Stochastic dynamics of migrating cells

Cell migration is critical in many physiological phenomena, including embryogenesis, immune response, and cancer. In all these processes, cells face a common physical challenge: they navigate confining extra-cellular environments, in which they squeeze through thin constrictions. The motion of cells is powered by a complex machinery whose molecular basis is increasingly well understood. However, a quantitative understanding of the functional cell behaviours that emerge at the cellular scale remains elusive. This raises a central question, which acts as a common thread throughout the projects in this thesis: do migrating cells exhibit emergent dynamical 'laws' that describe their behavioural dynamics in confining environments? To address this question, we develop data-driven approaches to infer the dynamics of migrating cells directly from experimental data. We study the migration of cells in artificial confinements featuring a thin constriction across which cells repeatedly squeeze. From the experimental cell trajectories, we infer an equation of cell motion, which decomposes the dynamics into deterministic and stochastic contributions. This approach reveals that cells deterministically drive themselves into the thin constriction, which is in contrast to the intuition that constrictions act as effective barriers. This active driving leads to intricate non-linear dynamics that are poised close to a bifurcation between a bistable system and a limit cycle oscillator. We further generalize this data-driven framework to detect and characterize the variance of migration behaviour within a cell population and to investigate how cells respond to varying confinement size, shape, and orientation. We next investigate the mechanistic basis of these dynamics. Cell migration relies on the concerted dynamics of several cellular components, including cell protrusions and adhesive connections to the environment. Based on the experimental data, we systematically constrain a mechanistic model for confined cell migration. This model indicates that the observed deterministic driving is a consequence of the combined effects of the variable adhesiveness of the environment and a self-reinforcement of cell polarity in response to thin constrictions. These results suggest polarity feedback adaptation as a key mechanism in confined cell migration. Finally, we investigate the dynamics of interacting cells. To enable inference of cell-cell interactions, we develop Underdamped Langevin Inference, an inference method for stochastic high-dimensional and interacting systems. We apply this method to experiments of confined pairs of cells, which repeatedly collide with one another. This reveals that non-cancerous (MCF10A) and cancerous (MDA-MB-231) cells exhibit distinct interactions: while the non-cancerous cells exhibit repulsion and effective friction, the cancerous cells exhibit attraction and a surprising 'anti-friction' interaction. These interactions lead to non-cancerous cells predominantly reversing upon collision, while the cancer cells are able to efficiently move past one another by relative sliding. Furthermore, we investigate the effects of cadherin-mediated molecular contacts on cell-cell interactions in collective migration. Taken together, the data-driven approaches presented in this thesis may help to provide a new avenue to uncover the emergent laws governing the stochastic dynamics of migrating cells. We demonstrate how these approaches can provide key insights both into underlying mechanisms as well as emergent cell behaviours at larger scales.Zellmigration ist ein Kernelement vieler physiologischer Phänomene wie der Embryogenese, dem Immunsystem und der Krebsmetastase. In all diesen Prozessen stehen Zellen vor einer physikalischen Herausforderung: Sie bewegen sich in beengten Umgebungen, in denen sie Engstellen passieren müssen. Die Zellbewegung wird von einer komplexen Maschinerie an- getrieben, deren molekulare Komponenten immer besser verstanden werden. Demgegenüber fehlt ein quantitatives Verständnis des funktionalen Migrationsverhaltens der Zelle als Ganzes. Die verbindende Fragestellung der Projekte in dieser Arbeit lautet daher: gibt es emergente dynamische 'Gesetze', die die Verhaltensdynamik migrierender Zellen in beengten Umgebungen beschreiben? Um dieser Frage nachzugehen, entwickeln wir datengetriebene Ansätze, die es uns erlauben, die Dynamik migrierender Zellen direkt aus experimentellen Daten zu inferieren. Wir untersuchen Zellmigration in künstlichen Systemen, in denen Zellen Engstellen wiederholt passieren müssen. Aus den experimentellen Zelltrajektorien inferieren wir eine Bewegungsgleichung, die die Dynamik in deterministische und stochastische Komponenten trennt. Diese Methode zeigt, dass sich Zellen deterministisch 'aktiv' in die Engstellen hineinbewegen, ganz entgegen der intuitiven Erwartung, dass Engstellen als Hindernis fungieren könnten. Dieser aktive Antrieb führt zu einer komplexen nichtlinearen Dynamik im Übergangsbereich zwischen einem bistabilen System und einem Grenzzyklus-Oszillator. Wir verallgemeinern diesen datenbasierten Ansatz, um die Varianz des Migrationsverhaltens innerhalb einer Zellpopulation zu quantifizieren, und analysieren, wie Zellen auf die Größe, Form und Orientierung ihrer Umgebung reagieren. Darauf aufbauend untersuchen wir die zugrundeliegenden Mechanismen dieser Dynamik. Zellmigration basiert auf verschiedenen zellulären Komponenten, wie unter Anderem den Zellprotrusionen und der Adhäsion mit der Umgebung. Auf Basis der experimentellen Daten entwickeln wir ein mechanistisches Modell für Zellmigration in beengten Systemen, welches zeigt, dass der beobachtete aktive Antrieb eine Konsequenz zweier Effekte ist: Einer variierenden Adhäsion mit der Umgebung und einer Zellpolarität, die sich in Engstellen selbst verstärkt. Diese Ergebnisse deuten darauf hin, dass die Anpassung der Zellpolarität an die lokale Geometrie ein Schlüsselmechanismus in beengter Zellmigration ist. Schließlich analysieren wir die Dynamik interagierender Zellen. Um Zell-Zell Interaktionen zu inferieren, entwickeln wir die Underdamped Langevin Inference, eine Inferenzmethode für stochastische hochdimensionale und interagierende Systeme. Wir wenden diese Methode auf Daten von eingeschlossenen Zellpaaren an, welche wiederholt miteinander kollidieren. Dies zeigt, dass gesunde (MCF10A) und krebsartige (MDA-MB-231) Zellen unterschiedliche Interaktionen aufweisen: Während gesunde Zellen mit Abstoßung und effektiver Reibung interagieren, zeigen Krebszellen Anziehung und eine überraschende 'Anti-Reibung'. Diese Interaktionen führen dazu, dass gesunde Zellen nach Kollisionen primär umkehren, während Krebszellen effizient aneinander vorbeigleiten. Darüberhinaus analysieren wir die Effekte von Cadherin-basierten Molekularkontakten auf Zell-Zell Interaktionen in kollektiver Migration. Zusammenfassend könnten die in dieser Arbeit präsentierten datengetriebenen Ans ̈atze dabei helfen, ein besseres Verständnis der emergenten stochastischen Dynamik migrierender Zellen zu erlangen. Wir zeigen, wie diese Methoden wichtige Erkenntnisse sowohl über die zugrundeliegenden Mechanismen als auch über das emergente Zellverhalten liefern können

