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Three-dimensional cell culture in engineered hydro gels is increasingly used in tissue engineering and regenerative medicine. The transfer of nutrients, gases, and waste materials through these hydrogels is of utmost importance for cell viability and response, yet the translation of diffusion coefficients into practical guidelines is not well established. Here, we combined mathematical modeling, fluorescent recovery after photobleaching, and hydrogel diffusion experiments on cell culture inserts to provide a multiscale practical approach for diffusion. We observed a dampening effect of the hydrogel that slowed the response to concentration changes and the creation of a diffusion gradient in the hydrogel by media refreshment. Our designed model combined with measurements provides a practical point of reference for diffusion coefficients in real-world culture conditions, enabling more informed choices on hydrogel culture conditions. This model can be improved in the future to simulate more complicated intrinsic hydrogel properties and study the effects of secondary interactions on the diffusion of analytes through the hydrogel.

A comparatively straightforward approach to accomplish more physiological realism in organ-on-a-chip (OoC) models is through substrate geometry. There is increasing evidence that the strongly, microscale curved surfaces that epithelial or endothelial cells experience when lining small body lumens, such as the alveoli or blood vessels, impact their behavior. However, the most commonly used cell culture substrates for modeling of these human tissue barriers in OoCs, ion track-etched porous membranes, provide only flat surfaces. Here, we propose a more realistic culture environment for alveolar cells based on biomimetically microcurved track-etched membranes. They recreate the mainly spherical geometry of the cells' native microenvironment. In this feasibility study, the membranes were given the shape of hexagonally arrayed hemispherical microwells by an innovative combination of three-dimensional (3D) microfilm (thermo)forming and ion track technology. Integrated in microfluidic chips, they separated a top from a bottom cell culture chamber. The microcurved membranes were seeded by infusion with primary human alveolar epithelial cells. Despite the pronounced topology, the cells fully lined the alveoli-like microwell structures on the membranes' top side. The confluent curved epithelial cell monolayers could be cultured successfully at the air-liquid interface for 14 days. Similarly, the top and bottom sides of the microcurved membranes were seeded with cells from the Calu-3 lung epithelial cell line and human lung microvascular endothelial cells, respectively. Thereby, the latter lined the interalveolar septum-like interspace between the microwells in a network-type fashion, as in the natural counterpart. The coculture was maintained for 11 days. The presented 3D lung-on-a-chip model might set the stage for other (micro)anatomically inspired membrane-based OoCs in the future.

Mathematical biology has emerged as a powerful approach to describe and understand biological systems. Here, we introduce an interactive teaching tool with a practical hands-on skill session plan to introduce students to the various components of a mathematical model with 4 different mathematical approaches (i.e., ordinary differential equations, partial differential equations, stochastic differential equations, and spatial stochastic differential equations) and their advantages and disadvantages. As such, we provide a didactic summary for instructors and students interested in using VCell MathModels for mathematical modeling; this work is also valuable for mathematics-savvy users who would like to exploit fully the capabilities of the VCell software.

Membrane binding and unbinding dynamics play a crucial role in the biological activity of several non-integral membrane proteins, which have to be recruited to the membrane in order to perform their functions. By localizing to the membrane, these proteins are able to induce downstream signal amplification in their respective signaling pathways. Here we present a 3D computational approach using reaction-diffusion equations to investigate the relation between membrane localization of Focal Adhesion Kinase (FAK), Ras homolog family member A (RhoA) and signal amplification of the YAP/TAZ signaling pathway. Our results show that the theoretical scenarios, in which FAK is membrane-bound, yield robust and amplified YAP/TAZ nuclear translocation signals. Moreover, we predict that the amount of YAP/TAZ nuclear translocation increases with cell spreading, confirming the experimental findings in the literature. In summary, our in silico predictions show that when the cell membrane interaction area with the underlying substrate increases, for example through cell spreading, this leads to more encounters between membrane-bound signaling partners and downstream signal amplification. Since membrane activation is a motif common to many signaling pathways, this study has important implications for understanding the design principles of signaling networks.

