Stability of asymmetric cell division: A deformable cell model of cytokinesis applied to C. elegans.

Cell division during early embryogenesis is linked to key morphogenic events such as embryo symmetry breaking and tissue patterning. It is thought that the physical surrounding of cells together with cell intrinsic cues act as a mechanical "mold," guiding cell division to ensure these events are robust. To quantify how cell division is affected by the mechanical and geometrical environment, we present a novel computational mechanical model of cytokinesis, the final phase of cell division. Simulations with the model reproduced experimentally observed furrow dynamics and describe the volume ratio of daughter cells in asymmetric cell divisions, based on the position and orientation of the mitotic spindle. For dividing cells in geometrically confined environments, we show how the orientation of confinement relative to the division axis modulates the volume ratio in asymmetric cell division. Further, we quantified how cortex viscosity and surface tension determine the shape of a dividing cell and govern bubble-instabilities in asymmetric cell division. Finally, we simulated the formation of the three body axes via sequential (a)symmetric divisions up until the six-cell stage of early C. elegans development, which proceeds within the confines of an eggshell. We demonstrate how model input parameters spindle position and orientation provide sufficient information to reliably predict the volume ratio of daughter cells during the cleavage phase of development. However, for egg geometries perturbed by compression, the model predicts that a change in confinement alone is insufficient to explain experimentally observed differences in cell volume. This points to an effect of the compression on the spindle positioning mechanism. Additionally, the model predicts that confinement stabilizes asymmetric cell divisions against bubble-instabilities.

The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model.

Actin protrusion dynamics plays an important role in the regulation of three-dimensional (3D) cell migration. Cells form protrusions that adhere to the surrounding extracellular matrix (ECM), mechanically probe the ECM and contract in order to displace the cell body. This results in cell migration that can be directed by the mechanical anisotropy of the ECM. However, the subcellular processes that regulate protrusion dynamics in 3D cell migration are difficult to investigate experimentally and therefore not well understood. Here, we present a computational model of cell migration through a degradable viscoelastic ECM. This model is a 2D representation of 3D cell migration. The cell is modeled as an active deformable object that captures the viscoelastic behavior of the actin cortex and the subcellular processes underlying 3D cell migration. The ECM is regarded as a viscoelastic material, with or without anisotropy due to fibrillar strain stiffening, and modeled by means of the meshless Lagrangian smoothed particle hydrodynamics (SPH) method. ECM degradation is captured by local fluidization of the material and permits cell migration through the ECM. We demonstrate that changes in ECM stiffness and cell strength affect cell migration and are accompanied by changes in number, lifetime and length of protrusions. Interestingly, directly changing the total protrusion number or the average lifetime or length of protrusions does not affect cell migration. A stochastic variability in protrusion lifetime proves to be enough to explain differences in cell migration velocity. Force-dependent adhesion disassembly does not result in faster migration, but can make migration more efficient. We also demonstrate that when a number of simultaneous protrusions is enforced, the optimal number of simultaneous protrusions is one or two, depending on ECM anisotropy. Together, the model provides non-trivial new insights in the role of protrusions in 3D cell migration and can be a valuable contribution to increase the understanding of 3D cell migration mechanics.

Distribution and propagation of mechanical stress in simulated structurally heterogeneous tissue spheroids.

The mechanical microenvironment of cells has been associated with phenotypic changes that cells undergo in three-dimensional spheroid culture formats. Radial asymmetry in mechanical stress - with compression in the core and tension at the periphery - has been analyzed by representing tissue spheroids as homogeneous visco-elastic droplets under surface tension. However, the influence of the granular microstructure of tissue spheroids in the distribution of mechanical stress in tissue spheroids has not been accounted for in a generic manner. Here, we quantify the distribution and propagation of mechanical forces in structurally heterogeneous multicellular assemblies. For this, we perform numerical simulations of a deformable cell model, which represents cells as elastic, contractile shells surrounding a liquid incompressible cytoplasm, interacting by means of non-specific adhesion. Using this model, we show how cell-scale properties such as cortical stiffness, active tension and cell-cell adhesive tension influence the distribution of mechanical stress in simulated tissue spheroids. Next, we characterize the transition at the tissue-scale from a homogeneous liquid droplet to a heterogeneous packed granular assembly.

