Graph-based Characterisations of Cell Types and Functionally Related

Modules in Promoter Capture Hi-C Data

Lelde Lace, Gatis Melkus, Peteris Rucevskis, Edgars Celms, Karlis Cerans, Paulis Kikusts,

artin¸

s Opmanis, Darta Rituma and Juris Viksna

Institute of Mathematics and Computer Science, University of Latvia, Rainis Boulevard 29, Riga, Latvia

lelde.lace, gatis.melkus, peteris.rucevskis, edgars.celms, karlis.cerans, paulis.kikusts, martins.opmanis, darta.rituma,

Keywords:

Hi-C Networks, Cell Type Speciﬁcity, Graph-Based Metrics, Graph Topology.

Abstract:

Current technologies, noteworthy Hi-C, for chromosome conformation capture allow to understand a broad

spectrum of functional interactions between genome elements. Although signiﬁcant progress has been made,

there are still a lot of open questions regarding best approaches for analysis of Hi-C data to identify bio-

logically signiﬁcant features. In this paper we approach this problem by focusing strictly on the topological

properties of Hi-C interaction graphs. Graph topological properties were analysed from the perspective of

two research questions: 1) are topological properties alone able to distinguish between different cell types

and assign biologically meaningful distances between them; 2) what is a typical structure of Hi-C interaction

graphs and can we assign a biological signiﬁcance to structural elements or features? The analysis was applied

to a set of Hi-C interactions in 17 human haematopoietic cell types. Promising results have been obtained at

answering both questions. Firstly, we propose a concrete set Base11 of 11 topology-based metrics that pro-

vide good discriminatory power between cell types. Secondly, we have explored the topological features

of connected components of Hi-C interaction graphs and demonstrate that such components tend to be well

conserved within particular cell type subgroups and can be well associated with known biological processes.

1 INTRODUCTION

The spatial organization of a genome inside of a liv-

ing cell’s nucleus has long been appreciated as an im-

portant determinant of genomic function. One of the

most important methods for studying this organiza-

tion has been chromosome conformation capture or

3C, in which closely associated genomic fragments

are cross-linked via formaldehyde treatment and then

puriﬁed, permitting closer study (Dekker et al., 2002).

Since its inception at the start of the previous decade,

the original 3C protocol has been adapted and com-

bined with other methods, including chromatin im-

munoprecipitation and next-generation sequencing to

assist in broadening the scope and depth of individ-

ual experiments. Particularly noteworthy among these

is Hi-C, which utilises a biotin-streptavidin puriﬁ-

cation method in combination with next-generation

sequencing technology to potentially create a com-

plete, unbiased genomic library of chromatin inter-

actions (Lieberman-Aiden et al., 2009; Belton et al.,

2012). However, in practice Hi-C produces highly

complex datasets that do not lend themselves easily

to the study of genomic contacts below a resolution

of 1 Mb, and to simplify such studies an additional

reﬁnement, capture Hi-C (cHi-C), was invented. In

cHi-C the complex Hi-C library is subjected to an ad-

ditional sequence capture step that obtains a subset

of interactions that occur with a preselected subset of

genomic regions known as ’bait fragments’, simplify-

ing the resulting data sufﬁciently to allow for statisti-

cally signiﬁcant results at a high genomic resolution

(Dryden et al., 2014; Mifsud et al., 2015). Capture

Hi-C has subsequently been used in other studies for

varying elements of interest including gene promot-

ers (Mifsud et al., 2015; Javierre et al., 2016), au-

toimmune disease-associated genomic variants (Mar-

tin et al., 2015), colorectal cancer risk loci (J

ager

et al., 2015), cardiovascular disease risk loci (Mon-

teﬁori et al., 2018) and more.

The basic analysis of Hi-C datasets is largely es-

tablished and well-documented (Lajoie et al., 2015).

However, the large amount of comprehensive data ob-

tained and the high cost of exhaustive and represen-

tative experiments utilising these methods mean that

it is important to consider how currently published

Lace, L., Melkus, G., Rucevskis, P., Celms, E., Cerans, K., Kikusts, P., Opmanis, M., Rituma, D. and Viksna, J.

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data.

