=Paper=
{{Paper
|id=Vol-2518/paper-ODLS3
|storemode=property
|title=Foundations of the Cell Tracking Ontology
|pdfUrl=https://ceur-ws.org/Vol-2518/paper-ODLS3.pdf
|volume=Vol-2518
|authors=Patryk Burek,Nico Scherf,Heinrich Herre
|dblpUrl=https://dblp.org/rec/conf/jowo/BurekSH19
}}
==Foundations of the Cell Tracking Ontology==
https://ceur-ws.org/Vol-2518/paper-ODLS3.pdf
Foundations of the Cell Tracking Ontology
Patryk BUREKa,1, Nico SCHERF b,c and Heinrich HERREd
a
Institute of Computer Science, Faculty of Mathematics, Physics and Computer
Science, Marii Curie-Sklodowskiej University, pl. Marii Curie-
Sklodowskiej 5, 20-031 Lublin, Poland
b
Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103
Leipzig, Germany
c
Institute for Medical Informatics and Biometry, Carl Gustav Carus Faculty of
Medicine, TU Dresden, Fetscherstr. 74, 01307 Dresden, Germany
d
Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig,
Haertelstr. 16-18, 04107 Leipzig, Germany
Abstract. Time-lapse microscopy gives us insight into the dynamic behaviour of
cells as they develop into tissues, organs, and entire organisms. Being able to
image and analyse these multi-cellular dynamics might provide the key to
understand the underlying organising principles. There is an ever increasing
amount of available cell tracking data that could be systematically integrated to
increase our knowledge of the organizing biological processes. This integration of
heterogeneous data demands the creation of frameworks suitable for rendering
extracted data searchable and interoperable between experiments and even data
from complementary measurements such as single cell sequencing. In the current
paper we discuss the fundamental concept of a cellular genealogy, a basic
knowledge structure forming conceptual and formal foundations of the Cell
Tracking Ontology (CTO) suitable for describing, querying and integrating data
from complementary experimental techniques in the domain of single cell analysis.
Cellular genealogies allow integration of cell tracking data, which typically consist
of sets of observations of cells at single time points organized into time indexed
sequences mapping the behaviour (e.g. cell division, cell death or differentiation)
of individual cells and their offspring into a common reference frame. The current
paper discusses the main ontological components of cellular genealogies: cells,
considered as material objects, having a lifetime and persisting through time;
temporal situations, composed of (continual) cells and relators connecting these
cells; snapshots of cells and of temporal situations; frames identified with
snapshots of temporal situations (they may be called presentic situations). All
these entities are organized into cellular genealogies, forming consistent, pedigree-
like structures supporting organization, querying and analysis of cell tracking data.
Keywords. Knowledge Representation and Management; Semantic annotation of
images and videos; Ontologies, Live Microscopy, Cell Tracking
1. Introduction
Live microscopy is a well established, experimental technique to study the dynamics
of single cells, cell colonies, tissues, organs and entire organisms [1,2,3,4]. The same
sample is imaged repeatedly over an extended period of time to create a time-lapse
1
Corresponding Author, E-mail: patryk.burek@poczta.umcs.lublin.pl. Copyright © 2019 for this paper
by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
movie, which is the subject of analysis in this work. Since manual analysis of such
large amounts of imaging data is largely infeasible, over the past years, a lot of work
has been dedicated to develop automated cell tracking methods [5, 6]. However, the
lack of a standard format for storing and annotating tracking results hinders integration,
and unified querying and analysis of the available data. Thus, a general and formal
annotation scheme for cell tracking results is needed to support both the integration of
experiment results as well as flexible and advanced analytics over the different
experimental results. That requires more than a classification scheme for some specific
types of entities but instead a model which supports traversing the data from a
collection of cell observations into the complex knowledge structures supporting
advanced queries.
Therefore, the fist and most important challenge is to design a knowledge structure
which supports these goals. We decided to use the most general concept of cellular
genealogies as a foundation for the Cell Tracking Ontology (CTO) [7] which is
intended for annotating cell tracking data. In the current paper we discuss ontological
basis of cellular genealogies in context of the General Formal Ontology (GFO) [8]
which provides the foundation for the CTO. We discuss the main ontological choices
underlying the CTO i.e. Presentials vs Time-Extended Entities, Objects vs Situations.
We also discuss the core notions of the CTO: cells, considered as material objects,
having a lifetime and persisting through time; temporal situations, composed of
(continual) cells; snapshots of cells and of temporal situations; finally cellular
genealogies, which serve as the backbone model upon which the integration of specific
biological ontologies into cell tracking experiments is made possible. The model
organizes single cell observations into temporally extended cells and supports
construction of entire developmental histories of cellular systems.