Intercellular Adhesion Stiffness Moderates Cell Decoupling as a Function of Substrate Stiffness.

The interplay between cell-cell and cell-substrate interactions is complex yet necessary for the formation and healthy functioning of tissues. The same mechanosensing mechanisms used by the cell to sense its extracellular matrix also play a role in intercellular interactions. We used the discrete element method to develop a computational model of a deformable cell that includes subcellular components responsible for mechanosensing. We modeled a three-dimensional cell pair on a patterned (two-dimensional) substrate, a simple laboratory setup to study intercellular interactions. We explicitly modeled focal adhesions and adherens junctions. These mechanosensing adhesions matured, becoming stabilized by force. We also modeled contractile stress fibers that bind the discrete adhesions. The mechanosensing fibers strengthened upon stalling. Traction exerted on the substrate was used to generate traction maps (along the cell-substrate interface). These simulated maps are compared to experimental maps obtained via traction force microscopy. The model recreates the dependence on substrate stiffness of the tractions' spatial distribution, contractile moment of the cell pair, intercellular force, and number of focal adhesions. It also recreates the phenomenon of cell decoupling, in which cells exert forces separately when substrate stiffness increases. More importantly, the model provides viable molecular explanations for decoupling: mechanosensing mechanisms are responsible for competition between different fiber-adhesion configurations present in the cell pair. The point at which an increasing substrate stiffness becomes as high as that of the cell-cell interface is the tipping point at which configurations that favor cell-substrate adhesion dominate over those favoring cell-cell adhesion. This competition is responsible for decoupling.

Mechanodegradation of Polymers: A Limiting Factor of Mechanochemical Activation in the Production of Amorphous Solid Dispersions by Cryomilling.

In this study, we report on the influence of mechanochemical activation on the chemical stability of amorphous solid dispersions made up of indomethacin and hydroxypropyl methyl cellulose (HPMC), poly(vinylpyrrolidone) (PVP), poly(vinylpyrrolidone vinylacetate) (PVPVA), or Soluplus. In agreement with our recently published work, all applied carriers were found to be prone to polymer degradation. Covalent bonds within the polymers were cleaved and mechanoradicals were generated. Furthermore, decomposition of indomethacin was also observed but occurred only in the presence of polymers. Hence, it is proposed that the generated mechanoradicals from the polymers are responsible for the chemical degradation of indomethacin. Our study also strongly suggests the existence of a critical polymer- and process-dependent molecular weight limit "M∞", below which only limited mechanodegradation takes place since the lower-molecular-weight polymer PVP K12PF had a less profound influence on the degradation of indomethacin in comparison to PVP K25.

Towards Mimicking the Fetal Liver Niche: The Influence of Elasticity and Oxygen Tension on Hematopoietic Stem/Progenitor Cells Cultured in 3D Fibrin Hydrogels.

