Dynamic Modeling of Hemato-poietic Stem Cell Organization – Design … · IMISE-REPORTS...

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Herausgegeben von Professor Dr. Markus Löffler ISSN 1610-7233

Ingo Röder

Dynamic Modeling of Hemato-poietic Stem Cell Organization – Design and Validation of the New Concept of Within-Tissue Plasticity Dissertation

IMISE-REPORT Nr. 1/2005

Medizinische Fakultät

Impressum Herausgeber: Prof. Dr. Markus Löffler Redakteur: Ingo Röder Institut für Medizinische Informatik, Statistik und Epidemiologie (IMISE) Härtelstraße 16-18, 04107 Leipzig Tel.: (0341) 97-16100, Fax: (0341) 97-16109 Internet: http://www.imise.uni-leipzig.de Druck des Einbands und Bindung: Buch- und Offsetdruckerei Herbert Kirsten Redaktionsschluss: Juli 2003 © IMISE 2007 Alle Rechte vorbehalten. Nachdruck nur mit ausdrücklicher Genehmigung des Herausgebers und mit Quellenangabe gestattet. ISSN 1610-7233

Dynamical Modeling of Hematopoietic Stem Cell Organization

– Design and Validation of the New Concept of

Within-Tissue Plasticity

Ingo Röder

Dissertation

Dynamical Modeling of

Hematopoietic Stem Cell Organization

–Design and Validation of the New Concept of

Within-Tissue Plasticity

Dissertation

zur Erlangung des akademischen Grades

Dr. rer. med.

an der Medizinischen Fakultät

der Universiẗat Leipzig

eingereicht von:

Dipl.-Math. Ingo R öder

geboren am 20. Juli 1967 in Dresden

angefertigt am:

Institut für Medizinische Informatik, Statistik und Epidemiologie

Universität Leipzig

Betreuer:

Prof. Dr. Markus Löffler

Beschluss ¨uber die Verleihung des Doktorgrades vom 16. Juli 2003

1. Gutachter: Prof. Dr. med. Markus L¨offler (Universität Leipzig)

2. Gutachter: Prof. Dr. rer. nat. Wolfgang Alt (Universit¨at Bonn)

3. Gutachter: Prof. Gary Van Zant, PhD (University of Kentucky)

Bibliographische Beschreibung

Röder, Ingo

Dynamische Modellierung hämatopoetischer Stammzellorganisation –

Entwurf und Validierung des neuartigen Konzepts der gewebsinternen Plastizität

(Dynamical modeling of hematopoietic stem cell organization –

Design and validation of the new concept of within-tissue plasticity)

Universität Leipzig, Dissertation

140 Seiten1, 146 Literaturangaben, 51 Abbildungen, 7 Tabellen

Referat:

In der vorliegenden Arbeit wird ein neues, umfassendes Konzept der Stammzellorga-

nisation im hämatopoetischen System vorgestellt. Dieses beschreibt dasStammzell-

potenzial, nicht wie in bisherigen Ansätzen, als eine explizit zelluläre Eigenschaft,

sondern als das Resultat eines dynamischen Selbstorganisationsprozesses.

Kernbestandteil des neuen Konzepts ist die Annahme, dass individuelle Zellen ihr

Repertoire möglicher Funktionalitäten, in Abhängigkeit von Einflüssen ihrer lokalen

Wachstumsumgebung, unterschiedlich nutzen. Zelluläre Eigenschaften können inner-

halb einer Menge von möglichen Optionen reversibel verändert werden. Diese po-

tenzielle Reversibilität wird alsgewebsspezifische Plastizität (within-tissue plasticity)

bezeichnet.

Die Überführung dieses Konzepts in ein mathematisches Modell ermöglicht eine Ana-

lyse mit Hilfe von Computersimulationen. Basierend auf zwei unterschiedlichen ma-

thematischen Repräsentationen, werden die Modellannahmen anhand von Vergleichen

der Simulationsergebnisse mit experimentellen Resultaten validiert.

Es wird gezeigt, dass das vorgestellte dynamische Modell alle Kriterien der funktio-

nalen Definition von Gewebsstammzellen erfüllt und gleichzeitig in der Lage ist, eine

konsistente Erklärung für viele experimentell und klinisch beobachtbare Phänomene

zu liefern.

1inklusive Zusammenfassung, Literaturverzeichnis und Appendix

Danksagung

Die vorliegende Arbeit wurde am Institut für Medizinische Informatik, Statistik und

Epidemiologie der Universität Leipzig unter der Betreuung von Herrn Prof. Dr. Markus

Löffler angefertigt, dem ich hiermit für die Überlassung des Themas sowie für die

freundschaftliche und engagierte Begleitung und Unterstützung ganz herzlich danke.

Des weiteren möchte ich mich bei Herrn Prof. Dr. Wolfgang Alt, Frau Dr. Angela

Stevens und Herrn Dr. Dirk Drasdo für ihre Hinweise und methodischen Ratschläge

zur mathematischen Modellierung bedanken.

Herrn Dr. Gerald de Haan, Herrn Prof. Dr. Albrecht Müller sowie Frau Prof. Dr.

Christa Müller-Sieburg danke ich für die konstruktiven Diskussionen und Erklärungen

bezüglich der biologischen Grundlagen und der experimentellen Methodik.

Herrn Dipl.-Informatiker Frank Meineke danke ich für seine Unterstützung bei der

programmiertechnischen Umsetzung des Modells.

Ebenfalls gilt mein Dank Herrn Dr. Allen Jackway, der es als fachfremder Mutter-

sprachler auf sich nahm, diese Arbeit hinsichtlich ihrer englischen Stilistik und Kor-

rektheit zu prüfen.

Bei Herrn Prof. Dr. Holger Dette möchte ich mich bedanken, dass er mich als erster

an das wissenschaftliche Arbeiten herangeführt und meine Leidenschaft dafür geweckt

hat.

Ich danke meinen Eltern, Gisela und Dr.-Ing. Fritz Röder, für ihre vielfältige Un-

terstützung.

Ein ganz besonderer Dank gilt meiner Frau, Annette Röder. Da sie mich von vielen

anderen familiären Aufgaben entlastete, trug sie entscheidend zum erfolgreichen Ab-

schluss dieser Arbeit bei.

Nicht zuletzt möchte ich mich an dieser Stelle auch bei meinen Kindern, Tara Helene,

Anselm Tim und Lina Augustine dafür entschuldigen, dass ich manchmal weniger Zeit

als gewünscht für sie aufbringen konnte.

Simple interactions can have consequences that are notpredictable by intuition based on biological experience alone.

Einfache Interaktionen können Konsequenzen haben, welchenicht durch alleinige, auf biologischer Erfahrung

beruhende Intuition, vorhersagbar sind.

Lee A. Segel, (1980). ed.

Mathematical Models in Molecular and Cellular Biology,

Cambridge University Press, Cambridge, England

Contents

1 Motivation and objective 1

1.1 Motivation . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objective . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Biological background 8

2.1 Stem cell systems . .. . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 The hematopoietic system .. . . . . . . . . . . . . . . . . . . . . . 10

2.3 Measuring methods and assay techniques. . . . . . . . . . . . . . . 13

2.3.1 Hematopoietic stem cell markers .. . . . . . . . . . . . . . . 13

2.3.2 Hematopoietic stem cell assays .. . . . . . . . . . . . . . . 14

2.3.3 Cell kinetic assays .. . . . . . . . . . . . . . . . . . . . . . 17

2.4 Observed phenomena. . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.1 Heterogeneity. . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.2 Microenvironmental dependence .. . . . . . . . . . . . . . . 19

2.4.3 Clonal fluctuation and competition. . . . . . . . . . . . . . . 19

2.4.4 Disturbances and regeneration . .. . . . . . . . . . . . . . . 20

3 Theoretical background 22

3.1 Biological concepts .. . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.1 Symmetric / asymmetric cell division . . . . .. . . . . . . . 22

3.1.2 Stem cell hierarchy .. . . . . . . . . . . . . . . . . . . . . . 24

3.1.3 Niche concept. . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.4 Screw model. . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.5 Clonal succession . .. . . . . . . . . . . . . . . . . . . . . . 26

