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In-silico patterning of vascular mesenchymal cells in three dimensions.

Danino T, Volfson D, Bhatia SN, Tsimring L, Hasty J - PLoS ONE (2011)

Bottom Line: Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis.We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells.Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
Cells organize in complex three-dimensional patterns by interacting with proteins along with the surrounding extracellular matrix. This organization provides the mechanical and chemical cues that ultimately influence a cell's differentiation and function. Here, we computationally investigate the pattern formation process of vascular mesenchymal cells arising from their interaction with Bone Morphogenic Protein-2 (BMP-2) and its inhibitor, Matrix Gla Protein (MGP). Using a first-principles approach, we derive a reaction-diffusion model based on the biochemical interactions of BMP-2, MGP and cells. Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis. We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells. Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.

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Initial and steady state patterns of cells produced by exogenous BMP-2.An initial condition of 2× higher concentration of BMP-2 is placed along the center (a) sphere or (b) cylinder and the cells are allowed to reach steady state. The stripe regime parameters were used and set as D = 0.005, q = 0.003, K = 0.25, B = 1.1, k = 0.7, c = 0.14, γ  = 600 with simulation box length set to 2 cm. The lowest values were made transparent for clarity while red color indicates higher cell density while blue indicates low. A cut of the simulation box in (a) 1/8 of cube and (b) 1/4 of cube was sliced out for easier visualization.
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pone-0020182-g004: Initial and steady state patterns of cells produced by exogenous BMP-2.An initial condition of 2× higher concentration of BMP-2 is placed along the center (a) sphere or (b) cylinder and the cells are allowed to reach steady state. The stripe regime parameters were used and set as D = 0.005, q = 0.003, K = 0.25, B = 1.1, k = 0.7, c = 0.14, γ  = 600 with simulation box length set to 2 cm. The lowest values were made transparent for clarity while red color indicates higher cell density while blue indicates low. A cut of the simulation box in (a) 1/8 of cube and (b) 1/4 of cube was sliced out for easier visualization.

Mentions: Fig. 4 shows the evolution of cells with an initial condition of a (a) spherical or (b) cylindrical region along the center axis containing at 2× higher BMP-2 concentration than the steady state. The surrounding region was set to the zero value. The parameters set for these simulations were those in the stripe pattern regime to mimic the previous experimental setting[11].


In-silico patterning of vascular mesenchymal cells in three dimensions.

Danino T, Volfson D, Bhatia SN, Tsimring L, Hasty J - PLoS ONE (2011)

Initial and steady state patterns of cells produced by exogenous BMP-2.An initial condition of 2× higher concentration of BMP-2 is placed along the center (a) sphere or (b) cylinder and the cells are allowed to reach steady state. The stripe regime parameters were used and set as D = 0.005, q = 0.003, K = 0.25, B = 1.1, k = 0.7, c = 0.14, γ  = 600 with simulation box length set to 2 cm. The lowest values were made transparent for clarity while red color indicates higher cell density while blue indicates low. A cut of the simulation box in (a) 1/8 of cube and (b) 1/4 of cube was sliced out for easier visualization.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3102094&req=5

pone-0020182-g004: Initial and steady state patterns of cells produced by exogenous BMP-2.An initial condition of 2× higher concentration of BMP-2 is placed along the center (a) sphere or (b) cylinder and the cells are allowed to reach steady state. The stripe regime parameters were used and set as D = 0.005, q = 0.003, K = 0.25, B = 1.1, k = 0.7, c = 0.14, γ  = 600 with simulation box length set to 2 cm. The lowest values were made transparent for clarity while red color indicates higher cell density while blue indicates low. A cut of the simulation box in (a) 1/8 of cube and (b) 1/4 of cube was sliced out for easier visualization.
Mentions: Fig. 4 shows the evolution of cells with an initial condition of a (a) spherical or (b) cylindrical region along the center axis containing at 2× higher BMP-2 concentration than the steady state. The surrounding region was set to the zero value. The parameters set for these simulations were those in the stripe pattern regime to mimic the previous experimental setting[11].

Bottom Line: Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis.We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells.Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America.

ABSTRACT
Cells organize in complex three-dimensional patterns by interacting with proteins along with the surrounding extracellular matrix. This organization provides the mechanical and chemical cues that ultimately influence a cell's differentiation and function. Here, we computationally investigate the pattern formation process of vascular mesenchymal cells arising from their interaction with Bone Morphogenic Protein-2 (BMP-2) and its inhibitor, Matrix Gla Protein (MGP). Using a first-principles approach, we derive a reaction-diffusion model based on the biochemical interactions of BMP-2, MGP and cells. Simulations of the model exhibit a wide variety of three-dimensional patterns not observed in a two-dimensional analysis. We demonstrate the emergence of three types of patterns: spheres, tubes, and sheets, and show that the patterns can be tuned by modifying parameters in the model such as the degradation rates of proteins and chemotactic coefficient of cells. Our model may be useful for improved engineering of three-dimensional tissue structures as well as for understanding three dimensional microenvironments in developmental processes.

Show MeSH