Hematopoietic stem/progenitor cells (HSPCs) are responsible for the generation of blood cells throughout life. It is believed that, in addition to soluble cytokines and niche cells, biophysical cues like elasticity and oxygen tension are responsible for the orchestration of stem cell fate. Although several studies have examined the effects of bone marrow (BM) niche elasticity on HSPC behavior, no study has yet investigated the effects of the elasticity of other niche sites like the fetal liver (FL), where HSPCs expand more extensively. In this study, we evaluated the effect of matrix stiffness values similar to those of the FL on BM-derived HSPC expansion. We first characterized the elastic modulus of murine FL tissue at embryonic day E14.5. Fibrin hydrogels with similar stiffness values as the FL (soft hydrogels) were compared with stiffer fibrin hydrogels (hard hydrogels) and with suspension culture. We evaluated the expansion of total nucleated cells (TNCs), Lin-/cKit+ cells, HSPCs (Lin-/Sca+/cKit+ (LSK) cells), and hematopoietic stem cells (HSCs: LSK- Signaling Lymphocyte Activated Molecule (LSK-SLAM) cells) when cultured in 5% O2 (hypoxia) or in normoxia. After 10 days, there was a significant expansion of TNCs and LSK cells in all culture conditions at both levels of oxygen tension. LSK cells expanded more in suspension culture than in both fibrin hydrogels, whereas TNCs expanded more in suspension culture and in soft hydrogels than in hard hydrogels, particularly in normoxia. The number of LSK-SLAM cells was maintained in suspension culture and in the soft hydrogels but not in the hard hydrogels. Our results indicate that both suspension culture and fibrin hydrogels allow for the expansion of HSPCs and more differentiated progeny whereas stiff environments may compromise LSK-SLAM cell expansion. This suggests that further research using softer hydrogels with stiffness values closer to the FL niche is warranted.

The Effect of Cortical Elasticity and Active Tension on Cell Adhesion Mechanics.

We consider a cell as an elastic, contractile shell surrounding a liquid incompressible cytoplasm and with nonspecific adhesion. We perform numerical simulations of this model to study the mechanics of cell-cell separation. By variation of parameters, we are able to recover well-known limits of the Johnson-Kendall-Roberts theory, the Derjaguin-Muller-Toporov model, adhesive vesicles with surface tension (Brochard-Wyart and de Gennes derivation), and thin elastic shells. We further locate biological cells on this parameter space by comparison to existing experiments on S180 cells. Using this model, we show that mechanical parameters can be obtained that are consistent with both dual pipette aspiration and micropipette aspiration, a problem not successfully tackled so far. We estimate a cortex elastic modulus of Ec ≈ 15 kPa, an effective cortex thickness of tc ≈ 0.3 µm, and an active tension of γ ≈ 0.4 nN/µm. With these parameters, a Johnson-Kendall-Roberts-like scaling of the separation force is recovered. Finally, the change of contact radius with applied force in a pull-off experiment was investigated. For small forces, a scaling similar to both the Brochard-Wyart and de Gennes derivation and the Derjaguin-Muller-Toporov model is found.

Discrete element modelling of tomato tissue deformation and failure at the cellular scale.

Bruise damage in fruit results from cell wall failure and inter-cellular separation. Despite the importance of the micro-mechanics of plant tissue with respect to its integrity, it remains largely unquantified and poorly understood, due to many difficulties during experimental characterization. In this article, a 3D micro-mechanical plant tissue model that is able to model cell rupture and inter-cellular debonding and thus provide more insight into the micro-mechanics was developed. The model is based on the discrete element method (DEM) and represents the tissue as a mass-spring system. Each plant cell is represented as a deformable visco-elastoplastic triangulated mesh under turgor pressure. To model cell wall rupture, it is assumed that a spring connection in the wall breaks at a certain critical stretch ratio and that a ruptured cell is turgorless. The inter-cellular contact model assumes brittle fracture between a cell's node and an adjacent cell's triangle when their bond distance exceeds a critical value. A high-speed tomato fruit cell compression test was simulated and the modelled force-strain curve compares well with the experimental data, including for strains above the elastic limit. By varying the shape of the cell in the compression simulation it was shown that the force-strain curve is highly dependent on the cell shape and thus parameter fitting procedures based on a spherical cell model will be inaccurate. Furthermore, the wall stiffness and thickness showed a positive linear relationship with the force at cell bursting. Besides simulating compression tests of single cells, we also simulated tensile and compression tests on small tissue specimens. Realistic tissue structures of tomato mesocarp tissue were generated by a novel method using DEM simulations of deformable cells in a shrinking cylinder. The cell area, volume and anisotropy distributions of the virtual tissue compared well with micro-CT images of real tomato mesocarp tissue (normalized root mean square error values smaller than 3%). The tissue compression and tensile test simulations demonstrated an important influence of the inter-cellular bonding energy and tissue porosity on the tissue failure characteristics and elastic modulus.