DOI: 10.5220/0007390800780089

In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019), pages 78-89

ISBN: 978-989-758-353-7

datasets could best be mined to answer additional bi-

ological questions. Several methods exist by which

the resolution of a Hi-C dataset can be theoretically

improved through more sophisticated interaction call-

ing algorithms. These include several algorithms with

broadly comparable performances for general Hi-C

data (Forcato et al., 2017) and also more speciﬁc tools

such as the CHiCAGO analysis pipeline meant specif-

ically for cHi-C datasets (Cairns et al., 2016), and

these algorithms can involve techniques ranging from

modelling technical biases (Ay et al., 2014) to em-

ploying a deep convolutional neural network (Zhang

et al., 2018). Another set of approaches that are dis-

tinct from these are clustering methods where avail-

able 3C and Hi-C data are analysed in the interest of

discovering functionally related modules of genes and

regulatory elements. These include the use of δ-teams

models for Hi-C data to identify both known and puta-

tive gene clusters (Schulz et al., 2018), hard- and soft-

clustering algorithms that could theoretically assist in

the interpretation of combined metagenomic sequenc-

ing and 3C data (DeMaere and Darling, 2016), and

also spectral clustering-based methods such as the

Arboretum-Hi-C framework that was found to be use-

ful in identifying chromatin features in mammalian

Hi-C datasets at several levels of organization and

pointed to the potential utility of graph-based cluster-

ing in both analysing and comparing Hi-C datasets in

general (Siahpirani et al., 2016).

Although the advantages of analysing Hi-C inter-

action data in graph-related terms are already well ac-

cepted – e.g approaches by (Siahpirani et al., 2016)

or (Cairns et al., 2016) explicitly discuss graph-based

formalisms and their methods have been success-

fully applied when analysing new data sets (Javierre

et al., 2016), only the properties of interaction ma-

trices (which can be considered as weighted graphs)

are mainly taken into account as well as some addi-

tional data (e.g. interaction segment distances and

associations with known gene regulations). Analysis

of topological features of these interaction graphs and

their biological signiﬁcance, however, remain largely

unexplored. (Although some studies explicitly men-

tion ’topological features’, these are very limited and

usually more related to the topology of chromosomes

rather than interaction graphs – e.g. in (Wang et al.,

2013) these are interpreted as the distributions of in-

teraction endpoints on chromosomes).

In this paper we focus explicitly only on the topo-

logical properties of Hi-C interaction graphs. These

properties were identiﬁed and analysed from the per-

spective of two research questions: 1) are topologi-

cal properties of Hi-C interaction graphs alone able

to distinguish between different cell types and assign

biologically meaningful distances between them; 2)

what is a typical structure of Hi-C interaction graphs

and can we assign some biological signiﬁcance to

structural elements or features of these graphs?

2 DATASET USED FOR THIS

STUDY

For this study we use a dataset of long-range inter-

actions between promoters and other regulatory el-

ements that was generated by The Babraham Insti-

tute and University of Cambridge (Javierre et al.,

2016). The data comprise interactions that were

determined by promoter capture Hi-C in 17 human

primary haematopoietic cell types. The measure-

ments have identiﬁed interaction regions of 31253

promoters across all chromosomes; from these high-

conﬁdence PCHi-C interactions have been selected

using CHiCAGO pipeline (Cairns et al., 2016) and se-

lecting interactions with score 5 or more. These data

are available from the Open Science Framework web-

site (Javierre et al., 2016). This data set is still largely

unique because it contains genome-wide data cover-

ing a representative subset of the entire haematopoi-

etic lineage collected using a uniﬁed protocol.

From these data we have constructed directed

graphs separately for each chromosome (few inter-

chromosome interactions were rejected and chromo-

some Y was not considered due to a very few interac-

tions) and for each cell type. The vertices of graphs

are chromosome segments that correspond either to

promoters (’baits’) or the detected interaction regions

(’other ends’), the edges correspond to interactions

and are directed from ’baits’ to ’other ends’. Un-

like most other analyses we only consider the topol-

ogy of interaction graphs, without assigning concrete

sets of genes to the vertices. In total we obtained

23 ×17 chromosome and cell type-speciﬁc graphs,

each of which can be considered as a subgraph of the

’complete interaction network’ having a total number

of vertices 251209 (with ranges between 2904 and

23079 per chromosome) and 723165 edges. Simi-

larly, each of these graphs can be considered as a sub-

graph of the ’interaction network’ of one of the chro-

mosomes, which is speciﬁc for a given cell type.

In a number of computational tests the graphs

were further modiﬁed by varying CHiCAGO scores

between thresholds for edge inclusion between 3 and

8. Although no comprehensive analysis was done, in

general such variations had a limited impact on the

stability of the results.

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data

3 EXPLAINING DIFFERENCES

BETWEEN CELL TYPES WITH

GRAPH-BASED METRICS

In this section we analyse the possibility to distin-

guish between cell types using sets of metrics that are

based on graph topological structure and propose a

concrete set Base11 of metrics having the largest dis-

criminatory power. The approach is somewhat simi-

lar to graphlet-based methods (Yaveroglu et al., 2015)

that have been successfully used for analysis of differ-

ent types of biological networks and also in our previ-

ous work on protein structure analysis (Viksna et al.,

2004; Celms et al., 2018). The graphlet methods rely

on network sampling for the presence of a predeﬁned

set of small subgraphs, for protein structure analysis

the graphs were derived from typical common sub-

graphs.

