be referred to as molecular building units Si26- with additional metallic and ionic contributions in the solid. In the covalent metal CaSi3, however, the bonding within the dumbbells falls short of fulfilling the octet rule. As a result, antibonding states of the Si2 building units are depopulated and attend metallic interactions, simultaneously giving rise to stronger covalent Si-Si bonds.

Optimal ligand discrimination by asymmetric dimerization and turnover of interferon receptors.

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an information-theoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands.

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.

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.

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.

KAHRP dynamically relocalizes to remodeled actin junctions and associates with knob spirals in Plasmodium falciparum-infected erythrocytes.

The knob-associated histidine-rich protein (KAHRP) plays a pivotal role in the pathophysiology of Plasmodium falciparum malaria by forming membrane protrusions in infected erythrocytes, which anchor parasite-encoded adhesins to the membrane skeleton. The resulting sequestration of parasitized erythrocytes in the microvasculature leads to severe disease. Despite KAHRP being an important virulence factor, its physical location within the membrane skeleton is still debated, as is its function in knob formation. Here, we show by super-resolution microscopy that KAHRP initially associates with various skeletal components, including ankyrin bridges, but eventually colocalizes with remnant actin junctions. We further present a 35 Å map of the spiral scaffold underlying knobs and show that a KAHRP-targeting nanoprobe binds close to the spiral scaffold. Single-molecule localization microscopy detected ~60 KAHRP molecules/knob. We propose a dynamic model of KAHRP organization and a function of KAHRP in attaching other factors to the spiral scaffold.

Microtubule number and length determine cellular shape and function in Plasmodium.

Microtubules are cytoskeletal filaments essential for many cellular processes, including establishment and maintenance of polarity, intracellular transport, division and migration. In most metazoan cells, the number and length of microtubules are highly variable, while they can be precisely defined in some protozoan organisms. However, in either case the significance of these two key parameters for cells is not known. Here, we quantitatively studied the impact of modulating microtubule number and length in Plasmodium, the protozoan parasite causing malaria. Using a gene deletion and replacement strategy targeting one out of two α-tubulin genes, we show that chromosome segregation proceeds in the oocysts even in the absence of microtubules. However, fewer and shorter microtubules severely impaired the formation, motility and infectivity of Plasmodium sporozoites, the forms transmitted by the mosquito, which usually contain 16 microtubules. We found that α-tubulin expression levels directly determined the number of microtubules, suggesting a high nucleation barrier as supported by a mathematical model. Infectious sporozoites were only formed in parasite lines featuring at least 10 microtubules, while parasites with 9 or fewer microtubules failed to transmit.

Ge32 Co9-x : Creating "Empty" Space by High Pressure.

The compound Ge32 Co9-x (x=0.54(6), a=10.9861(3) Å, space group Im 3 ‾ $\bar 3$ m) prepared under high pressure and at high temperature is metastable under ambient conditions. It crystallizes in a new structure type, Pearson symbol cI82-1.08. The crystal structure represents a slightly distorted cubic primitive arrangement of germanium atoms with part of the Ge cubes filled by cobalt. Analysis of the chemical bonding by real-space methods revealed three-core cluster units Ge16 Co3 and seemingly empty regions comprising either covalent inter-polyhedral Ge-Ge bonds or lone-pairs located at the germanium atoms. The electrical conductivity is metal-like.

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.

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.

A Borosilicide with Clathrate VIII Structure.

The high-pressure phase Na8BxSi46-x (3 < x < 5) is the first representative of a borosilicide crystallizing in the rarely occurring clathrate VIII type structure. Crystals with composition Na8B4Si42 (space group I43̅m; a = 9.7187(2) Å; Pearson symbol cI54) were obtained at 5-8 GPa and 1200 K. The clathrate I modification exists for the same composition at lower pressure with a larger cell volume (Pm3̅n; a = 9. 977(2) Å; cP54). Profound structural adaptions allow for a higher density of the clathrate VIII type than clathrate I, opening up the perspective of obtaining clathrate VIII type compounds as high-pressure forms of clathrate I.

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.

Kinetically Controlled Reduction of ß-Vanadyl(V) Orthophosphate: Synthesis and Characterization of New Metastable Polymorphs of Vanadium(III) Phosphate.

Two thermodynamically metastable polymorphs of vanadium(III) phosphate, VIIIPO4-m1 and VPO4-m2, have been obtained via reduction of ß-VVOPO4 by moist hydrogen. The XRPD pattern of VPO4-m1 can be assigned based on the crystal structure of ß-VVOPO4, though with distinctly different lattice parameters (VPO4-m1/ß-VOPO4: Pnma, a = 7.3453(12)/7.7863(5) Å, b = 6.4001(12)/6.1329(3) Å, c = 7.3196(13)/6.9673(5) Å). The XRPD pattern of VPO4-m2 was found to be very similar to that of Fe2(VO)(P2O7)(PO4) (VPO4-m2: P21/m, Z = 2, a = 8.792(4) Å, b = 5.269(2) Å, c = 10.398(6) Å, ß = 112.60(4)°). The crystal structure models for VPO4-m1 and VPO4-m2 have been optimized by DFT calculations. Polymorph m1 contains the unprecedented butterfly shaped [VIIIO4] chromophore and has been further characterized by magnetic measurements, by powder reflectance spectroscopy (NIR/vis/UV), and IR spectroscopy. For six polymorphic forms of VPO4 (m1', m1'', m2, m3, m4, and m5), DFT calculations have been performed. For the existence of VPO4-m1', -m1'', and -m2, our experiments provide evidence. VPO4-m3, -m4, and -m5 were obtained by structure optimization based on reduced ß-VOPO4. Their stability is predicted by the DFT calculations.

Two types of magnetic shape-memory effects from twinned microstructure and magneto-structural coupling in Fe1+y Te.

A detailed experimental investigation of Fe1+y Te (y = 0.11, 0.12) using pulsed magnetic fields up to 60 T confirms remarkable magnetic shape-memory (MSM) effects. These effects result from magnetoelastic transformation processes in the low-temperature antiferromagnetic state of these materials. The observation of modulated and finely twinned microstructure at the nanoscale through scanning tunneling microscopy establishes a behavior similar to that of thermoelastic martensite. We identified the observed, elegant hierarchical twinning pattern of monoclinic crystallographic domains as an ideal realization of crossing twin bands. The antiferromagnetism of the monoclinic ground state allows for a magnetic-field-induced reorientation of these twin variants by the motion of one type of twin boundaries. At sufficiently high magnetic fields, we observed a second isothermal transformation process with large hysteresis for different directions of applied field. This gives rise to a second MSM effect caused by a phase transition back to the field-polarized tetragonal lattice state.