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As a theoretical framework for understanding the self-assembly of living cells into tissues, Steinberg proposed the differential adhesion hypothesis (DAH) according to which a specific cell type possesses a specific adhesion apparatus that combined with cell motility leads to cell assemblies of various cell types in the lowest adhesive energy state. Experimental and theoretical efforts of four decades turned the DAH into a fundamental principle of developmental biology that has been validated both in vitro and in vivo. Based on computational models of cell sorting, we have developed a DAH-based lattice model for tissues in interaction with their environment and simulated biological self-assembly using the Monte Carlo method. The present brief review highlights results on specific morphogenetic processes with relevance to tissue engineering applications. Our own work is presented on the background of several decades of theoretical efforts aimed to model morphogenesis in living tissues. Simulations of systems involving about 10⁵ cells have been performed on high-end personal computers with CPU times of the order of days. Studied processes include cell sorting, cell sheet formation, and the development of endothelialized tubes from rings made of spheroids of two randomly intermixed cell types, when the medium in the interior of the tube was different from the external one. We conclude by noting that computer simulations based on mathematical models of living tissues yield useful guidelines for laboratory work and can catalyze the emergence of innovative technologies in tissue engineering.

White blood cells slowly roll along the walls of blood vessels, due to the coordinated formation and breakage of chemical selectin-carbohydrate bonds. Using detailed computer simulations of cells rolling on a selectin surface under flow, we show the time series of the cell translational velocity to be fractal in nature over time scales ranging from 2²–2¹¹ ms. A rescaled range analysis was performed to determine the Hurst exponent of the velocity time series, for simulations of cells rolling on either a uniform or punctate distribution of P-selectin molecules. The rolling behavior was found to exhibit two very distinct regimes, with a negative Hurst exponent ranging from -(1.2-0.6) over time scales of 2³-2⁷ ms, and a positive Hurst exponent of +0.47±0.03 over time scales of 2⁷-2¹¹ ms. The short-time Hurst exponent was found to be a strong function of the molecular distribution and also a function of average molecular density, while the long-time Hurst exponent was unchanged over all conditions studied. The implication is that the short-time adhesive behavior of cells interacting with a reactive surface is sensitive to the spatial arrangement of molecules, and the total number of molecules on the surface.

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Inspired by the complex biophysical processes of cell adhesion and detachment under blood flow in vivo, numerous novel microfluidic devices have been developed to manipulate, capture, and separate bio-particles for various applications, such as cell analysis and cell enumeration. However, the underlying physical mechanisms are yet unclear, which has limited the further development of microfluidic devices and point-of-care (POC) systems. Mathematical modeling is an enabling tool to study the physical mechanisms of biological processes for its relative simplicity, low cost, and high efficiency. Recent development in computation technology for multiphase flow simulation enables the theoretical study of the complex flow processes of cell adhesion and detachment in microfluidics. Various mathematical methods (e.g., front tracking method, level set method, volume of fluid (VOF) method, fluid–solid interaction method, and particulate modeling method) have been developed to investigate the effects of cell properties (i.e., cell membrane, cytoplasma, and nucleus), flow conditions, and microchannel structures on cell adhesion and detachment in microfluidic channels. In this paper, with focus on our own simulation results, we review these methods and compare their advantages and disadvantages for cell adhesion/detachment modeling. The mathematical approaches discussed here would allow us to study microfluidics for cell capture and separation, and to develop more effective POC devices for disease diagnostics.

Complex three-dimensional (3D) porous scaffolds with macro-pore size of 400–800 μm based on polyvinyl alcohol (PVA) powder were successfully developed by selective laser sintering (SLS) technology. The PVA scaffolds had customizable shape, controlled and totally interconnected porous structure, and high porosity. The microstructure and mechanical property were performed for their suitability for tissue engineering (TE). The results showed that PVA did not decompose while the degree of crystallization decreased in a given sintering condition. Moreover, there were micro-pores with sizes of 20–100 μm in the scaffold. The actual porosity of sintered scaffolds could be up to 82.35%, which was higher than the value of the designed models. An in vitro biocompatibility test showed MG-63 cells could well spread on the scaffold surface. The presented work demonstrates the favorable potential of PVA powder as TE scaffolds fabricated via SLS.

Cell adhesion to the extracellular matrix is accomplished by the clustering of receptor–ligand bonds into focal contacts on the cell-substrate interface. The contractile forces applied onto these focal contacts lead to elastic deformation of the surrounding, which results into a cellular mechanosensory capability that plays a key role in cell adhesion, spreading, and migration, among many others. The mechanosensitivity can be manipulated by the substrate anisotropy, by which focal contacts may align into certain directions so to minimize the total mechanical potential energy. Using the elastic anisotropic contact analysis, this work systematically analyzes the dependence of the alignment on the elastic anisotropy, and more importantly, the direction of the inclined contractile forces. The contact displacement fields are a complex function of the elastic constants, so simple analysis based on tensile or shear softest direction cannot properly predict the alignment orientation. It is also proved that if these focal contacts are of elongated shape, the major axis will be parallel to the alignment direction.