Neither of these approaches, however, seem to be

directly applicable to Hi-C interaction graphs due to

lack of well deﬁned common topological substruc-

tures (partially because the presence of edges depends

on weight thresholds, and neither of the aforemen-

tioned methods are well suited to weighted graphs).

Whilst features that are explicitly based on graph

metrics sometimes have been used to analyse certain

types of biomolecular interactions (e.g. in (Quadrini

and Emanuela, 2018) for RNA structure analysis),

such metrics, however, usually are more related to

vertex or edge weights or labels rather than to graph

topological properties.

In our set of proposed metrics we have tried to in-

clude more global graph properties, which are easy to

compute and also remain comparatively stable under

changing weight thresholds (at least for this particular

dataset of Hi-C interaction graphs).

3.1 Graph-based Metrics

The initial set Base57 contains 57 different metrics

characterising graph topology. The selection of these

metrics were based on manual exploration of graphs,

however, short of including all the possible counts of

different small subgraphs (from which only cliques

and cycles of length 2 are considered), they cover

most of usually considered graph topological prop-

erties that can be computed efﬁciently. The set con-

sists of the following metrics: CCnE – a number of

connected components with n edges, CCnV – a num-

ber of connected components with n vertices, BCnE –

a number of vertex bi-connected components with n

edges, BCnV – a number of vertex bi-connected com-

ponents with n vertices, SCnE – a number of strongly

connected components with n edges, SCnV – a num-

ber of strongly connected components with n vertices

and CLnV – a number of cliques (ignoring edge di-

rections) of size n, with values of n ranging from

3 to 8+ (8 or more). Metrics CCmaxV, CCaverV

denote maximal and average (for cell types) num-

bers of vertices in connected components, and CC-

maxE, CCaverE, BCmaxV, BCaverV, BCmaxE, BCa-

verE, SCmaxV, SCaverV, SCmaxE, SCaverE are de-

ﬁned similarly for numbers of edges and vertices and

bi-connected and strongly connected components. Fi-

nally, CLmaxV and CLaverV denote maximal and av-

erage clique sizes, and antiparallelEdges is number

of cycles of length 2.

Apart from these additional 4 metrics were con-

sidered that are closely related to the sizes of graphs:

V – the number of vertices, E – the number of edges,

E9 – the number of edges, which are not shared by 9

or more (i.e. by no more than 50% of all) cell types

and E17 – the number of edges, which are not shared

by all 17 cell types.

To minimise the effect of the measure of cell type

distances being based simply on different numbers of

particular features (which very likely will be strongly

correlated to the difference in sizes of interaction

graphs) the values of metrics were normalised, i.e.,

for a metric m its value m(i, j) for cell types i and

j was deﬁned as m(i, j) = m

i, j

√

×m

, where m

and m

are the numbers of features in graphs of cell

types i and j and m

i, j

is the number of features in the

largest common subgraph of these graphs. Such val-

ues m(i, j) were computed for all 61 metrics and all

136 distinct tissue pairs i and j.

One clearly expects a high correlation between the

values of metrics V, E, E9 and E17; however, there

are also high correlations between certain pairs from

Base57 set, in particular, between numbers of vertices

and edges in speciﬁc types of components. Only one

of the metrics was kept for pairs with correlations of

0.93 and above (after which there is a slight drop, al-

though the main reason for choosing this threshold

was very clear correlations between metrics measur-

ing numbers of vertices and numbers of edges), lead-

ing to the removal of CCnV, BCnV, SCnV for all val-

ues of n and also the removal of CCmaxV, CCaverV,

BCmaxV, BCaverV as well as CLmaxV (strongly cor-

relating with CLmaxV). For the further studies the re-

maining subset Base34 of 34 metrics from Base57

was chosen.

3.2 Cell Type Distances

While the molecular mechanisms underlying

haematopoiesis in humans are incompletely under-

stood, the general pattern of haematopoietic stem

BIOINFORMATICS 2019 - 10th International Conference on Bioinformatics Models, Methods and Algorithms

cell differentiation into erythroid, megakaryocytic,

myeloid and lymphoid lineages is generally agreed

upon and commonly represented in haematopoietic

trees (e.g. Robb et al. 2007). Although hierarchical

classiﬁcation of blood cell types from varying lin-

eages is occasionally performed, e.g. on the basis

of ribosomal protein expression (Guimaraes and

Zavolan, 2016), it is usually done with the intent

of validating results by examining their consistency

with well-known conceptions of haematopoiesis. The

situation is similar with CHiCAGO based clustering

of Hi-C data from (Javierre et al., 2016), however,

this study assigns easily quantiﬁable distances, and,

since we are working with the same Hi-C dataset,

seems the most appropriate for comparison.

