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

The influence of swelling on elastic properties of polyacrylamide hydrogels

Polyacrylamide (PAM) hydrogels are commonly used as substrates for cell mechanical and mechanobiological studies because of their tunable stiffness and ease of handling. The dependence of bulk rheological and local elastic properties (assessed by Atomic Force Microscopy, or AFM) of PAM hydrogels on its composition and polymerization temperature has been extensively studied. PAM hydrogels swell when immersed in media, but the influence of swelling on local elastic properties is poorly characterized. Direct measurements of the effect of swelling on PAM elastic properties are scarce. We report here, for the first time, the direct measurements of volumetric swelling and local elastic properties of PAM gels throughout the post-polymerization swelling process until equilibrium. First, local and global elastic properties (measured by rheology), were obtained during polymerization in the absence of swelling, and showed good agreement with each other. Four PAM hydrogel compositions were characterized thus, with corresponding storage shear moduli (as measured immediately after polymerization) of 4,530 Pa (termed stiffest), 2,900 Pa (stiff), 538 Pa (soft), and 260 Pa (softest). Next, all compositions were subjected to swelling in phosphate buffered saline. Swelling ratios and local elastic moduli were measured at 0, 3, 6, 9, 12, and 24 h post-polymerization for the soft and softest compositions, and once daily till 6 days post-polymerization for all four compositions. For the stiffest and stiff gels, swelling ratio, and local elastic modulus changed negligibly with time, while for the soft and softest gels, substantial changes between Day 0 and Day 1 were found for both swelling ratio (increased by 21.6 and 133%, respectively), and local elastic modulus decreased (by 33.7 and 33.3%, respectively), substantially. Experimental data were analyzed by a model that combined ideal elastomer mechanics and poroelastic swelling kinetics model. Model predictions confirmed the validity of present measurements with respect to past studies where swelling and elastic properties were not measured simultaneously. The present study underlines the important effect swelling can have on PAM elastic properties and provides detailed quantitative data to guide the duration taken to reach equilibrium—a useful information for cell mechanics experiments. In addition, the simultaneous measurements of swelling and local elastic moduli provide novel data for the validation of theoretical models

Fibrin structural and diffusional analysis suggests that fibers are permeable to solute transport

Fibrin hydrogels are promising carrier materials in tissue engineering. They are biocompatible and easy to prepare, they can bind growth factors and they can be prepared from a patient’s own blood. While fibrin structure and mechanics have been extensively studied, not much is known about the relation between structure and diffusivity of solutes within the network. This is particularly relevant for solutes with a size similar to that of growth factors. A novel methodological approach has been used in this study to retrieve quantitative structural characteristics of fibrin hydrogels, by combining two complementary techniques, namely confocal fluorescence microscopy with a fiber extraction algorithm and turbidity measurements. Bulk rheological measurements were conducted to determine the impact of fibrin hydrogel structure on mechanical properties. From these measurements it can be concluded that variations in the fibrin hydrogel structure have a large impact on the rheological response of the hydrogels (up to two orders of magnitude difference in storage modulus) but only a moderate influence on the diffusivity of dextran solutes (up to 25% difference). By analyzing the diffusivity measurements by means of the Ogston diffusion model we further provide evidence that individual fibrin fibers can be semi-permeable to solute transport, depending on the average distance between individual protofibrils. This can be important for reducing mass transport limitations, for modulating fibrinolysis and for growth factor binding, which are all relevant for tissue engineering

Modeling extracellular matrix viscoelasticity using smoothed particle hydrodynamics with improved boundary treatment

We propose viscoelastic smoothed particle hydrodynamics (SPH) with extended boundary conditions as a new method to model the extracellular matrix (ECM) in contact with a migrating cell. The contact mechanics between a cell and ECM is modeled based on an existing boundary method in SPH that corrects for the well-known missing kernel support problem in Fluid Structure Interactions (FSI). This boundary method is here extended to allow the modeling of moving boundaries in contact with a viscoelastic solid. To validate the method, simulations are performed of tractions applied to a viscoelastic solid, Stokes flow around an array of square pillars, and indentation of a viscoelastic material with a circular indenter. By drop out of the inertial terms in the SPH equations of motion, the new SPH formulation allows to solve problems in a low Reynolds environment with a timestep independent of the particle spacing, permitting to model processes at the cellular scale (i.e. -scale). The potential of the method to capture cell–ECM interactions is demonstrated by simulation of a self propelling object that locally degrades the ECM by fluidizing it to permit migration. This should enable us to model and understand realistic cell–matrix interactions in the future

Occurrence and Treatment of Bone Atrophic Non-Unions Investigated by an Integrative Approach

Recently developed atrophic non-union models are a good representation of the clinical situation in which many nonunions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures

Relating the Chondrocyte Gene Network to Growth Plate Morphology: From Genes to Phenotype

During endochondral ossification, chondrocyte growth and differentiation is controlled by many local signalling pathways. Due to crosstalks and feedback mechanisms, these interwoven pathways display a network like structure. In this study, a large-scale literature based logical model of the growth plate network was developed. The network is able to capture the different states (resting, proliferating and hypertrophic) that chondrocytes go through as they progress within the growth plate. In a first corroboration step, the effect of mutations in various signalling pathways of the growth plate network was investigated

Fibrodysplasia ossificans progressiva: what have we achieved and where are we now?: Follow-up to the 2015 Lorentz workshop

Fibrodysplasia ossificans progressiva (FOP) is an ultra-rare progressive genetic disease effecting one in a million individuals. During their life, patients with FOP progressively develop bone in the soft tissues resulting in increasing immobility and early death. A mutation in the ACVR1 gene was identified as the causative mutation of FOP in 2006. After this, the pathophysiology of FOP has been further elucidated through the efforts of research groups worldwide. In 2015, a workshop was held to gather these groups and discuss the new challenges in FOP research. Here we present an overview and update on these topics.Diabetes mellitus: pathophysiological changes and therap

The importance of loading frequency, rate and vibration for enhancing bone adaptation and implant osseointegration

Mechanical loading is one of the key factors that influence bone mass and the osseointegration of bone-anchored implants. From a clinical point of view, mechanical stimulation may be used to enhance bone strength and implant osseointegration. Among the many loading parameters that influence the response to mechanical loading, the effects of loading frequency and rate have been investigated in many studies. In this paper the most relevant animal studies that have addressed the effect of loading frequency, rate, and vibration on either bone adaptation or implant osseointegration are systematically reviewed. Apparently contradictory results are discussed and interpreted within the context of mechanotransduction and mechanoregulation of bone. A combined experimental and computational approach is suggested to address some of the remaining research questions