Various cell surface receptors play an important role in the differentiation and self-renewal of human mesenchymal stem cells (hMSCs). One example of such receptors are the cadherins, which maintain cell–cell adhesion and mechanically couple cells together. Recently, cadherin-11, which is a member of the type II classical cadherin family, has been shown to be involved in the fate commitment of hMSCs. Interestingly, cadherin-11 has no known intrinsic signaling activity and is thought to affect cell behavior via interactions with other cell surface receptors. Members of the platelet-derived growth factor receptor (PDGFR) family are hypothesized to be one of the interaction partners of cadherin-11. Experiments confirmed that PDGFR-α binding to extracellular cadherin-11 regions increases the PDGFR-α activity, whereas the interaction between PDGFR-β and cadherin-11 suppresses the activity of the growth factor receptor. Cadherin-11 knockdown experiments also decreased cell proliferation. These interactions between cadherin-11 and PDGFRs indicate a crosstalk between these receptors and their downstream signaling activities but the nature of this crosstalk is not entirely known. In this study, we used a computational model to represent the experimentally proven interactions between cadherin-11 and the two PDGFRs and we inspected whether the crosstalk also exists downstream of the signaling initiated by the two receptor families. The computational framework allowed us to monitor the relative activity levels of each protein in the network. We performed model simulations to mimic the conditions of previous cadherin-11 knockdown experiments and to predict the effect of crosstalk on cell proliferation. Overall, our predictions suggest the existence of another layer of crosstalk, namely between β-catenin (downstream to cadherin-11) and an ERK inhibitor protein (e.g. DUSP1), different than the crosstalk at the receptor level between cadherin-11 and PDGFR-α and -β. By investigating the multi-level crosstalk between cadherin and PDGFRs computationally, this study contributes to an improved understanding of the effect of cell surface receptors on hMSCs proliferation.

OBJECTIVE Bone biopsy (BB) performed by a surgeon or an interventional radiologist is recommended for suspicion of osteomyelitis underlying diabetic foot ulcer (DFU). To facilitate its practice, we developed a procedure allowing bedside blind bone biopsy (B4) by a diabetologist. RESEARCH DESIGN AND METHODS We conducted a three-step observational study consisting of a feasibility and safety phase (phase 1) to assess the success and side effects of B4, a validity phase (phase 2) to compare DFU outcomes between positive (B4+) and negative (B4−) bone cultures, and a performance phase (phase 3) to compare B4 with the conventional surgical or radiological procedure basic bone biopsy (B3). Primary end points were the presence of bone tissue (phase 1) and complete DFU healing with exclusive medical treatment at 12 months (phases 2 and 3). RESULTS In phase 1, 37 consecutive patients with clinical and/or radiological suspicion of DFU osteomyelitis underwent B4. Bone tissue was collected in all patients with few side effects. In phase 2, a B4+ bone culture was found in 40 of 79 (50.6%) participants. Among B4+ patients, complete wound healing after treatment was 57.5%. No statistical difference was observed with patients with B4− bone culture not treated with antibiotics (71.8%, P = 0.18). In phase 3, the proportion of patients with positive BB was lower in B4 (40 of 79, 50.6%) than in B3 (34 of 44, 77.3%, P < 0.01). However, complete healing was similar (64.6% vs. 54.6%, P = 0.28). No difference in rate of culture contamination was observed. CONCLUSIONS B4 is a simple, safe, and efficient procedure for the diagnosis of DFU osteomyelitis with a similar proportion of healing to conventional BB.

The complex interaction of cells with biomaterials (i.e., materiobiology) plays an increasingly pivotal role in the development of novel implants, biomedical devices, and tissue engineering scaffolds to treat diseases, aid in the restoration of bodily functions, construct healthy tissues, or regenerate diseased ones. However, the conventional approaches are incapable of screening the huge amount of potential material parameter combinations to identify the optimal cell responses and involve a combination of serendipity and many series of trial-and-error experiments. For advanced tissue engineering and regenerative medicine, highly efficient and complex bioanalysis platforms are expected to explore the complex interaction of cells with biomaterials using combinatorial approaches that offer desired complex microenvironments during healing, development, and homeostasis. In this review, we first introduce materiobiology and its high-throughput screening (HTS). Then we present an in-depth of the recent progress of 2D/3D HTS platforms (i.e., gradient and microarray) in the principle, preparation, screening for materiobiology, and combination with other advanced technologies. The Compendium for Biomaterial Transcriptomics and high content imaging, computational simulations, and their translation toward commercial and clinical uses are highlighted. In the final section, current challenges and future perspectives are discussed. High-throughput experimentation within the field of materiobiology enables the elucidation of the relationships between biomaterial properties and biological behavior and thereby serves as a potential tool for accelerating the development of high-performance biomaterials.

