Role of Physical Mechanisms in Biological Self-Organization

Organs form during morphogenesis, the process that gives rise to specialized biological structures of specific shape and function in early embryonic development. Morphogenesis is under strict genetic control, but shape evolution itself is a physical process. Here we report the results of experimental and modeling biophysical studies on in vitro biological structure formation. Experimentally, by controlling the interaction between cells and their embedding matrices, we were able to build living structures of definite geometry. The experimentally observed shape evolution was reproduced by Monte Carlo simulations, which also shed light on the biophysical basis of the process. Our work suggests a novel way to engineer biological structures of controlled shape.

Figure 1

Special purpose 3D bioprinter with two mechanically driven extruders (left panel). One of the extruders hosts the bioink cartridge (right panel), a micropipette (the one shown has $500\mu \mathrm{m}$ inner diameter) with the spherical aggregate-bioink particles. The other extruder prints the biopaper-hydrogel scaffold. The $x\mathrm{\text{−}}y$ stage and the $z$ directional motion of the extruders are fully computer controlled.

Figure 2

Sheet formation depends on the initial configuration and the tissue-matrix interfacial tension. Two initial states, made of model cell aggregates, 925 cells each, packed in (a) a hexagonal and (b) a square lattice, after 250 000 MCS evolve into configurations shown in panels (c) (${\gamma }_{cg}/E_T=0.8$) and (d) (${\gamma }_{cg}/E_T=1.4$), respectively. For identical parameters, fusion from the hexagonal initial configuration is considerably faster. (e),(f) Similar structures of 25 aggregates of CHO cells ($500\mu \mathrm{m}$ in diameter) were embedded in $1.0\mathrm{mg}/\mathrm{ml}$ collagen type I. Compact sheets after 144 h of incubation are shown in panels (g) and (h).

Figure 3

(a) Tube formation with model cells of the same type. In each ring, 10 aggregates, of 257 cells each, are placed contiguously along circles, and rings are closely packed in the vertical direction such that each aggregate touches two others from below and above. In a simulation, with ${\gamma }_{cg}/E_T=2$, after $2\times {10}^5$ MCS the result is the tube shown in the middle, whereas for ${\gamma }_{cg}/E_T=0.4$ the structure breaks up into two spheroids. (b) Spontaneous tube formation. The initial aggregates (left) are made of cells wrapping a gel core (index 2 below), embedded in a different type of gel (index 1 below). One composite aggregate includes 4169 lattice sites, part of which is occupied by cells, the rest by gel. The two final structures, in the middle and on the right, reached after ${10}^5$ MCS, were both simulated with ${\gamma }_{c{g}_1}/E_T=0.7$, ${\gamma }_{c{g}_2}/E_T=0.3$, and ${\gamma }_{{\mathrm{g}}_1{\mathrm{g}}_2}/E_T=1.5$; the respective cell occupancies (of each aggregate’s volume) were 66% and 50%. (c) Tissue self-assembly in a 4-phase system made of two types of cells randomly intermixed in each aggregate (30% type 2, green) and two types of gel. The initial state (left) consists of 10 rings of 10 aggregates of 257 cells each. On the right side, an axial cross section of the final state, reached after ${10}^5$ MCS is depicted. We associate indices 0 and 1, respectively, with the embedding gel and the gel in the interior of the tube. Indices 2 and 3 designate, respectively, the green and red cell types. The interfacial energy parameters are ${\gamma }_{01}/E_T=1.8$, ${\gamma }_{02}/E_T=1.2$, ${\gamma }_{03}/E_T=0.7$, ${\gamma }_{12}/E_T=0.7$, ${\gamma }_{13}/E_T=1.2$, and ${\gamma }_{23}/E_T=0.4$.

Figure 4

The total interaction energy vs the number of MCS for the various simulations. (a) The single ringlike configuration (i.e., a one-layer tube; not shown). (b) The sheet simulation of Figs. 2a, 2c. (c) The tube in the middle of Fig. 3a. (d) The tube undergoing the pearlinglike instability on the right of Fig. 3a. (e) The tube on the right of Fig. 3b. (f) The long-lived tube in Fig. 3c.