Ilka B. Bischofs

Cell organization in soft media due to active mechanosensing

Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one unifying principle, namely that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness. Using linear elasticity theory to model the extracellular environment, we calculate optimal cell organization for several situations of interest and find excellent agreement with experiments for fibroblasts, both on elastic substrates and in collagen gels: cells orient in the direction of external tensile strain; they orient parallel and normal to free and clamped surfaces, respectively; and they interact elastically to form strings. Our method can be applied for rational design of tissue equivalents. Moreover, our results indicate that the concept of contact guidance has to be reevaluated. We also suggest that cell–matrix contacts are up-regulated by large effective stiffness in the environment because, in this way, build-up of force is more efficient.

Filamentous Network Mechanics and Active Contractility Determine Cell and Tissue Shape

For both cells and tissues, shape is closely correlated with function presumably via geometry-dependent distribution of tension. In this study, we identify common shape determinants spanning cell and tissue scales. For cells whose sites of adhesion are restricted to small adhesive islands on a micropatterned substrate, shape resembles a sequence of inward-curved circular arcs. The same shape is observed for fibroblast-populated collagen gels that are pinned to a flat substrate. Quantitative image analysis reveals that, in both cases, arc radii increase with the spanning distance between the pinning points. Although the Laplace law for interfaces under tension predicts circular arcs, it cannot explain the observed dependence on the spanning distance. Computer simulations and theoretical modeling demonstrate that filamentous network mechanics and contractility give rise to a modified Laplace law that quantitatively explains our experimental findings on both cell and tissue scales. Our model in conjunction with actomyosin inhibition experiments further suggests that cell shape is regulated by two different control modes related to motor contractility and structural changes in the actin cytoskeleton.

Elastic interactions of active cells with soft materials

Anchorage-dependent cells collect information on the mechanical properties of the environment through their contractile machineries and use this information to position and orient themselves. Since the probing process is anisotropic, cellular force patterns during active mechanosensing can be modeled as anisotropic force contraction dipoles. Their buildup depends on the mechanical properties of the environment, including elastic rigidity and prestrain. In a finite sized sample, it also depends on sample geometry and boundary conditions through image strain fields. We discuss the interactions of active cells with an elastic environment and compare it to the case of physical force dipoles. Despite marked differences, both cases can be described in the same theoretical framework. We exactly solve the elastic equations for anisotropic force contraction dipoles in different geometries (full space, half space, and sphere) and with different boundary conditions. These results are then used to predict optimal position and orientation of mechanosensing cells in soft material.

Metabolic cross-feeding via intercellular nanotubes among bacteria

Bacteria frequently exchange metabolites by diffusion through the extracellular environment, yet it remains generally unclear whether bacteria can also use cell-cell connections to directly exchange nutrients. Here we address this question by engineering cross-feeding interactions within and between Acinetobacter baylyi and Escherichia coli, in which two distant bacterial species reciprocally exchange essential amino acids. We establish that in a well-mixed environment E. coli, but likely not A. baylyi, can connect to other bacterial cells via membrane-derived nanotubes and use these to exchange cytoplasmic constituents. Intercellular connections are induced by auxotrophy-causing mutations and cease to establish when amino acids are externally supplied. Electron and fluorescence microscopy reveal a network of nanotubular structures that connects bacterial cells and enables an intercellular transfer of cytoplasmic materials. Together, our results demonstrate that bacteria can use nanotubes to exchange nutrients among connected cells and thus help to distribute metabolic functions within microbial communities.

