Centrosomes are microtubule-based organelles composed of two centrioles and peri-centriolar material, involved in the formation and organization of the mitotic spindle, serving as microtubule-organizing center and involved in ciliogenesis. Supernumerary centrosomes are detrimental for cell physiology and activate the PIDDosome, a multi-protein complex that serves as a platform for the activation of Caspase-2, composed of: PIDD1, RAIDD and Caspase-2 itself. Caspase-2’s preferred cleavage site based on peptide screening is VDVAD, however Caspase-2, when activated via the PIDDosome, cleaves its bona fide substrate MDM2 (negative p53 regulator) in the FDVPD sequence. Here, I present evidence for VDVADase activity in apoptotic cells lacking Caspase-2, which suggests that this cleavage site is not Caspase-2 specific when the Caspase-2 activation occurs via the PIDDosome. In order to investigate if the mode of activation of Caspase-2 determines its substrate specificities I performed a Caspase-2 rescue experiment and introduced several mutations affecting the Caspase-2 autoproteolytic-processing. Furthermore, I present evidence that exogenous Caspase-2 is able to form the PIDDosome and cleaves MDM2 but when key autoproteolytic sites are mutated no MDM2 cleavage is detectable. Supernumerary centrosomes also accumulate upon overexpression of PLK4 (a kinase regulator of the centriole duplication). Immunofluorescence images of cells overexpressing PLK4 were taken following the centrioles quantification over time. Consequently, a large amount of image data was accumulated, which necessitated the development of a semi-automated pipeline for centrioles counting. This pipeline was generated using the image processing and analysis tool ImageJ and the deep learning segmentation tool MitoS together with the pretrained MitoSegNet model, which was finetuned to count centrioles stained against different centrosomal epitopes, namely Centrin 1, γ-Tubulin and ANKRD26. This semi-automated method of centrioles quantification is easy to use, reproducible and faster than manual quantification. Using this pipeline to quantify centrioles in p53, SCLT1 or ANKRD26 lacking cells we demonstrate accumulation of supernumerary centrosomes in these cells similar to parental cells. / I centrosomi sono organelli cellulari a base di microtubuli, composti da due centrioli e dal materiale pericentriolare che li circonda. I centrosomi sono coinvolti nell'organizzazione dei microtubuli, nella formazione del fuso mitotico e nella ciliogenesi. I centrosomi soprannumerari sono dannosi per la fisiologia cellulare e attivano il PIDDosoma, un complesso multiproteico, composto da PIDD1, RAIDD e Caspasi-2, che funge da piattaforma per l'attivazione della caspasi stessa. Il sito preferenziale di proteolisi di Caspasi-2 è stato individuato tramite screening peptidico nella sequenza VDVAD. Nonostante ciò, quando attivata tramite il PIDDosoma, Caspasi-2 scinde il suo substrato di elezione MDM2 (regolatore negativo di p53) a livello della sequenza FDVPD. In questa tesi presento evidenze di attività VDVAD-asica in cellule apoptotiche prive di Caspasi-2, suggerendo che questo sito di taglio non sia specifico di Caspasi-2 quando la sua attivazione avviene tramite il PIDDosoma. Al fine di indagare se la modalità di attivazione della proteasi determina le sue specificità di substrato, ho eseguito esperimenti di complementazione di Caspasi-2 facendo uso di diversi mutanti che influenzano il suo processamento autoproteolitico. Inoltre, presento prove che Caspasi-2 esogena è in grado di assemblare il PIDDosoma e proteolizzare MDM2 ma quando i suoi siti chiave di autoproteolisi sono mutati non è rilevabile il taglio di MDM2. I centrosomi soprannumerari si accumulano anche in caso di sovraespressione di PLK4 (chinasi regolatrice della duplicazione dei centrioli). Immagini di immunofluorescenza di cellule che sovraesprimono PLK4 sono state acquisite seguendo la cinetica di accumulo dei centrioli nel tempo. Di conseguenza, l’ingente mole di dati generati ha reso necessario lo sviluppo di una procedura semiautomatica per la conta dei centrioli. Questa pipeline è stata generata utilizzando il programma di elaborazione e analisi di immagini ImageJ e il programma di segmentazione basato su deep learning MitoS, insieme al modello MitoSegNet, che è stato affinato per la conta dei centrioli evidenziati tramite immunofluorescenza diretta contro diversi epitopi centrosomiali, ossia: Centrin 1, γ-Tubulina e ANKRD26. Questo metodo semiautomatico di quantificazione dei centrioli è facile da usare, riproducibile e più veloce della quantificazione manuale. Utilizzando questa procedura per quantificare i centrioli nelle cellule prive di p53, SCLT1 o ANKRD26, dimostriamo che l'accumulo di centrosomi soprannumerari in queste cellule è simile a quello riscontrato nelle cellule parentali.

