Assessing Preferred Proximity between Different Types of Embryonic

Stem Cells

Minhong Wang

1 a

, Athanasios Tsanas

1 b

, Guillaume Blin

2 c

and Dave Robertson

3 d

Usher Institute, The University of Edinburgh, Edinburgh, U.K.

MRC Center for Regenerative Medicine, The University of Edinburgh, Edinburgh, U.K.

School of Informatics, The University of Edinburgh, Edinburgh, U.K.

Keywords:

Embryonic Stem Cells, Different Types of Stem Cells, Statistical Analysis, Minimum Spanning Tree.

Abstract:

Embryonic stem cells (ESCs) studies play an important role for understanding the molecular events that un-

derlie cell lineage commitment and serve as models for the development of disease. However, the interactions

between neighboring embryonic stem cells are not fully understood. Assessing proximity between different

types of embryonic stem cells might provide more information about distinct behaviors of embryonic stem

cells. In this study, we processed 186 cell colonies on disc constrained microdomains and 152 cell colonies on

ellipse. We grouped cell colonies based on different observed patterns and grouped cells by their locations. By

applying two measurements on embryonic stem cell colonies, minimum spanning tree and average distance to

the ﬁve closest objects, we investigated the difference of proximity between different types of embryonic stem

cells, the difference between grouped cell colonies and the difference between grouped cells. We found one

type of ESC has a smaller average path based on minimum spanning tree and higher proximity than the other

type. We report consistent results for different types of embryonic stem cells: these ﬁndings may be useful to

set benchmarks for empirical models which replicate ESC behaviors.

1 INTRODUCTION

Embryonic stem cells (ESCs) have shown potential

for regenerative medicine towards the development of

novel therapies for a wide range of diseases or injuries

(Wu and Hochedlinger, 2011). ESCs can self-renew

and differentiate into almost any type of mature cells.

Due to the special properties of ESCs, they are use-

ful for: 1) understanding the molecular events that

regulate stemness and cell lineage commitment (Ivey

et al., 2008)(Gan et al., 2007); 2) modeling develop-

ment of disease (Avior et al., 2016).

Previous work has demonstrated that stem cells

have the ability to socialize with their neigh-

bors while interacting with their micro-environment

(Fuchs et al., 2004). Recent studies illustrate that

different types of ESCs have distinct dynamic social

behaviors, such as variable migration speed and pre-

ferred number of neighbors (Phadnis et al., 2015).

https://orcid.org/0000-0001-7041-7045

https://orcid.org/0000-0002-0994-8100

https://orcid.org/0000-0002-9295-237X

https://orcid.org/0000-0001-9574-849X

However, the neighboring effects in ESCs are still

not fully understood as the underlying mechanisms of

their communication are highly complex (Madl and

Heilshorn, 2018)(Watt and Hogan, 2000). Under-

standing neighboring effects can beneﬁt the investi-

gation of behaviors in ESCs, which would be helpful

for controlling differentiation and contribute towards

the development of new stem cell therapies.

Brachyury (T) is a marker of early mesendoder-

mal expression (Beddington et al., 1992)(Wilkinson

et al., 1990). T+ cells are early differentiated cells as

they are marked by Brachyury (T), while T- cells are

naive ESCs. The process of spatial pattern formation

in differentiated stem cells is essential for establish-

ing functional mammalian tissue. Blin and colleagues

demonstrated that T+ and T- cells prefer different

numbers of neighboring cells, with T- cells preferring

more neighbors than T+ cells (Blin et al., 2018).

In this study we extend on these ﬁndings and look

into the preferred proximity (closeness) of neighbors

between the two types of cells. We applied two new

measurements to quantify the proximity of T+ and

T- cells in ESC colonies and assess the difference of

proximity within different patterning constraints.

Wang, M., Tsanas, A., Blin, G. and Robertson, D.

Assessing Preferred Proximity Between Different Types of Embryonic Stem Cells.

DOI: 10.5220/0009368903770381

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 4: BIOSIGNALS, pages 377-381

ISBN: 978-989-758-398-8; ISSN: 2184-4305

377

2 METHODS

2.1 Empirical Data

We used previous data of ESC colonies consisting of

186 images for disc experiments and 152 images for

ellipse experiments (Blin et al., 2018)(Wang et al.,

2018). Each image corresponds to a single cell colony

that was captured 48 hours after the initial seeding

of the stem cells. Each colony was randomly seeded

with both T+ and T- cells. Populations of each cell

type were isolated in the images by thresholding la-

belled image data. We extracted the cells’ locations

(described by x and y values) based on the centers of

the nuclei. For disc experiments, we selected cells

within 95.5 µm from the center of the disc; for ellipse

experiments, we selected cells within the ellipse with

the semi-major axis as 193.5 µm and semi-minor axis

as 47 µm. Cells outside these deﬁned constrained ar-

eas were considered as random noise and discarded.