The remainder of the paper is structured as follows. Section 2 gives some
introduction into the underlying framework of the GFO and into the main assumptions
taken in the presented work. Sections 3 and 4 discuss the core notions of the CTO:
cells, divisions and cellular genealogies as well as their ontological interpretation in
terms of Presentials, Time-Extended Entities, Objects and Situations. Finally, section 5
presents conclusions, discussion and future work.
2. The Ontological Framework (GFO)
The term entity refers to anything which has a mode of existence. Entities are classified
into categories and individuals. In the General Formal Ontology (GFO) the basic
entities of space and time are topoids and time-intervals, also called chronoids. The
ontology of space and time of GFO is inspired by ideas of Franz Brentano [10] and is
presented in [11].
In the current paper we restrict the GFO-framework to the main elements relevant
in the context of cell tracking experiments. We take a minimal ontological commitment
and a pragmatic approach i.e. a minimal subset of GFO concepts, which is suitable for
modelling the domain of cell tracking is distilled and used as a foundation of the Cell
Tracking Ontology.
The main ontological categories relevant in context of the cell tracking
experiments are:
● Cells, considered as material objects, having a lifetime and persisting through
time.
● Temporal situations, composed of (continual) cells and relators connecting
these cells.
● Snap-shots of cells and of temporal situations. Frames can be identified with
snap-shots of temporal situations (they may be called presentic situations).
3. Cells as Presentials and Time-Extended Entities
Typically, the data obtained from cell tracking experiments consists of sets of
observations of cells at single time points, which in the next step are organized into
temporally ordered sequences. In order to represent the data adequately we introduce
two distinct kinds of temporal locations: Time Points and Time Periods and establish a
membership relation between them, denoted x ∈ y meaning that a time point x is an
element of a time period y. Additionally, we rely on the following relations of temporal
algebra: temporal order of time temporal locations x, y, denoted x < y; temporal
location of an entity z at some time location x, denoted at(z,x).
Basing on the above we introduce the notion of Presential - an entity existing at
exactly one time point and as such immutable. The term “presential” indicates the fact
that presentials exist fully in the presence, which has no temporal extension, hence,
happens at a time-point.
Pres(x) ↔df ∃ !y (TimePoint(y) ∧ at(x,y) (1)
Presentials are contrasted with Time Extended Entities, which we understand as
entities that exist at/over a time period.
TimeExtEntity(x) ↔df ∃ ! y (TimePeriod(y) ∧ at(x,y)) (2)
A snapshot relation, denoted snapshot(x,y), is gluing together presentials with time
extended entities in a sense that presentials are snapshots of time extended entities - for
each presential there exists a time extended entity which the presential is a snapshot of.
Clearly, the space of possible temporal locations of a snapshot is limited to the
elements of the temporal location of the entity it is a snapshot of, i.e. if x is snapshot of
y, then the time point of x is an element of time interval of y. The following axioms
specify the interplay between time extended entities and presentials.
∀ x,y (snapshot(x,y) → Pres(x) ∧ TimeExtEntity(y)) (3)
∀ x (Pres(x) → ∃ ! y (TimeExtEntity(y) ∧ snapshot(x,y))) (4)
∀ x,y (snapshot(x,y) → ∃ v,w (at(x,v) ∧ at(y,w) ∧ v ∈ w )) (5)
Having the above in place we focus now on analysing the content of a single cell
tracking observation. The objects identified at each observation are typically cells
considered as entities present at a time of observation. The time of observation is
considered as temporal point. In this sense, we may classify the elements of the
observation as Presential Cells and denote them PresCell(x). Cells, denoted Cell(x), in
contrast to presential cells, are not temporally flat objects, but instead are the entities
extended in time and as such having a life time. This is the first fundamental explicit
ontological distinction made in the CTO, which, if left implicit, leads to ambiguity of
the notion of cell in context of cell tracking experiments. Now, having the presential
cells identified we may detect cells with the help of the following formula.
∀ x (PresCell(x) → ∃ y (Cell(y) ∧ snapshot(x,y))) (6)
4. Objects and Situations: Cells, Divisions and Cellular Genealogies
The second distinction applied to the CTO is made between Objects, denoted Obj(x),
and Situations, denoted Sit(x). The notion of object is broadly used, yet it imposes some
ambiguity. In context of ontology engineering (and especially in context of the
discussion between 3D and 4D approaches) the object is considered as a mutable entity
that persists in time. In this sense objects are contrasted mainly to processes which
usually in 3D ontologies are understood as entities that depend on objects. The relation,
connecting both is a kind of participation, i.e. objects can participate in processes. In
contrast, in object-oriented software engineering an object is a basic unit of code and in
this sense its understanding is very broad - consequently every element of a domain,
including processes, is represented as an object. However, some approaches to domain
modelling with object-oriented paradigm provide a more detailed classification of
objects. For instance, the Domain Driven Design [12] distinguishes between mutable
objects, having a sort of conceptual identity, called Entities, and Aggregates combining
one or more Entities into wholes.
