Higher-order Emergence in Collective AI Systems from Computational Model of Dictyostelium discoideum to Swarm Robotics

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Thesis

Reference

Higher-order Emergence in Collective AI Systems from

Computational Model of Dictyostelium discoideum to Swarm Robotics

PARHIZKAR, Mohammad

Abstract

In this thesis, we show how to apply the method, the frameworks, and how to derive agent-based models of both first- and second-order emergence on the specific case of the social amoeba Dictyostelium discoideum. Overall, this thesis proposes a new design pattern

“leader-follower”, describing a mechanism for achieving higher-order emergent behavior in artificial systems, derived from D.discoideum behavior. We eventually translate this pattern into swarms of Kilobots. In general, our computational simulations can replicate the behaviors of D. discoideum system it parallels and to do so based on the present, identified characteristics of the system from aggregation until slug formation. To achieve this goal, it is required to model different steps for each phase of the D. discoideum life cycle. Overcoming this challenge is possible by experimental1 and theoretical studies. These studies cover understanding the implications of the conceptual and main algorithmic steps of the model for each phase.

PARHIZKAR, Mohammad. Higher-order Emergence in Collective AI Systems from Computational Model of Dictyostelium discoideum to Swarm Robotics. Thèse de doctorat : Univ. Genève, 2020, no. SdS 141

DOI : 10.13097/archive-ouverte/unige:141766 URN : urn:nbn:ch:unige-1417669

Available at:

http://archive-ouverte.unige.ch/unige:141766

Disclaimer: layout of this document may differ from the published version.

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UNIVERSITÉ DE GENÈVE Institute of Information Service Science

Systèmes d’Information Professeur Giovanna Di Marzo Serugendo

Higher-order Emergence in Collective AI Systems

from Computational Model of

Dictyostelium discoideum to Swarm Robotics.

THÈSE

présentée à la Faculté des Sciences de la Société Institute of Information Service Science Centre Universitaire d’Informatique (CUI)

l’Université de Genève pour obtenir le grade de Docteur ès Sciences de la Société mention Systèmes d’Information

par

Mohammad Parhizkar

de

Orumiyeh (Iran)

Thèse N^◦ 141 GENÈVE

Repro-Mail - Université de Genève février 2020

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To

My Twin Brother

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Acknowledgements

I express my deepest gratitude to my thesis advisor, Prof. Giovanna Di Marzo Serugendo, for the countless hours that she devoted to this thesis. Her knowledge and expertise in my area of research significantly developed the contents of this thesis; I couldn’t have chosen a better supervisor! If it were not for her, I would not be studying in this school in the first place, and this thesis would not exist. I have also learned many life lessons from her over the five years, which I will keep them with me for my whole life.

I wish to express my sincere appreciation to Prof. Thierry Soldati, who convincingly guided and encouraged me to know more about the biological aspects of my Ph.D. project. I would like to recognize the invaluable assistance that you provided during my study.

I am indebted to Prof. Thomas Schmickl and Prof. Salima Hassas, for inviting me as a guest researcher to their labs in Graz and Lyon. I want to thank our colleagues Jahn Nitschke and Louis Hellequin, from the University of Geneva, Department of Biochemistry.

They provided insight and expertise that greatly assisted the research, also they grant the video and images ofD. discoideum life cycle.

This research is supported by the Swiss National Science Foundation (SNSF) [205321 179023].

I would like to thank my committee members, Prof. Jean-Henry Morin, Prof. Salima Hassas, Prof. Thierry Soldati, Dr. Jose-Luis Fernandez-Marquez, for accepting to assess my thesis and taking the time to read it.

I want to offer my special thanks to the past and current members of Centre Universitaire d’Informatique (CUI) of Geneva, for creating such a productive environment for research and learn new aspects of computer science and information system. I have enjoyed every second of our invaluable collaborations, excellent lunch and coffee breaks, other activities, as well. There is no way to express how much it meant to me to have been a member of CUI. I have been very fortunate to know and to be officemate with two incredible friends: Allan Francisco Berrocal Rojas and Alex de Masi. Some particular words of appreciation go to my friends who have always celebrated each accomplishment and been a significant source of the guide when things would get a bit discouraging: Farid, Vahid, Massih, Golzar, Kasimir, Sina, Maryam, Francesco, Meghdad, Mina, Mohsen. Thanks guys, for always being there for me.

I would also like to thank my incredible friend Sohrab Ferdowsi to whom I owe many of the lessons I have learned in life. I would not hesitate for a second to call him brother.

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Words do not describe my appreciation for my family. I would like to appreciate first my strong sister, Mahsa. Thanks for always supporting Reza and me since the first day of our life. You were educating us how to read and write at home before our school days have even begun. It had a significant impact on the ease and confidence with which we pursued afterward. I am also very grateful to my brother-in-law, Nima. I really appreciate your true brothership. Your pieces of advice always help me to think deeper and pull myself together. Indeed, my deepest gratitude and appreciation go to my father and mother, Ali and Soudabeh, for their unlimited love, tenderness, patience and support.

My twin brother, Reza, has been and will be an inseparable part of me. Thank you so much for your priceless effort to give me this opportunity to do my study in Switzerland.

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Résumé

Emergence d’ordre supérieur dans les systèmes d’intelligence artificielle collective

des modèles computationnels du

Dictyostelium disciodeum à la robotique en essaim.

Le comportement collectif dans la nature constitue une source d’inspiration pour la conception de systèmes collectifs artificiels d’adaptation, en raison de mécanismes favorisant l’adaptation aux changements environnementaux et permettant à un comportement émergent complexe de naître d’un comportement relativement simple des entités individuelles. L’ingénierie des mécanismes de modélisation de l’émergence de premier-ordre, également appelée intelligence des essaims, est bien étudiée et identifiée, comme le gradient, la répulsion ou la recherche de fourmi, mais pas encore pour l’émergence de second-ordre ou d’ordre supérieur. Cependant, le comportement de l’émergence d’ordre supérieur n’a pas encore fait l’objet de beaucoup d’attention. Le comportement émergent de second-ordre résulte des interactions entre les individus, qui sont elles-mêmes le résultat d’un comportement émergent de premier-ordre.

