ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.1.3 Budding and Growth
We assume that the proliferating yeast cells are in the exponential growth phase. Because the
intracellular biology of the cell cycle is not explicitly modelled, only the changes of cell shape
during the cell cycle have to be taken into account, as they will influence the cellular interaction
forces. Morphologically, the cell cycle can be subdivided into two important stages: cellular
growth and cytokinesis. According to [9], cellular growth can be described by:
dm
dt = K [R]Ao, (4)
in which the rate of mass change in time (dm/dt) is proportional to the outer surface area of the
cell just after division (Ao) and the total ribosome content, which we assume to remain constant.
Cells of S. Cerevisiae divide by budding. The daughter cell appears as a small bulge from the
cell wall of the mother cell, and steadily grows while still attached until it separates from the
mother cell. Analogous to how binary fission can be described by two overlapping spheres with
changing distance and radius ([4, 3]), we approximate the budding mechanism geometrically by a
combination of two spheres. During the budding process, the increase in volume over time of the
mother-bud complex is assumed to remain constant and the average time for the budding process to
complete is set. Next, the appropriate bud radius r and displacement d are calculated accordingly.
Figure 1 shows how two overlapping spheres are connected to approximate the shape of budding
cells.
R
✗✔
✗✔
✗✔
r
r = Ri r = Ri r = Ri
✖✕
Ri ✤✜ < r < R0
✣✢
✖✕
✛ ✲
d = R − Ri R − Ri < d < R d = R
Ri < r < R0
R < d < R + R0 R < d < R + R0 d = R + R0
✖✕
Figure 1: Approximation of a budding cell by two overlapping spheres. Initially, the minor sphere (bud) has
a predetermined radius Ri and is completely inside the mother cell. The displacement d increases
until r = Ri. Next, both radius and displacement increase until the bud separates from the mother
cell when r = Ro.
We model mechanical inhibition of cell division by including a division force Fd. Biologically, this
force arises from the assembly of cytoskeleton and polysaccharides in the cell wall. The magnitude
of Fd is dependent on the mechanical environment: a higher force is required when the cell is
closely surrounded by other cells than when the cell is freely suspended in liquid. In the model
Fd is adjusted dynamically in order to complete division in the prescribed time. Furthermore, a
maximum value for Fd is set which corresponds with the threshold for mechanical inhibition.
3.2 Model parameters
The model parameters used for the simulations are listed in table 1. This set represents the standard
conditions for a growing colony starting with both one FLO + and one f lo − cell.
3.3 Measuring sorting
There are several ways to measure, how “well sorted” the system is at any point during a simulation.
R0