La réponse cellulaire humaine aux agents génotoxiques est essentielle pour le maintien de l'intégrité génétique. Elle implique une régulation coordonnée de nombreuses voies métaboliques qui déclencheront un arrêt du cycle cellulaire et la réparation des macromolécules endommagées, l'inflammation et l'apoptose. La Réparation Globale du Génome par Excision de Nucléotides (GG-NER) est une voie majeure de réparation de l'ADN pour la prévention de la cancérogenèse car elle élimine une grande variété de lésions induites par les rayonnements ultraviolets, des carcinogènes chimiques et d'autres facteurs de notre environnement. Ces lésions sont reconnues par XPC, qui est le premier facteur protéique impliqué dans cette voie de réparation. XPC forme un complexe avec Rad23B. Nous avons montré qu'in vivo le complexe XPC/Rad23B comportait également la centrine 2. Le mode d'interaction de XPC avec la centrine 2 est très conservé de la levure à l'homme indiquant une participation de ce complexe à un processus biologique général à tous les eucaryotes. La centrine 2 est impliquée dans la division cellulaire en régulant la duplication du centrosome. Rad23B intervient dans le contrôle stabilité/dégradation des protéines par le protéasome 26S. Nous avons montré que l'existence de ce complexe ancré à la chromatine permettait son accumulation immédiate sur les sites des lésions induites par les UV ou après l'impact d'un laser à 405 nm. Cette localisation dépend uniquement de la présence de XPC. Nous avons montré que XPC régulait le niveau basal et l'équilibre de la centrine 2 entre le noyau et le centrosome. Ceci pourrait être primordial pour coordonner la réparation de l'ADN et la division cellulaire. De plus, nous avons observé que Rad23B promouvait la survie cellulaire en stabilisant XPC après une irradiation aux UVC. Enfin, nos résultats montrent que la présence de XPC est requise pour l'accumulation des transcrits centrine 2 et Rad23B suite à une irradiation aux UV. Ceci conforte l'idée que XPC pourrait faire partie d'un système de signalisation qui induit l'expression de gènes après la reconnaissance des dommages de l'ADN. Cet hétérotrimère regroupe donc des protéines aux fonctions distinctes qui sont localisées précocement sur les dommages de l'ADN. Nous proposons que ce complexe coordonne différents processus biologiques immédiatement après la reconnaissance des lésions par XPC : la régulation du cycle cellulaire par la centrine 2, le contrôle stabilité/dégradation de protéines, dont XPC, par Rad23B et le déclenchement de la réparation et l'induction de l'expression de gènes par XPC. Des études récentes montrent que XPC serait également impliquée dans d'autres voies de réparation comme la réparation par excision de bases et la réparation des cassures double-brin. L'ensemble de ces observations suggère que ce complexe multifonctionnel pourrait avoir un rôle global dans la réponse cellulaire aux agents génotoxiques.