En plus d’étudier les mécanismes de l’émergence d’ordre supérieur, nous proposons dans cette thèse une méthode d’analyse et de modélisation de l’émergence de premier-ordre et d’ordre supérieur dans les systèmes collectifs. Cette méthode s’appuie sur deux cadres existants : Generic Emergence Framework (GEF) pour la mise en forme de différents niveaux d’émergence et les quadrants MASQ pour la mise en forme du comportement individuel et collectif des agents. Ils nous aident à concevoir des modèles basés sur les agents, en particulier pour distinguer les comportements de premier et de second-ordre, et identifier les déclencheurs de changement (GEF) ; pour identifier les états internes, les comportements individuels, les interactions et les propriétés émergentes du premier et du second-ordre (MASQ). Nous montrons comment appliquer la méthode, les cadres et comment dériver des modèles basés sur les agents de l’émergence du premier et du second-ordre sur le cas spécifique de l’amibe socialeDictyostelium discoideum. Les cellules deD. discoideumsont capables de modifier leur comportement pour survivre en réponse à la privation de nutriments. Les cellules individuelles se déplacent d’elles-mêmes lorsqu’il y a de la nourriture en abondance. Lorsque la nourriture est rare, les cellules s’auto-agrègent vers des cellules centrales spontanées (comportement émergent de premier-ordre) pour construire un super-organisme, similaire à une limace (Slug).

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Ce super-organisme présente un système à un niveau de complexité plus important qu’une cellule individuelle, sans la complexité d’un système nerveux. Une limace multicellulaire, qui est le résultat de l’agrégation de 105 cellules affamées, se déplace dans son ensemble et interagit avec d’autres limaces (comportement émergent de second-ordre) [1].

Dans cette thèse, nous soulignons que le mouvement de la limace et son comportement émergent de second ordre résultent de l’action chimiotactique organisée des cellules individuelles duD. discoideum de chaque limace [1]. La limace se déplace en réaction à la lumière, à la température et à l’ammoniac à la surface du sol [1]. Bien que le comportement de la limace soit dû au comportement collectif des amibes, elle présente des propriétés qu’aucune des cellules n’a en soi (par exemple, la sensibilité à la lumière, à la température et à l’ammoniac).

Une fois que la limace s’est installée dans un endroit approprié, l’extrémité postérieure s’étend avec l’extrémité antérieure établie dans l’air pour développer un corps fructifiant, qui contient une boule de spores, et une mince tige. Ensuite, lors de la dispersion, les spores germent et les cellules reprennent leur comportement individuel. Il est intéressant de noter que chaque spore de cet organisme social germe à un rythme différent et indépendamment des autres spores [2].

En ce qui concerne les comportements émergents de premier-ordre, les résultats montrent une sélection autonome des centres, une formation de nouveaux centres, une taille similaire des territoires d’agrégation. De plus, en ce qui concerne les comportements émergents de second-ordre, les résultats montrent un mouvement collectif pendant la phase de migration, le phototaxis des limaces, l’effet ammoniac, la fusion des limaces, ou de nouvelles caractéristiques comme la sensibilité à la lumière. Dans l’ensemble, cette thèse propose un nouveau modèle de conception “leader-follower”, décrivant un mécanisme permettant d’obtenir un comportement émergent d’ordre supérieur dans les systèmes artificiels, dérivé du comportement duD. discoideum. Nous traduisons finalement ce modèle en essaims de Kilobots. Le modèle de conception proposé et nos nouveaux modèles à base d’agents aideront les chercheurs à passer des algorithmes traditionnels d’intelligence des essaims aux mécanismes de comportement collectif d’ordre supérieur. En général, nos simulations informatiques sont capables de reproduire les comportements du systèmeD. discoideum auquel il est parallèle et de le faire en se basant sur les caractéristiques actuelles et identifiées du système depuis l’agrégation jusqu’à la formation des limaces. Pour atteindre cet objectif, il est nécessaire de modéliser différentes étapes pour chaque phase du cycle de vie du D. discoideum. Il est possible de surmonter ce défi par des études expérimentales1 et théoriques. Ces études portent sur la compréhension des implications des étapes conceptuelles et des principales étapes algorithmiques du modèle pour chaque phase.

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Abstract

Collective behavior in nature provides a source of inspiration to engineer artificial collective adaptive systems, due to mechanisms favoring adaptation to environmental changes and enabling complex emergent behavior to arise from a relatively simple behavior of individual entities. Engineering of the mechanisms for modeling the first-order emergence, also referred to as swarm intelligence, is well studied and identified, such as gradient, repulsion, or ant foraging, but not yet for the second- or higher-order emergence. However, higher-order emergent behavior has not received much attention yet. Second-order emergent behavior arises from the interactions of individuals, which are themselves the result of first-order emergent behavior.

In addition to studying mechanisms for higher-order emergence, we propose in this thesis a method for analyzing and modeling first- and higher-order emergence in collective systems.

This method relies on two existing frameworks: the Generic Emergence Framework (GEF) for shaping different levels of emergence and the MASQ quadrants for shaping individual, collective agent behavior. They help us to design agent-based models, in particular, to discriminate first- from second-order behavior, and identify triggers of change (GEF); to identify internal states, individual behaviors, interactions, and emerging properties of both first- and second-order (MASQ).

We show how to apply the method, the frameworks, and how to derive agent-based models of both first- and second-order emergence on the specific case of the social amoeba Dictyostelium discoideum.

D. discoideum cells are able to change their behavior to survive in response to nutrient starvation. Individual cells move around on their own when there is plenty of food. When food is scarce, cells self-aggregate toward leading, spontaneous center cells (first-order emergent behavior) to build a super-organism, similar to a slug. This super-organism presents a system at a level of complexity more significant than an individual cell, without the complexity of a nervous system. A multicellular slug, which is a result of the aggregation of up to10⁵starving cells, moves as a whole and interacts with other slugs (second-order emergent behavior) [1].

In this thesis, we emphasize that the slug movement and it’s second-order emergent behavior result from organized chemotactic action of the individualD. discoideum cells in each slug [1].

The slug relocates in reaction to light, temperature, and ammonia to the surface of the soil [1].

Although the slug’s behavior is due to the collective behavior of the amoebae, it displays

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properties that none of the cells have on its own (e.g., sensitivity to light, temperature, and ammonia). Following the slug settles into one suitable place, the posterior end reaches out with the anterior end established in the air to develop a fruiting body, which contains a ball of spores (sorus) and a slender stalk. Afterward, upon dispersal, the spores germinate, and cells resume their individual behavior. Interestingly, each spore of this social organism germinates at a different rate and independent of the other spores [2]. Regarding first-order emergent behaviors, the results show autonomous center selection, streaming, and stream-breaking, new center formation, similar aggregation territories size. Moreover, regarding second-order emergent behaviors, the results exhibit collective movement during the migration phase, slug’s phototaxis, ammonia effect, merging of slugs, or new features as sensitivity to light.

Overall, this thesis proposes a new design pattern “leader-follower”, describing a mechanism for achieving higher-order emergent behavior in artificial systems, derived from D.discoideum behavior. We eventually translate this pattern into swarms of Kilobots.