It should be emphasised that our goal is not

to replicate the same results using slightly different

methods. Our approach is distinct from (Javierre

et al., 2016) in that we analyse the interactions not as

a weight matrix, but in graph-topology speciﬁc terms.

The question, therefore, is whether there exists a set

of speciﬁc topological properties that can be utilized

to distinguish between different forms of chromatin

interactions captured in Hi-C data, and whether these

properties are potentially useful in describing and pre-

dicting coordinated genomic processes.

On basis of these data we consider two distance

measures: Dcont ranging from 0.00 to 1.00 that

are proportional to distances from (Javierre et al.,

2016) and a binarised version Db with values 0 and

1 applying cut-off threshold 0.50 (see Figure 1). We

also consider two distances based only on biologi-

cally well-accepted cell type similarities: Dt that is

equal to 0 for cell types within the same (lymphoid

and myeloid) subgroups and equal to 1 for cells

from different subgroups, and D4 based on their

respective positions in the haematopoietic tree and

(in the case of endothelial precursors EP) functional

similarities. This separates cells into 5 subgroups:

= {MK,Ery}, G

2,1

= {Mac0,Mac1, Mac2},

2,2

= {EP,Mon, Neu}, G

3,1

{aCD4,naCD4,tCD4, nCD4, nCD8,tCD8,FoetT}

and G

3,2

= {nB,tB} and assigns distance D4 equal to

0.33 between different members of the same group,

distances 0.67 between pairs from groups G

2,1

, G

2,2

and G

3,1

, G

3,2

and distances 1.0 between pairs from

other groups. For a pair of the same cell types D4 is

In addition we also tested 3 distances DA, DB and

DC to check the possibility to separate some closely

related cell subgroups from the other cell types in the

tree (see Figure 1).

Figure 1: Haematopoietic tree of 17 cell types. The contin-

uous distances Dcont range from 0 to 1 and are proportional

to distances in the tree according to the scale shown. Binary

distances Db are deﬁned to be equal to 0 for Dcont < 0.5

and equal to 1 otherwise. Dt is deﬁned according to cell

subtypes – it is equal to 1 between lymphoid and myeloid

types and equal to 0 between cells of the same subtype. Ad-

ditionally binary distances DA, DB and DC were used to test

separability of subtrees ’cut’ correspondingly at points A, B

and C.

3.3 Discrimination Between Different

Cell Types

To estimate the discriminatory power of metrics

from Base34 and of 4 ’counting’ metrics V, E, E9

and E17 we constructed linear regression models

for the prediction of cell distances on the basis of

the values of these metrics. We also applied step-

wise regression (using Akaike information criterion

(Sakamoto et al., 1986) and its implementation in AIC

function, which is available in language R core li-

brary) to select the most discriminatory metrics from

Base34. As statistically signiﬁcant were identiﬁed

11 metrics: CC8+E, antiparallelEdges, CCaverE,

CCmaxE, BCaverE, SCmaxE, CL3V, CL4V, CL5V,

SC4E, BC8+E with the ﬁrst 7 being signiﬁcant for all

four distances Dcont, Db, Dt and D4 (see Figures 2

and 3). The set of these 11 metrics is called Base11.

Some interesting features of this set are the fact

that sizes of connected components have compara-

tively high signiﬁcance, high signiﬁcance has also the

number of components of size 8 or more (this is also

partially implied by results from Section 4). The num-

ber of cliques is also important, the dominance of

CL3V could be explained by the overall larger num-

ber of them. The importance of antiparallelEdges

probably could be explained by its ’counting’ char-

acter, but potentially might be related also to gene

regulation, since such interactions are possible only

between ’bait’ regions, which, by deﬁnition, are asso-

ciated with genes.

The correlations between predictions of regres-

sion models and the actual distances are summarised

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data

Figure 2: The most discriminating metrics for cell type dis-

tances Dcont (top) and Db (bottom). The relative discrimi-

natory power of any pair of metrics is proportional to the ra-

tio of their absolute values of ”effect size” shown on y axis.

The exact ranges of ”effect size” are data-dependent and

are not directly comparable between different cell type dis-

tances, and (even more notably) between full genome and

single chromosome metrics data.

in Table 1. To some extent, it shows the suitability

of different metrics for discrimination between cell

types, although the obtained correlation values are

likely inﬂuenced by over-ﬁtting and should be treated

with caution (although the results are very stable –

10 repeated bootstrapping tests with training sets con-

taining 75% of data produced at most 2% deviations).