Biological cells consist of many subunits that form distinct compartments and work together to allow for life. These compartments are clearly separated from each other and their sizes are often strongly correlated with cell size. Examples for those structures are centrosomes, which we consider in this thesis. Centrosomes are essential for many processes inside cells, most importantly for organizing cell division, and they provide an interesting example of cellular compartments without a membrane. Experiments suggest that such compartments can be described as liquid-like droplets. In this thesis, we suggest a theoretical description of the growth phase of centrosomes. We identify a possible mechanism based on phase separation by which the centrosome may be organized. Specifically, we propose that the centrosome material exists in a soluble and in a phase separating form. Chemical reactions controlling the transitions between these forms then determine the temporal evolution of the system. We investigate various possible reaction schemes and generally find that droplet sizes and nucleation properties deviate from the known equilibrium results. Additionally, the non-equilibrium effects of the chemical reactions can stabilize multiple droplets and thus counteract the destabilizing effect of surface tension. Interestingly, only a reaction scheme with autocatalytic growth can account for the experimental data of centrosomes. Here, it is important that the centrioles found at the center of all centrosomes also catalyze the production of droplet material. This catalytic activity allows the centrioles to control the onset of centrosome growth, to stabilize multiple centrosomes, and to center themselves inside the centrosome. We also investigate a stochastic version of the model, where we find that the autocatalytic growth amplifies noise. Our theory explains the growth dynamics of the centrosomes of the round worm Caenorhabditis elegans for all embryonic cells down to the eight-cell stage. It also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with disturbed centrioles. Our example thus suggests a general picture of the organization of membrane-less organelles. / Biologische Zellen bestehen aus vielen Unterstrukturen, die zusammen arbeiten um Leben zu ermöglichen. Die Größe dieser meist klar voneinander abgegrenzten Strukturen korreliert oft mit der Zellgröße. In der vorliegenden Arbeit werden als Beispiel für solche Strukturen Zentrosomen untersucht. Zentrosomen sind für viele Prozesse innerhalb der Zelle, insbesondere für die Zellteilung, unverzichtbar und sie besitzen keine Membran, welche ihnen eine feste Struktur verleihen könnte. Experimentelle Untersuchungen legen nahe, dass solche membranlose Strukturen als Flüssigkeitstropfen beschrieben werden können. In dieser Arbeit wird eine theoretische Beschreibung der Wachstumsphase von Zentrosomen hergeleitet, welche auf Phasenseparation beruht. Im Modell wird angenommen, dass das Zentrosomenmaterial in einer löslichen und einer phasenseparierenden Form existiert, wobei der Übergang zwischen diesen Formen durch chemische Reaktionen gesteuert wird. Die drei verschiedenen in dieser Arbeit untersuchten Reaktionen führen unter anderem zu Tropfengrößen und Nukleationseigenschaften, welche von den bekannten Ergebnissen im thermodynamischen Gleichgewicht abweichen. Insbesondere verursachen die chemischen Reaktionen ein thermisches Nichtgleichgewicht, in dem mehrere Tropfen stabil sein können und der destabilisierende Effekt der Oberflächenspannung unterdrückt wird. Konkret kann die Wachstumsdynamik der Zentrosomen nur durch eine selbstverstärkende Produktion der phasenseparierenden Form des Zentrosomenmaterials erklärt werden. Hierbei ist zusätzlich wichtig, dass die Zentriolen, die im Inneren jedes Zentrosoms vorhanden sind, ebenfalls diese Produktion katalysieren. Dadurch können die Zentriolen den Beginn des Zentrosomwachstums kontrollieren, mehrere Zentrosomen stabilisieren und sich selbst im Zentrosom zentrieren. Des Weiteren führt das selbstverstärkende Wachstum zu einer Verstärkung von Fluktuationen der Zentrosomgröße. Unsere Theorie erklärt die Wachstumsdynamik der Zentrosomen des Fadenwurms Caenorhabditis elegans für alle Embryonalzellen bis zum Achtzellstadium und deckt dabei auch Fälle mit anormaler Zentrosomenanzahl und veränderter Zellgröße ab. Das Modell kann auch Situationen mit unterschiedlich großen Zentrosomen erklären, welche auftreten, wenn die Struktur der Zentriolen verändert wird. Unser Beispiel beschreibt damit eine generelle Möglichkeit, wie membranlose Zellstrukturen organisiert sein können.

Dissertation (Ph.D.)--University of South Florida, 2009. / Title from PDF of title page. Document formatted into pages; contains 155 pages. Includes vita. Includes bibliographical references.