In this work, the membrane surface of poly(acrylonitrile-co-2-hydroxyethyl methacrylate) (PANCHEMA) was chemically modified by anchoring of phospholipid moieties. The process involved the reaction of hydroxyl groups on the membrane surface with 2-chloro-2-oxo-1,3,2-dioxaphospholane (COP) followed by the ring-opening reaction of COP with trimethylamine. Chemical differences between the original and the modified membranes were characterized by FT-IR and XPS. It was found that the amount of macrophage adhered on the modified membrane surface is substantially lower than that on polyacrylonitrile (PAN) and PANCHEMA membranes under the same condition. The morphological change of the adherent cell is also suppressed by the generation of phospholipid moieties on the membrane surface.

Human colon carcinoma (HCT-8) cells show a stable, metastasis-like phenotype (MLP) when cultured on appropriate soft substrates (21 ~ 47 kPa). Initially epithelial (E) in nature, the HCT-8 cells become rounded (R) and show a number of metastatic hallmarks after only seven days of culture on soft substrate (Tang et al., [2010] "Mechanical force affects expression of an in vitro metastasis-like phenotype in HCT-8 cells," Biophysical Journal99, 2460–2469; Tang et al., [2012a] "Attenuation of cell mechanosensitivity in colon cancer cells during in vitro metastasis," PlosONE7, e50443). Here, we studied the surface nonspecific adhesion of HCT-8 cells throughout the in vitro metastasis process. A novel bio-MEMS force sensor was used to measure the cell-probe nonspecific adhesion. The adhesion characteristics are analyzed using fracture mechanics theory. Our results indicate that the post-metastatic HCT-8 cells (dissociated R cells) display remarkably diminished surface adhesion and are potentially more invasive than original pre-metastatic HCT-8 cells (E cells). To the best of our knowledge, this is the first report of quantitative data showing the changes in cancer cell adhesion and other cellular mechanical properties during the expression of in vitro metastasis-like phenotype.

Cellular adhesion is mediated by the formation and rupture of specific molecular bonds between ligands and receptors. As an idealized model, based on the Markov process assumption, we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds between two rigid bodies with curved interfaces under displacement- and force-controlled loadings, respectively. Regarding the equilibrium cluster size, strength, bond distribution and life time, exact solutions from the corresponding one-step master equations are obtained for the special cases of clusters with fixed separations or clusters with flat interfaces, while the general cases of those with curved interfaces are dealt with numerical techniques. Especially, Monte Carlo simulations are performed to verify the proposed analytical results and to demonstrate interesting differences between stochastic adhesion behaviors of the clusters under loading protocols of fixed separations and fixed forces, respectively.

Many studies have demonstrated that microscale changes to surface chemistry and topography affect cell adhesion, proliferation, differentiation, and gene expression. More recently, studies have begun to examine cell behavior interactions with structures on the nanoscale since in vivo, cells recognize and adhere to cell adhesion receptors that are spatially organized on this scale. These studies have been enabled through various fabrication methods, many of which were initially developed for the semiconductor industry. This review explores cell responses to a variety of controlled topographical and biochemical cues using an assortment of nanoscale fabrication methods in order to elucidate which pattern dimensions are beneficial for controlling cell adhesion and differentiation.

In sickle cell disease (SCD), hemoglobin molecules polymerize intracellularly and lead to a cascade of events resulting in decreased deformability and increased adhesion of red blood cells (RBCs). Decreased deformability and increased adhesion of sickle RBCs lead to blood vessel occlusion (vaso-occlusion) in SCD patients. Here, we present a microfluidic approach integrated with a cell dimensioning algorithm to analyze dynamic deformability of adhered RBC at the single-cell level in controlled microphysiological flow. We measured and compared dynamic deformability and adhesion of healthy hemoglobin A (HbA) and homozygous sickle hemoglobin (HbS) containing RBCs in blood samples obtained from 24 subjects. We introduce a new parameter to assess deformability of RBCs: the dynamic deformability index (DDI), which is defined as the time-dependent change of the cell's aspect ratio in response to fluid flow shear stress. Our results show that DDI of HbS-containing RBCs were significantly lower compared to that of HbA-containing RBCs. Moreover, we observed subpopulations of HbS containing RBCs in terms of their dynamic deformability characteristics: deformable and non-deformable RBCs. Then, we tested blood samples from SCD patients and analyzed RBC adhesion and deformability at physiological and above physiological flow shear stresses. We observed significantly greater number of adhered non-deformable sickle RBCs than deformable sickle RBCs at flow shear stresses well above the physiological range, suggesting an interplay between dynamic deformability and increased adhesion of RBCs in vaso-occlusive events.

Polymeric scaffolds, in the form of porous membranes, modified to favour cell adhesion and proliferation on their surface, were prepared using an innovative technique of functionalization, based on molecularly imprinting technology.

A series of membranes based on poly-ε-caprolactone were obtained through phase inversion using different solvents and non-solvents. Diffusion tests showed that prepared membranes exhibited a good permeability towards important nutrients such as folic acid and glucose. The ability of membranes, modified with imprinted nanoparticles, to facilitate cell adhesion and proliferation was evaluated by cell culture method using murine fibroblast cell line. SEM analysis at 72 h after seeding revealed an improved cell distribution on the surface of the membranes functionalized by deposition of molecularly imprinted nanoparticles.