The proposed design pattern and our new agent-based models will help researches to move forward from traditional swarm intelligence algorithms to the higher-order collective behavior mechanisms.

In general, our computational simulations are able to replicate the behaviors of D. dis- coideum system it parallels and to do so based on the present, identified characteristics of the system from aggregation until slug formation. To achieve this goal, it is required to model different steps for each phase ofD. discoideum life cycle. Overcoming this challenge is possible by experimental¹, and theoretical studies. These studies cover understanding the implications of the conceptual and main algorithmic steps of the model for each phase.

1This thesis uses images and videos from biological experiments ofAx2(ka)strain ofD. discoideum, which have been done by our colleagues at the University of Geneva, Louis Hellequin, Jahn Nitschke, from the Department of Biochemistry, Prof. Thierry Soldati’s group, as part of the SNSF 205321 179023 project.

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Research Output Resources

Conference papers:

• Mohammad Parhizkar, and Giovanna Di Marzo Serugendo, Social Amoeba Dic- tyostelium discoideum As an Inspiration for Swarm Robotics. In9th IEEE International Conference on Self-Adaptive and Self-Organizing Systems (SASO). MIT, USA, 2015.

• Mohammad Parhizkar and Giovanna Di Marzo Serugendo, An agent-based model for collective behaviors of social amoeba Dictyostelium discoideum morphogenesis:

Aggregation phase. InSWAMR’17: The 2nd International Symposium on Swarm Behavior and Bio-Inspired Robotics, Japan, 2017.

• Mohammad Parhizkar, Giovanna Di Marzo Serugendo, Salima Hassas, Leaders and Followers: a Design Pattern for Second-Order Emergence. In 4th IEEE International Workshops on Foundations and Applications of Self* Systems (FAS*W), Sweden, 2019.

• Mohammad Parhizkar, Jahn Nitschke, Louis Hellequin, Thierry Soldati, Giovanna Di Marzo Serugendo, Self-organising Agent-Based Model to Study Stream-breaking Phenomenon During Aggregation Phase of Dictyostelium discoideum. In SWARM’19:

The 3rd International Symposium on Swarm Behavior and Bio-Inspired Robotics, Japan, 2019.

Journal papers:

• Mohammad Parhizkar and Giovanna Di Marzo Serugendo, Agent-based models for first- and second-order emergent collective behaviors of social amoeba Dictyostelium discoideumaggregation and migration phases,Artificial Life and Robotics Journal, Volume 23, Issue 4, pp. 498–507, 2018.

Project’s website:

• UNIGE Collective Adaptive Systems Group Projects: Dicty Project Website YouTube URL link to the experiments’ videos:

• YouTube Channel: Dicty Project Channel Simulation source codes:

• GitHub Repository: Dicty Project Repository

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Chapter 1 Introduction

Understanding collective behavior in nature and its potential links to the engineering of decentralized self-organization systems, in terms of collective artificial behavior, e.g., swarm robotics [3, 4], modular robots [5, 6], and sensor networks [7, 8] attracts many researchers from biology and computer science. Researchers are interested in different scientific and industrial topics such as cell biology, cancer study, environment cleaning, swarms of drones, unmanned robots, and, more generally, in collective adaptive systems based on IoT (Internet of Things) or massive ICT (Information and Communications Technology) deployment.

Most of the theoretical and experimental researches on collective social behavior has concentrated on animals [9]. However, this thesis focuses on the social amoebaDictyostelium discoideummulticellular development process as a unique and exciting form of collective system in nature. This introductory chapter reflects the Ph.D. project’s overview, the motivation, research questions, our contribution, and, eventually, the impacts and applications of the project.

1.1 Overview

Dictyostelium discoideum is a social amoeba, able to change its behavior to survive in response to nutrient starvation [10]. Most of its life, the organism lives in the soil as a single amoeba and feeds on bacteria [11] (see D. discoideum life cycle inFig. 2.1). Individual cells move around on their own when there is plenty of food. Then, when food is scarce, the cells start a multicellular developmental process. Up to a million amoeboid cells artfully self-aggregate via pattern formation [12] (first-order emergent behavior) to build a coherent and cohesive super-organism, similar to a motile slug. This complex super-organism has several properties that individual cells do not have on their own, for example, sensitivity to the light and heat.

The slug moves as a whole (second-order emergent behavior) looking for a suitable place (high light and low humidity) to transform into a fruiting body [12]. The fruiting body, consisting of a stalk, in which about20% of the cells [13] die to lift the remaining cells up

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to a better place for sporulation and dispersal on the surface of the soil [14]. Interestingly, at this point, the cells resume their individual behavior.

The social amoeba D. discoideum is one of the eight species selected as unicellular model organisms for biomedical researches [15]. Despite its unique and relatively simple life cycle, it has been exploited for the study and modeling of various behaviors, such as cell motility, chemotaxis, pattern formation, phagocytosis, cell-cell contact, gene- expression, cell death.

Studies of the developmental cycle inD. discoideumrepresent the best examples of the use of mathematical modeling in developmental biology [16]. Moreover, the mentioned ability of alternation between unicellular and multicellular forms makes D. discoideum an ideal organism to study social and self-organized behaviors, as well different levels of emergent properties. This specific feature inspired us to investigate the relationship between the first-order and the higher-order collective behaviors in terms of emergence.

First-order complex collective behavior can emerge from the local interactions of simple agents. Second-order emergent behavior, however, arises from the interactions of individuals, which are themselves the result of first-order emergent societies. According to Sawyer’s book [17], the second-order emergence refers to systems in which agents recognize the existence of groups that emerged from their own collective behaviors.

In the case ofD. discoideum, higher-order emergent behavior refers to collective behavior at the level of slugs, as a dynamic process of “wholeness”. Slugs themselves are the result of collective behavior at the level of cells.

(see Chapter 6: Second-order Collective Behavior–Page 79) The key objectives of this thesis can be delegated into two classes:

• To provide methods and comprehensive frameworks from natural systems, to analyze and design collective artificial systems exhibiting first- and higher-levels of emergent behavior.

• To derive appropriate mechanisms for higher-order emergent behavior and provide them as design patterns for artificial systems.

1.2 Motivation and Research Questions

The Ph.D. project, therefore, involves the combination of different disciplines - cell biology, self-organizing systems, and swarm intelligence into one activity. Among them, advancements of the state-of-the-art in swarm intelligence and swarm robotics is another objective of this thesis, which can be pursued by relying on bio-inspired swarm systems composed of a large number of autonomous robots presenting various physical behavior. To this end, tools development and methodologies that enable the use of such systems is necessary(see Chapter 4: Framework of Agent-based Model–Page 35).