Emergent structures and dynamics of cell colonies by contact inhibition of locomotion.

Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing tissue phenotypes. These include regular distributions of cells, dynamic cell clusters, gel-like networks, collectively migrating monolayers, and 3D aggregates. We give analytical predictions for transitions between noncohesive, cohesive, and 3D cell arrangements. We explicitly show how CIL yields an effective repulsion that promotes cell dispersal, thereby hindering the formation of cohesive tissues. Yet, in continuous monolayers, CIL leads to collective cell motion, ensures tensile intercellular stresses, and opposes cell extrusion. Thus, our work highlights the prominent role of CIL in determining the emergent structures and dynamics of cell colonies.

Immersed Boundary Models for Quantifying Flow-Induced Mechanical Stimuli on Stem Cells Seeded on 3D Scaffolds in Perfusion Bioreactors.

Perfusion bioreactors regulate flow conditions in order to provide cells with oxygen, nutrients and flow-associated mechanical stimuli. Locally, these flow conditions can vary depending on the scaffold geometry, cellular confluency and amount of extra cellular matrix deposition. In this study, a novel application of the immersed boundary method was introduced in order to represent a detailed deformable cell attached to a 3D scaffold inside a perfusion bioreactor and exposed to microscopic flow. The immersed boundary model permits the prediction of mechanical effects of the local flow conditions on the cell. Incorporating stiffness values measured with atomic force microscopy and micro-flow boundary conditions obtained from computational fluid dynamics simulations on the entire scaffold, we compared cell deformation, cortical tension, normal and shear pressure between different cell shapes and locations. We observed a large effect of the precise cell location on the local shear stress and we predicted flow-induced cortical tensions in the order of 5 pN/µm, at the lower end of the range reported in literature. The proposed method provides an interesting tool to study perfusion bioreactors processes down to the level of the individual cell's micro-environment, which can further aid in the achievement of robust bioprocess control for regenerative medicine applications.

Mathematical model suitable for efficient simulation of thin semi-flexible polymers in complex environments.

We present an alternative approach to simulations of semi-flexible polymers. In contrast with the usual bead-rod compromise between bead-spring and rigid rod models, we use deformable cylindrical segments as basic units of the polymer. The length of each segment is not preserved with end points diffusing under constraints keeping the polymer chain nature intact. The model allows the simulation of tension transport and elasticity properties. In particular we describe a new cooperative regime in the relaxation of the polymer from its fully elongated configuration.

Analysis of initial cell spreading using mechanistic contact formulations for a deformable cell model.

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cell's cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

Anomalous diffusion of nanoparticles in the spatially heterogeneous biofilm environment.

Biofilms contain extracellular polymeric substances (EPS) that provide structural support and restrict penetration of antimicrobial treatment. To overcome limited penetration, functionalized nanoparticles (NPs) have been suggested as carriers for antimicrobial delivery. Using microscopy, we evaluate the diffusion of nanoparticles in function of the structure of Salmonella biofilms. We observe anomalous diffusion and heterogeneous mobility of NPs resulting in distinct NPs distribution that depended on biofilm structure. Through Brownian dynamics modeling with spatially varying viscosity around bacteria, we demonstrated that spatial gradients in diffusivity generate viscous sinks that trap NPs near bacteria. This model replicates the characteristic diffusion signature and vertical distribution of NPs in the biofilm. From a treatment perspective, our work indicates that both biofilm structure and the level of EPS can impact NP drug delivery, where low levels of EPS might benefit delivery by immobilizing NPs closer to bacteria and higher levels hamper delivery due to shielding effects.

Stirred culture of cartilaginous microtissues promotes chondrogenic hypertrophy through exposure to intermittent shear stress.