3.1.6 Regulated proliferation and self-renewal . . . .. . . . . . . . 27

3.2 Mathematical models. . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Differential equation models . . .. . . . . . . . . . . . . . . 28

i

CONTENTS ii

3.2.2 Stochastic single cell based models . . . . . .. . . . . . . . 29

3.2.3 Cellular automaton models . . . .. . . . . . . . . . . . . . . 30

4 Model description 32

4.1 General model assumptions .. . . . . . . . . . . . . . . . . . . . . . 33

4.2 Mathematical representation. . . . . . . . . . . . . . . . . . . . . . 40

4.2.1 Cellular properties .. . . . . . . . . . . . . . . . . . . . . . 40

4.2.2 Transition between growth-environments . . .. . . . . . . . 41

4.2.3 Development within growth-environments . . .. . . . . . . . 43

4.2.4 Simulation procedure. . . . . . . . . . . . . . . . . . . . . . 44

5 Simulation results 46

5.1 General model behavior . . .. . . . . . . . . . . . . . . . . . . . . . 46

5.1.1 Dependence on� and� . . . . . . . . . . . . . . . . . . . . . 46

5.1.2 Dependence on�� . . . . . . . . . . . . . . . . . . . . . . . . 48

5.1.3 Dependence on�� and�� . . . . . . . . . . . . . . . . . . . 49

5.1.4 Dependence on�� and�� . . . . . . . . . . . . . . . . . 55

5.1.5 Dependence on initial conditions .. . . . . . . . . . . . . . . 55

5.1.6 Parameter choice . .. . . . . . . . . . . . . . . . . . . . . . 57

5.2 Heterogeneity . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2.1 Cellular model properties . . . . .. . . . . . . . . . . . . . . 59

5.2.2 Clonogenic potential. . . . . . . . . . . . . . . . . . . . . . 65

5.2.3 Repopulating potential . . . . . .. . . . . . . . . . . . . . . 68

5.2.4 Cycling activity . . .. . . . . . . . . . . . . . . . . . . . . . 70

5.3 Microenvironmental influence . . . . . .. . . . . . . . . . . . . . . 71

5.4 Clonal fluctuation and competition . . . .. . . . . . . . . . . . . . . 72

5.4.1 Cell populations with identical properties . . .. . . . . . . . 72

5.4.2 Cell populations with different properties . . .. . . . . . . . 75

5.4.3 Fluctuations and competition on the single cell level . . . . . 77

5.5 Disturbances and regeneration . . . . . .. . . . . . . . . . . . . . . 81

5.5.1 Regeneration from acute cell kill .. . . . . . . . . . . . . . . 81

5.5.2 Continuous cell kill .. . . . . . . . . . . . . . . . . . . . . . 84

6 Differential equation approach 86

6.1 The uncoupled system . . .. . . . . . . . . . . . . . . . . . . . . . 87

6.1.1 Derivation of the model equations. . . . . . . . . . . . . . . 87

CONTENTS iii

6.1.2 Solutions of the model equations .. . . . . . . . . . . . . . . 90

6.2 The complete system. . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.2.1 Derivation of the model equations. . . . . . . . . . . . . . . 93

6.2.2 Solutions of the model equations .. . . . . . . . . . . . . . . 94

6.3 Numerical results . .. . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.3.1 Stable systems . . .. . . . . . . . . . . . . . . . . . . . . . 98

6.3.2 System disturbances. . . . . . . . . . . . . . . . . . . . . . 99

6.3.3 Cycling systems . .. . . . . . . . . . . . . . . . . . . . . . 101

6.3.4 Exhausting systems .. . . . . . . . . . . . . . . . . . . . . . 102

6.3.5 Unstable systems . .. . . . . . . . . . . . . . . . . . . . . . 102

7 Discussion 105

7.1 Conclusions and biological implications .. . . . . . . . . . . . . . . 105

7.1.1 Change of the stem cell paradigm. . . . . . . . . . . . . . . 106

7.1.2 Definition of tissue stem cells . .. . . . . . . . . . . . . . . 108

7.1.3 Compatibility with experimental results and model predictions 109

7.2 Relation to previous stem cell models . .. . . . . . . . . . . . . . . 113

7.3 Comparision of PDE and Monte-Carlo approach . . . .. . . . . . . . 114

7.4 Limitations . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8 Summary 120

A Computer implementation 137

A.1 Parameter file . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 138

A.2 Control sequence file. . . . . . . . . . . . . . . . . . . . . . . . . . 138

B Specific mathematical abbreviations 140

Chapter 1

Motivation and objective

1.1 Motivation

Stem cells play a prominent role in biology and life sciences. Not only in basic research

fields such as cell or developmental biology, but also in medicine and clinical research

their importance is growing more and more. The main reason underlying this broad

interest in stem cells is their capacity to reconstitute functional tissues after disturbance

or injury. They are able to produce a huge number of differentiated, functional cells

and, at the same time, they maintain or even re-establish their own population.

This functionality makes them target-cells for many therapeutic approaches. One

example is gene-therapy where a genetic deficiency of a (regenerative) tissue is aimed

to be corrected by the transplantation of few genetically manipulated cells [Dunbar,

1996; Dick, 2000]. For the success of such a strategy it is necessary that these ma-

nipulated cells, firstly, engraft to the recipient tissue and, secondly, contribute to the

production of functional cells over a long time. Therefore, it is clear that these manip-

ulated cells have to generate and maintain a cell population which is able to coexist

with or to replace the deficient cells.

A second example of stem cell use is the treatment of clonal disorders, such as

leukemia [Champlin et al., 1988; Carella et al., 1997; Shimoni et al., 2000]. At the

moment bone marrow or (mobilized) stem cell transplantation is the only potentially

curative treatment for various forms of leukemia. Depending on the actual circum-

stances the patient will mostly receive a transplant of cells from a healthy related or

unrelated donor after a pre-treatment by chemotherapy or irradiation. These donor

cells are expected to completely overtake the production of functional hematopoietic

cells.

1

CHAPTER 1. MOTIVATION AND OBJECTIVE 2

The third and last example of the broad application spectrum of stem cells given

here is their potential use for therapeutic cloning of organs or tissues [Colman and

Kind, 2000; Chang, 2001]. It has been shown that some very primitive, pluripotent

stem cells, which can be found in embryonic tissues, are able to differentiate into a

pre-specified tissue type if specifically treated in culture [Doetschman et al., 1985;

Schuldiner et al., 2000; Yamashita et al., 2000]. This ability has raised the hope to be

able to grow whole organs or tissue complexes for transplantation purposesin vitro.

Moreover, in the last few years it has been shown that tissue stem cells which have

already been committed to a specific tissue (e.g. hematopoietic or neuronal stem cells)

are much more flexible than previously thought. There seems to be evidence that these

cells can be redirected in their developmental direction. It has been demonstrated that

hematopoietic cells can contribute to the production of neuronal cells and vice versa.

The same holds for hematopoietic and muscle cells, and there are more of these “tissue

switching” phenomena [Mertelsmann, 2000; Goodell et al., 2001].

To avoid misunderstandings and confusion, one should point out that there are two

general classes of stem cells which have to be distinguished: the so calledembryonic

stem cells (ESC) and the somatictissue stem cells (TSC). These two classes differ

largely in their properties. Section 2.1 will briefly discuss the most important differ-

ences and similarities of these two general classes. The focus of this thesis, however,

is the theoretical investigation of one particular type of somatic tissue stem cells, the

hematopoietic stem cell (HSC). Biological specificities of the hematopoietic system

will be introduced in section 2.2.

After referring to the great therapeutic potential of stem cells in general, the ques-

tion arises, how these specific cells can be separated from other, less potential, cells.

Because embryonic stem cells are derived from a small and well characterized cell

population of the inner cell mass of the blastocyst [Evans and Kaufman, 1981; Martin,

1981; Thomson et al., 1998], their separation is straightforward. The problem is that

an early embryo needs to be sacrificed to extract these cells as the source for culturing

ESC. Especially in the human situation this causes serious ethical questions [McKay,

2000; Wolfrum, 2001]. In contrast, hematopoietic stem cells can be found in the bone

marrow or even in the peripheral blood of adult organisms. Besides the unresolved

question whether TSC are equally potent as ESC there is a further major problem.

These stem cells cannot be distinguished from other primitive, non-differentiated cell

types morphologically.

Many efforts in using specific phenotypic markers (see section 2.3.1) have been


made to identify hematopoietic stem cells. Although correlations of these markers with

the ability for long-term repopulation could be demonstrated [Uchida et al., 1996],

there is presently no way to determine for a given cell whether it is a stem cell and

which developmental potential it will have prospectively. One reason for this is the

huge range of different markers and marker combinations which characterize the ac-

tual status of the cells. It is likely that different marker combinations are linked to

similar properties (redundancy) or that identical marker combinations characterize dif-

ferent potentials under e.g. different environmental influences (pleiotropy). It is highly

questionable whether there exists a single marker pattern uniquely characterizing HSC.

Another problem in the use of phenotypic markers is the fact that these are generally

not stable. Many phenotypic properties, currently used as stem cell markers, show

reversible changes (e.g.�� [Sato et al., 1999]). Because of this phenotypic

plasticity it is impossible to make a definite statement about the future potentiality of

a certain cell solely on the basis of its actual marker status.