Of larger interest is the comparative performance of

different metrics in cell type differentiation. Good

performance of ’counting’ metrics V, E, E9 and E17

is not surprising, since one should expect that more

closely related cell types will share more common Hi-

C interactions. Nevertheless, they alone do not out-

perform sets of Base metrics (apart from E9, which

counts the interactions that are common to no more

than 50% of cell types, and thus is dataset depen-

dent). Surprising, however, is the low performance

of these metrics for identiﬁcation of select clusters

of closely related cell types (distances DA, DB and

DC). Overall, however, these results conﬁrm that the

Base topology-based metrics, particularly the Base11

subset, perform well in lineage-based identiﬁcation of

blood cell types in chromatin interaction data.

Figure 3: The most discriminating for cell type distances Dt

(top) and D4 (bottom).

Table 1: Pearson correlations between cell type distances

and predictions of their values.

Dcont Db Dt D4 DA D8 DC

Base57 0.79 0.68 0.67 0.72 0.77 0.44 0.63

Base34 0.78 0.67 0.66 0.71 0.76 0.42 0.62

Base11 0.78 0.67 0.66 0.70 0.74 0.40 0.58

Base11 + V 0.81 0.69 0.67 0.73 0.75 0.46 0.62

Base11 + E 0.80 0.68 0.67 0.72 0.75 0.45 0.61

Base11 + E17 0.80 0.68 0.67 0.72 0.75 0.45 0.61

Base11 + E9 0.87 0.72 0.73 0.76 0.75 0.55 0.71

V 0.67 0.57 0.56 0.55 0.47 0.36 0.45

E 0.78 0.66 0.65 0.70 0.68 0.29 0.25

E17 0.78 0.66 0.65 0.70 0.68 0.29 0.25

E9 0.86 0.71 0.72 0.75 0.69 0.33 0.31

An interesting feature can be observed from com-

paring the performance of Base11 on different chro-

mosomes (shown by heatmaps in Figure 4). The chro-

mosomes are grouped in a number of similarity clus-

ters, which is not the case for randomised data. The

clusters, however, strongly depend on the used cell

type distance (although there are few stably related

pairs of chromosomes as well as few persistent out-

liers).

For Dcont distance Figure 5 shows the statistical

signiﬁcance of Base11 metrics for which it correlates

well with metrics signiﬁcance for the whole chromo-

some set.

BIOINFORMATICS 2019 - 10th International Conference on Bioinformatics Models, Methods and Algorithms

Figure 4: Heatmaps of similarity between pairs of chromo-

somes using the four metrics giving the best predictions of

cell type distances Dcont (top left), Db (top right), Dt (bot-

tom left) and D4 (bottom right).

Figure 5: Statistical signiﬁcance of metrics for Dcont dis-

tance and chromosome 15, which well correlate with met-

rics for the whole chromosome set.

Figure 6 illustrates examples of metrics statistical

signiﬁcance of chromosome 19 (belonging to another

well correlating group) and chromosome 5 (an ’out-

lier’). Notably that Base11 predictions for Dcont dis-

tance based solely on data from chromosomes 15, 19

and 5 gives correspondingly correlations 0.85, 0.88

and 0.91. The fact that these values exceed overall

value of 0.78 is the most likely result of larger over-

ﬁtting effect due to smaller datasets; however, these

numbers indicate that there are no strictly ’dominant’

chromosomes that could be used for cell type differ-

entiation. The exact reasons why such clusters of

chromosomes are formed remain unclear, but might

be the result of some more complex dependencies be-

tween Base11 metrics, which can not be detected by

regression models.

Figure 6: Statistical signiﬁcance of metrics for Dcont dis-

tance and chromosomes 19 (belongs to a block of 6 corre-

lating chromosomes), and an ’outlier’ chromosome 5.

4 THE STRUCTURE OF HI-C

INTERACTION GRAPHS

In this section we more closely explore the struc-

ture of graphs describing Hi-C interactions. The ini-

tial graphs (see Section 2) are deﬁned separately for

each of the 23 chromosomes (chromosome Y is omit-

ted due to a very low number of interactions) and

for each of the 17 cell types. Each of these graphs

can be considered as a subgraph of a ’complete net-

work’ for a speciﬁc chromosome, with vertices cor-

responding to chromosome segments between which

interactions have been measured and (for simplicity)

with isolated (non-interacting) vertices removed for

a graph corresponding to a speciﬁc cell type. The

number of vertices for chromosome and cell type spe-

ciﬁc graphs ranges between 773 (chromosome 22)

and 11118 (chromosome 1) and the number of edges

on average is slightly less than the number of vertices

multiplied by 2. The vertices are denoted by the mid-

dle genomic coordinate of their respective segment

mapped on a speciﬁc chromosome, and the gene an-

notations used are from the original data.

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data

The questions we are trying to answer here are: 1)

what is a ’typical structure’ of Hi-C interaction graph?

2) how do the structures of graphs change if we con-

sider common subgraphs for given sets of cell types?