Cartilage microtissues are promising tissue modules for bottom up biofabrication of implants leading to bone defect regeneration. Hitherto, most of the protocols for the development of these cartilaginous microtissues have been carried out in static setups, however, for achieving higher scales, dynamic process needs to be investigated. In the present study, we explored the impact of suspension culture on the cartilage microtissues in a novel stirred microbioreactor system. To study the effect of the process shear stress, experiments with three different impeller velocities were carried out. Moreover, we used mathematical modeling to estimate the magnitude of shear stress on the individual microtissues during dynamic culture. Identification of appropriate mixing intensity allowed dynamic bioreactor culture of the microtissues for up to 14 days maintaining microtissue suspension. Dynamic culture did not affect microtissue viability, although lower proliferation was observed as opposed to the statically cultured ones. However, when assessing cell differentiation, gene expression values showed significant upregulation of both Indian Hedgehog (IHH) and collagen type X (COLX), well known markers of chondrogenic hypertrophy, for the dynamically cultured microtissues. Exometabolomics analysis revealed similarly distinct metabolic profiles between static and dynamic conditions. Dynamic cultured microtissues showed a higher glycolytic profile compared with the statically cultured ones while several amino acids such as proline and aspartate exhibited significant differences. Furthermore, in vivo implantations proved that microtissues cultured in dynamic conditions are functional and able to undergo endochondral ossification. Our work demonstrated a suspension differentiation process for the production of cartilaginous microtissues, revealing that shear stress resulted to an acceleration of differentiation towards hypertrophic cartilage.

Permissive aggregative group formation favors coexistence between cooperators and defectors in yeast.

In Saccharomyces cerevisiae, the FLO1 gene encodes flocculins that lead to formation of multicellular flocs, that offer protection to the constituent cells. Flo1p was found to preferentially bind to fellow cooperators compared to defectors lacking FLO1 expression, enriching cooperators within the flocs. Given this dual function in cooperation and kin recognition, FLO1 has been termed a "green beard gene". Because of the heterophilic nature of the Flo1p bond however, we hypothesize that kin recognition is permissive and depends on the relative stability of the FLO1+/flo1- versus FLO1+/FLO1+ detachment force F. We combine single-cell measurements of adhesion, individual cell-based simulations of cluster formation, and in vitro flocculation to study the impact of relative bond stability on the evolutionary stability of cooperation. We identify a trade-off between both aspects of the green beard mechanism, with reduced relative bond stability leading to increased kin recognition at the expense of cooperative benefits. We show that the fitness of FLO1 cooperators decreases as their frequency in the population increases, arising from the observed permissive character (F+- = 0.5 F++) of the Flo1p bond. Considering the costs associated with FLO1 expression, this asymmetric selection often results in a stable coexistence between cooperators and defectors.

Agaric acid reduces Salmonella biofilm formation by inhibiting flagellar motility.

Salmonella biofilms are a common cause of contaminations in the food or feed industry. In a screening for novel compounds to combat biofilm-associated foodborne outbreaks, we identified agaric acid as a Salmonella Typhimurium biofilm inhibitor that does not affect planktonic growth. Importantly, the remaining biofilm cells after preventive treatment with agaric acid were significantly more sensitive to the common disinfectant hydrogen peroxide. Screening of a GFP-promoter fusion library of biofilm related genes revealed that agaric acid downregulates the transcription of genes responsible for flagellar motility. Concurrently, swimming motility was completely abrogated in the presence of agaric acid, indicating that biofilm inhibition occurs via interference with the motility phenotype. Moreover, agaric acid also reduced biofilm formation of Pseudomonas aeruginosa, Staphylococcus aureus and Escherichia coli. Agaric acid thus shows potential as an anti-virulence compound that inhibits both motility and biofilm formation.

Model-Driven Controlled Alteration of Nanopillar Cap Architecture Reveals its Effects on Bactericidal Activity.