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1.3 Contribution and Project Phases 7 In the biology field, althoughD. discoideum provides a promising research path, not all phases are currently understood and modeled at the micro-level. From the computer science and artificial systems perspectives, the first-order emergence is well studied, but higher-order levels of emergent behavior have not received much attention yet.

Finally, from the artificial intelligence perspective, there is no attempt at applying higher-order emergent behavior to this type of system. To this end, we could identify three main phases of this project as: (1) provide agent-based models of the different phases of D. discoideum life cycle, (2) extract pertinent mechanisms for higher-order emergent behavior and provide them as design patterns for artificial systems; and (3) eventually translate these mechanisms into swarms of real multi-modular, self-configuring, self-adaptive micro-robots, such as Kilobots.

This thesis addresses these points and tackles the following research questions:

• What are the social relations and configurations of D. discoideum behaviors at the different phases of its life cycle and how to model them?

• What are the mechanisms favoring higher-order emergence in swarms and artificial collective behavior?

• How to translate and implement those mechanisms into collective adaptive systems?

This thesis substantially advances state of the art by providing:

• Fine-grained understanding of D. discoideum individual cells behaviors at all phases of its life cycle and provision of corresponding agent-based models validated with actual biological experiments;

• Novel self-organizing mechanisms for higher-order emergent behaviors expressed and defined as design patterns for artificial systems.

1.3 Contribution and Project Phases

Inspired byD. discoideum pattern formation and the social evolution behaviors, we envision to apply some parts of the process to the swarms of robots. Fig. 1.1 illustrates the main tasks of the four phases of the Ph.D. project. Phase 1 and Phase 2 are related to our contribution from a biological perspective; however, Phase 3 and Phase 4 are linked to the thesis contributions from an artificial intelligence engineering perspective.

Our main contributions, from a biological perspective, can be categorized in the following four steps:

1. Understanding the different mechanisms ofD. discoideum during its whole life cycle as a continuous process, with several sequences of life stages.

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2. Obtaining the details, curiously highlighting individual phases, and finding out their emergent properties.

3. Surveying state of the art in the development of D. discoideum with a focus on the modeling collective behaviors, identifying cells’ behavior pertaining to the first- and the second-order behavior, which includes distinguishing cells’ internal transition from first- to second-order emergent behavior.

4. Consequently, simulating the Aggregation and Migration phases of the process and visualize their results.

Phase 1

Understanding and Modeling D. discoideum First-order

Emergent Behaviors

Understanding D. discoideum first-order emergent behaviors (vegetative, streaming, pre-aggregation)

Applying emergence framework to D.

Discoideum (first-order)

D. discoideum agent-based model of first-order emergent behaviors

Algorithms and simulations Biological illustration 1.1

1.2 1.3

1.4 1.5

Phase 2

Understanding and Modeling D. discoideum Higher-order

Understanding D. discoideum higher-order emergent behaviors (aggregation, migration, culmination)

Applying emergence framework to D.

Discoideum (higher- order)

D. discoideum agent-based model of higher-order emergent behaviors

Algorithms and simulations Biological illustration 2.1

2.2 2.3

2.4 2.5

Phase 3

Identifying Mechanisms and Defining Design Patterns for Higher-order

Identifying mechanisms for higher-order emergent behaviors

Defining new design patterns Implementation and Validation 3.1

3.2 3.3

Phase 4

Translating D. discoideum higher-order emergent

behaviors to robots

Understanding swarm robotics (software and hardware perspective)

Translating first- and higher order collective model into the small Kilobots

Finalizing writing PhD manuscript 4.1

4.2 4.3

Fig. 1.1 |Ph.D. project: The main tasks of four phases of the Ph.D. project.

From an engineering perspective, swarm robotics relies on a high number of robots with identical algorithms to provide global behaviors as a single robot unit. Such a cooperative

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1.4 Relevance and Impact 9 social behavior is analogous to cell biology in which individual amoebae communicate themselves and work together to sustain their life. By constructing computational models of the behavior of the cells, we pass the following facts at the same time:

• Getting an insight into connections between individual and global behaviors.

• Developing a computational theory for how agents/robots operate.

• Understanding how we might program swarm robotics to accomplish tasks that we specify.

Novel bio-inspired self-organizing design patterns

During the last20 years, mechanisms, and design patterns for understanding and modeling first-order emergent behavior are well documented and studied [18]. However, there are not eagerly available tool, and design patterns that collectively produce higher-order emergent behavior. Frameworks for analyzing different levels of emergence remain in their infancy or are not applied to artificial systems. As mentioned before, one of the main objectives of this project is to derive engineering principles inspired by D. discoideum to develop collective adaptive artificial systems (e.g., swarm robotics).

InD. dicoideumsystem, two main entities can be recognized: (1) the D. discoideum cells, which cooperates and form an organization in the process, and (2) the environment and its changing circumstances, which is a physical location where the organization is established.

The environment affords food resources – bacteria – that the population can use, events that can be recognized by the cells, and make the adaptation, which can produce changes in the whole system (the starvation). Cells can interact with each other by chemical signals, measure different factors from the environment, and act individually or collaboratively over the situation. We know that individual cells are self-governing and proactive, and they have partial, incomplete knowledge of the population size and the environment. Moreover, the resources in the environment are changing, and it influences the behaviors of the organisms significantly. In this system, the interaction between the organisms is direct and indirect;

cells use one to one communication like pulling or pushing, or they use the environment to release and collect information.

(see Chapter 7: Design pattern–Page 97)

1.4 Relevance and Impact

This section describes the potential repercussions and impacts of the thesis on science, medicine, and industry:

• For researchers in biology: This thesis delivers the advantages of computer simulations to biology. Researchers can use our proposed simulation models for an individual cell

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to speed up their research. Success with this agent-based collective model will generate the necessary foundation for then tackling more complex and biologically relevant organisms. For example, the principal part of our first-order emergence model is about cell-cell interactions, which provides how cells communicate with their surrounding environment and each other. In this model, we incorporate many different systems that are at play in a cell (e.g., cell’s age, releasing and sensing various chemical signals, cell density). Therefore, it will deliver researchers a comprehensive platform for studying a much higher set of questions.