The above two paradigms share some common intuitions. First, in both objects
have some sort of conceptual identity and, secondly, they can be organized into bigger,
more complex structures which are still perceived as wholes. Basing on this intuitions
we distinguish Objects from Situations. It is out of scope of the current paper to discuss
the notion of identity, which has a rich literature in context of ontology engineering,
(among others [13]). In our approach, as soon as we can identify an entity (by whatever
rules and means) it becomes a candidate for being classified as an object and since in
the CTO we are dealing only with observable physical objects the identification is
made simply by visual detection.
Following the GFO we understand situations as special configurations, which can
be comprehended as wholes and which satisfy certain conditions of unity. Situations
are built upon individualized relations connecting objects - we say that objects
participate in situations, which essentially are aggregating objects into comprehensible
wholes. For every situation S there exists an object participating in S. Under this
interpretation even a single object Obj can be considered as a situation, since Obj can
be represented/understood as a whole, which is composed of individual
properties/qualities, which are connected by the inherence relation. In the ontology of
Tegtmeier [14] situations (called by him state of affairs) are the basic entities and all
other entities (object, processes etc.) are special cases of state of affairs.
∀ x,y (participates_in(x,y) → Obj(x) ∧ Sit(y)) (7)
∀ x (Sit(x) → ∃ y (Obj(y) ∧ participates_in(y,x))) (8)
The distinction drawn between objects and situations does not impose any
temporal characteristics of those entities. In this approach both objects and situations
can be located at time points or time periods. That means we may, in the first place,
speak about Presential Objects and Presential Situations and define them as follows:
PresObj(x) ↔df Pres(x) ∧ Obj(x) (9)
PresSit(x) ↔df Pres(x) ∧ Sit(x) (10)
Since a situation is meant to be an aggregate of some objects which posses some
sort of unity, it cannot exist temporally detached from its participants and therefore it
must be present at the same time on which they are present. For presentials that means
that both a situation and its participant must be located at the same time point:
∀ x,y (PresSit(x) ∧ participates_in(y,x) → PresObj(y) ∧
∃ z ( at(x,z) ∧ at(y,z))) (11)
The distinction between objects and situations can be applied to time extended
entities as well. In this case we introduce two additional types of entities - Continuant
and Temporal Situation. The former is a broadly used and discussed concept, here we
understand it by following GFO: “Continuants persist through time and have a
lifetime; they correspond to ordinary objects, as cars, balls, trees etc. The lifetime of a
continuant is presented by a time interval of non-zero duration”[8].
Cont(x) ↔df TimeExtEntity(x) ∧ Obj(x) (12)
In turn, a temporally extended situation (or temporal situation) is a system which
can be comprehended as a whole and which consists of participating continuants
(objects).
TempSit(x) ↔df TimeExtEntity(x) ∧ Sit(x) (13)
Analogously as in case of presentials, a temporal situation must not be temporally
detached from its participants, otherwise one could not speak about participation and a
situation forming a comprehensive whole over its participants. However, in contrast to
presentials, that condition is not simply reduced to having equal temporal extensions.
For instance, an object can participate in many situations, yet it does not mean that its
lifetime must be limited to the duration of the situations (as many of them can be much
shorter). On the other hand, a situation can have a duration, which exceeds the lifetime
of an object which participate (partially) into it. In this sense one could say that an
object participates in a (temporal) part of situation. The ontological analysis of that
interplay is the topic exceeding the scope of the current paper. Here we take a generic
approach, in which we enforce some sort of co-occurrence between situation and its
participant. That means that their temporal extensions somehow overlap at least at a
single time point.
∀ x,y,v,w (TempSit(y) ∧ participates_in(x,y) ∧ at(x,v) ∧ at(y,w) →
∃ z (z ∈ v ∧ z ∈ w )) (14)
Having the above in place, we may introduce the notion of Cellular Division,
which is a well grounded concept in biology, understood as a process transforming a
mother cell into two daughter cells. We may specify cell division as a temporal
situation, in which there are exactly three participants i.e. one mother cell and two
daughter cells. We identify those two different types of participants by means of
specific participation relations: participates_as_mother(x,y) → participates_in(x,y),
and participates_as_daughter(x,y) → participates_in(x,y). The two relations enable
the introduction of the direct link between a mother and daughter cells.