3) can we assign some biological signiﬁcance to the

structural elements or features of these graphs?

4.1 General Topological Properties of

Interaction Graphs

Since the data that we have used are focused par-

ticularly on small-scale interactions, it is not unex-

pected that our interaction graphs separate easily into

connected components. Approximately 29% of these

contain just 2 vertices (isolated edges or cycles of

length 2), there are comparatively few components of

size 3-7 (29%) and the remaining 45% contain 8 or

more vertices. Very few of them are comparatively

large (up to 150 vertices), with a typical range be-

ing 10-70 vertices and an average size being 32 ver-

tices. A sample distribution of connected compo-

nent sizes is shown in Figure 7. To investigate how

these components change for different cell types we

further consider components of 10 or more vertices

(although chosen somewhat arbitrary, this threshold

seems well suited to largely reduce random ’noise’

in graphs). The average number of such components

in each chromosome and cell type-speciﬁc graph is

around 50.

Figure 7: The distribution of sizes of connected components

for chromosome 1. Component size is shown on the hori-

zontal axis.

More interesting is the fact that connected com-

ponents have a tendency to remain largely unchanged

when shared by a number of different (component-

speciﬁc) cell types and to be largely (or completely)

absent in others. A typical reduction of sizes of com-

ponents for chromosome and cell type-speciﬁc graph,

when only parts of components shared by all cell

types are considered, is shown in Figure 8 for chro-

mosome 5 and Mon cell type. The proportion of com-

ponents that are shared by Mon and at least one other

cell type and that are almost absent in at least one

other cell type is around 25%. Comparatively few

(around 5%) components remain little changed in all

of the cell types. The remaining 70% could be further

subdivided in not very strictly separated subclasses,

ranging from ones for which part of the component

shows good cell type speciﬁcity, to quite noisy ones

(full statistics is lacking, but manual inspections indi-

cate that the ﬁrst of these behaviours tends to be more

common).

Figure 8: The reduction of sizes of connected components

(with 10 or more vertices) for chromosome 5 and Mon cell

type when the component is replaced by a subgraph shared

by all 17 cell types. The remaining component size (in %)

is shown on the horizontal axis and the percentage of com-

ponents on the vertical axis.

As an example, the following ﬁgures illustrate a

connected component of chromosome 5 and cell type

EP. The complete initial component is shown in Fig-

ure 9. Figure 9 shows the parts of the component that

are shared by Mac0, Mac1 and Mac2 – although a

number of interactions and nodes are lost the topo-

logical structure remains mostly preserved; and also

additionally is shared by cell type tCD8, in which case

only a few vertices and interactions remain. The com-

ponent is completely absent in cell type Neu.

Figure 9: A connected component of Hi-C interactions in

chromosome 5 and cell type EP.

BIOINFORMATICS 2019 - 10th International Conference on Bioinformatics Models, Methods and Algorithms

Figure 10: The parts of EP Hi-C interactions component

shared with cell types Mac0, Mac1 and Mac2 (top) and ad-

ditionally with tCD8 (bottom). There are no common inter-

actions shared with cell type Neu.

4.2 Biological Interpretation of Hi-C

Interaction Components

The observation that connected components in Hi-C

interaction graphs are either largely shared by two

cell types, or are present in one of them and largely

absent in another strongly suggest that they have bi-

ological roles. These, however, might differ between

the components and the very large number of these

make comprehensive analysis practically infeasible.

Still, we have performed limited analyses that con-

ﬁrm a strong relation of a component structure with

known biological interactions and we have explored

several illustrative components in more detail.

In order to ascertain whether the clusters previ-

ously obtained by linking bait-to-bait and bait-to-end

interactions contained likely candidates for function-

ally related gene modules we ﬁrst chose a sequence

of related cell types from the myeloid haematopoietic

lineage to examine for cell type-speciﬁc chromatin

architecture. Starting from a large pool of common

connected components for resting Mac0 and inﬂam-

matory macrophages Mac1, we sequentially added

more cell types to the selection criteria – alternatively

activated macrophages Mac2, monocytes Mon, neu-

trophils Neu and endothelial precursors EP – to nar-

row the range of clusters and establish the speciﬁcity

of graph components lost at each step.

The connected components were then assessed for

the proportion of nodes lost and grouped according

to their degree of preservation along the course of

cell type addition, from well-preserved (75-100% of

nodes in common between all cell types) to entirely

lost (no nodes in common between all cell types) with

several groups in between (Table 2). The majority of

components found tended to be highly speciﬁc, show-

ing 0-25% retention in the ﬁnal set of linked nodes

and edges – however, the most speciﬁc components

also tended to have the smallest number of nodes.

