Three-Dimensional Continuum Model of Lumen Formation in a Cluster of Cells Immersed in an Extracellular Matrix: The Role of Mechanical Factors

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Abstract

The extent of participation of mechanisms such as the active interactions of cells with each other and with the extracellular matrix, the increased hydrostatic pressure in intercellular fluid, and enzymatic activity of cells that lead to the destruction of the extracellular matrix in the process of formation of cavities in clusters of cells formed during cluster vasculogenesis is studied. The problem of evolution of a single cluster of cells immersed in a deformable extracellular matrix is solved within the framework of a previously developed continuum multiphase model of the medium formed by two actively interacting solid phases and a fluid and the role of various cellular mechanisms discussed in the formation of hollow structures is studied. The calculations showed that the dominance of active interactions of the cell-matrix type over the intercellular interactions leads to a displacement of cells towards the outer boundary of the cluster and the creation of conditions for the formation of a cavity inside the cluster. The enzymatic activity of cells helps to free up a headroom for compaction of the cluster, due to the active intercellular interactions, and to slow down the formation of the increasing concentration profile of the cellular phase. An increase in the fluid pressure in the area occupied by cells leads to acceleration of the redistribution of concentrations of the cellular phase and matrix. The fluid pressure promotes accumulation of the cellular phase near the cluster boundary and increase in the matrix concentration in its central part. And only the joint participation of all the mechanisms considered leads to the formation of a structure in which a layer formed by the cellular phase surrounds a fluid-occupied cavity, while the matrix concentration in the cavity demonstrates the trend to its complete disappearance.

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About the authors

S. A. Logvenkov

National Research University “Higher School of Economics”; Moscow State University

Author for correspondence.
Email: logv@bk.ru

Institute of Mechanics

Russian Federation, Moscow; Moscow

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Supplementary files

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2. 1. Schematic representation of a cluster of cells immersed in a matrix. The letters c and m, circled in small circles, indicate the presence of cells and matrix in different areas. The coordinate r = Rc(t) is the radius of the sphere bounding the cells, the sphere of radius Rm(t) bounds the matrix.

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3. Fig. 2. Concentration distributions of the cell phase (a) and matrix phase (b) at different time points at mcm = 42, mc = 36 in the problem with free fluid flow across the boundary r = Rc(t): 1 and 2 at t = 1.15 and t = 1.62, respectively; dotted curves – initial distributions.

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4. Fig. 3. Distributions of concentrations of the cell phase and matrix (1 and 2 for and, respectively) obtained in the problem with free fluid flow across the boundary r = Rc(t) at mcm = 42, mc = 36 in the absence of matrix destruction (dashed curves) and at (solid lines) at the same time at the same time, t = 1.62.

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5. Fig. 4. (a) Solutions to the problem that takes into account the appearance of an osmotic barrier at r = Rc(t) and the problem with free fluid flow. The distributions of the concentrations of the cell phase and matrix (1 and 2 for and, respectively) were obtained at time t = 1.15 at the values of the parameters mcm = 42, mc = 36, . Dotted curves are solutions to the problem with free fluid flow, dashed and solid curves are solutions to the problem with an osmotic barrier at and, respectively; (b) the dependence of the asymmetry parameter of the cell phase distributions at time t = 1.15 on the hydrostatic pressure in the osmotic barrier problem.

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6. Fig. 5. Solutions to the problem involving all mechanisms. (a) The distribution of concentrations of the cell phase and matrix (1 and 2 for and, respectively) in the area jointly occupied by them, at different time points at the values of the parameters mcm = 42, mc = 36, g = 12 and . Dotted curves – t = 1.56, dashed curves – t = 1.66 and solid curves – t = 1.74 (b) Time dependence of the average concentration of the matrix in the area occupied jointly with the cells .

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