Figure 1 shows the indicative plots for disc and ellipse

experiments.

Figure 1: Indicative plots for A) disc and B) ellipse experi-

ments. Blue circles represent T- cells; orange circles repre-

sent T+ cells.

2.2 Pattern Grouping

For both disc and ellipse experiments, we applied 2D

kernel density estimation (Botev et al., 2010) to ob-

tain the density maps of aggregated T- and T+ cells

separately. Since we are interested in the locations of

T+ cells, we thresholded the aggregated density map

of T+ cells based on the mean of max and min density

of each pixel to obtain the areas with high density T+

cells. The borders of high density areas (HDA) were

smoothed by least squared circle or ellipse function.

Figure 2 shows indicative plots for HDA on the disc

and ellipse constrained microdomain. In the disc ex-

periments, the HDA is a ring shaped area due to the

symmetry of the disc. In the ellipse, the HDA is fo-

cused at the tips of the major axis of the ellipse. We

compared the ratio of HDA/non-HDA size to the ra-

tio of HDA/non-HDA cell number to get an indica-

tion of cell spacing. Subsequently we obtained three

distinct groups of different cell patterns based on the

grouping of T+ cells: 1) cell colonies with relatively

higher density of T+ cells on HDA; 2) cell colonies

with relatively low density of T+ cells on HDA; 3)

cell colonies with no T+ cells.

Figure 2: Indicative plots for HDA on A) disc and B) ellipse

experiments.

2.3 Measurements of Neighboring

Effects

2.3.1 Minimum Spanning Tree

We built a connected graph (Wilson, 1996) for T+ or

T- cells in each cell colony by taking each cell as a

node and connecting any two nodes with an edge. The

weight of each edge was deﬁned as the Euclidean dis-

tance between the two nodes. A spanning tree is a

sub-graph that connects every node in the graph with-

out any cycles (Kruskal, 1956). As there are different

spanning trees for the graph, the minimum spanning

tree is the spanning tree connecting the nodes through

edges and has the smallest total weight (Prim, 1957).

Therefore, the minimum spanning tree calculates the

shortest path that connects all T+ or T- cells within the

colony. We calculated the average path distance be-

tween two nodes (cells) by dividing the path distance

of the minimum spanning tree by the number of T+ or

T- cells respectively. A smaller average path distance

indicates a higher proximity. Following this, we ap-

plied kernel density estimation (Botev et al., 2010) of

the average path distance we received from T+ and

T- cells from each cell colony. The number of mesh

points used in the kernel density estimation was 256.

We also calculated the minimum spanning tree for T+

and T- cells in each pattern group.

2.3.2 Quantifying Average Distance of Each

Query Object to Five Nearest Targets

For each T+ or T- cell (i.e., object) within disc and

ellipse experiments, we found the ﬁve closest T+ and

T- cells (i.e., targets). We calculated the average dis-

tance from each object to its targets (referred to as D).

The data presented four different cases of calculating

D: 1) the object is a T- cell with T- cell targets; 2) the

object is a T- cell with T+ cell targets; 3) the object

SERPICO 2020 - Special Session on Mining Self-reported Outcome Measures, Clinical Assessments, and Non-invasive Sensor Data

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is a T+ cell with T- cell targets; and 4) the object is a

T+ cell with T+ cell targets. For these four cases, we

applied kernel density estimation (Botev et al., 2010)

of D from all cells within each pattern group. Based

on the borders of the HDA, we applied kernel den-

sity estimation of the cells in the HDA and cells out-

side the HDA separately to investigate the difference

in proximity between the different cell type with both

regions.

3 RESULTS

3.1 Pattern Groups

Figure 3 shows the percentage of different patterns

observed in the disc and ellipse experiments. We de-

ﬁned pattern 1 as a relatively higher density of T+

cells within the HDA. In pattern 2, the density of T+

cells within the HDA was lower than the density of T+

cells within the remaining areas. On pattern 3, there

were no T+ cells.

Figure 3: The percentage of the 3 different patterns ob-

served within the A) disc and B) ellipse experiments. Pat-

tern 1: high density of T+ cells within the HDA. Pattern 2:

density of T+ cells within the HDA was lower than the den-

sity of T+ cells within the remaining areas. Pattern 3: no

T+ cells.

3.2 Minimum Spanning Tree Results

The results of the overall distribution of average path

distance based on the minimum spanning tree are

shown in Figure 4. The overall aggregate results for

the disc and the ellipse were consistent. It is note-

worthy that T- cells have much smaller average path

distance than T+ cells. The results indicate that T-

cells have a higher proximity than T+ cells, and the

variation in proximity of T+ cells was greater than in

T- cells.