Table 2: Macrophage-speciﬁc graph component retention

in myeloid cells and endothelial progenitors after sequential

addition of cell types. n – a number of graph components, n

- a number of graph components containing over 20 nodes

initially.

Chr

75% −100%

retained, n(n

)

50% −75%

retained, n(n

)

25% −50%

retained, n(n

)

0% −25%

retained, n(n

)

retained, n(n

)

Total, n(n

)

1 23(5) 15(10) 45(36) 39(29) 111(14) 233(94)

2 14(1) 12(10) 36(31) 38(29) 96(17) 196(88)

3 13(1) 9(4) 34(24) 29(26) 83(11) 168(66)

4 7(3) 10(5) 15(11) 24(17) 80(14) 136(50)

5 9(3) 11(5) 30(25) 17(15) 80(8) 147(56)

6 7(2) 16(10) 26(22) 20(15) 79(8) 148(57)

7 11(3) 13(6) 20(16) 22(21) 84(10) 150(56)

8 6(0) 13(4) 14(10) 15(12) 73(13) 121(39)

9 7(0) 13(7) 16(12) 19(16) 65(8) 120(43)

10 17(3) 9(5) 15(12) 26(24) 65(10) 132(54)

11 11(2) 18(8) 29(19) 28(22) 67(3) 153(54)

12 8(0) 13(7) 24(17) 12(11) 87(13) 144(48)

13 7(0) 3(1) 11(8) 13(11) 31(5) 65(25)

14 9(2) 8(4) 12(9) 12(5) 62(9) 103(29)

15 11(0) 8(5) 19(9) 17(13) 68(3) 123(30)

16 7(1) 9(8) 18(6) 8(5) 47(4) 89(24)

17 10(1) 18(6) 24(18) 21(19) 67(3) 140(47)

18 2(0) 5(1) 13(9) 10(4) 38(9) 68(23)

19 18(1) 16(7) 18(7) 6(2) 48(0) 106(17)

20 10(1) 8(4) 12(10) 7(5) 38(5) 75(25)

21 4(0) 2(1) 5(4) 5(3) 24(4) 40(12)

22 6(0) 5(3) 9(4) 11(7) 34(3) 65(17)

X 4(1) 16(7) 20(13) 14(11) 66(2) 120(34)

Total 221

(30)

250

(128)

465

(332)

413

(322)

1493

(176)

2842

(988)

After collecting data about node retention, the

largest components showing high (75-100%) or low

(0-25%) retention in chromosomes of interest ac-

cording to our previous graph analysis (chromosomes

5, 9, 14, 15 and 19) were analysed for enrichment

with registered transcription factor protein-protein in-

teractions, known transcription factor binding sites,

co-expressed transcription factors and binding mo-

tifs with the Enrichr web tool (Chen et al., 2013;

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data

Figure 11: A component of Hi-C interactions shared by cell types Mac0, Mac1 and Mac2, Mon, Neu and EP. The initial larger

component, shown with dashed lines, is present in Mac0.

Kuleshow et al., 2016).

The analysed lists featured between 6 and 200

genes depending on component size. The analy-

sis uncovered a variety of transcription factors that

associated with different components, including an

array of broadly tissue macrophage-associated fac-

tors such as STAT5, GATA6, PPARγ and MAF

(Lavin et al., 2016) as well as more speciﬁc factors

found primarily in monocyte-derived macrophages

– JUN, JUNB, MAFK, EGR3 and others (Ramirez

et al., 2017), and even lipopolysaccharide treatment-

induced transcription factors including BCL3, USF1

and SREBF2 signifying inﬂammatory macrophage

activity or interleukin-4 and 13 activated factors such

as MITF (Das et al., 2018). These speciﬁc factors

were primarily, but not exclusively found in compo-

nents with very little retention across all cell types

analysed, such as one particular component which

showed a particular enrichment for STAT5 binding

during analysis and was completely lost when search-

ing for common chromatin conformations with en-

dothelial precursors (Figure 11).

The pattern previously described partly holds for

better-retained components as well, which contain

genes associated with transcription factors signiﬁcant

for other cell types, notably monocytes with GATA2,

CEBPB and KLF4, or more basal hematopoietic tran-

scription factors like RUNX1 (Zhu et al., 2016), or

even FLI1 which is known to negatively regulate

myeloid differentiation and function as a master con-

troller transcription factor in endothelial cells (Zhu

et al., 2016; Kanki et al., 2017). These compo-

nents particularly tend to taper off sharply in node

count when neutrophils and endothelial precursors

are included, such as one component associated with

GATA2 and CEBPB as well as less speciﬁc tran-

scription factors like CTCF and SIN3A, the for-

mer of which is a well-known insulator in vertebrate

genomes (Ong and Corces, 2014) and the latter an im-

portant factor in stem cell proliferation (Figure 11)

(McDonel et al., 2012).