Besides the use of specific markers, HSC are also characterized by several kinds

of assays systems (see section 2.3.2), which check specific functionalities and future

potentials of the cells. For example, colony-forming assays demonstrate the poten-

tial of the cells to form colonies of differentiated cells. But this is only one facet of

stem cell potentiality. The only way to demonstrate the stem cell character of a cell

is the use ofin vivo systems which check the ability of transplanted candidate cells

to repopulate depleted hosts. But even thesein vivo assays are not able to answer the

frequently posed question: “Isthis cell a stem cell?”. Such a question implies the idea

that one can decide about the capabilities of a given cell without relating it to other

cells and without testing the capabilities functionally. However, the main attributes of

stem cells relate to their potential in the future and can only be studied by placing the

considered cells in a situation where they have the opportunity to express their poten-

tial (e.g. an appropriate assay system). In doing so, one alters the circumstances and

inevitably loses the original cell. This situation is similar to Heisenberg’s uncertainty

principle in quantum physics [Heisenberg, 1927], which says that the act of measur-

ing the properties of a certain system inevitably changes its characteristics. Therefore,

the measuring process itself introduces an uncertainty in the evaluation of the system

properties. The analogy of this principle in the analysis of tissue stem cells assays has

been extensively discussed elsewhere [Potten and Loeffler, 1990; Loeffler and Potten,

1997; Loeffler and Roeder, 2002]. It implies that it is not possible to make a defini-

tive statement about whether or not a given cell will act as a tissue stem cell. All


statements about a cell under consideration will necessarily be probabilistic statements

about its future behavior under particular conditions. These remarks make clear, that

it is essential to incorporate the experimental procedure, i.e. the assay and sampling

techniques, into the investigation of tissue stem cell organization. Otherwise, there is

the danger that confounding effects of the measuring process could be interpreted as

intrinsic features of the stem cells.

Compared to the extensive experimental effort, only very little theoretical work

has been done in the field of tissue stem cells research so far. However, the more

it becomes obvious that it is a misleading expectation to be able to determine tissue

stem cells directly by a specific marker or assay procedure, one realizes the need for

theoretical concepts (see also [Loeffler and Roeder, 2002]).

The application of predictive quantitative theories and simulation models has sev-

eral advantages. They are important tools for the discovery of generic rules and con-

struction principles of different stem cell systems and they help to understand how

common mechanisms of regulation and organization are biologically implemented in a

specific system such as hematopoiesis. Furthermore, theoretical models are necessary

to understand the complex molecular networks underlying the macroscopically ob-

servable phenomena. For example, recent experimental insights into gene expression,

transcription factor activation, and signal transduction [Heyworth et al., 1999; Zhang

et al., 1999; Brandon et al., 2000] demonstrate the high number of potentially involved

genes. These numbers together with the universe of interactions among them make

it clear that the resulting regulation network is too complex to be decoded without a

theoretically supported simplification. Another point is the ability of theoretical mod-

els to explain and link a variety of observed phenomena and reveal how far different

experimental results are consistent with one another or with hypothesized underlying

mechanisms. Moreover, they are able to highlight and isolate misleading experimental

results (e.g. confounding of stem cell functionality with assay effect) and to generate

new, experimentally testable hypotheses. Not only in basic stem cell research, but also

in clinical situations, the use of theoretical concepts and simulation models of tissue

stem cell organization might be relevant. One promising example is the model based

or supported design of new treatment strategies for hematological disorders. Here, a

theoretical analysis can serve to optimize treatment effects and to minimize potential

risks [Loeffler et al., 1998].

A description of some important theoretical concepts and mathematical models,

which have been applied to processes of tissue stem cell organization in the past, will


be given in chapter 3. Most of them rely on the classical assumption that tissue stem

cells are predetermined entities with fixed, stem cell specific properties (e.g. the abil-

ity of self-maintaining, asymmetric cell division) which are gradually lost during the

process of differentiation. This irreversible loss of functionalities implies a strict one-

directional hierarchy of the stem cell systems.

However, as already mentioned above, recent experimental results demonstrate the

potential of somatic stem cells to change their tissue-specific differentiation program.

One of the first experiments, reporting this, so calledtissue (or stem cell) plasticity,

has been published by Bjornson et al. [1999]. This group observed the contribution

of neuronal cells to hematopoietic tissue formation when these cells are placed into a

bone marrow environment. Meanwhile, many other such tissue plasticity phenomena

involving hematopoietic, neuronal, muscle, or liver cells have been reported [Brazelton

et al., 2000; Seale and Rudnicki, 2000; Goodell et al., 2001].

Furthermore, evidence has been accumulating that also within a tissue, gene- and

marker-expression can be reverted and redirected. In the murine system, lineage re-

stricted properties have been shown to be reversible (e.g. for B-lymphocyte precursors

by knocking out the Pax5-gene [Rolink et al., 1999]), and gene-expression pattern can

be switched from adult to embryonic type and vice versa by changing the environmen-

tal context of the cells [Geiger et al., 1998]. Furthermore, phenotypic traits, such as the

expression of the transmembran glycoprotein CD34 [Goodell, 1999; Sato et al., 1999],

the adhesion protein expression, and the engraftment/homing behavior show reversible

changes [Habibian et al., 1998; Frimberger et al., 2001]. Even the long-term reconsti-

tuting ability seems to vary reversibly depending on the actual cell cycle position of

the cell [Quesenberry et al., 2001]. This remarkable plasticity potential is clearly not

consistent with the classical view of an one-directional, predetermined differentiation

hierarchy.

Besides this reversibility of stem cell characteristics, there is a variety of other ex-

perimental findings and observed phenomena, including heterogeneity of the stem cell

population, microenvironmental influences, stem cell – stroma interactions, or clonal

fluctuation phenomena (see section 2.4), which lack a comprehensive and conclusive

explanation. None of the classical concepts of tissue stem cell organization is able to

cover the whole range of observed phenomena.


1.2 Objective

As argued in the last section, there is the need for a new theoretical framework of

the organization of tissue stem cells in general and for hematopoietic stem cells in

particular. It is the objective of this thesis to develop and validate a new theoretical

model of hematopoietic stem cell organization, focusing on regulation processes of

self-renewal and repopulating ability.

To overcome the deficiencies of the classical concepts, such a theory has to meet

several criteria. It shall account for the realization that tissue stem cells are no fixed

entities with a predetermined developmental fate. Therefore, it will be necessary to

abandon the classical paradigm of a prespecified, one-directional differentiation hi-

erarchy within the population of hematopoietic stem cells. The new perspective on

stem cell systems as networks of different cell types and their interactions implies that

stemness should not be treated as an explicit cellular property, but as the result of a dy-

namic self-organization process. Stem cell – microenvironment interactions and their

specific effects on proliferation and differentiation have to be embedded in the concept.

Furthermore, the model has to consistently explain the broad variety of experimental

observations, as there are cell kinetic heterogeneity, microenvironmental dependence

of reconstituting ability, clonal fluctuation and competition, plasticity of cellular prop-

erties within one tissue, and regeneration after disturbances. It is intended to link these

macroscopic phenomena to underlying (latent) microscopic mechanisms. To include

experimental observations which describe individual cell and clone1 behavior into the

analysis, the model shall be able to describe single cell as well as cell population be-

havior. In addition to these requirements, the model has to fulfill the criteria of the

functional definition of tissue stem cells (see table 2.1 below).

To be able to investigate general system properties of such a concept and to ob-

tain experimentally testable predictions, it is necessary to translate the concept into a

mathematical representation. This will be done using a single cell based, stochastic

Monte-Carlo approach. To perform simulation studies, this mathematical representa-

tion has to be implemented in a computer program. Fitting of model parameters and

validation of model assumptions will be realized by the comparison of simulation re-

sults with experimental data. In order to detect confounding effects of experimental

procedures, and to be able to compare simulations directly to experimental results,

also the measuring and sampling process has to be incorporated into the simulation

1progeny of one specific, individual cell


procedure.

Another objective is the investigation of an alternative mathematical approach,

namely the description of the concept by a system of partial differential equations.

There are two major motivations for such a strategy. Firstly, the second mathematical

representation should serve as a consistency check of the established model assump-

tions. Furthermore, the differential equation approach allows a more efficient simu-

lation of the average system behavior compared to a single cell based model. Both

mathematical approaches will be compared with respect to their adequacy to describe

the considered biological problem.

Chapter 2

Biological background

2.1 Stem cell systems

As already mentioned in the introduction, one has to distinguish between two general

classes of stem cells: embryonic stem cells (ESC) and tissue stem cells (TSC). To

clearly illustrate the difference, it is helpful to look at the development of a mammalian

organism (Fig. 2.1).

Maturecells

Progenitorcells

Somaticstem cells

Ectoderm Mesoderm

Blastocyst

MuscleBrain Gut Liver

EndodermBloodSkin

Zygote

Figure 2.1: Simplified illustration of organismal development (after [Wei et al., 2000]). Shownare major developmental steps and some important examples of established tissue systems,each one supplied by a specific type of somatic tissue stem cells. These stem cells produceprogenitor cells, which amplify and differentiate/maturate during several steps within the re-spective tissues to form mature functional cells.