The mitotic spindle is a bipolar microtubule-based structure that mediates proper cell division by segregating the genetic material and by positioning the cytokinesis cleavage plane. Spindle assembly is a complex process, involving the modulation of microtubule dynamics, microtubule focusing at spindle poles and the formation of stable microtubule attachments to chromosomes. The cellular events leading to spindle formation are highly regulated, and mitotic kinases have been implicated in many aspects of this process. However, little is known about their counteracting phosphatases. A screen for genes required for early embryonic cell divisions in C. elegans identified rsa-1 (for regulator of spindle assembly 1), a putative Protein Phosphatase 2A (PP2A) regulatory subunit whose silencing causes defects in spindle formation. Upon rsa-1(RNAi), spindle poles collapse onto each other and microtubule amounts are strongly reduced. My thesis work demonstrates that RSA-1 indeed functions as a PP2A regulatory subunit. RSA-1 associates with the PP2A enzyme and recruits it to centrosomes. The centrosome binding of PP2A furthermore requires the new protein RSA-2 as well as the core centrosomal protein SPD-5 and is based on a hierarchical protein-protein interaction pathway. When PP2A is lacking at centrosomes after rsa-1(RNAi), the centrosomal amounts of two critical mitotic effectors, the microtubule destabilizer KLP-7 and the kinetochore microtubule stabilizer TPXL-1, are altered. KLP-7 is increased, which may account for the reduction of microtubule outgrowth from centrosomes in rsa-1(RNAi) embryos. TPXL-1 is lost from centrosomes, which may explain why spindle poles collapse in the absence of RSA-1. TPXL-1 physically associates with RSA-1 and RSA-2, suggesting that it is a direct target of PP2A. In summary, this work defines the role of a novel PP2A complex in mitotic spindle assembly and suggests a model for how different microtubule re-organization steps might be coordinated during spindle formation.

Biological cells consist of many subunits that form distinct compartments and work together to allow for life. These compartments are clearly separated from each other and their sizes are often strongly correlated with cell size. Examples for those structures are centrosomes, which we consider in this thesis. Centrosomes are essential for many processes inside cells, most importantly for organizing cell division, and they provide an interesting example of cellular compartments without a membrane. Experiments suggest that such compartments can be described as liquid-like droplets. In this thesis, we suggest a theoretical description of the growth phase of centrosomes. We identify a possible mechanism based on phase separation by which the centrosome may be organized. Specifically, we propose that the centrosome material exists in a soluble and in a phase separating form. Chemical reactions controlling the transitions between these forms then determine the temporal evolution of the system. We investigate various possible reaction schemes and generally find that droplet sizes and nucleation properties deviate from the known equilibrium results. Additionally, the non-equilibrium effects of the chemical reactions can stabilize multiple droplets and thus counteract the destabilizing effect of surface tension. Interestingly, only a reaction scheme with autocatalytic growth can account for the experimental data of centrosomes. Here, it is important that the centrioles found at the center of all centrosomes also catalyze the production of droplet material. This catalytic activity allows the centrioles to control the onset of centrosome growth, to stabilize multiple centrosomes, and to center themselves inside the centrosome. We also investigate a stochastic version of the model, where we find that the autocatalytic growth amplifies noise. Our theory explains the growth dynamics of the centrosomes of the round worm Caenorhabditis elegans for all embryonic cells down to the eight-cell stage. It also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with disturbed centrioles. Our example thus suggests a general picture of the organization of membrane-less organelles.:1 Introduction 1.1 Organization of the cell interior 1.2 Biology of centrosomes 1.2.1 The model organism Caenorhabditis elegans 1.2.2 Cellular functions of centrosomes 1.2.3 The centriole pair is the core structure of a centrosome 1.2.4 Pericentriolar material accumulates around the centrioles 1.3 Other membrane-less organelles and their organization 1.4 Phase separation as an organization principle 1.5 Equilibrium physics of liquid-liquid phase separation 1.5.1 Spinodal