Altogether the gene set enrichment analysis sup-

ports the hypothesis that the genes we have linked

together into connected components may form func-

tionally related modules, broadly ﬁtting a loose model

of speciﬁcity applied through examining the overlap

between chromatin architectures of diverse cell types.

4.3 Software Availability

Web-based software components, developed

by the authors, for visualisation and explo-

ration of Hi-C interaction graphs is avail-

able at GitHub: https://github.com/IMCS-

Bioinformatics/HiCGraphAnalysis. It includes

the datasets of graphs used in this study, which

the users can replace with their own. The current

functionality is limited to the exploration of changes

in graph components being shared between different

subsets of cell types.

BIOINFORMATICS 2019 - 10th International Conference on Bioinformatics Models, Methods and Algorithms

Figure 12: Another chromosome 5 component of Hi-C interactions shared by cell types Mac0, Mac1 and Mac2, Mon, Neu

and EP. The initial larger component, shown with dashed lines, is present in Mac0.

5 CONCLUSIONS

In this paper we have analysed the topological prop-

erties of Hi-C interaction graphs from two related,

but somewhat different perspectives: 1) are topo-

logical properties of these graphs alone able to dis-

tinguish between different haematopoietic cell types

and assign biologically meaningful distances between

them; 2) what is a typical structure of Hi-C interac-

tion graphs and can we assign some biological sig-

niﬁcance to structural elements or features of these

graphs?

In general, we think that we have obtained af-

ﬁrmative answers to both these questions. Regard-

ing characterisation of interactions graphs in terms of

their topological properties we propose a set Base11

of 11 metrics based on graph topological features

that can be used to distinguish between different cell

types for 7 different distance measures that we have

tested. Although the Base11 metrics are related to

graph properties, which unlikely could be directly as-

sociated with concrete biological mechanisms, they

seem very appropriate for characterisation of interac-

tions that are speciﬁc for a particular cell type. If dis-

crimination between the cell types is the main priority

then Base11 can be used in combination with ’count-

ing metrics’ V, E, E9 and E17 to obtain correlations

between the distance-deﬁned and predicted values of

up to 0.87. Although the usefulness of these ’counting

metrics’ can be anticipated since one should expect

that more closely related cell types will share more

common interactions, they perform much better when

used in combination with Base11, and an interesting

non-obvious feature is their linearity, i.e. the fact that

they perform well in linear regression models.

The observed clustering of chromosomes accord-

ing to regression coefﬁcients that are assigned to dif-

ferent Base11 metrics is an interesting feature, in par-

ticular since such clustering is observed for different

cell type distances D, but the clusters are different

for different distances D. The exact reasons why such

clusters of chromosomes are formed remain unclear,

but a probable explanation is that they could be the re-

sult of some complex (interaction graph-speciﬁc) de-

pendencies between Base11 metrics, or biological re-

lations between graph components (which is not taken

into account by the current topological approach).

The analysis of topology of Hi-C interaction

graphs showed that they decompose in comparatively

small connected components, which can be either par-

tially shared by all cell types, or can be pronouncedly

cell type-speciﬁc – largely conserved in a speciﬁc set

of cell types and practically absent in others. A de-

tailed inspection of two of such components showed

that they can be well explained by biological fac-

tors/properties that are shared by some of the cell

types, but not all of them.

Regarding further developments, it would be very

Graph-based Characterisations of Cell Types and Functionally Related Modules in Promoter Capture Hi-C Data

interesting to test our approach on another genome-

wide PCHi-C interaction dataset, in order to assess

both: 1) the applicability of Base11 metrics for dis-

crimination between cell types, other than blood cells

studied here; and 2) to analyse the similarity of topo-

logical structure and component behaviour of interac-

tion graphs in order to assess how the properties ob-

served for haematopoietic cells generalises to other

cell types. Unfortunately, as far as we know, an-

other appropriate PCHi-C dataset covering multiple

cell types has yet to become available.

There is also a good potential to further extend

the graph topology based approach that we have used

here. It has been quite successful to show that topo-

logical properties alone could be quite informative

for discrimination between different cell types and

also for assigning biological meaning to speciﬁc com-

ponents on interaction graphs. At the same time

some useful information in the current graph repre-

sentation is absent, notably, an edge in an interac-

tion graph might represent an interaction that forms

a well-deﬁned loop on a chromosome (if the distance

between interaction segments is limited and there are

no intermediate interactions between them), or it can

represent a long range interaction with a far less ob-

vious biological role. We have plans to further de-

velop the mathematical formalism for description of

interaction graphs in order to incorporate and analyse

such features, although additional studies are needed

to determine the best way to achieve this.

ACKNOWLEDGEMENTS

The research was supported by ERDF project

1.1.1.1/16/A/135.

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