IndeedD. discoideum is increasingly used for the investigation of human disease genes and the crosstalk between host and pathogen [19]. Several of these issues have already been the subject of studies [20–23]. Additionally, D. discoideum has been used to identify targets for drugs used to treat human diseases: cisplatinum, an anticancer agent [11, 24], lithium used to treat bipolar disorder [25], and bisphosphonates used to treat osteoporosis [26]. These studies are reviewed in Müller [19] and Williams’s recent work [27]. Besides, Williams [27] emphasizes in his paper the similarities between legionella infection inD. discoideumand animal cells. Additionally, collective migration inD. discoideum (and other lower eukaryotes), comprises similar actin dynamics and cell-cell binding to collective migration in multicellular vertebrates and among cancer cells [28].

• For researchers in agent-based, collective artificial intelligence systems: Additional pat- terns for first-order collective behaviors complete the catalog of patterns [18], most importantly providing novel higher-order collective behavior design patterns that go well beyond current first-order ones. They can then be applied to cyber-physical-systems, socio-technical systems, interacting smart objects, and more generally smart cities scenarios to design large-scale autonomous systems that adapt to unforeseen situations.

• For researchers in swarm robotics: Applying the identified design patterns to engineer first-order and higher-order emergent behaviors into swarms of robots. With our new models and design patterns, the researchers in this field can achieve the desired collective behavior, which will emerge from the intercommunications between the robots and interactions of the robots with the environment.

• For commercial and other research sectors: Swarm robotics provide explications for commercial and research areas to elucidate the benefits of collective emergence and its potential to deliver practical resolutions for real-world problems. In general, our bio-inspired models can be used in swarms of Kilobots or the development of other new robotic swarms for different purposes in a host of swarm robotics industries. These collective intelligence models are valuable for different applications such as autonomous exploration in unknown environments like collapsed construction to find survivors, dangerous tasks in hazardous workplaces, and self-assembling to create a specific composition.

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Chapter 2 Dictyostelium discoideum

Since 1869, when Oskar Brefeld discovered Dictyostelium, the organism has been named slime molds [10]. However, among different species,Dictyostelium discoideum is the most often-studied social amoebae [29], which was discovered by Kenneth Raper in 1935 [30].

Recently, many workers, such as R. Kessin in his book [10], have chosen the terminology Dictyostelium discoideum or social amoeba to use. Therefore, in this thesis, we will use D. discoideum or social amoeba. This chapter first presents a brief glossary of terms and a summary of the development of D. discoideum, and then, its first and second-order collective behaviors during its life cycle.

2.1 D. discoideum Behavior

D. discoideum is a social amoeba (from Dictyostelid family [10]) able to adopt a unique strategy for multi-cellular development; to change behavior and to display different emergent collective properties during its life cycle. Its typical length is about 10 µm in diameter [31, 32], and its movements are 20µm per 100 secperiod for each cell [33].

The Dictyostelids¹ have engrossed biologists for over 150 years [11] with their ability to recruit and aggregate up to a million amoebae to create a single migration super-organism [12], which after seeking out a spot for spore dispersal, revolutionizes to a complex fruiting body.

Fig. 2.1shows the different phases ofD. discoideumlife cycle. The life cycle rises following the release of the spores from a mature fruiting body. At high enough concentrations (high cell density), the amoebae enter into a new mode of existence characterized by the expression of genes associated with collective behaviors.

During the “Vegetative” phase, the amoebae divide by mitosis, are attracted by folic acid, feed on bacteria, yeast, and grow as independent single cells. The amoebae continuously monitor the ratio of the population of amoeba over the bacteria by secreting the prestarvation factor (PSF) [34].

1More details aboutDictyostelium can be found inhttps//www.dictybase.org

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When the supply of bacteria is depleted, a self-organized developmental program is triggered. After approximately4-6 h of starvation [35], the amoebae enter the “Aggregation”

phase during which up to10⁵cells [10] gather toward the main oscillatory center by secreting and responding to the chemo-attractant: cyclic Adenine Monophosphate (cAMP²). At the end of the aggregation phase, cells’ first differentiation is limited to two major categories, pre-stalk (PST) and pre-spore (PSP) types, which will become the spore and stalk cells, respectively. Pre-stalk cells take place at the tipped of the “Mound”. At this stage, the cells begin to pile up, forming a three-dimensional mount. Then, the mound extends up to the air to make the “Tipped finger” structure. The tipped finger falls over after approximately 16 h of starvation [35] and starts to migrate away in a polar fashion, toward light and heat.

This motile organization of cells, which is also known as “Migrating Slug”, made by 2×10⁴ - 1×10⁵ cells [36, 37]. These new phototaxis and thermotaxis behavior of the slug help it to go to the surface of the soil [37, 38]. The slug consists of two parts: anterior (tip), which includes PST cells and posterior (tail), which includes PSP cells. The tip is the organizer and is responsible for the direction of the slug. Each slug is about2-4 mm long and is protected by a cellulose sheath [39, 40]. Once the slug finds a suitable spot, it stops the forward-only direction movement. Afterward, the anterior part rises up in the air, and the posterior part spreads out to make a “Mexican hat” shape structure. Two other fascinating behaviors concerning emergence deserve to mention here:

• If either the anterior or the posterior of a slug is cut off, the remaining cells of the slug reorganize it. Therefore, some of the cells with interchangeable ability, transdifferentiate into the other cell type until a new ordinarily patterned slug is formed [41].

• Slugs fuse and separate all the time; they also mop up single cells when they go over them.

(see D. discoideum slug’s tip characteristics in Section 2.4 – page 23) Then, the front part of the Mexican hat forms a cellulose tube. The posterior cells climb up the outside of the tube until the top, and in the meantime, the pre-stalk cells move down.

This multicellular structure is known as “Fruiting body” about 4 mm high consisting of a

“Stalk” supporting a “Spore mass”. Eventually, after a process of8-10 hours [42], the mature fruiting body is fully formed, which is characterized by their ability to disperse the spores by the air. Eventually, a whole cycle begins over again by releasing spores after the sporocarps burst out. Usually, a multicellular stalk supports aloft the sporocarp, which contains the mass of 80’000spores, which are dispersed for reproduction [43].

The red arc of Fig. 2.1presents the vegetative phase and the aggregation phases, where we observe the first-order emergent behavior of D. discoideum, when individual cells behave collectively as a swarm. Also, the blue arc ofFig. 2.1demonstrates the mound, tipped finger,

2cAMP as a molecule, which the amoebae realize during chemotaxis, will be explained in detail in future sections.

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2.1D. discoideum Behavior 13 slug formation, and migration phases. In this part, we investigate the second-order emergent behavior, when the cells form a higher-order structure as the slug. The slug migrates and behaves as a single organism with new properties. This collective migration allows the population to move for longer distances and more efficiently than individuals, also reduce the risk of predators [10].