The development starts with a single cell, the zygote. This cell (potentially) gives

8

CHAPTER 2. BIOLOGICAL BACKGROUND 9

rise to a complete organism and could, therefore, be denoted as the ultimate stem cell

of the organism. After a few cell divisions one reaches the early embryonic state of the

blastocyst which comprises about 150 cells in mice and 250 in humans [Kirschstein

and Skirboll, 2001]. The blastocyst represents the embryo prior to implantation in the

uterine wall. It consists of an outer layer (the trophectoderm), a fluid-filled cavity (the

blastocoel), and a cluster of cells in the interior (the inner cell mass). From this inner

cell mass, which is composed of about 30 cells (in human) [Kirschstein and Skirboll,

2001], one can derive the embryonic stem cells by culturing these cells under specific

conditions [Evans and Kaufman, 1981; Martin, 1981; Thomson et al., 1998].

These embryonic stem cells arepluripotent in nature, i.e. they are able to give

rise to all tissues of an embryo. However, they lack the capacity to form a complete

new organism [Reubinoff et al., 2000; Odorico et al., 2001]. Furthermore, embryonic

stem cells can self-maintain their population without differentiation under specific cul-

ture conditions for more than two years undergoing about 300 population doublings

[Odorico et al., 2001]. They seem to represent a transient cell population whose mem-

bers differentiate into different layers, the germ line, the ectoderm (external layer),

the mesoderm (middle layer), and the endoderm (internal layer). Because so far no-

body has been successful in finding truly pluripotent stem cells in an adult organism,

it is unclear whether these are only difficult to detect or if all of them have lost their

pluripotency in the developmental process from an embryo to an adult organism.

From the ectodermal, the mesodermal, and the endodermal layers (see figure 2.1)

different tissues are developing. Various regenerative tissues, e.g. the blood system,

the skin, and the intestine as well as the brain and the spinal cord, are fed by specific

populations of somatic tissue stem cells (TSC). These stem cell populations are self-

maintaining during the whole life of the organism in an unperturbedin vivo situation.

However, the preservation of this self-maintaining ability inin vitro settings seems to

be very problematic for some of these tissues (e.g. the hematopoietic system) [Varas

et al., 1998; Szilvassy et al., 1999].

Another difference between ESC and TSC is their differentiation ability. Whereas

ESC are pluripotent (see above), TSC are classically denoted asmultipotent. That

means, they have a differentiation potential which is restricted to the different lineages

of a pre-specified tissue. For example, it is assumed that hematopoietic stem cells can

give rise to all hematopoietic lineages, but not to other tissues. However, exactly this

assumption about the restricted differentiation potential of TSC has become strongly

debated during the last few years. The recently described plasticity phenomena of TSC


[Bjornson et al., 1999; Goodell et al., 2001] provide strong evidence for their capacity

to change their tissue-specific differentiation program (see also section 1.1).

As already mentioned, in an adult organism different tissues are assumed to be

maintained by their tissue-specific stem cell populations. Although the produced func-

tional cell types differ tremendously (e.g. comparing red blood cells with epithelial

cells in the gut) the general task of all these stem cell types is very similar. They have

to ensure a constant production of (most often) short lived functional cells (i.e. to guar-

antee homeostasis) and, at the same time, to maintain their own population. Potten and

Loeffler [1990] formulated a general definition of tissue stem cells which is based on

their functional attributes. In the light of new insight into the biology of stem cells

regarding heterogeneity, lineage plasticity, clonal fluctuation, and cell – environment

interactions this definition has recently been discussed by Markus L¨offler and myself

[Loeffler and Roeder, 2002]. The conclusion of this work is an amended definition of

tissue stem cells, which is shown in table 2.1.

Stem cells of a particular tissue are

a (potentially heterogeneous) population of functionally undifferentiated cells (C1)

capable of

– homing to an appropriate growth-environment (C2)

– proliferation (C3)

– production of a large number of differentiated progeny (C4)

– self-renewing or self maintaining their population (C5)

– regenerating the functional tissue after injury (C6)

with flexibility and reversibility in the use of these options (C7)

Table 2.1: Definition of tissue stem cells (after [Loeffler and Roeder, 2002]). Criteria labels(C1) - (C7) are given for later referencing.

2.2 The hematopoietic system

The hematopoietic system is responsible for the production and maintenance of all

types of blood and immune cells. This comprises the supply of functional cells of


various different lineages: immune (lymphoid) cells, including B-lymphocytes, T-

lymphocytes, and natural killer cells, white blood cells, among them granulocytes,

monocytes, and macrophages, red blood cells (erythrocytes), and the platelet cells

(thrombocytes). All these cells have only limited life spans ranging from less than

a day for granulocytes, over about 4 months for erythrocytes, to several years for T-

lymphocytes1. Therefore, a source of cell production which is preserved throughout

the entire life of the organism is needed. This source is the population of hematopoi-

etic stem cells (HSC). From these primitive cells over several steps of intermediate

premature cell stages (so called precursor cells) functional blood cells are derived. The

enormous demand for functional blood cells2 is met via a two stage process: the out-

put of precursor and progenitor cells from the HSC population and the amplification

due to proliferation of these premature cells. Figure 2.2 is a structural scheme of the

hematopoietic system clearly showing the classically assumed irreversible hierarchy

[Uchida et al., 1993] of the differentiation status.

Figure 2.2: Hierarchical structure of the hematopoietic system (after [Kirschstein and Skir-boll, 2001]). Direction of arrows indicate the irreversible direction of differentiation towardsfunctional blood cells.

As one specific type of tissue stem cells, the hematopoietic stem cells have to fulfill

the characterization criteria (C1-C7) listed in the general definition of TSC (table 2.1).

This is indeed the case as demonstrated by the following experimental results:

It has been shown experimentally that the population of HSC is heterogeneous

(C1) with respect to a variety of phenotypic, cell kinetic and functional characteris-

1life spans for human cells2daily production in humans: 2 x 10�� erythrocytes, 1.6 x 10� thrombocytes, 10�� granulocytes


tics [Uchida et al., 1993; Hao et al., 1996; Lord, 1997]. In section 2.4 some of these

observations will be discussed more detailed. Besides this heterogeneity, all members

of the HSC population share one common property: none of them expresses lineage-

specific surface markers [Uchida et al., 1993]. This property is used to classify them as

undifferentiated cells (C1) with respect to progenitors (which are already committed

to a specific lineage) and functional end cells. Furthermore, it has been demonstrated

Figure 2.3: Schematic illustration of the stem cell microenvironment in the bone marrow (after[Kirschstein and Skirboll, 2001]).

that HSC need an appropriate microenvironment (C2) to express their specific prolif-

erative and regenerative potential [Schofield, 1978; Wineman et al., 1996; Lemischka,

1997]. This microenvironment is predominantly found in the bone marrow (see figure

2.3). Other important blood production sites are the spleen (especially in mice) or the

liver. In addition, HSC can also be found in the peripheral blood. It seems to be clear

that there is an ongoing mobilization (into the blood stream) and homing (in the bone

marrow) process of HSC [Papayannopoulou and Craddock, 1997; Quesenberry and

Becker, 1998].

The ability of HSC to proliferate (C3), to produce large numbers of differentiated

cells (C4), to self-maintain or self-renew their population (C5), and to fully regener-

ate the hematopoietic system after depletion or injury (C6) can be demonstrated by

several types of repopulation assays (see section 2.3.2). It is possible to reconstitute

the hematopoietic system of (lethally) irradiated mice by the transplantation of bone

marrow cells from a donor mouse [Neben et al., 1991]. It can be shown that after re-

population the entire spectrum of functional blood cells of all lineages is present in the

recipient animal, which demonstrates the characteristics (C4) and (C6). The presence

of HSC in these repopulated animals can be shown by the repopulation of secondary

recipients using bone marrow of the primary recipients [Iscove and Nawa, 1997]. It


has been shown that even the repopulation with very low numbers of HSC can provide

the same result of a fully reconstituted hematopoietic system including normal num-

bers of HSC [Osawa et al., 1996]. This is strong evidence for the capability of HSC to

proliferate (C3), to maintain, and even to self-renew (C5) their own population.

The last point in the definition of TSC highlights the flexibility and reversibility

of HSC in using the above mentioned capabilities (C7). This criterion has attracted

specific attention since the first experiments about stem cell (tissue) plasticity [Bjorn-

son et al., 1999; Brazelton et al., 2000; Seale and Rudnicki, 2000] and about reverting

and redirecting of gene- or marker-expression of cells within one tissue [Geiger et al.,

1998; Rolink et al., 1999; Sato et al., 1999] have emerged.

