Limited predictive value of blastomere angle of division in trophectoderm and inner cell mass specification

The formation of trophectoderm (TE) and pluripotent inner cell mass (ICM) is one of the earliest events during mammalian embryogenesis. It is believed that the orientation of division of polarised blastomeres in the 8- and 16-cell stage embryo determines the fate of daughter cells, based on how asymmetrically distributed lineage determinants are segregated. To investigate the relationship between angle of division and subsequent fate in unperturbed embryos, we constructed cellular resolution digital representations of the development of mouse embryos from the morula to early blastocyst stage, based on 4D confocal image volumes. We find that at the 16-cell stage, very few inside cells are initially produced as a result of cell division, but that the number increases due to cell movement. Contrary to expectations, outside cells at the 16-cell stage represent a heterogeneous population, with some fated to contributing exclusively to the TE and others capable of contributing to both the TE and ICM. Our data support the view that factors other than the angle of division, such as the position of a blastomere, play a major role in the specification of TE and ICM.

If the line we have added is equally likely to point in any direction, it is equally likely to touch the sphere at any point. Consequently, the probability a randomly generated line makes an angle θ that lies in the range θ1<θ< θ1+dθ1 (where dθ1is a very small increment) with the z--axis is simply proportional to the fraction of the area of the sphere that lies in this range. The slither of sphere with these values of θ is sketched below.
This thin slither of sphere can be unwrapped to form a strip approximated (exactly in the limit of small dθ1) by a rectangle with dimensions dθ1 and 2 π sin(θ1), giving it a total area of 2 π sin(θ1) dθ1. Since the whole sphere has area 4 π, this corresponds to a fraction of the surface of the sphere of 2 π sin(θ1) dθ1/(4 π)=(1/2) sin(θ1) dθ1, so a the probability a line drawn at random makes an angle θ1<θ< θ1+dθ1 with the z axis is P(θ1)dθ1 =(1/2) sin(θ1) dθ1, the sin(θ) distribution.
In terms of cell division, the above sphere should be thought of as embedded in the mother cell, with the z axis pointing out from the center of the embryo, through the center of the mother, to the outside. The line that is added is the line between the centers of the two daughter cells, translated to run exactly through the origin of the sphere. Consequently, in our case there is no distinction between division angles of θ and π--θ, since if one daughter cell is at θ the other is at π--θ. Thus, we are effectively only interested in the upper half--sphere, which has area 2 π, so we have P(θ1)dθ1 =sin(θ1) dθ1.

Definition of the center of each cell
For calculating quantities such as cell velocity and division angles we have to assign a point position to each cell. There are several ways one might do this. To assign this position we took the three--dimensional surface corresponding to the cell membrane and imagined filling it with a uniformly dense substance then calculated where the center of mass of such an object would lie. To do this calculation, we imagined a plane running though the cell, and broke the volume of the cell into long thin prismatic objects made by sweeping the triangles of the cells surface down to the plane (along the planes normal). Each of these basic objects has a known volume (i.e. `mass'') mi and a known position of its center of mass ri. The center of mass of the complex shaped cell, R, is then given as =

Definition of the velocity of each cell
To calculate the velocity of a cell we could have simply divided the distance between the center of the cell in two adjacent time steps by the time elapsed. However, sometimes the whole embryo rotates, which gives all the cells a velocity but doesn't imply any internal change in the embryo. To eliminate this problem, we first rotated the embryo in the second frame until the centers of the cells were as close as possible to the centers of the same cells in the previous time step (specifically minimum total squared distance between cells, implemented using mathematica's NMinnimize function) then calculated the cell velocities as above. To calculate the radial velocity of a cell we simply projected the velocity vector onto the line connecting the CoM of the cell to the CoM of the embryo.
Supplementary Movie 1. Time-lapse sequence of an embryo developing from morula to early blastocyst. The panel at left shows fluorescence and the panel at right shows the bright-field image. The embryo expresses myr-TdTomato in the plasma membrane (magenta) and H2B-GFP in the nucleus (green).
Supplementary Movie 2. Time-lapse sequence of an embryo developing from morula to early blastocyst. Montage of all the z-levels of the embryo shown in movie 1. The embryo expresses myr-TdTomato in the plasma membrane (magenta) and H2B-GFP in the nucleus (green).
Supplementary Movie 3. Segmentation of embryo blastomeres. Animation illustrating how bitmap image data is converted to vector representations of individual blastomeres. One starts with a 3D (or in our case, 4D) data-set, and outlines blastomeres one at a time across the various focal planes, to segment them. This is repeated across the different time-points, to segment entire lineages.