Fig. 2.1 | Schematic diagram of D. discoideum life cycle: The development process is highly regulated and depends on the local cell density [44]. From 10³ to 10⁵ cells [10]

aggregate together (after approximately4-6 h of starvation [35]) in response to cAMP signals emanating from the center of an aggregation territory. The whole morphogenesis development happens in24 hours [45]. (A reproduction inspired from www.dictybase.org)

The whole transformation process is regulated by 349 different proteins secreted by developing cells [46]. Nonetheless, the most significant agents in our models are PSF, CMF, Adenosine, PDE, CF, and3’,5’ -cyclic adenosine monophosphate (cAMP). In fact, a key role in aggregation is caused by periodic cAMP secretion (Fig. 2.4) and is amplified by surrounding starved cells, which results in cell polarization and stream formation [47].

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2.2 Vegetative and Pre-aggregation Phases

As explained in the previous section, during the vegetative phase, the unicellular amoebae divide by binary division as they feed on bacteria, and monitor their own density [48]. On exhaustion of the food supply, the developmental phase starts when hundreds of od thousands the cells aggregate and go through a sequence of morphogenetic phases [10].

Nutrient Sensing and Vegetative State

As long as the food is present, the vegetative cells monitor food bacteria within a limited area and respond to folic acid (FA) as a derived metabolite [49]. Each cell reacts autonomously to FA as a chemoattractant generating a spatial cue that cells use to hunt bacteria [50].

Prestarvation Factor (PSF): The constant interaction between cells is essential for the development of D. discoideum, and depends on the identification of emitted signals [45].

Fig. 2.2demonstrates the releasing time of various signals. Starvation makes the cells less responsive to FA and also causes the emergence of different new genes, which are essential for chemotaxis toward cAMP [10]. PSF is an autocrine factor that is secreted by growing cells until early multicellularity development [48]. It has two significant roles: measuring cell density and the ratio of bacteria toD. discoideum cells [50].

starvation

t = 0

PSF CMF

t = 5 hr

adenosine, (cAMP + PDE) , CF

t = 12 hr

aggregation

Fig. 2.2 | Chemical signals: Times of continuously synthesizing and secreting autocrine factors before and after starvation.

Conditioned Media Factor (CMF): Another crucial factor forD. discoideumdevelopment is CMF(an 80-kDa glycoprotein), which is secreted by starved cells slowly and simultaneously as preparation for aggregation [37]. CMF secretion serves to synchronize the beginning of the aggregation, signaling when the number of starved cells passed a critical threshold.

Single-cell Self-analysis

We discuss here the behavior of single cells, how they analyze themselves, and undertake differentiation toward becoming regular cells or centers (i.e., recruiting regular cells to form an aggregation territory, which will later become a slug).

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2.2 Vegetative and Pre-aggregation Phases 15 Cell growth cycle and cell differentiation: Aggregation begins for starved cells, which are in theS phase of their growth cycle(see Fig. 2.3: Cell growth cycle); this occurs between 2 h to 3 h and also between 6 h to 7 h after release [51]. When cells are synchronized in S phase, approximately 50% of the population initiates centers. However, when cells are synchronized in the late G2 phase (T7 cells), only7.5% of the population initiates centers [51]. Thus, in a population containing homogeneous cells in different phases of their cell cycles, it may be the S-phase cells that differentiate earliest and possibly initiate centers.

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Fig. 2.3 | D. discoideum cell growth cycle: the whole doubling time is approximately 7.2hr and most of it, is G₂ phase – (Inspired from Maeda’s work [49].)

Spontaneous Center Selection

As described in the previous section, some starved amoebae have the potential to initiate the aggregation centers, but there are three facts we should keep in mind:

1. Some researchers [52] commonly stated that cells with the capability of aggregation initiation are not genetically distinct. Being an aggregation initiator only depends on the cell’s random location in the population. However, these randomly selected initiators have to first meet a crucial threshold of density as a physiological environment by sensing the level of concentration of CMF. Moreover, there are other researchers [53, 54], who believe that initiators are genetically distinct from regular cells, in terms of dimension and capabilities. They declare that this particular type of cell is usually needed to launch the aggregation phase in the D. discoideumlife cycle after starvation [55]. The large cells (I-cells) [53] are the initiator cells in the population of smaller cells that are responder cells (R-cells). I-cells can be identified by their large dimensions, their more significant activity, and their peculiar structure [53].

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2. D. discoideum cells are sensitive to the inhibition action of adenosine, released by already initiated centers. The concentration of adenosine at5mM impedes aggregation center initiation without any competition concerning cAMP and the signal relay [56].

3. Amoeba’s position in its growing cell cycle at the onset of development influences the differentiation of the population.

Approximately400 per eachmm² is a critical density to reach the cAMP concentration threshold; less than it, the aggregative signal cannot be stimulated in the population [10].

During the aggregation phase, the movement of cells consists of cell adhesion and making streams, then the streams converge to the significant streams, and finally, they gather in the centers.

(To see the single cell self-analysis in our model check Section 5.1.3 – Page 54)

Sussman’s work [57] indicates that the number of aggregative centers is both a function of the number of the cells and the population density. Then, in the optimal population densities, the number of centers is constant at the different developmental stages.

Chemotaxis

Chemotaxis inD. discoideum morphogenesis is the movement of the amoebae (Fig. 2.4), as a reaction to starvation, which is determined by spatial and temporal leads of the dynamic cAMP gradients as a chemical stimulus.

Cyclic Adenosine Monophosphate (cAMP): As mentioned in Section 2.1, individual amoebae acquire new and unique abilities such as synthesis, detection, and degradation of cAMP after starvation. During aggregation and even after it, the centers release short, periodic pulses of cAMP autonomously. The other cells make a positive feedback loop. Starved amoebae gather by periodically synthesizing and secreting cAMP into the extracellular medium and also responding to it by small step forward. Fig. 2.5shows the increasing levels of cAMP threshold regulating, respectively, the appearance of new centers, the relay of cAMP by regular cells, and the chemotaxis threshold is inducing cell movements and streaming [58].

Phosphodiesterase (PDE): Secreted cAMP is the principal signal in the development of D. discoideum, and its degradation is regulated by an extracellular cyclic nucleotide phosphodiesterase (PDE). It is specifically responsible for converting cyclic-3’, 5’-AMP to 5’-AMP [60]. Since PDE is released to the external medium by cells at the same time as cAMP production, at higher cell densities, higher degradation rates are expected.

Refractory period: As a highly organized system, during the cAMP signal propagation, there is a delay between receiving and releasing the cAMP pulse, which is called the “Refractory period” [61]. As the cAMP waves move through the population directionally from the center, the responding amoebae must become insensitive for a short time after relying on. Otherwise, they would react to the reflection of their own relayed signals.

