SUPPORTING MATERIAL
Agent-based simulations
Agent-based modeling in NetLogo39 was used to explore the feasibility of cell clustering in the absence of longrange interactions. The in silico world in which this model exists consists of a 50x50x7 arrangement of patches,
each of which is a unit cube with dimensions equaling the diameter of a cell (20 m), and wraps in the XY
plane. Cells were represented as individual spherical agents each centered in a unit cell. The cells possess a
limited number of available actions regulated by strictly defined rules. These actions include binding to other
cells, breaking bonds with other cells and moving within the simulation space. Cells may form multiple bonds
such that one cell may have as many as six, one bond each at its up, right, down, left, top and bottom sides.
Once a cell is bound to another cell it is no longer free to move within the simulation space, until it breaks all of
its cell-cell bonds to become an “unbound” cell. With respect to movement, during one iteration each unbound
cell has a chance to move determined by both a probability of movement, as well as the availability of
unoccupied spaces to move. To explain this in more detail, cells are first randomly assigned which of four
directions (N, E, S and W) they will try to move in. Only if this neighboring region is unoccupied will the cell
move into this space. If this space is occupied a cell will try to climb up to one of two potential spots (Fig. 5A). A
potential spot must not only be unoccupied but also supported by four cells (bound or unbound) that form a
platform upon which the center is an available site. As a result of cells having to be supported by four cells,
cells on successive levels are offset from each other 0.5 patches in the X and Y directions. Unbound cells that
are on a higher level follow the same rules as unbound cells on the base level, except that, since they are not in
contact with the matrix, they are not inhibited from climbing onto higher levels due to the cell-substrate
adhesion probability parameter and, since they have cells beneath them, they may bind to cells on their
bottom side. Therefore these unbound cells may move to unoccupied neighboring areas on the same level,
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bind to other neighboring cells and climb up to other levels where proper support and vacancy exists. In the
event that a cell moves to a region unsupported by four cells on a lower level it will fall down. If a cell on a
lower level moves away causing a cell on the level above to no longer have the support of four cells the higher
cell will break all of its cell-cell bonds and fall down to replace the lower level cell’s previous position. This
model does not include proliferation or cell death.
All simulations were run at 40% confluence, a value chosen to help distinguish conditions that support
clustering and those that do not. To help explain the choice of this value, we must first explain that a cluster
was defined as a contiguous network of cells, regardless of shape. At initial conditions and in the absence of
cell-cell binding, as confluence increases the average number of neighbors each cell has also increases, along
with the average size of contiguous networks of cells. At high values, all cells are increasingly likely to be
connected as one very large network. Therefore, high values of confluence do not allow for distinguishing
differences between conditions through the measurement of average cluster size. As the value for confluence
decreases, cells on average become spread further apart, limiting the maximal average cluster size that can be
formed by random migration and cell-cell adhesion. 40% is an empirically chosen value falling within a range
that balances these two competing issues.
The probabilities that cells will form and break bonds to other cells was controlled by a single parameter for
cell-cell adhesion probability (%). The probability a cell will form a bond with an adjacent cell was set as equal
to the cell-cell adhesion probability with the probability a cell will unbind set as (100% - cell-cell adhesion
probability). Therefore, both the probability of binding and unbinding add to 100%. Cell-substrate adhesion
probability (%) is another variable in the model. This parameter serves only to restrict cells on the base level
from climbing to the second level. The probability for a cell to be allowed to climb is defined as (100% - cellsubstrate adhesion probability). For example, 70% cell-substrate probability will mean that cells will be allowed
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to climb 30% of the time. Therefore, low values of cell-substrate adhesion probability are less restrictive and a
value of 100% prevents all cells from climbing from the first level to the second. Although cell-substrate
adhesion probability may in reality affect other cell behaviors such as migration, this coupling was not included
in the model. The probability of movement has been observed to have a moderate influence cluster size and
density, but was not explored for these experiments and was set arbitrarily at 50%.
Cell-cell adhesion probability was explored at seven levels (0%, 10%, 30%, 50%, 70%, 90% and 99%) and cellsubstrate adhesion probability at seven levels (0%, 10%, 30%, 50%, 70%, 90% and 100%) for a total of 49
unique combinations (n = 10). Cell-cell adhesion probability of 100% was not used since the probability for a
cell to break its bonds to other cells would be 0%. The consequence for this would be that within the first few
iterations all cells would form cell-cell bonds and be locked in place throughout the rest of the simulation.
Three approaches were used to quantify the degree of clustering: average cluster size, average height and
compactness. Average height was calculated by dividing the total number of cells by the footprint, or area
clusters occupy on the base level. Roughly, this value represents the average cluster height in cells and
provides a measure of three-dimensionality. Compactness was used as a way to quantify how closely the cells
are arranged. It was calculated as the percentage of neighboring sites occupied by cells and ignored whether
the cells were bound together or simply adjacent. The following examples will aid this concept of compactness.
A cell has six sides and an isolated cell having zero neighboring cells would have a compactness of 0%. If this
cell were to have one neighbor, the compactness of the two neighboring cells with 12 sides together, two of
which possess adjacent cells, would be 16.7%. Eight cells forming a 2x2x2 cube, an arrangement not possible in
this model due to the staggering of successive cell levels, would have 48 sides in total, 24 of which possess
neighboring cells, for a compactness of 50%.
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All models were run for 15,000 iterations; each iteration represents the application of all the relevant rules to
all the cells. All rules in our model were probabilistic and the order of the cells to which the rules were applied
each iteration was random. Therefore, simulations with the same initial conditions will almost certainly have
different outcomes. The length of simulation time was determined by how long it took all simulations in a
preliminary set to reach a state of equilibrium. Equilibrium was determined by averaging and comparing values
for average height and compactness in the final 1000-point ranges (i.e., (13,001 – 14,000) and (14,001 –
15,000)). If the average values for both parameters varied by less than 2% the model was determined to be at
equilibrium. The average value for the final 1000-point range (i.e., 14,001 – 15,000) was used as the value for
average height and compactness and only data from simulations that had reached equilibrium are reported
here. Average cluster size was calculated after the final iteration.
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Figure S1. Polar histograms
Polar histograms (rose diagrams) for the total distance cells migrated in relation to the cluster when
using a motility filter (A-C) or longer 30-min intervals (D-F). The direction toward the central cluster
(solid arrow) and mean resultant vector (dashed arrow) are overlain on each figure. For experiments
without a central cluster the solid arrow points to an arbitrary central point. The magnitude of the
mean resultant vector is included in each panel (range 0% - 100%).
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Figure S1. Holfinger
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