Graphical abstract, The interactions between cells and their extracellular matrix (ECM) are critically important for homeostatic control of cell growth, proliferation, differentiation and apoptosis. Transmembrane integrin molecules facilitate the communication between ECM and the cell. Since the characterization of integrins in the late 1980s, there has been great advancement in understanding the function of integrins at different subcellular levels. However, the versatility in molecular pathways integrins are involved in, the high diversity in their interaction partners both outside and inside the cell as well as on the cell membrane and the short lifetime of events happening at the cell–ECM interface make it difficult to elucidate all the details regarding integrin function experimentally. To overcome the experimental challenges and advance the understanding of integrin biology, computational modeling tools have been used extensively. In this review, we summarize the computational models of integrin signaling while we explain the function of integrins at three main subcellular levels (outside the cell, cell membrane, cytosol). We also discuss how these computational modeling efforts can be helpful in other disciplines such as biomaterial design. As such, this review is a didactic modeling summary for biomaterial researchers interested in complementing their experimental work with computational tools or for seasoned computational scientists that would like to advance current in silico integrin models.

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic setups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights. Impact StatementAlthough in recent years the use of mathematical and computational sciences has increased in the Tissue Engineering and Regenerative Medicine (TERM) field, we believe that a further integration of experimental and computational approaches has a huge potential for advancing the field due to the ability of models to explain and predict experimental results and efficiently optimize TERM product and process designs. By providing an overview of existing computational models, how they have contributed to the field, as well as a future perspective, this review represents an important step to help realize TERM's ultimate goal: a cure instead of care.

BackgroundLower limb arterial calcification is a frequent, underestimated but serious complication of diabetes. The DIACART study is a prospective cohort study designed to evaluate the determinants of the progression of lower limb arterial calcification in 198 patients with type 2 diabetes.MethodsLower limb arterial calcification scores were determined by computed tomography at baseline and after a mean follow up of 31.20 ± 3.86 months. Serum RANKL (Receptor Activator of Nuclear factor kB Ligand) and bone remodeling, inflammatory and metabolic parameters were measured at baseline. The predictive effect of these markers on calcification progression was analyzed by a multivariate linear regression model.ResultsAt baseline, mean ± SD and median lower limb arterial calcification scores were, 2364 ± 5613 and 527 respectively and at the end of the study, 3739 ± 6886 and 1355 respectively. Using multivariate analysis, the progression of lower limb arterial log calcification score was found to be associated with (β coefficient [slope], 95% CI, p-value) baseline log(calcification score) (1.02, 1.00–1.04, p ConclusionIn patients with type 2 diabetes, lower limb arterial calcification is frequent and can progress rapidly. Circulating RANKL and triglycerides are independently associated with this progression. These results open new therapeutic perspectives in peripheral diabetic calcifying arteriopathy.Trial registrationNCT02431234

Objective: To describe the rates of healing, major amputation and mortality after 12 months in patients with a new diabetic foot ulcer (DFU) and their care in a French diabetic foot service (DFS). Method: A prospective single-centre study including patients from March 2009 to December 2010. The length of time to healing, minor amputation, major amputation and mortality rate after inclusion were analysed using the Kaplan–Meier method. Results: Some 347 patients were included (3% lost to follow-up), with a median follow-up (IQR) of 19 (12–24) months. The mean (SD) age was 65±12 years, 68% were male, and the median duration of the ulcer was 49 (19–120) days. Complications of the DFU were ischaemia (70%), infection (55%) and osteomyelitis (47%). Of the patients, 50% were inpatients in the DFS at inclusion (median duration of hospitalisation 26 (15–41) days). The rate of healing at one year was 67% (95% confidence interval (CI): 61–72); of major amputation 10% (95% CI: 7–17); of minor amputation 19% (95% CI: 14–25), and the death rate was 9% (95% CI: 7–13). Using an adjusted hazard ratio, the predictive factors of healing were perfusion and the area of the wound. The risk factors for a major amputation were active smoking and osteomyelitis. The risk factors for mortality were perfusion and age. Conclusion: This study confirms the need to treat DFUs rapidly, in a multidisciplinary DFS.

In vivo cells reside in a complex extracellular matrix (ECM) that presents spatially distributed biochemical and ‑physical cues at the nano- to micrometer scales. Chemical micropatterning is successfully used to generate adhesive islands to control where and how cells attach and restore cues of the ECM in vitro. Although chemical micropatterning has become a powerful tool to study cell–material interactions, only a fraction of the possible micropattern designs was covered so far, leaving many other possible designs still unexplored. Here, a high-throughput screening platform called “Galapagos chip” is developed. It contains a library of 2176 distinct subcellular chemical patterns created using mathematical algorithms and a straightforward UV-induced two-step surface modification. This approach enables the immobilization of ligands in geometrically defined regions onto cell culture substrates. To validate the system, binary RGD/polyethylene glycol patterns are prepared on which human mesenchymal stem cells are cultured, and the authors observe how different patterns affect cell and organelle morphology. As proof of concept, the cells are stained for the mechanosensitive YAP protein, and, using a machine-learning algorithm, it is demonstrated that cell shape and YAP nuclear translocation correlate. It is concluded that the Galapagos chip is a versatile platform to screen geometrical aspects of cell–ECM interaction.

