Math connects vascular network to the universe

Endothelial cells (ECs) plated on a surface of Matrigel, a basement membrane matrix, spontaneously form a capillary network that is very similar to capillary beds formed in vivo. Now, Guido Serini, Federico Bussolino (University of Torino, Torino, Italy), Davide Ambrosi, Andrea Gamba (Polytechnic of Torino, Torino, Italy) and colleagues have used a combination of mathematical modeling and in vitro experiments to demonstrate that the key parameters in the pattern formation are the density of ECs and the biochemical properties of the chemoattractant.

The group found that if they disrupted either variable in the cell culture system then the capillary network formed was aberrant. For example, with fewer than 100 cells/mm², the cells form a continuous network, but more than 200 cells/mm² led to a Swiss cheese–like mat. And when the researchers swamped out the natural VEGF-A chemoattractant gradient, which forms as a result of secretion from the ECs, the cells fail to aggregate.

All of the results could be accurately modeled using a nonlinear diffusion equation, called the adhesion model, which implies that the behavior of ECs and the pattern follow simple mathematical laws. And by combining the two approaches, the group was able to define specific characteristics about the chemoattractant, such as its diffusion coefficient, that they otherwise would not have known. But perhaps most exciting, says Bussolino, is that the same type of equation can be used to describe the formation of many patterns in nature such as bacterial colony formation and Dictyostelium morphogenesis—and, oddly enough, the events that occurred just after the big bang that gave rise to the universe. ▪

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