∀ x (CellDivision(x) → ∃ y,v,w (Cell(y) ∧ Cell(v) ∧ Cell(w) ∧
participates_as_mother(y,x) ∧ participates_as_daughter(v,x) ∧
participates_as_daughter(w,x) ∧ y ≠ v ∧ y ≠ w ∧ v ≠ w )) (15)
∀ x,y,v,w (CellDivision(x) ∧ Cell(y) ∧ Cell(v) ∧ Cell(w) ∧
participates_as_mother(y,x) ∧ participates_as_daughter(v,x) ∧
participates_as_daughter(w,x) →
parent_cell(y,v) ∧ parent_cell(y,w)) (16)
Cell tracking data sets usually do not contain information on cell division, however
this information can be reconstructed from observations of presential cells, e.g. basing
on morphological characteristics of observed cells. That way the presential snapshot of
a cell division, called Presential Cell Division considered as presential situation, can be
detected. Since observations contain always information on presential objects the
presential division never links both mother and daughter participants as they never co-
exist at the same time point. Instead, a presential division can be detected on a frame
where either a mother or daughter cells are present.
∀ x (PresCellDivision(x) → ∃ y (PresCell(y) ∧
participates_as_mother(y,x) ∨ participates_as_daughter(y,x))) (17)
Next, a temporal cell division can be reconstructed from presential cell division
similarly as a cell has been reconstructed from presential cells:
∀ x (PresCellDivision(x) → ∃ y (CellDivision(y) ∧ snapshot(x,y))) (18)
Finally, cells and their divisions can be organized into Cellular Genealogies,
denoted CellGen(x). Cellular genealogy is interpreted as a situation, in which
continuant cells and division situations that link those cells participate. It always has a
structure having exactly one root and an arbitrary number of leaf cells. In cellular
genealogy the root of the tree represents the founder cell and its progeny is arranged in
the branches of the tree. Each branching represents a cell division.
∀ x (CellGen(x) → ∃ ! v ∃ w (root_cell(v,x) ∧ leaf_cell(w,x))) (19)
∀ x,y (root_cell(x,y) → ∃ z (particp(z,y) ∧ parent_cell(z,x))) (20)
∀ x,y (leaf_cell(x,y) → ∃ z (particp(z,y) ∧ parent_cell(x,z))) (21)
Cellular genealogies can be enriched by annotating additional properties measured
during the experiments such as e.g. number of cell generations or shape of the tree. It
also supports advanced queries such as e.g. returning undifferentiated cells whose
second generation descendants were differentiated and underwent apoptosis. However,
some aspects of a cell, such as shape or cell state defined by gene expression profiles
can be only attributed to the presential interpretation of a cell, whereas other attributes
are only well-defined for a time-extended object (e.g. motion characteristics, changes
of gene expressions).
5. Conclusions, Applications and Future Work
The current paper discusses the main ontological categories underlying the Cell
Tracking Ontology - an ontology designed for annotating, sharing and querying cell
tracking experiment results. As discussed in [7] the Cell Tracking Ontology allows for
analysis of tracking results based on the underlying model of cellular genealogies,
which links the raw experimental data (i.e. presential cell measurements) and builds an
expressive knowledge structure out of it. To achieve this, our model itself has a
minimal ontological commitment with respect to the number of its elements. The main
ontological distinctions underlying the CTO are: (1) presentials vs time extended
entities, (2) objects vs situations. Basing on the above four concepts all the main
components of the CTO are introduced: cells, divisions and cellular genealogies.
Additionally, the ambiguity of cells understood either as time extended entities or as
objects observed at time points is solved by explicit separation of cells as presentials
from cells as time extended entities.
The current paper neglects one additional but important aspect of the CTO, namely
the concept of property applicable to all of the mentioned above components of the
model. This is a crucial aspect necessary for real life applications of the CTO and
should be a subject of further research. Another vector of extending the core model of
the CTO is the introduction of interactions between cells that go beyond the “family
relationships” captured in the genealogies such as, for instance, cell-cell contact.
In the long run, the integration of the CTO with existing tools for live cell
microscopy [6, 15-18] can dramatically shorten the path from the cell tracking
experiment to the analysis of its results. Currently, we are working on tools, which can
automatically annotate raw data sets with CTO. That is a step towards the ultimate
goal, which is to support automated generation of annotated data on cells and cellular
genealogies directly out of raw movies without the assistance of a user.
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