Whereas a lot is known about the regulation processes of blood production in the

more mature cell stages (e.g. by cytokines [de Haan, 1995; de Haan et al., 1996;

Roeder et al., 1998]), the mechanisms which rule proliferation and differentiation on

the level of HSC are not understood at the moment. It is unclear how stem cells de-

cide whether to differentiate into a more mature cell stage or to keep their primitive

undifferentiated character. Furthermore, if the cells have decided to differentiate there

is the question into which lineage? Also the control mechanisms of these lineage com-

mitment processes are still unknown. However, they will not be in the focus of this

work.

2.3 Measuring methods and assay techniques

2.3.1 Hematopoietic stem cell markers

There is a zoo of different phenotypic markers which are used to separate HSC from

other cell types or at least to enrich cell populations for these HSC. Generally, mon-

oclonal antibodies are used to stain the cells for flow-cytometry (FACS) analysis and

cell sorting. An overview of these methods including a collection of references has

been given e.g. by Neben et al. [1991], Uchida et al. [1993], and Rebel et al. [1996].

In the following, a short selection of a few important markers will be presented.

First of all, HSC should not express lineage-specific markers, such as TER-119 for

erythroid cells, B220 for B cells, Mac-1 for monocytes, Gr-1 for granulocytes, or CD3,

CD4, and CD8 for T cells. If none of these markers can be found, the cells are denoted

as Lineage-negative (��).

A second set of criteria for HSC separation is a low expression of the cell-surface


antigen Thy-1.1 (� �-�� or high expression of the antigen Sca-1 (��-��).

A further sub-classification is sometimes done using the mitochondria binding dye

Rhodamine(��)123 and the DNA-binding dye Hoechst(��)33342. These two fluores-

cence markers subdivide populations of HSC mainly on the basis of their quiescence

status, with the most primitive cells showing a��

��

phenotype.

The surface molecule that binds wheat germ agglutinin (� ��) is also used as a

stem cell marker. Whereas cells with low levels of WGA affinity (� ��) show on

average stable long-term repopulating ability (see below: HSC assays), cells with high

WGA affinity (� ��) only provide short-term repopulation.

Commonly used combinations for the enrichment of HSC are for example

� �-��-�� [Spangrude et al., 1991] or��-��-�� [de Haan

et al., 2000]. The latter one also includes the expression of the stem cell factor (SCF)

receptorc-kit.

Especially for human cells, the cell surface glycoprotein CD34 is routineously

used to separate HSC [Goodell, 1999]. The combination of CD34 positive and CD38

(another glycoprotein) negative cells has been shown to define a subpopulation of

hematopoietic precursors which is highly enriched in primitive HSC expressing long-

term repopulating ability (see 2.3.2).

2.3.2 Hematopoietic stem cell assays

Long-term culture initiating cell (LTC-IC) assay

This in vitro assay establishes conditions which allow a long-term culture of bone

marrow cells. Stromal elements are induced to form an adherent layer in the culture

which serves as an appropriate environment forin vitro hematopoiesis. To ensure that

no endogenous hematopoiesis is confounding the culture, the stromal layer is irradi-

ated before the seeding of bone marrow cells. If the bone marrow contains primitive

hematopoietic cells, these can produce colonies of differentiated cells for 5 to 8 weeks

under these conditions. These primitive cells are therefore called long-term culture

initiating cells (LTC-IC). Frequency estimates of LTC-IC range between 1 and 10 in

�� bone marrow cells [Sutherland et al., 1990; Bertolini et al., 1997; Cho and Muller-

Sieburg, 2000]. Although clonogenic cells from these cultures are not able to compete

with fresh bone marrow for long-term repopulation of irradiated hosts (see competi-

tion assays below) the LTC-IC assay is often used as a practicable measure of primitive

progenitors especially in the human situation [Lord, 1997].


Cobblestone area forming cell (CAFC) assay

The CAFC assay [Ploemacher et al., 1989] is a specific form of a stroma-dependent

bone marrow culture as already described in the LTC-IC setting. In contrast to this

assay, the endpoint is not the colony forming ability as such, but the formation of so

called “cobblestone areas” (CA) beneath the stromal layer. These are visible by light

microscopy. Some of the CA stay beneath the stroma layer for a long time and keep on

growing, others migrate up to the culture surface and become differentiated cell types.

The number of CA is determined at different time points (usually at day 7, 14, 21, 28,

35). Before counting the CA all supernatant cells are washed out from the culture.

This procedure does not disturb the cells beneath the stroma layer. It has been shown

that the time point of CA appearance is correlated with the Rhodamine (��) retention,

and therefore, indirectly with the primitiveness of the cells [Ploemacher et al., 1989].

Colony-forming unit in the spleen (CFU-S) assay

This technique, which is sometimes referred to as the first modern stem cell assay,

was introduced by Till and McCulloch [1961]. Bone marrow cells of a donor mouse

are transplanted into an irradiated recipient. After 10 - 12 days macroscopic colonies

can be found in the spleen of the recipient. These so called colony forming units in

spleen (CFU-S) have been shown to be clonally derived from one cell each. Therefore,

taking into account that only a fraction of all potential CFU-S cells will seed in the

recipient spleen, the assay is used to estimate the number of these clonogenic cells. The

primary spleen colonies themselves contain CFU-S cells, as shown by the generation of

secondary spleen colonies after transplantation of individual primary spleen colonies

into a secondary irradiated hosts (serial CFU-S assay). This fact has been used to proof

the self-renewing potential of these cells. CFU-S cells have, therefore, been denoted

as hematopoietic stem cells for a long time. However, it has been shown [van der Loo

et al., 1994] that CFU-S cells can only achieve short-term repopulation of irradiated

hosts and not a (long-term) regeneration of functional tissue, as required in the stem

cell definition.

Marrow repopulating ability (MRA) assay

This assay is used to demonstrate the repopulation ability of bone marrow cells if trans-

planted into an irradiated recipient [Lord, 1997]. The repopulating ability is shown by

the existence of CFU-S cells in the bone marrow of irradiated animals 13 days af-


ter having received a bone marrow transplant of a normal donor mouse. However, as

already mentioned in the last paragraph, this demonstrates only a short-term repopu-

lating ability and is not a proof of the existence of HSC in the sense of the above given

definition (table 2.1).

Long-term repopulating ability (LTRA) assay

This functional assay is still the hallmark for demonstrating the existence of HSC in

a given cell population [Lord, 1997]. Similar to the MRA assay, an investigated cell

population is transplanted into ablated (e.g. by irradiation) recipients. In contrast to

the former assay, the endpoint is not the CFU-S content after 13 days, but the donor

contribution in all the hematopoietic lineages after 6 or more months. This can be

controlled by the use of differently marked donor and recipients cells, e.g. male donors

and female recipients, using the Y-chromosome as a marker.

If one is interested in the comparison of the repopulating ability of two cell popula-

tions one can use a derivative of the LTRA assay, the so called competition assay. Here,

two populations of distinguishable cell types are transplanted into an ablated host. The

contribution of each of these cell types to the blood cell production of the repopulated

animal is then monitored by the sequential analyses of peripheral blood sampling or

bone marrow biopsies.

Individual clone tracking assay

All the above described assay techniques do investigate the fate of populations of cells,

i.e. they can only detect the existence of cells, inducing e.g. positive CFU-S or LTRA

results. It is not possible to follow the fate of a predefined cell and its progeny. The

possibility of an unique, inheritable labeling of cells by retro- or lenti-viral marking

[Jordan and Lemischka, 1990; Drize et al., 1996] enables the investigator to follow

the fate of the clone founded by the marked cell. To do so, the target cells have to

be infected by the viruses which requires specific culture conditions. Thereafter, these

cells will be transplanted into recipients (see LTRA assay), and finally, the contribution

of the individual clones has to be monitored in these animals over time. This is done

e.g. by the use of blood samples or partial splenectomies. The individual marking

patterns are identified by Polymerase Chain Reaction (PCR) or Southern blot analysis

of the sampled cell populations. Another way of monitoring the contribution of marked

clones is the use of colonies which have been initiated by individual cells obtained from


repeated bone marrow samples. These colonies are analyzed for the clone marking

pattern of the initiating cells, again using PCR or Southern blot analysis. Due to the

fact that the colonies are clonally derived, the marking signal is amplified considerably.

Because PCR and Southern blot have a certain detection threshold it is clear that the

second method, which uses clonally expanded cell populations, is more sensitive to

find the labeling pattern than the first one. However, the individual cells used for

induction of the colonies represent only a very small sample out of the total population.

Therefore, the high sensitivity of detecting the marker in a single cell has to be paid by

a substantial chance of missing long-term contributing clones.

2.3.3 Cell kinetic assays

Hydroxyurea suicide

This assay is used to estimate the proliferative fraction, i.e. the proportion of cells in

DNA-synthesis (S-phase) [de Haan et al., 1997]. To do this, a sample of cells is split

into two groups. To one of these groups one adds a certain dose of Hydroxyurea (HU).