Nanostructured surfaces can be engineered to kill bacteria in a contact-dependent manner. The study of bacterial interactions with a nanoscale topology is thus crucial to developing antibacterial surfaces. Here, a systematic study of the effects of nanoscale topology on bactericidal activity is presented. We describe the antibacterial properties of highly ordered and uniformly arrayed cotton swab-shaped (or mushroom-shaped) nanopillars. These nanostructured surfaces show bactericidal activity against Staphylococcus aureus and Pseudomonas aeruginosa. A biophysical model of the cell envelope in contact with the surface, developed ab initio from the infinitesimal strain theory, suggests that bacterial adhesion and subsequent lysis are highly influenced by the bending rigidity of the cell envelope and the surface topography formed by the nanopillars. We used the biophysical model to analyse the influence of the nanopillar cap geometry on the bactericidal activity and made several geometrical alterations of the nanostructured surface. Measurement of the bactericidal activities of these surfaces confirms model predictions, highlights the non-trivial role of cell envelope bending rigidity, and sheds light on the effects of nanopillar cap architecture on the interactions with the bacterial envelope. More importantly, our results show that the surface nanotopology can be rationally designed to enhance the bactericidal efficiency.

Modeling of Mechanosensing Mechanisms Reveals Distinct Cell Migration Modes to Emerge From Combinations of Substrate Stiffness and Adhesion Receptor-Ligand Affinity.

Mesenchymal cell migration is an integral process in development and healing. The process is regulated by both mechanical and biochemical properties. Mechanical properties of the environment are sensed through mechanosensing, which consists of molecular responses mediated by mechanical signals. We developed a computational model of a deformable 3D cell on a flat substrate using discrete element modeling. The cell is polarized in a single direction and thus moves along the long axis of the substrate. By modeling discrete focal adhesions and stress fibers, we implement two mechanosensing mechanisms: focal adhesion stabilization by force and stress fiber strengthening upon contraction stalling. Two substrate-associated properties, substrate (ligand) stiffness and adhesion receptor-ligand affinity (in the form of focal adhesion disassembly rate), were varied for different model setups in which the mechanosensing mechanisms are set as active or inactive. Cell displacement, focal adhesion number, and cellular traction were quantified and tracked in time. We found that varying substrate stiffness (a mechanical property) and adhesion receptor-ligand affinity (a biochemical property) simultaneously dictate the mode in which cells migrate; cells either move in a smooth manner reminiscent of keratocytes or in a cyclical manner reminiscent of epithelial cells. Mechanosensing mechanisms are responsible for the range of conditions in which a cell adopts a particular migration mode. Stress fiber strengthening, specifically, is responsible for cyclical migration due to build-up of enough force to elicit rupture of focal adhesions and retraction of the cellular rear. Together, both mechanisms explain bimodal dependence of cell migration on substrate stiffness observed in the literature.

Robust scalable synthesis of a bis-urea derivative forming thixotropic and cytocompatible supramolecular hydrogels.

Synthetic hydrogels address a need for affordable, industrially scalable scaffolds for tissue engineering. Herein, a novel low molecular weight gelator is reported that forms self-healing supramolecular hydrogels. Its robust synthesis can be performed in a solvent-free manner using ball milling. Strikingly, encapsulated cells spread and proliferate without specific cell adhesion ligands in the nanofibrous material.

Increasing robustness against changes in the interferent structure by incorporating prior information in the augmented classical least-squares framework.

A class of multivariate calibration methods called augmented classical least squares (ACLS) has been proposed which combines an explicit linear additive model with the predictive power of inverse models, such as principal component regression (PCR) and partial least squares (PLS). Because of its use of the explicit linear additive model, ACLS provides an interesting framework to incorporate different sources of prior information, such as measured pure component spectra, in the model. In this study, the predictive power of ACLS models incorporating different amounts of prior information has been compared to that of PCR and PLS using two examples, a designed experiment and one with biological samples. In both cases, the ACLS models showed predictive power comparable to PLS under idealized validation conditions. When a different interferent structure was present in the validation samples, the predictive power of the inverse models (PCR and PLS) dramatically decreased, with an increase in root-mean-squared error of prediction by a factor of 3.5 for the first example and a factor of 2 in the second example. The incorporation of prior information in the ACLS framework was found to considerably reduce or even completely remove these dramatic effects, especially when the pure component contributions for the interferents were taken into account.