decomposition and droplet formation 1.5.2 Formation of a single droplet 1.5.3 Ostwald ripening destabilizes multiple droplets 1.6 Non-equilibrium phase separation caused by chemical reactions 1.7 Overview of this thesis 2 Physical Description of Centrosomes as Active Droplets 2.1 Physical description of centrosomes as liquid-like droplets 2.1.1 Pericentriolar material as a complex fluid 2.1.2 Reaction-diffusion kinetics of the components 2.1.3 Centrioles described as catalytic active cores 2.1.4 Droplet formation and growth kinetics 2.1.5 Complete set of the dynamical equations 2.2 Three simple growth scenarios 2.2.1 Scenario A: First-order kinetics 2.2.2 Scenario B: Autocatalytic growth 2.2.3 Scenario C: Incorporation at the centrioles 2.3 Diffusion-limited droplet growth 2.4 Discussion 3 Isolated Active Droplets 3.1 Compositional fluxes in the stationary state 3.2 Critical droplet size: Instability of small droplets 3.3 Droplet nucleation facilitated by the active core 3.4 Interplay of critical droplet size and nucleation 3.5 Perturbations of the spherical droplet shape 3.5.1 Linear stability analysis of the spherical droplet shape 3.5.2 Active cores can center themselves in droplets 3.5.3 Surface tension stabilizes the spherical shape 3.5.4 First-order kinetics destabilize large droplets 3.6 Discussion 4 Multiple Interacting Active Droplets 4.1 Approximate description of multiple droplets 4.2 Linear stability analysis of the symmetric state 4.3 Late stage droplet dynamics and Ostwald ripening 4.4 Active droplets can suppress Ostwald ripening 4.4.1 Perturbation growth rate in the simple growth scenarios 4.4.2 Parameter dependence of the stability of multiple droplets 4.4.3 Stability of more than two droplets 4.5 Discussion 5 Active Droplets with Fluctuations 5.1 Stochastic version of the active droplet model 5.1.1 Comparison with the deterministic model 5.1.2 Ensemble statistics and ergodicity 5.1.3 Quantification of fluctuations by the standard deviation 5.2 Noise amplification by the autocatalytic reaction 5.3 Transient growth regime of multiple droplets 5.4 Influence of the system geometry on the droplet growth 5.5 Discussion 6 Comparison Between Theory and Experiment 6.1 Summary of the experimental observations 6.2 Estimation of key model parameters 6.3 Fits to experimental data 6.4 Dependence of centrosome size on cell volume and centrosome count 6.5 Nucleation and stability of centrosomes 6.6 Multiple centrosomes with unequal sizes 6.7 Disintegration phase of centrosomes 7 Summary and Outlook Appendix A Coexistence conditions in a ternary fluid B Instability of multiple equilibrium droplets C Numerical solution of the droplet growth D Diffusion-limited growth of a single droplet E Approximate efflux of droplet material F Determining stationary states of single droplets G Droplet size including surface tension effects H Distortions of the spherical droplet shape H.1 Harmonic distortions of a sphere H.2 Physical description of the perturbed droplet H.3 Volume fraction profiles in the perturbed droplet H.4 Perturbation growth rates I Multiple droplets with gradients inside droplets J Numerical stability analysis of multiple droplets K Numerical implementation of the stochastic model / Biologische Zellen bestehen aus vielen Unterstrukturen, die zusammen arbeiten um Leben zu ermöglichen. Die Größe dieser meist klar voneinander abgegrenzten Strukturen korreliert oft mit der Zellgröße. In der vorliegenden Arbeit werden als Beispiel für solche Strukturen Zentrosomen untersucht. Zentrosomen sind für viele Prozesse innerhalb der Zelle, insbesondere für die Zellteilung, unverzichtbar und sie besitzen keine Membran, welche ihnen eine feste Struktur verleihen könnte. Experimentelle Untersuchungen legen nahe, dass solche membranlose Strukturen als Flüssigkeitstropfen beschrieben werden können. In dieser Arbeit wird eine theoretische Beschreibung der Wachstumsphase von Zentrosomen hergeleitet, welche auf Phasenseparation beruht. Im Modell wird angenommen, dass das Zentrosomenmaterial in einer löslichen und einer phasenseparierenden Form existiert, wobei der Übergang zwischen diesen Formen durch chemische Reaktionen gesteuert wird. Die drei verschiedenen in dieser Arbeit untersuchten Reaktionen führen unter anderem zu Tropfengrößen und Nukleationseigenschaften, welche von den bekannten Ergebnissen im thermodynamischen Gleichgewicht abweichen. Insbesondere verursachen die chemischen Reaktionen ein thermisches Nichtgleichgewicht, in dem mehrere Tropfen stabil sein können und der destabilisierende Effekt der Oberflächenspannung unterdrückt wird. Konkret kann die Wachstumsdynamik der Zentrosomen nur durch eine selbstverstärkende