Complexity in bacterial cell–cell communication: Quorum signal integration and subpopulation signaling in the Bacillus subtilis phosphorelay

A common form of quorum sensing in Gram-positive bacteria is mediated by peptides that act as phosphatase regulators (Phr) of receptor aspartyl phosphatases (Raps). In Bacillus subtilis, several Phr signals are integrated in sporulation phosphorelay signal transduction. We theoretically demonstrate that the phosphorelay can act as a computational machine performing a sensitive division operation of kinase-encoded signals by quorum-modulated Rap signals, indicative of cells computing a “food per cell” estimate to decide whether to enter sporulation. We predict expression from the rapA-phrA operon to bifurcate as relative environmental signals change in a developing population. We experimentally observe that the rapA-phrA operon is heterogeneously induced in sporulating microcolonies. Uninduced cells sporulate rather synchronously early on, whereas the RapA/PhrA subpopulation sporulates less synchronously throughout later stationary phase. Moreover, we show that cells sustain PhrA expression during periods of active growth. Together with the model, these findings suggest that the phosphorelay may normalize environmental signals by the size of the (sub)population actively competing for nutrients (as signaled by PhrA). Generalizing this concept, the various Phrs could facilitate subpopulation communication in dense isogenic communities to control the physiological strategies followed by differentiated subpopulations by interpreting (environmental) signals based on the spatiotemporal community structure.

Memory in microbes: quantifying history-Dependent behavior in a bacterium.

Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy.

Effect of adhesion geometry and rigidity on cellular force distributions.

The behavior and fate of tissue cells are controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force distributions for cells adhering to adhesive patterns with different geometries and rigidities. For continuous adhesion along a closed contour, forces are predicted to be localized to the corners. For discrete sites of adhesion, the model predicts the forces to be mainly determined by the lateral pull of the cell contour. With increasing distance between two neighboring sites of adhesion, the adhesion force increases because the cell shape results in steeper pulling directions. Softer substrates result in smaller forces. Our predictions agree well with experimental force patterns measured on pillar assays.

Contractile network models for adherent cells

Cells sense the geometry and stiffness of their adhesive environment by active contractility. For strong adhesion to flat substrates, two-dimensional contractile network models can be used to understand how force is distributed throughout the cell. Here we compare the shape and force distribution for different variants of such network models. In contrast to Hookean networks, cable networks reflect the asymmetric response of biopolymers to tension versus compression. For passive networks, contractility is modeled by a reduced resting length of the mechanical links. In actively contracting networks, a constant force couple is introduced into each link in order to model contraction by molecular motors. If combined with fixed adhesion sites, all network models lead to invaginated cell shapes, but only actively contracting cable networks lead to the circular arc morphology typical for strongly adhering cells. In this case, shape and force distribution are determined by local rather than global determinants and thus are suited to endow the cell with a robust sense of its environment. We also discuss nonlinear and adaptive linker mechanics as well as the relation to tissue shape.

Effect of poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and antiferroelastic phases as a function of the Poisson ratio.

A modular view of the diversity of cell-density-encoding schemes in bacterial quorum-sensing systems.

Certain environmental parameters are accessible to cells only indirectly and require an encoding step for cells to retrieve the relevant information. A prominent example is the phenomenon of quorum sensing by microorganisms, where information about cell density is encoded by means of secreted signaling molecules. The mapping of cell density to signal molecule concentration and the corresponding network modules involved have been at least partially characterized in many bacteria, and vary markedly between different systems. In this study, we investigate theoretically how differences in signal transport, signal modification, and site of signal detection shape the encoding function and affect the sensitivity and the noise characteristics of the cell-density-encoding process. We find that different modules are capable of implementing both fairly basic as well as more complex encoding schemes, whose qualitative characteristics vary with cell density and are linked to network architecture, providing the basis for a hierarchical classification scheme. We exploit the tight relationship between encoding behavior and network architecture to constrain the network topology of partially characterized natural systems, and verify one such prediction by showing experimentally that Vibrio harveyi is capable of importing Autoinducer 2. The framework developed in this research can serve not only to guide reverse engineering of natural systems but also to stimulate the design of synthetic systems and generally facilitate a better understanding of the complexities arising in the quorum-sensing process because of variations in the physical organization of the encoder network module.