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2.3 Aggregation Phase and Stream Formation 17

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Fig. 2.4 | Amoeba polarization and signal emitting: The left image demonstrates the D. discoideum cell movement toward cAMP emitted from a source. The right image demonstrates the chemical diffusion from cell to the extracellular medium.

cAMP concentration for a regular cell New center threshold Relaying threshold

Chemotaxis threshold

Fig. 2.5 | Different levels of cAMP thresholds: After the first threshold, cells start to move chemotactically toward the higher cAMP concentration. If the cAMP concentration is higher than the second threshold, cells begin to relay the cAMP signal, at the same time, they move. Nevertheless, if the concentration of cAMP is higher than the third one –“new center formation”– one of the regular cells will be allowed to become a spontaneous center. These thresholds are defined by considering the refractory period [59]. To see the use of these three different thresholds in our first-order collective behavior model, see Section 5.1 – Page 49.

2.3 Aggregation Phase and Stream Formation

As explained in previous sections, the remarkable feature of D. discoideumcells is that food exhaustion triggers a relatively simple program of multicellular development, the starved cells switch behavior to survive. This multicellularity, in many ways, resembles animal development [62, 63]. This ability consists of self-aggregation, dynamic self-assembly, and self-disassembly.

Fig. 2.6 highlights schematically the differences between first- and second-order emergence:

a. First-order emergent behaviors during vegetative phase:

i. Small individual cells interact with each other.

ii. Cells recognize themselves within an aggregation territory, as a community.

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b. Second-order emergent behaviors:

iii. Slugs formation and slugs interaction - new property emerge such as: thermotaxis and phototaxis, uniform distribution of slugs in the environment [38].

iv. Slugs can merge with other slugs and divide into several small slugs. A slug is also able to mop up single cells or aggregates when it goes over them.

i. vegetative ii. aggregation iii. slugs formation iv. slugs behaviours

a. First-order b. Second-order

Fig. 2.6 | Differences between first- and second-order emergence: During D. dis- coideumlife cycle, different levels of behaviors emerge, whereby more comprehensive organisms like slug arise through simple interactions among individual cells.

a. b. c.

d. e. f.

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10:30 11:40 14:35

Fig. 2.7 | Aggregation phase of D. discoideum life cycle: Aggregation of starved Ax2(ka) cells strain during D. discoideum life cycle –Lab experiment and photography by UNIGE, Department of Biochemistry, Prof. Thierry Soldati’s group, Jahn Nitschke.

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2.3 Aggregation Phase and Stream Formation 19 Fig. 2.7illustrates the different stages of the D. discoideumlife cycle. In the vegetative phase (a.), individual mononucleated amoeba move around on their own grazing food. Once the food is scarce, cells gather in response to cAMP signals (b.,c.), which emanates from the centers. Centers are pacemaker cells which begin spontaneously, to secrete cAMP.

Once D. discoideum cells receive the cAMP signal, they start to relay it and aggregate chemotactically toward the higher cAMP concentration area (d.), which has a locally higher cell density [64]. The cells migrate collectively like streams(d., e.) toward the spontaneous centers. Afterward, streams aggregate and form a hemispherical mass (e.), which is called mound. In this state, the cells start to differentiate into several different cell types, e.g., pre-stalk cells, which will make the stalk and the basal disk [64], upper and lower part of the fruiting body; and pre-spore cells, which will transform into spores.

Aggregation Territory Size and Late Centers

When D. discoideum cells grow, and the population begins to rise, largely unaware of each other, a set of factors is used to measure the ideal amoeba numbers required to form a complete multicellular organism. Basically, cells use different substances to monitor the population size, extracellular environment, and control the choice between growth and differentiation.

In previous sections, we identified CMF and PSF. In this section, we identify CF as another significant biochemical signal during the development ofD. discoideum life cycle.

Counting Factor (CF): In addition to CMF, CF affects the developmental process in order to regulate the size of a group of cells. It is involved in sensing the number of cells in an aggregation stream. The high concentration of CF causes large aggregation streams to divide into small groups [65].

To achieve the optimal spore dispersal, a fruiting body has to hold the spore mass as high as possible from the ground. In that way, there might be a relation between the number of dead cells in the stalk and the number of spores in the sporangium. Thus, on the one hand, the process tries to survive the maximum number of cells, and on the other hand, increasing the number of cells in the sporangium, there should be a proper sturdy stalk to keep them safe. Thus, in a field of starving D. discoideum, there are an upper threshold and lower threshold on a number of cells in each aggregation center. In other words, depending on the planting density and the type of species, the average size territories usually are the same [66].

2.3.1 Stream-Breaking Phenomenon

As mentioned before, during the aggregation phase, starved cells migrate forming patterns, very similar to veins or branches; this phenomenon is called streaming. Afterward, streams aggregate and form a hemispherical mass, which is called mound.

In higher density zones, the cells relay the cAMP signal more strongly, which attracts more cells compared to the low-density regions. Consequently, they attract additional cells.

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As discussed before, cells at high-density produce more CF. On the other hand, we know that the cell’s motive force, the force involved in the movement of the cells, depends on the strength of the cAMP signal, which also depends on the cell density and cell’s distance from the spontaneous center. Thus the combination of CF with motive force (cell-cell interaction) causes stream break-up. The moving streams break into shorter streams, smaller aggregates develop, and new centers arise. Fig. 2.8illustrates the stream formation during aggregation phase.

a. b. c.

06:25 07:00 07:35

Fig. 2.8 |Streaming and stream break-up: Different stages of the aggregation of starved Ax2(ka) cells strain during D. discoideum life cycle. a.Early aggregation phase. b. Waves in a streaming aggregate. c. Streams break, and new centers develop, a mound will develop after the streams reach the aggregate.–Lab experiment and photography by UNIGE, Department of Biochemistry, Prof. Thierry Soldati’s group, Jahn Nitschke (hh:mm after starvation onset at frame 1 of the video: 05:30).

(see our agent-based model of stream break-up phenomenon in Section 2.3.1 – Page 19).

D. discoideum: first-order emergence

The first-order emergent behavior of D. discoideum happens during the vegetative and the aggregation phases (red arc on Fig. 2.1), where free-living individuals communicate with each other like a swarm. From the perspective of the mathematical modeler, in D.

discoideum life cycle, collective behaviors arise by starvation of amoebae, in which cells produce, secrete slowly, and detect small molecules (cAMP). At high concentrations (high cell density), the amoebae enter into a new mode of existence characterized by the expression of genes associated with collective behaviors. From this point up to several hundreds of thousands of cells aggregate chemotactically to form a multicellular structure, which is called slug (Fig 2.9) [58].

