Distinguishing between Directed and Undirected Cell Motility within an Invading Cell Population

Cell-Based Modeling of Tissue Developing in the Scaffold Pores of Varying Cross-Sections

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows us to obtain complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.

Non-HLA antibodies targeting angiotensin II type 1 receptors and endothelin-1 type A receptors impair endothelial repair via a β2-arrestin link to the mTOR pathway

Functional non-HLA antibodies (antibodies to non-human leukocyte antigens) targeting the G protein-coupled receptors angiotensin II type 1 receptor (AT1R) and endothelin-1 type A receptor (ETAR) are implicated in the pathogenesis of transplant vasculopathy. While ERK signaling (a regulator of cell growth) may represent a general cellular response to agonist stimulation, the molecular link between receptor stimulation and development of vascular obliteration has not been fully established. Here we hypothesize involvement of the versatile adaptor proteins, β-arrestins, and the major regulator of cell growth, PI3K/mTOR signaling, in impaired endothelial repair. To test this, human microvascular endothelial cells were treated with AT1R/ETAR antibodies isolated from patients with kidney transplant vasculopathy. These antibodies activated both mTOR complexes via AT1R and ETAR in a PI3K-dependent and ERK-independent manner. The mTOR inhibitor, rapamycin, completely abolished activation of mTORC1 and mTORC2 after long-term treatment with receptor antibodies. Imaging studies revealed that β2- but not β1-arrestin was recruited to ETAR in response to ET1 and patient antibodies but not with antibodies isolated from healthy individuals. Silencing of β2-arrestin by siRNA transfection significantly reduced ERK1/2 and mTORC2 activation. Non-HLA antibodies impaired endothelial repair by AT1R- and ETAR-induced mTORC2 signaling. Thus, we provide evidence that functional AT1R/ETAR antibodies induce ERK1/2 and mTOR signaling involving β2-arrestin in human microvascular endothelium. Hence, our data may provide a translational rational for mTOR inhibitors in combination with receptor blockers in patients with non-HLA receptor recognizing antibodies.

Mechanical boundary conditions bias fibroblast invasion in a collagen-fibrin wound model

Because fibroblasts deposit the collagen matrix that determines the mechanical integrity of scar tissue, altering fibroblast invasion could alter wound healing outcomes. Anisotropic mechanical boundary conditions (restraint, stretch, or tension) could affect the rate of fibroblast invasion, but their importance relative to the prototypical drivers of fibroblast infiltration during wound healing--cell and chemokine concentration gradients--is unknown. We tested whether anisotropic mechanical boundary conditions affected the directionality and speed of fibroblasts migrating into a three-dimensional model wound, which could simultaneously expose fibroblasts to mechanical, structural, steric, and chemical guidance cues. We created fibrin-filled slits in fibroblast-populated collagen gels and applied uniaxial mechanical restraint along the short or long axis of the fibrin wounds. Anisotropic mechanical conditions increased the efficiency of fibroblast invasion by guiding fibroblasts without increasing their migration speed. The migration behavior could be modeled as a biased random walk, where the bias due to multiple guidance cues was accounted for in the shape of a displacement orientation probability distribution. Taken together, modeling and experiments suggested an effect of strain anisotropy, rather than strain-induced fiber alignment, on fibroblast invasion.

Building macroscale models from microscale probabilistic models: a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.