Bioengineering of tissues and organs has the potential to generate functional replacement organs. However, achieving the full-thickness vascularization that is required for long-term survival of living implants has remained a grand challenge, especially for clinically sized implants. During the pre-vascular phase, implanted engineered tissues are forced to metabolically rely on the diffusion of nutrients from adjacent host-tissue, which for larger living implants results in anoxia, cell death, and ultimately implant failure. Here it is reported that this challenge can be addressed by engineering self-oxygenating tissues, which is achieved via the incorporation of hydrophobic oxygen-generating micromaterials into engineered tissues. Self-oxygenation of tissues transforms anoxic stresses into hypoxic stimulation in a homogenous and tissue size-independent manner. The in situ elevation of oxygen tension enables the sustained production of high quantities of angiogenic factors by implanted cells, which are offered a metabolically protected pro-angiogenic microenvironment. Numerical simulations predict that self-oxygenation of living tissues will effectively orchestrate rapid full-thickness vascularization of implanted tissues, which is empirically confirmed via in vivo experimentation. Self-oxygenation of tissues thus represents a novel, effective, and widely applicable strategy to enable the vascularization living implants, which is expected to advance organ transplantation and regenerative medicine applications. ispartof: ADVANCED FUNCTIONAL MATERIALS vol:31 issue:42 ispartof: location:Germany status: published

Surface topography is a tool to endow biomaterials with bioactive properties. However, the large number of possible designs makes it challenging to find the optimal surface structure to induce a specific cell response. The TopoChip platform is currently the largest collection of topographies with 2176 in silico designed microtopographies. Still, it is exploring only a small part of the design space due to design algorithm limitations and the surface engineering strategy. Inspired by the diversity of natural surfaces, it is assessed as to what extent the topographical design space and consequently the resulting cellular responses can be expanded using natural surfaces. To this end, 26 plant and insect surfaces are replicated in polystyrene and their surface properties are quantified using white light interferometry. Through machine-learning algorithms, it is demonstrated that natural surfaces extend the design space of the TopoChip, which coincides with distinct morphological and focal adhesion profiles in mesenchymal stem cells (MSCs) and Pseudomonas aeruginosa colonization. Furthermore, differentiation experiments reveal the strong potential of the holy lotus to improve osteogenesis in MSCs. In the future, the design algorithms will be trained with the results obtained by natural surface imprint experiments to explore the bioactive properties of novel surface topographies.

Bone healing process is a complicated phenomenon regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound (US) accelerates bone ossification and has a multiple influence on cell differentiation and angiogenesis. In a recent work of the authors, a bioregulatory model for providing bone-healing predictions was addressed, taking into account for the first time the salutary effect of US on the involved angiogenesis. In the present work, a mechanobioregulatory model of bone solidification under the US presence incorporating also the mechanical environment on the regeneration process, which is known to affect cellular processes, is presented. An iterative procedure is adopted, where the finite element method is employed to compute the mechanical stimuli at the linear elastic phases of the poroelastic callus region and a coupled system of partial differential equations to simulate the enhancement by the US cell angiogenesis process and thus the oxygen concentration in the fractured area. Numerical simulations with and without the presence of US that illustrate the influence of progenitor cells' origin in the healing pattern and the healing rate and simultaneously demonstrate the salutary effect of US on bone repair are presented and discussed. ispartof: JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA vol:145 issue:2 pages:1048-1059 ispartof: location:United States status: published

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.

Integrin transmembrane proteins conduct mechanotransduction at the cell–extracellular matrix interface. This process is central to cellular homeostasis and therefore is particularly important when designing instructive biomaterials and organoid culture systems. Previous studies suggest that fine-tuning the extracellular matrix composition and mechanical properties can improve organoid development. Towards the bigger goal of fully functional organoid development, we hypothesize that resolving the dynamics of extracellular matrix–integrin interactions will be highly instructive. To this end, we developed a mathematical model that enabled us to simulate three main interactions, namely integrin activation, ligand binding and integrin clustering. Different from previously published computational models, we account for the binding of more than one type of ligand to the integrin. This competition between ligands defines the fate of the system. We have demonstrated that an increase in the initial concentration of ligands does not ensure an increase in the steady state concentration of ligand-bound integrins. The ligand with higher binding rate occupies more integrins at the steady state than does the competing ligand. With cell type specific, quantitative input on integrin-ligand binding rates, this model can be used to develop instructive cell culture systems.

