Figure 4. Different morphologies can be obtained by varying boundary conditions (Figure 4—video 1).

(A) A hollow sphere emerges if polarities are fixed and initially point radially out from the center of mass. (B) A hollow tube is obtained if polarities point radially out from a central axis. (C) Two flat planes pointing in opposite directions are obtained if polarities point away from a central plane. (D) For all three initial conditions (A–C), if the polarities are allowed to change dynamically and the noise is high (η = 10⁰ compared to η = 10⁻¹ in A–C), the resulting shape consists of three nested ‘Russian doll’-like hollow spheres that will never merge due to opposing polarities. In contrast to the random initial condition in Figure 3, the initial conditions in (D) are symmetric.

Figure 4—video 1. Dynamics when the polarities have restricted orientations.

Download video file ^{(4.1MB, mp4)}

DOI: 10.7554/eLife.38407.015

In all three simulations, an aggregate consisting of 8000 cells develops into three simple morphologies due to polarities being fixed in different directions. (A) One big lumen forms when the polarities are restricted to point radially out from the center-of-mass. At an early stage, a small lumen forms around the center-of-mass. Later the shell transiently consists of multiple cell layers. However, in the end, these layers merge into a single cell layer (Figure 4A). (B) A tube emerges when the polarities are restricted to point away from a central axis. Similar to (A) a small tube appears at an early stage deep inside the aggregate, and transiently it contains multiple cell layers (Figure 4B). (C) Finally, two opposing planes form when the polarities are restricted to orient away from a central plane. This develops in a similar way as (A) and (B) without rotating any cells (Figure 4C). Throughout all three simulations, dt = 0.1 and the noise parameter η = 0.1.