Abstracted functions for engineering the autonomous growth and formation of patterns

Natural biological patterns arise via the growth, differentiation, death, differential adhesion, communication, and movement of or among cells. Synthetic biologists typically impose explicit genetic control of cell-cell communication and programmable cell state to realize engineered biological patterns. Such engineering approaches do not usually consider the underlying physical properties of individual cells that inevitably contribute to pattern development. To better integrate synthetic genetic systems engineering with natural growth and patterning we derived abstract functions that relate how changes in basic cell properties such as growth rate, length, and radius of curvature result in differences in the curvature, end-point reliability, and texture of borders that define boundaries among growing cell lineages. Each abstracted border function is derived holistically as an emergent consequence of underlying cell physical properties. We experimentally demonstrate control of border curvature to angles of 60{degrees} from initial trajectories, control of end-point variability to within 15{degrees} of desired target endpoints, and control of border texture between 10 to 60 unit cell lengths. In combination with synthetic genetic control systems, we grow arbitrary two-dimensional patterns including phases of the moon, PacMen, and a yinyang-like pattern. Differences between the idealized and observed behavior of abstracted border functions highlight opportunities for realizing more precise control of growth and form, including better integration of synthetic genetic systems with native cellular properties and processes.