The distribution of signaling molecules following mechanical or chemical stimulation of a cell defines cell polarization, with regions of high active Cdc42 at the front and low active Cdc42 at the rear. As reaction-diffusion phenomena between signaling molecules, such as Rho GTPases, define the gradient dynamics, we hypothesize that the cell shape influences the maintenance of the “front-to-back” cell polarization patterns. We investigated the influence of cell shape on the Cdc42 patterns using an established computational polarization model. Our simulation results showed that not only cell shape but also Cdc42 and Rho-related (in)activation parameter values affected the distribution of active Cdc42. Despite an initial Cdc42 gradient, the in silico results showed that the maximal Cdc42 concentration shifts in the opposite direction, a phenomenon we propose to call “reverse polarization”. Additional in silico analyses indicated that “reverse polarization” only occurred in a particular parameter value space that resulted in a balance between inactivation and activation of Rho GTPases. Future work should focus on a mathematical description of the underpinnings of reverse polarization, in combination with experimental validation using, for example, dedicated FRET-probes to spatiotemporally track Rho GTPase patterns in migrating cells. In summary, the findings of this study enhance our understanding of the role of cell shape in intracellular signaling.

Kidney dialysis is the most widespread treatment method for end-stage renal disease, a debilitating health condition common in industrialized societies. While ubiquitous, kidney dialysis suffers from an inability to remove larger toxins, resulting in a gradual buildup of these toxins in dialysis patients, ultimately leading to further health complications. To improve dialysis, hollow fibers incorporating a cell-monolayer with cultured kidney cells have been proposed; however, the design of such a fiber is nontrivial. In particular, the effects of fluid wall-shear stress have an important influence on the ability of the cell layer to transport toxins. In the present work, we introduce a model for cell-transport aided dialysis, incorporating the effects of the shear stress. We analyze the model mathematically and establish its well-posedness. We then present a series of numerical results, which suggest that a hollow-fiber design with a wavy profile may increase the efficiency of the dialysis treatment. We investigate numerically the shape of the wavy channel to maximize the toxin clearance. These results demonstrate the potential for the use of computational models in the study and advancement of renal therapies.

We previously found that surface topographies induce the expression of the Scxa gene, encoding Scleraxis in tenocytes. Because Scxa is a TGF-beta responsive gene, we investigated the link between mechanotransduction and TGF-beta signaling. We discovered that mesenchymal stem cells exposed to both micro-topographies and TGF-beta 2 display synergistic induction of SMAD phosphorylation and transcription of the TGF-beta target genes SCX, alpha-SMA, and SOX9. Pharmacological perturbations revealed that Rho/ROCK/SRF signaling is required for this synergistic response. We further found an activation of the early response genes SRF and EGR1 during the early adaptation phase on micro-topographies, which coincided with higher expression of the TGF-beta type II receptor gene. Of interest, PKC activators Prostratin and Ingenol-3, known for inducing actin reorganization and activation of serum response elements, were able to mimic the topography-induced TGF-beta response. These findings provide novel insights into the convergence of mechanobiology and TGF-beta signaling, which can lead to improved culture protocols and therapeutic applications.

Lipid starvation results in skeletal progenitors favouring commitment to chondrogenic over osteogenic fate, a process mediated by FOXO transcription factors and SOX9. The avascular nature of cartilage makes it a unique tissue(1-4), but whether and how the absence of nutrient supply regulates chondrogenesis remain unknown. Here we show that obstruction of vascular invasion during bone healing favours chondrogenic over osteogenic differentiation of skeletal progenitor cells. Unexpectedly, this process is driven by a decreased availability of extracellular lipids. When lipids are scarce, skeletal progenitors activate forkhead box O (FOXO) transcription factors, which bind to the Sox9 promoter and increase its expression. Besides initiating chondrogenesis, SOX9 acts as a regulator of cellular metabolism by suppressing oxidation of fatty acids, and thus adapts the cells to an avascular life. Our results define lipid scarcity as an important determinant of chondrogenic commitment, reveal a role for FOXO transcription factors during lipid starvation, and identify SOX9 as a critical metabolic mediator. These data highlight the importance of the nutritional microenvironment in the specification of skeletal cell fate.