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2.4 Migration Phase and Fruiting Body Formation 21

pst cells psp cells

(a) (b) (c) (d) (e) (f)

Fig. 2.9 | From mound aggregation until slug formation: After aggregation, pre- stalk (PST) and pre-spore (PSP) cells arrange themselves into a slug. They first make a mound (a, b), which elongates and finally tips over (c, d). Fig. (e) shows the cylindrical finger that falls over onto the substratum and migrates like a slug (f). The PST (shown in red) cells position themselves in the anterior part and the PSP cells (shown in blue) relocate themselves in the posterior part.

2.4 Migration Phase and Fruiting Body Formation

After aggregation and mound formation, the cells make a coherent and cohesive organization, which is enclosed by the slime sheath [39]. This superficial morphology is similar to a slug without organs. The multicellular organization displays phototaxis and thermotaxis behavior.

These two sophisticated slug characteristics lead the cell mass upward toward the surface of the soil in a coordinated way [37, 38]. Usually, after about 24 hours of development, the cell mass transforms into a new organization called a fruiting body consisting of a globe of spore cells on top of a slender cellular stalk [67]. Its function is to hold the spore mass off the ground for optimal spore dispersal [37]. Eventually, this complex multicellular organization disperses again, spores germinate, each releasing a new amoeba. At this point, the cells resume their individual behavior. This social, relatively simple but yet powerful behavior is particularly appealing to inspire the engineering of swarm robotics, where a large number of simple, self-organized and homogeneous robots adapt and coordinate themselves with the environment changes.

Additionally, at the migrating stage of D. discoideum life cycle, slugs, which consist of up to10⁵ cells [68–70, 36, 71], show unique movements without any muscles or nerves. Each slug consists of 20% anterior (PST cells), and 80% posterior (PSP cells) parts [32]. If we compare the movement speed of two similar slugs regarding the number of consisting cells and age of formation, the one which is shorter and fatter will move slower than the one which is thinner. Also, Inouye [72] illustrates that the slug with less formation age (younger slug) moves faster.

D. discoideum: second-order emergence

During mound formation (Fig. 2.10-a), tipped finger (Fig. 2.10-b), and migration phases (Fig. 2.10-c, d) – blue arc onFig. 2.1– we observe the second-order emergent behavior of

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D. discoideum. In these phases cells form a higher-order structure (slug), which moves and behaves as a single organism with its own new property. Collective migration allows the cells to move more efficiently and for longer distances than individuals and reduce the risk of predation.

a. b. c. d.

02:20 04:05 05:50 06:25

Fig. 2.10 | Collective movement ofD. discoideum cells: Slug formation during Ax2(ka) strain D. discoideum life cycle, from the Mound formation phase until the Migration phase –

Lab experiment and photography by UNIGE, Department of Biochemistry, Prof. Thierry Soldati’s group, Jahn Nitschke (hh:mm after starvation onset at frame 1 of the video: 17:40).

In the second-order of emergence, specific perturbations of the system are amplified [73].

Due to a specific structural and functional organization, collective systems represent several essential challenges for researchers [74]. Adaptive and self-developmental processes happen in different phases of D. discoideum life cycle as a collective system. What distinguishes the first-order collective behavior (swarm mode) [74] explicitly from the higher-order collective behavior (organism mode) [74] is the fact that, in organism mode, even though cells still retain individual behavior, the slug acts as a single organism.

Table 2.1 demonstrates the categorization of different behaviors of D. discoideum cells from a separate emergence order. Self-organized cells have different characteristics in swarm mode and organism mode. In swarm mode, the D. discoideum population cells perform parallel swarm responsibilities such as search, quorum sensing, food localization. Then, the environmental conditions impose the cells to self-assemble into a specific structure (aggregation).

This change in the system’s state can be called the transition from swarm mode to organism mode (slug formation). In organism mode, a new higher-level of processes, interactions, and communication with the environment happens. This transition creates a macroscopic regulative formation and delivers self-recognition of the slug’s cognitive capabilities, such as merging with other slugs or sensitivity to the light and heat. The slug as a new structure has a self-repairing behavior; for example, if the tip is amputated, the slug is able to reproduce a new tip. The cells inside the slug have macro-actuation behavior, which supports them to migrate as a “whole” to reach a suitable location. The new location setting initiates a

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2.4 Migration Phase and Fruiting Body Formation 23 Table 2.1 | Main differences betweenD. discoideum swarm mode and organism mode. In this thesis, the terminology of swarm modeand organism modehas been chosen to use, which is presented in P. Levi et al. book [74].

Characteristics Vegetative phase Slug phase

(swarm mode) (organism mode)

Reproduction Self-replication No

Ingesting Self-organization No

Movement Randomly Strong coordinated

Structure amoebae with pseudopods Dynamic changing Coordination cAMP, Chemical secretion cAMP, Connected

behaviors Generalized Strong specialized

Functionality Emerged Dynamic change: Evolved

Mono-functionality Macro-functionality

Adaption Aggregation Changing position

Defense mechanism Self-regulation Homeostasis, Self-healing Advantages Self-organization Plasticity, Reliability, Stability

new homeostatic phase (culmination). Then, the system begins self-disassembly to make the second transition from organism mode to swarm mode.

More specific behavior and properties of both first- and second-order will be discussed along with the corresponding agent-based models in Chapter 5 and Chapter 6.

Characteristics of D. discoideum aggregation tip

It is confirmed that the tip has an important role in D. discoideum morphogenesis. It ensures the morphological integrity of the organism [75]; however, the complexity of its functionality is unexplored [76]. This is also established that the tip controls the slug’s behavior by performing as a source of extracellular signaling [77].

Here, we identify five fundamental characteristics of the tip of a slug:

1. The tip has unique organizer-like properties. It acts the same at all phases, from the aggregation phase to fruiting body formation [78]. The slug particularizes anterior- posterior polarity [79].

2. The tip acts as the source of inhibition for late tip development [80].

3. The tip is the sensitive sector to light stimuli [81].

4. An amputated slug is able to regenerate a fresh tip [82]

5. The tip decides between extending the slug migration phase or staying for fruiting-body formation (timing of entry into the culmination phase) [76, 77].

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Additionally, during the slug phase, the sheath is produced by leader cells to support the cells in the interior part. It supports the traction for collective movement in the slug [39, 83].

In terms of tip inhibition, there are two factors which define the size of aD. discoideum slug [84]:

1. The strength of the tip to organize the following cells from competing

2. The strength of the following cells to continue being constrained to the first tip by ignoring the newly arisen tip.