Produktion der phasenseparierenden Form des Zentrosomenmaterials erklärt werden. Hierbei ist zusätzlich wichtig, dass die Zentriolen, die im Inneren jedes Zentrosoms vorhanden sind, ebenfalls diese Produktion katalysieren. Dadurch können die Zentriolen den Beginn des Zentrosomwachstums kontrollieren, mehrere Zentrosomen stabilisieren und sich selbst im Zentrosom zentrieren. Des Weiteren führt das selbstverstärkende Wachstum zu einer Verstärkung von Fluktuationen der Zentrosomgröße. Unsere Theorie erklärt die Wachstumsdynamik der Zentrosomen des Fadenwurms Caenorhabditis elegans für alle Embryonalzellen bis zum Achtzellstadium und deckt dabei auch Fälle mit anormaler Zentrosomenanzahl und veränderter Zellgröße ab. Das Modell kann auch Situationen mit unterschiedlich großen Zentrosomen erklären, welche auftreten, wenn die Struktur der Zentriolen verändert wird. Unser Beispiel beschreibt damit eine generelle Möglichkeit, wie membranlose Zellstrukturen organisiert sein können.:1 Introduction 1.1 Organization of the cell interior 1.2 Biology of centrosomes 1.2.1 The model organism Caenorhabditis elegans 1.2.2 Cellular functions of centrosomes 1.2.3 The centriole pair is the core structure of a centrosome 1.2.4 Pericentriolar material accumulates around the centrioles 1.3 Other membrane-less organelles and their organization 1.4 Phase separation as an organization principle 1.5 Equilibrium physics of liquid-liquid phase separation 1.5.1 Spinodal decomposition and droplet formation 1.5.2 Formation of a single droplet 1.5.3 Ostwald ripening destabilizes multiple droplets 1.6 Non-equilibrium phase separation caused by chemical reactions 1.7 Overview of this thesis 2 Physical Description of Centrosomes as Active Droplets 2.1 Physical description of centrosomes as liquid-like droplets 2.1.1 Pericentriolar material as a complex fluid 2.1.2 Reaction-diffusion kinetics of the components 2.1.3 Centrioles described as catalytic active cores 2.1.4 Droplet formation and growth kinetics 2.1.5 Complete set of the dynamical equations 2.2 Three simple growth scenarios 2.2.1 Scenario A: First-order kinetics 2.2.2 Scenario B: Autocatalytic growth 2.2.3 Scenario C: Incorporation at the centrioles 2.3 Diffusion-limited droplet growth 2.4 Discussion 3 Isolated Active Droplets 3.1 Compositional fluxes in the stationary state 3.2 Critical droplet size: Instability of small droplets 3.3 Droplet nucleation facilitated by the active core 3.4 Interplay of critical droplet size and nucleation 3.5 Perturbations of the spherical droplet shape 3.5.1 Linear stability analysis of the spherical droplet shape 3.5.2 Active cores can center themselves in droplets 3.5.3 Surface tension stabilizes the spherical shape 3.5.4 First-order kinetics destabilize large droplets 3.6 Discussion 4 Multiple Interacting Active Droplets 4.1 Approximate description of multiple droplets 4.2 Linear stability analysis of the symmetric state 4.3 Late stage droplet dynamics and Ostwald ripening 4.4 Active droplets can suppress Ostwald ripening 4.4.1 Perturbation growth rate in the simple growth scenarios 4.4.2 Parameter dependence of the stability of multiple droplets 4.4.3 Stability of more than two droplets 4.5 Discussion 5 Active Droplets with Fluctuations 5.1 Stochastic version of the active droplet model 5.1.1 Comparison with the deterministic model 5.1.2 Ensemble statistics and ergodicity 5.1.3 Quantification of fluctuations by the standard deviation 5.2 Noise amplification by the autocatalytic reaction 5.3 Transient growth regime of multiple droplets 5.4 Influence of the system geometry on the droplet growth 5.5 Discussion 6 Comparison Between Theory and Experiment 6.1 Summary of the experimental observations 6.2 Estimation of key model parameters 6.3 Fits to experimental data 6.4 Dependence of centrosome size on cell volume and centrosome count 6.5 Nucleation and stability of centrosomes 6.6 Multiple centrosomes with unequal sizes 6.7 Disintegration phase of centrosomes 7 Summary and Outlook Appendix A Coexistence conditions in a ternary fluid B Instability of multiple equilibrium droplets C Numerical solution of the droplet growth D Diffusion-limited growth of a single droplet E Approximate efflux of droplet material F Determining stationary states of single droplets G Droplet size including surface tension effects H Distortions of the spherical droplet shape H.1 Harmonic distortions of a sphere H.2 Physical description of the perturbed droplet H.3 Volume fraction profiles in the perturbed droplet H.4 Perturbation growth rates I Multiple droplets with gradients inside droplets J Numerical stability analysis of multiple droplets K Numerical implementation of the stochastic model