Both groups are then incubated for one hour. After a washing process, a nucleated cell

count is performed. Because Hydroxyurea is incorporated only during S-phase and

because its incorporation causes cell death, it is possible to estimate the proportion of

cells in S-phase during the one hour period of HU co-culture by the ratio of the cell

number difference in the two groups and the cell number in the untreated group.

Continuous Bromodeoxyuridine labeling

Bromodeoxyuridine (BrdU) is a labeling substance which is also incorporated only

during the S-phase of the cell cycle. In contrast to HU it does not kill the cell, but it

can be detected by the use of antibody analysis. Because the BrdU label is inherited to

the daughter cells it is possible to determine the cumulative proportion of cells which

have gone through S-phase at least once by a continuous administration of BrdU (e.g.

in the drinking water of mice) [Bradford et al., 1997; Cheshier et al., 1999].

2.4 Observed phenomena

As pointed out in section 1.2, an appropriate model of hematopoietic stem cell organi-

zation has to be able to explain a broad variety of experimentally observed phenomena.


The following phenomena list does not claim to be complete, but it represents a selec-

tion which is suitable to serve as a representative check list.

2.4.1 Heterogeneity

In the early days of stem cell research it had been assumed that hematopoietic stem

cells are members of a homogenous population. Later, it became obvious that sub-

populations expressing different properties and functionalities can be distinguished

among the HSC. It has been documented that hematopoietic stem cells behave hetero-

geneously e.g. with respect to cycling activity, colony-forming ability, repopulating

and self-renewal potential. Furthermore, they show a heterogeneous expressions of

phenotypic markers.

The markers expression heterogeneity has already been discussed in section 2.3.1.

As mentioned, correlations of specific phenotype combinations with the ability for

long- and short-term repopulation could be demonstrated. Different assay techniques

(e.g. CAFC or LTC-IC) have been used to estimate the frequency of stem cells in

these subpopulations, suggesting very low numbers (� � per ��) of long-term and

larger numbers (about 1 per��) of short-term repopulating cells [Harrison et al., 1988;

Bertolini et al., 1997; Lord, 1997; Cho and Muller-Sieburg, 2000]. These findings

are generally taken as evidence for a developmental hierarchy associated with a grad-

ual, but irreversible decline of self-renewing and repopulating potential of HSC [Lord,

1997]. It has been shown that HSC are heterogeneous with respect to their ability to

form colonies (clonogenic potential) [Till et al., 1964; Hao et al., 1996]. There are

differences in the number of clonogenic cells per colony, in the time to appearance of

the colonies, and in the duration of colony-formation.

Furthermore, it has been documented that the hematopoietic stem cell population

is heterogeneous with respect to cycling activity [Eaves and Eaves, 1988b; Lerner

and Harrison, 1990]. This has been demonstrated by different sensitivities of cells

to the treatment with S-phase-specific cytostatica, such as Hydroxyurea (HU) or 5-

Fluorouracil (5-FU). Different groups [Ogawa, 1989; Down et al., 1995; Lord, 1997]

suggested that stem cells with a higher repopulating potential belong to a silent, non-

proliferative subpopulation. However, it turned out that the cycling status of HSC is

a reversible property. It has been shown by long-term labeling studies that some cells

may leave the cell cycle for many days and even months, but that almost all re-enter

the cycle at some point in time [Bradford et al., 1997; Cheshier et al., 1999].


2.4.2 Microenvironmental dependence

The hematopoietic microenvironment, a complex of local and systemic growth factors,

stroma cells, and extra-cellular matrix components has been shown to play an impor-

tant role in the regulation of stem cell organization [Lemischka, 1997; Lord, 1997].

The niche-concept, introduced by Schofield [1978], is a widely accepted theory about

specific, separated regions in the bone marrow (the niches) where HSC have to reside

to express their self-renewal potential.

It has been known for a long time that different types of cytokines influence the

regulation of hematopoietic cell production. For the more mature cell stages these reg-

ulatory networks have been extensively studied (see e.g. [de Haan et al., 1995a, 1996;

Roeder et al., 1998]). But not only these cells, also the most primitive HSC are influ-

enced by growth-factor signaling [de Haan et al., 1995b; Petzer et al., 1997]. Because

the production site of many cytokines are stroma cells, it was obvious that these cells

should, at least indirectly via the cytokines, affect the stem cell development. However,

it could be shown that stroma cells influence stem cell properties also directly. Wine-

man et al. [1996] demonstrated that thein vitro maintenance of stem cell repopulating

potential depends on the direct contact of stem and stroma cells. Whereas co-culture

of stem cells on stromal layers could preserve the repopulating ability of these cells,

the blocking of direct attachment (while preserving the exchange of the produced cy-

tokines) leads to a quick loss of the repopulating ability.

There is also another level of microenvironmental dependence. As already men-

tioned (section 1.1), hematopoietic and other tissue stem cells are highly plastic with

respect to their differentiation program [Bjornson et al., 1999; Brazelton et al., 2000],

but also with respect to gene expression [Geiger et al., 1998] and phenotypic traits

[Sato et al., 1999; Frimberger et al., 2001]. All these changes of cell-specific proper-

ties or functions seem to be induced by an alteration of microenvironmental signals.

2.4.3 Clonal fluctuation and competition

Another class of phenomena which is important in understanding the dynamics of

hematopoietic stem cell organization are fluctuation and competition processes in the

contribution of stem cells to blood production. The investigation of these processes can

help to understand regulatory mechanisms about stem cell activation/deactivation, to

separate stochastic from systematic effects, or to specify differences between diverse

types of stem cells or stem cell populations.


It has been shown that populations of differently, but neutrally marked cell pop-

ulations show fluctuating contributions to blood productions. Abkowitz et al. [1996]

demonstrated these fluctuations by monitoring the composition of committed progen-

itor cells of cat chimeras over more than 6 years. They investigated unperturbed cats

as well as cats which had received an autologous bone marrow transplantation after an

irradiation pretreatment and reported that the fluctuations in the clonal contribution of

the two markers are especially pronounced shortly after transplantation.

Fluctuations in the clonal contribution have also been observed in the competition

situation of kinetically different cell types. Such scenarios have been described for the

mouse model [Van Zant et al., 1992; Kamminga et al., 2000] and for human clonal

disorders [Carella et al., 1997; Eaves et al., 1998; Mauro and Druker, 2001]. There

are examples where the complete replacement of one cell type by another is reversible.

Such a dis- and reappearance of clones has been observed in DBA/2-C57BL/6 mouse

chimeras [Van Zant et al., 1992]. In these animals the contribution of the DBA/2 cells

to blood production disappears completely after a couple of months. A reactivation

can be induced by the transplantation of bone marrow from these animals into lethally

irradiated (primary) host mice. However, the achieved DBA/2 contribution is again

only transient. This behavior can be repeated in yet another (secondary) host.

Similar effects are observable in some treatment situations of clonal disorders. For

example, it is possible to achieve a reactivation of normal cells in chronic myeloid

leukemia patients, which initially have 100% malignant cells in the peripheral blood,

by treatment with Interferon-� [Hochhaus et al., 1997; Hehlmann et al., 2000]. How-

ever, depending on the degree of reactivation, and therefore inversely on the degree of

residual disease, there is still a substantial chance of relapse [Hochhaus et al., 2000].

Modern experimental techniques, such as retroviral marking, permit investigation

of individual cell clones. Largely different in design, these studies have produced

seemingly contradictory results. Whereas some groups report a high proportion of

long-lived clones (oligo-clonal situation) [Jordan and Lemischka, 1990; Capel et al.,

1990], other groups observed the simultaneous activity of many short-lived clones

(poly-clonal situation) [Drize et al., 1996].

2.4.4 Disturbances and regeneration

The hematopoietic system including the population of HSC is able to cope with dif-

ferent kinds of disturbances and injuries. Several feedback mechanisms have been

proposed to be responsible for controlling the maintenance, and if necessary, the re-


establishment of homeostasis of blood production [Loeffler and Wichmann, 1980;

Wichmann and Loeffler, 1985; de Haan, 1995]. For understanding the mechanisms

underlying these dynamic regulations, the regeneration situation after disturbance is

particularly informative. Therefore, two different types of irradiation injury are con-

sidered in this work to check whether the model is able to adequately reproduce the

experimentally observed regeneration kinetics of stem cells numbers.

In the murine system, it has been reported by several groups (e.g. Brecher et al.

[1967]; Beran [1973]; Blackett and Botnick [1981]) that acute cell kill by a single, but

relatively high irradiation dose causes a severe reduction of HSC numbers (measured

by CFU-S numbers) which is followed by a rapid recovery to normal cell numbers. In

the case of continuous (chronic) low dose irradiation the picture is changing. Here, it

seem to possible to drive the system into a new steady state at lower cell numbers than

in the unperturbed situation. The reached level depends on the used irradiation dose

[Wu et al., 1983; Kalina, 1985].

Table 2.2 summarizes the described phenomena classes and provides links to ref-

erences of experimental data and to figures comparing these data to simulation results.

