Fig 2. First embryonic cell divisions in the sea urchin
Using the sea urchin as a model organism, Prof. Akiyama and his co-workers have focused on the very early cleavage patterns. The fertilized egg goes through alternating meridional and latitudinal cleavages: 1st
latitudinal… This highly orchestrated sequence of consecutive cell cleavages eventually gives rise to a multicellular sphere: the blastula. Prof. Akiyama's 3D simulation model is based on a small defined set of premises, the most important being:
* The positions and movements of both centrosomes are depicted as two vectors (r1, r2) in a Cartesian coordinate system, representing one cell.
* Through diffusion, two different chemical substances form a concentration gradient from the poles towards the equator of the cell: substance A diffuses from the animal pole, while substance B diffuses from the vegetal pole. This double gradient assumption was based on the pioneering work of the Swedish embryologist Sven Hörstadius (1898-1996), who experimentally demonstrated the existence of such gradients in sea urchin embryos.
* In response to this double gradient, both centrosomes show chemo-repulsion, away from the animal pole and chemo-attraction, towards the vegetal pole.
* Both centrosomes (connected through microtubuli) create a repulsive force against each other and towards the cell membrane. As a result, a second repulsive force is generated from the membrane.
Fig 3. Some essential features of the 3D model, simulating early cell divisions during sea urchin developmentt
In other words, the 3D model postulates that an elaborate interplay between mechanical and chemical forces directs the movement of both centrosomes towards a given position, resulting in a specific cleavage pattern: meridional or latitudinal. Depending on the cleavage plane, the daughter cells will adopt a characteristic size and shape (e.g. spherical or rugby ball shaped), which will influence the quantitative values of the parameters - in the new Cartesian coordinate system of each daughter cell - and consequently the next cleavage type.
Translating these a priori
assumptions into the language of Mathematics - through formulating a defined set of equations - Prof. Akiyama and his team could indeed simulate the developmental program of the early cleavage pattern, characteristic of a sea urchin. But that was not the end of the story: resetting the quantitative values for specific parameters resulted in different spatio-temporal sequences of meridional and latitudinal cleavages in silico
. Amazingly, such alternative morphogenetic strategies are employed by nature itself: the 3D model could infallibly recapitulate the early embryonic cleavage patterns of other echinoderms, such as sea stars and sea cucumbers…