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The mechanics of animal cells is strongly determined by stress fibers, which are contractile filament bundles that form dynamically in response to extracellular cues. Stress fibers allow the cell to adapt its mechanics to environmental conditions and to protect it from structural damage. While the physical description of single stress fibers is well-developed, much less is known about their spatial distribution on the level of whole cells. Here, we combine a finite element method for one-dimensional fibers embedded in an elastic bulk medium with dynamical rules for stress fiber formation based on genetic algorithms. We postulate that their main goal is to achieve minimal mechanical stress in the bulk material with as few fibers as possible. The fiber positions and configurations resulting from this optimization task alone are in good agreement with those found in experiments where cells in 3D-scaffolds were mechanically strained at one attachment point. For optimized configurations, we find that stress fibers typically run through the cell in a diagonal fashion, similar to reinforcement strategies used for composite material., Comment: 37 pages, 11 figures, 72 references

Migration of animal cells is based on the interplay between actin polymerization at the front, adhesion along the cell-substrate interface, and actomyosin contractility at the back. Active gel theory has been used before to demonstrate that actomyosin contractility is sufficient for polarization and self-sustained cell migration in the absence of external cues, but did not consider the dynamics of adhesion. Likewise, migration models based on the mechanosensitive dynamics of adhesion receptors usually do not include the global dynamics of intracellular flow. Here we show that both aspects can be combined in a minimal active gel model for one-dimensional cell migration with dynamic adhesion. This model demonstrates that load sharing between the adhesion receptors leads to symmetry breaking, with stronger adhesion at the front, and that bistability of migration arises for intermediate adhesiveness. Local variations in adhesiveness are sufficient to switch between sessile and motile states, in qualitative agreement with experiments., Comment: Revtex, 33 pages, 7 figures, minor revisions to original version

Clathrin-mediated endocytosis is the main pathway used by eukaryotic cells to take up extracellular material, but the dominant physical mechanisms driving this process are still elusive. Recently several high-resolution imaging techniques have been used on different cell lines to measure the geometrical properties of clathrin-coated pits over their whole lifetime. Here we first show that the combination of all datasets with the recently introduced cooperative curvature model defines a consensus pathway, which is characterized by a flat to-curved transition at finite area, followed by linear growth and subsequent saturation of curvature. We then apply an energetic model for the composite of plasma membrane and clathrin coat to this consensus pathway to show that the dominant mechanism for invagination could be coat stiffening, which might originate from cooperative interactions between the different clathrin molecules and progressively drives the system towards its intrinsic curvature. Our theory predicts that two length scales determine the invagination pathway, namely the patch size at which the flat-to-curved transition occurs and the final pit radius., Comment: revtex, 13 pages, 5 figures in PDF-format

Biological systems are remarkably susceptible to relatively small temperature changes. The most obvious example is fever, when a modest rise in body temperature of only few Kelvin has strong effects on our immune system and how it fights pathogens. Another very important example is climate change, when even smaller temperature changes lead to dramatic shifts in ecosystems. Although it is generally accepted that the main effect of an increase in temperature is the acceleration of biochemical reactions according to the Arrhenius equation, it is not clear how it effects large biochemical networks with complicated architectures. For developmental systems like fly and frog, it has been shown that the system response to temperature deviates in a characteristic manner from the linear Arrhenius plot of single reactions, but a rigorous explanation has not been given yet. Here we use a graph theoretical interpretation of the mean first passage times of a biochemical master equation to give a statistical description. We find that in the limit of large system size and if the network has a bias towards a target state, then the Arrhenius plot is generically quadratic, in excellent agreement with experimental data for developmental times in fly and frog., Comment: 14 pages, 7 figures

Epithelial monolayers are a central building block of complex organisms. Topological defects have emerged as important elements for single cell behavior in flat epithelia. Here we theoretically study such defects in a three-dimensional vertex model for spherical epithelia like cysts or intestinal organoids. We find that they lead to the same generic morphological instability to an icosahedral shape as it is known from spherical elastic shells like virus capsids, polymerized vesicles or buckyballs. We derive analytical expressions for the effective stretching and bending moduli as a function of the parameters of the vertex model, in excellent agreement with computer simulations. These equations accurately predict both the buckling of a flat epithelial monolayer under uniaxial compression and the faceting transition around the topological defects in spherical epithelia. We further show that localized apico-basal tension asymmetries allow them to reduce the transition threshold to small system sizes., Comment: 5 pages, 5 figures, supplemental material

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. We first introduce and verify our computational method and then study several applications of large relevance. 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 viscoelasticity and cortical tension., Comment: 15 pages, 8 figures

Our goal is to describe superconformal structures on super Riemann surfaces (SRS), based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and the deformations using Strebel differentials and certain \v{C}ech cocycles for a specific covering, which we reproduce from a fatgraph data, consisting of $U(1)$-graph connection and odd parameters at the vertices. Then we consider dual $(1|1)$-supermanifolds and related superconformal structures for $N=2$ super Riemann surfaces. The superconformal structures $N=1$ SRS are computed as the fixed points of involution on supermoduli space of $N=2$ SRS., Comment: v2: 25 pages, minor revisions