Phenomena Experiment Simulation

HeterogeneityClonogenic potential Till et al. [1964] Figure 5.13Clonal appearance Hao et al. [1996] Figure 5.14Repopulation potential Down and Ploemacher [1993] Figure 5.15Cycling activity Cheshier et al. [1999], Figure 5.16

Bradford et al. [1997]Microenvironmental dependence

Stroma dependence Wineman et al. [1996] Figure 5.17Clonal fluctuation / competition

Cat chimeras Abkowitz et al. [1996] Figure 5.18Mouse chimeras Van Zant et al. [1992] Figure 5.19Clone tracking Drize et al. [1996], Figure 5.24

Jordan and Lemischka [1990]Disturbances / regeneration

Acute cell kill Brecher et al. [1967] and othersFigure 5.25Continuous cell kill Kalina [1985], Wu et al. [1983] Figure 5.27

Table 2.2: Summary of experimentally observed phenomena used for the model validation.Description and figures of simulation results in chapter 5.

Chapter 3

Theoretical background

In this chapter the most common concepts used to describe the organization of

hematopoietic stem cells will be described. In accordance with the objective of this

thesis, the focus will be on theories about the realization of self-renewal and repopu-

lating ability, leaving aside the problem of lineage specification. The chapter will be

separated into sections on biological theories and on mathematical models. The latter

ones are based on a biological concept, however, they exceed a simple description by

a formal representation which allows an analytic or simulation analysis.

3.1 Biological concepts

3.1.1 Symmetric / asymmetric cell division

The most common concept to explain the self-renewal ability of HSC is the assumption

of stem cell specific types of cell division.

The first kind is the asymmetric division of a mother stem cell into one stem and

one differentiated daughter cell [Till et al., 1964; Ogawa and Mosmann, 1985] (figure

3.1a). This division regime ensures a constant population of stem cells and, at the

same time, a constant production rate of differentiated cells. However, it does not

allow a dynamic regulation in the sense of reduced or enhanced self-renewal rates

depending on the system’s needs. To be precise, one cannot speak of a self-renewal

potential because the individual stem cell and the stem cell population only express

self-maintenance (see [Loeffler and Potten, 1997]). Neither the stem cell number nor

a specific stem cell property can berenewed if it has previously been lost.

To overcome the inflexibility of constant self-renewing / differentiation rates one

22

CHAPTER 3. THEORETICAL BACKGROUND 23

assumed two possible types of stem cell division, namely the symmetric divisions into

two identical stem cells or into two differentiated daughter cells [Vogel et al., 1969;

Loeffler and Grossmann, 1991] (figure 3.1b, c). If these two types of cell division

are realized at equal rates, one ends up, on average, in the same situation as with

asymmetric division. By a change of these rates, however, one can induce a growth or

a reduction of the stem cell population. Therefore, using this type of division scheme

and its regulation, one can achieve a real self-renewal of the stem cell pool with respect

to cell numbers. A self-renewal with respect to other cellular properties is not possible

within this paradigm because the differentiation process is assumed to be irreversible

(see also 3.1.2). Sometimes, also mixtures of the above concepts are assumed, i.e. stem

cells are assumed to divide either symmetrically / asymmetrically into two stem cells

or symmetrically into two differentiated cells [Loeffler and Grossmann, 1991; Loeffler

and Potten, 1997].

There is also another conceptual possibility to explain these processes without as-

suming different types of cell division. Starting from the assumption of an identical

doubling of the mother cell (symmetric self-replicating division) stem cells are induced

to differentiate independently from the division process. Depending on the time scales

of interest, one could subsume these two processes (symmetric cell division and dif-

ferentiation step) into the theoretical construct of the asymmetric division (see figure

3.1d).

S

S

D

(a)

S

S

S

(b)

D

S

D

(c)

S

S S

S D

(d)

Figure 3.1: Different concepts for stem cell specific types of cell division. (a) Asymmetricdivison into one stem cell (S) and one differentiated cell (D); (b) Symmetric reproduction ofthe stem cell; (c) Symmetric division into two differentiated cells (differentiation linked to celldivision); (d) Symmetric reproduction followed by a cell division independent differentiationevent.


3.1.2 Stem cell hierarchy

Many classical concepts assumed a homogenous population of tissue stem cells . How-

ever, as it has become obvious that the stem cell population is highly heterogeneous, it

was necessary to incorporate some degree of substructure into the description. The

majority of these theories share the concept of a developmental hierarchy of HSC

(for a review see [Lord, 1997]). Similar to the structure of the entire hematopoietic

system (see section 2.2), an irreversible developmental hierarchy with decreasing self-

renewing potential (repopulating ability) towards more differentiated cell stages is as-

sumed for the HSC compartment (see Figure 3.2). Most of the time these hierarchical

models assume a dependence of cell division and differentiation.

D

D

D

D

D

D

high low

S

S

S

S

S

S

S

none

... ...

Self−renewal potential

Figure 3.2: Hierarchy concept of hematopoietic stem cells (S). The self-renewing potential(ability to perform self-renewing divisions, illustrated by the curved arrows) is gradually, butirreversibly lost with each cell division. Differentiated cells (D) are assumed to have lost theself-renewing potential completely.

3.1.3 Niche concept

A specific combination of the hierarchical model and the asymmetric cell division is

the niche concept which was introduced by Schofield [1978] (see figure 3.3). It states

that hematopoietic stem cells reside in a specific micro-environmental niche. If such

a cell is induced to divide, one daughter cell will remain in the niche while the other

cell will have to leave it. Without the influence of the niche the cells will undergo

irreversible differentiation steps. If there are empty niches, stem cells will have the


chance to re-enter a niche. However, according to the paradigm of an irreversible,

one-directional hierarchy, proliferative potential lost during one or more differentia-

tion steps cannot be regenerated. The niche only supports a maintenance of the current

status of the cells. This effect of an environment (niche) induced differentiation ar-

rest has also been adopted by Muller-Sieburg and Deryugina [1995]. They extended

this concept, assuming a differentiation block of HSC induced by their attachment to

stroma cells. The proposed mechanism is the occupation of receptor molecules by

the attachment process which, otherwise, could receive and transmit differentiation

signals.

(a)

��

��

(b)

��

��

��

��

(c)

Figure 3.3: Niche concept (after [Lord, 1997]). (a) Hematopoietic stem cell in a micro-environmental niche; (b) If the stem cell is induced to divide, one daughter cell leaves theniche and starts forming a clone (hatched triangle) by further differentiating divisions. It is stillpossible for cells which have already underwent few differentiating divisions to re-occupy anempty stem cell niche. However, the proliferative potential (potential size of produced clones)of these cells is already reduced (c).

3.1.4 Screw model

The concept, known as thescrew model, which postulates proliferation and differen-

tiation to be two independent processes, has been formulated and discussed by Potten

and Loeffler [1990], Loeffler and Potten [1997]. Besides the self-replicating division

process of stem cells, some of them will, ruled by an independent process, differenti-

ate into another state and become so called transient cells. These transit cells do still

have a proliferative potential. In the steady state (figure 3.4a) this proliferation process

will be inevitably overlaid by the process of differentiation. Therefore, while dividing,

the cells will develop further towards a more mature differentiation state. In contrast


to this scenario, the transit cells will express the potential to perform self-replicating

divisions (i.e. blocking of the differentiation process) in regenerative situations (figure

3.4b). Moreover, the concept includes the possibility for transit cells to rejuvenate un-

der certain circumstances. These assumptions also implicate the notion of actual and

potential stem cells, where the latter group (transit cells) will perform self-maintenance

or even self-renewal only on demand. It should be mentioned that this model was orig-

Figure 3.4: Screw-model (after [Loeffler and Potten, 1997]). This concept assumes prolifer-ation and differentiation/maturation to be independent processes. In the scheme proliferation(cell cycle) is represented by the horizontal plane and differentiation/maturation by the verticaldirection. The notion S represents stem cells, T� to T� different types of transit cells and Mfunctional mature cells. Cell cycle phases are given by��, �� and� �. (a) Steady state situ-ation, with self-maintenance only at the stem cells level. (b) Regeneration situation, with thepossibility of self-maintenance and even self-renewal (rejuvenation) of transient cells.

inally developed for the intestinal crypt. However, its general principles should also be

applicable to other stem cell systems such as the hematopoietic one.

3.1.5 Clonal succession

A further conceptual approach is the clonal succession theory which has been proposed

by Kay [1965]. It postulates a restricted division potential of each cell. Consequently,

one has to assume the existence of a dormant (non-proliferating) stem cell reserve

pool. Kay hypothesized that this reserve pool is formed during embryogenesis. On


self

differentiation

renewal

S D

SS

SD D

D

DS

S

DS

S

Figure 3.5: Concept of clonal succession. On demand, stem cells (S) from a reserve pool areactivated to initiate a differentiating clone (D). Symmetric self-renewing divisions are poten-tially allowed for the cells in the reserve pool.

demand, individual cells from this reserve can be activated to initiate the production of

a differentiated clone. Introducing the potential to undergo symmetric, self-renewing

divisions for the stem cells in the reserve pool, one arrives at an extension of the clonal

succession theory (see figure 3.5) which has been proposed by Abkowitz et al. [1996].