Figure 5 shows the kernel density estimation re-

sults from the pattern groups described in 3.1. The

difference found in T- cells between the pattern

groups was relatively small. For Pattern 3, in which

there are no T+ cells, T- cells have the highest prox-

imity. T+ cells in Pattern 1 (more T+ cells on HDA)

Figure 4: Kernel density estimation of average path distance

(µm) of A) T- cells and B) T+ cells within disc and ellipse

experiments.

are slightly more compact than T+ cells in Pattern 2.

Again, the results from disc and ellipse experiments

are consistent. The double peaks of T+ cells on el-

lipse experiments might due to the fact that in some

colonies T+ cells were more dense at one tip of the el-

lipse and in some colonies T+ cells were more dense

at both tips.

Figure 5: Kernel density estimation of average path distance

of A) T- cells on disc experiments; B) T+ cells on disc ex-

periments; C) T- cells on ellipse experiments; D) T+ cells

on ellipse experiments.

3.3 Results of Average Distance of Each

Object to Five Nearest Targets

Figure 6 shows the kernel density estimation results

of average distance from the object to the ﬁve closest

targets (D) from the aggregated cells on disc and el-

lipse experiments. The case of T- as the object and T-

cells as the target results in the highest peak density

in both disc and ellipse experiments. This is consis-

tent with the results from the minimum spanning tree

which showed that T- cells have a high proximity. For

the case in which T- cells are taken as objects and T+

cells as targets the distribution of D has a high mean

value and a wide spread. This result could be due to

Assessing Preferred Proximity Between Different Types of Embryonic Stem Cells

379

the fact that there are more T- cells than T+ cells on

the colonies. Hence, for T- cells it takes longer dis-

tance to retrieve for the closest T+ cells in average.

For T+ cells, the distribution of D to its ﬁve closest

T+ or T- cells are relatively similar.

Figure 7 shows the kernel density estimation re-

sults of D which is grouped by cell locations. It shows

for all object T- cells the average D of the ﬁve closest

T- cells showed relatively low variety whether con-

tained within the HDA or not. For T- cells not in the

HDA, the average distance to the ﬁve closest T+ cells

is higher than for T- cells in the HDA. Interestingly,

for the cases in which T+ cells are taken as objects,

and both T- or T+ cells as targets, the T+ cells in the

HDA have a higher average D than T+ cells not in the

HDA and the distribution of D is slightly more spread

out.

Figure 6: Kernel density estimation results of D from the

aggregated cells on A) disc and B) ellipse experiments.

Figure 7: Kernel density estimation results of D from the

aggregated A) object cells on HDA on disc; B) object cells

on remaining areas on disc; C) object cells on HDA on el-

lipse; D) object cells on remaining areas on ellipse.

4 DISCUSSION

In this study, we quantiﬁed the proximity of different

types of cells in ESC colonies on different shaped mi-

crodomains. We assessed cells’ proximity in different

patterns groups, and the difference of the proximity

between different types of cells depending on location

(as shown in Figure 5 and Figure 7). The obtained re-

sults are consistent across discs and ellipses, which

provides some conﬁdence on the generalizability of

the extracted concepts (as shown in Figure 4 and Fig-

ure 6).

The results of the average path distance based

minimum spanning tree indicate that T- cells prefer

a higher proximity than T+ cells. The T+ cells in

colonies that formed the pattern with more cells in

the HDA (Pattern 1) have a higher proximity than the

T+ cells in the other pattern groups. The results from

D are consistent with the results from the minimum

spanning tree that T- cells have a higher proximity

than T+ cells. It also suggests that T+ cells have a

tendency to stay away from other cells as they have

a relatively low proximity to both T- and other T+

cells, compared to the high proximity we observed in

T- cells.

Compared to our previous work, we have provided

a more thorough analysis of the distribution of differ-

ent measurements by applying kernel density estima-

tion. We also analysed the difference between dif-

ferent observed patterns and different types of cells.

This information further improves our understanding

of the difference between types of stem cells, which

could be useful for controlling the differentiation in

ESCs. To the best of our knowledge, we are not aware

of other studies in literature which have investigated

the proximity in embryonic stem cells with the marker

Brachyury (T).

Currently, we are building diverse ESC compu-

tational models to reproduce the pattern formation

by investigating parsimonious, minimal sets of differ-

ent social behaviors of different types of ESCs which

replicate experimental data. This study is a step to-

wards informing the hypothesis that we can test in our

models as T+ cells tend to stay away from other cells.

In conclusion, we provided quantitative informa-

tion regarding the proximities of T- and T+ cells. T+

cells have a tendency to stay away from other cells

according to the results from the minimum spanning

tree and D. This ﬁnding could be useful in the analysis

of different social behaviors between different types

of ESCs.

ACKNOWLEDGEMENTS

MW would like to thank Sally Lab for supporting

data.

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Towards Facilitating Diagnosis, Longitudinal Monitoring, and Treatment

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