Cell crawling on flat substrates is based on intracellular flows of the actin cytoskeleton that are driven by both actin polymerization at the front and myosin contractility at the back. The new experimental tool of optogenetics makes it possible to spatially control contraction and thereby possibly also cell migration. Here we analyze this situation theoretically using a one-dimensional active gel model in which the excluded volume interactions of myosin and their aggregation into minifilaments is modeled by a supercritical van der Waals fluid. This physically simple and transparent, but nonlinear and thermodynamically rigorous model predicts bistability between sessile and motile solutions. We then show that one can switch between these two states at realistic parameter ranges via optogenetic activation or inhibition of contractility, in agreement with recent experiments. We also predict the required activation strengths and initiation times., Comment: 12 pages including supplement, 5 main and 4 supplemental figures

Complex energy landscapes often arise in biological systems, e.g. for protein folding, biochemical reactions or intracellular transport processes. Their physical effects are often reflected in the first-passage times arising from these energy landscapes. However, their calculation is notoriously challenging and it is often difficult to identify the most relevant features of a given energy landscape. Here we show how this can be achieved by coarse-graining the Fokker-Planck equation to a master equation and decomposing its first-passage times in an iterative process. We apply this method to the electrostatic interaction between two rods of nonmuscle myosin II (NM2), which is the main molecular motor for force generation in nonmuscle cells. Energy landscapes are computed directly from the amino acid sequences of the three different isoforms. Our approach allows us to identify the most relevant energy barriers for their self-assembly into nonmuscle myosin II minifilaments and how they change under force. In particular, we find that antiparallel configurations are more stable than parallel ones, but also show more changes under mechanical loading. Our work demonstrates the rich dynamics that can be expected for NM2-assemblies under mechanical load and in general shows how one can identify the most relevant energy barriers in complex energy landscapes., Comment: Revtex, 34 pages, 8 figures, minor revisions compared to original version

The actin cytoskeleton of cells is in continuous motion due to both polymerization of new filaments and their contraction by myosin II molecular motors. Through adhesion to the substrate, such intracellular flow can be converted into cell migration. Recently, optogenetics has emerged as a new powerful experimental method to control both actin polymerization and myosin II contraction. While optogenetic control of polymerization can initiate cell migration by generating protrusion, it is less clear if and how optogenetic control of contraction can also affect cell migration. Here we analyze the latter situation using a minimal variant of active gel theory into which we include optogenetic activation as a spatiotemporally constrained perturbation. The model can describe the symmetrical flow of the actomyosin system observed in optogenetic experiments, but not the long-lasting polarization required for cell migration. Motile solutions become possible if cytoskeletal polymerization is included through the boundary conditions. Optogenetic activation of contraction can then initiate locomotion in a symmetrically spreading cell and strengthen motility in an asymmetrically polymerizing one. If designed appropriately, it can also arrest motility even for protrusive boundaries., Comment: 16 pages, 11 figures. Revisions compared to first version mainly concern Eqs. 1, 3, 6, 8, 14 and Fig. 3 (effect of objective derivative)

The rheology of biological cells is not only determined by their cytoskeletal networks, but also by the molecular motors that crosslink and contract them. Recently it has been found that the assemblies of myosin II molecular motors in non-muscle cells are mixtures of fast and slow motor variants. Using computer simulations and an analytical mean field theory of a crossbridge model for myosin II motors, here we show that such motor ensembles effectively behave as active Maxwell elements. We calculate storage and loss moduli as a function of the model parameters and show that the rheological properties cross over from viscous to elastic as one increases the ratio of slow to fast motors. This suggests that cells tune their mechanical properties by regulating the composition of their myosin assemblies., Comment: 5 pages, 5 figures

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate non-muscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the crossbridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds upon a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching., Comment: 15 pages, 6 figures, 4 supplemental figures

Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of the free membrane does not play an important role for tensed and loose membranes, in the intermediate regime it leads to an important energy barrier. Here we show that this barrier is similar to but different from an effective line tension and suggest a simple analytical approximation for it. We then explore the rich dynamics of uptake for particles of different shapes and present the corresponding dynamical state diagrams. We also extend our model to include stochastic fluctuations, which facilitate uptake and lead to corresponding changes in the phase diagrams., Comment: 20 pages, 19 figures

The cellular uptake of nanoparticles or viruses requires that the gain of adhesion energy overcomes the cost of plasma membrane bending. It is well known that this leads to a minimal particle size for uptake. Using a simple deterministic theory for this process, we first show that, for the same radius and volume, cylindrical particles should be taken up faster than spherical particles, both for normal and parallel orientations. We then address stochastic effects, which are expected to be relevant due to small system size, and show that, now, spherical particles can have a faster uptake, because the mean first passage time profits from the multiplicative noise induced by the spherical geometry. We conclude that stochastic effects are strongly geometry dependent and may favor spherical shapes during adhesion-driven particle uptake., Comment: 5 pages, 4 figures