Although originating from different historical and biological backgrounds the clonal

succession theory with an self-renewing stem cell pool (figure 3.5) and the “pseudo”-

asymmetric cell division (symmetric self-renewing + differentiation event independent

from cell division; figure 3.1d) are conceptually equivalent if phases of cycling inac-

tivity are allowed in the latter model.

3.1.6 Regulated proliferation and self-renewal

As a last example of previously proposed concepts describing organization of HSC, the

concept of dynamically regulated proliferation and self-renewal, proposed by Wich-

mann and Loeffler [1985], will be presented. This concept combines ideas of different

kinds of cell division (see 3.1.1), activation of normally non-proliferating stem cell

(see 3.1.5), and a feedback regulated control of these processes. The proportion of

stem cells which are actively proliferating as well as their probability for self-renewing

divisions depend on the number of stem cells (S) and on the number of granulopoietic

(G) and erythropoietic (E) bone marrow cells. Whereas the proliferative fraction (a)

decreases likewise for higher numbers of S, E, and G, the self-renewing probability (p)

increases/decreases for decreasing/increasing numbers of S, but increasing/decreasing

numbers of E and G. A scheme of this concept, illustrating the influence of the demand

for stem cell and progenitors on the proliferative fraction and on the self-renewing

probability, is given in figure 3.6.


Figure 3.6: Schematic representation of the concept of dynamically regulated stem cell prolif-eration after [Wichmann and Loeffler, 1985]. The balances illustrate the effect of the demand(high demand�� heavy weight) for stem cells “S”, erytropoietic “E” or granlulopoietic “G”bone marrow cells on the proliferative fraction “a” (proportion of stem cells in active cell cy-cle) and on the self-renewing probability “p”.

3.2 Mathematical models

There are several ways to obtain a mathematical representation of a biologically mo-

tivated model. The choice of the appropriate approach largely depends on the precise

scientific question to be answered. In the following section the main ideas of three

important classes of mathematical models which have been used to describe the orga-

nization of HSC will be presented.

3.2.1 Differential equation models

One possible modeling approach uses a deterministic description of the dynamic pro-

cesses of cell proliferation, maturation, and differentiation on the population level. The

cells are considered as members of different cell pools (compartments), which contain

cells with equal (or similar) properties. The dynamics of cell numbers or densities in

these pools are mathematically described by systems of differential equations. In the

simple case of no substructure (e.g. with respect to spatial arrangement, cell age, or

maturation status) inside the different pools, this leads to systems of ordinary differen-

tial equations (ODE). If one is not only interested in the temporal changes, but also in

the dynamics with respect to further variables (e.g. space, maturation status) one has

to extend the description to partial differential equations (PDE).


One example of an ODE model is the mathematical representation of the con-

cept of dynamically regulated stem cell proliferation and self-renewal [Loeffler and

Wichmann, 1980; Wichmann and Loeffler, 1985]. This compartment model includes

different cell populations: stem cells, differentiated erythropoietic and granulopoietic

cells. The cells inside theses compartments are assumed to be homogeneous. The stem

cells divide or differentiate at certain rates which themselves depend on the number of

stem cell and differentiated cells, respectively. These feed-back mechanisms induce a

dynamic regulation of the system.

Other differential equation models describing processes of hematopoietic stem cell

proliferation and differentiation have been proposed as well. For example, Furusawa

and Kaneko [2001] proposed an ODE system to model intra-cellular chemical dynam-

ics. The chemical substances are assumed to rule the decision of stem cells to differen-

tiate. The authors show that their deterministic system produces chaotic behavior and

they interpret this as a possible reason for the observed stochasticity in the decision of

stem cells to differentiate or to self-renew.

Also the cell kinetic status of hematopoietic stem cells has been modeled using

an ODE approach [Mackey, 1978, 2001]. Here, the stem cell population is regarded

as consisting of two subpopulations: a proliferative and a dormant (non-proliferating)

one. The dynamics of HSC in this system are assumed to be governed by two coupled

delay differential equations.

A property shared by all the differential equation models is that they describe the

average behavior of cell populations. They are well suited to study dynamic properties

and feed-back effects in systems with high cell numbers, where the essential informa-

tion about the cellular dynamics (even in the case of stochastic effects on the individual

level) can be collapsed into an average behavior. If, besides the average, information

about the variability in the system behavior is needed, it is possible to use stochastic

differential equations (SDE) as an appropriate mathematical tool [Gardiner, 1985]. In

the case of low cell number systems with increasing importance of stochastic fluctua-

tions and if individual cell fates are of interest, another class, the so called single cell

based models, are more appropriate.

3.2.2 Stochastic single cell based models

These models assume rules for the behavior of individual cells. According to these

rules all cells in the system are updated at specified time points allowing the fate of

each cell to be follow over time. If the decision rules are (partially) random, one can


model the cellular behavior by a stochastic process [Gardiner, 1985].

One example of a time-discrete stochastic birth and death process for the descrip-

tion of stem cell self-renewal and differentiation is the model proposed by Till et al.

[1964]. It assumes that each stem cell can either divide symmetrically into two stem

cells (birth) or differentiate (death). Both processes occur with predefined probabili-

ties (see also section 3.1.1). Generalized versions of this model have been investigted

e.g. by Vogel et al. [1969] who include the additional chance of an asymmetric divi-

sion into one stem and one differentiated cell, by Ogawa and Mosmann [1985] who

incorporated a stochastic selection of one of several lineage types in case of a differ-

entiation event, or by Loeffler and Grossmann [1991] who suggested such as concept

for the stem cell system in the intestinal crypt. A further extension of the concept of

self-renewing division or differentiation of HSC has been proposed by Abkowitz et al.

[1996]. This group did not assume predefined generation times at which one of the two

options is realized. Instead, they introduced intensities (probabilities per time unit) of

self-replication (�) and differentiation (�). The probability of an increase (replication)

or decrease (differentiation) of the stem cell number by one in a small time interval�

is assumed to be linear in� (Poisson process). As a consequence of the Markov prop-

erty1 of this process, the time to the next replication or differentiation is exponentially

distributed with parameters�� or ��, respectively. The replication / differentiation

process of HSC is now realized by the simulation of these sojourn times combined with

the appropriate event. In contrast to the other sketched single cell based approaches,

the Abkowitz model does not allow the tracing of individual cell or clone fates, be-

cause the state space of the stochastic process is defined by the total stem cell numbers

and not by the state of individual cells or cell clones.

3.2.3 Cellular automaton models

Another type of single cell based approaches, a cellular automaton, has been used by

Agur et al. [2002] to model the dynamics of stem cell organization. Here, the decision

of a stem cell to replicate or to differentiate depends on the state of all neighboring

cells. One implication of the assumed rules is that a stem cell only differentiates if

its local neighborhood is saturated with stem cells. Another important assumption

which ensures a de-synchronization of neighboring cells, is the existence of an internal

clock which determines the differentiation onset. Using these rules the model is able

1i.e. the future development of the process depends only on its present state not on the past [Taylorand Karlin, 1984].


to explain homeostasis and reconstitution of the stem cell system without assuming

stochastic decisions about self-replication and differentiation.

All the described concepts and models stick to the classical view on stem cells as

prespecified entities which are subjected to an irreversible developmental hierarchy.

Although some of them include influences of the microenvironment on the develop-

ment of the stem cells, none of them understands this interaction as a necessity for the

generation of stem cell function. However, such a functional view on stem cell popu-

lations as self-organizing systems is, in my opinion, necessary to be able to explain the

experimentally described plasticity and flexibility of tissue stem cells.

In the next chapter, a new concept of stem cell organization, which is based on

self-organizing principles, will be introduced. It links the macroscopic emergent sys-

tem behavior to microscopic mechanism on the cellular level. Moreover, it is able

to explain experimental observations on the population and on the single cell level,

which is necessary to include all the different kinds ofin vitro andin vivo assays into

the model analysis.

Chapter 4

Model description

This chapter describes the assumptions of a new model of hematopoietic stem cell

organization. According to the aims listed in the objective section (1.2) it should

� replace the classical view on stem cells as prespecified, fixed entities by an ex-

planation of stem cell organization as the result of a dynamic, self-organizing

process,

� fulfill all criteria of the definition of tissue stem cells, and

� consistently explain a broad variety of experimentally observed phenomena.

Herein, specific attention will be paid to an incorporation of new experimental insights

with respect to microenvironmental influences, specifically on stem cell - stroma in-

teractions, to plasticity and reversibility phenomena, and to the description of clonal

fluctuation and competition effects including the behavior

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