Inferring the dynamics of underdamped stochastic systems

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference (ULI), which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualizing the emergent behavior of cells. We first review how this inference problem has been addressed in freely migrating cells on two-dimensional substrates and in structured, confining systems. Moreover, we discuss how data-driven methods can be connected with molecular mechanisms, either by integrating mechanistic bottom-up biophysical models, or by performing inference on subcellular degrees of freedom. Finally, we provide an overview of applications of data-driven modelling in developing frameworks for cell-to-cell variability in behaviours, and for learning the collective dynamics of multicellular systems. Specifically, we review inference and machine learning approaches to recover cell-cell interactions and collective dynamical modes, and how these can be integrated into physical active matter models of collective migration

Innovating quality control mechanisms in aseptic drug manufacturing by means of isothermal microcalorimetry and tunable diode laser absorption spectroscopy

Aseptic manufacturing refers to bringing the sterile drug solution into decontaminated containers in a way that product sterility and therapeutic effectiveness is maintained. At this stage the produced drug has a significant value, reflecting relatively large financial risk in case of failure during manufacturing procedures. Therefore, environmental monitoring activities strictly control production surroundings to ensure that no accidental product contamination occurs. Media fills are part of environmental monitoring activities and imitate the aseptic (free from pathogenic microorganisms) filling procedure with microbial growth medium instead of the liquid drug product. After filling, media fills are inspected visually on turbidity, which represents the control on filling line asepticity. Such inspection is time-consuming, manually performed and therefore considered for potential automation. A laser-based technology was used (called tunable diode laser absorption spectroscopy) abbreviated as TDLAS to determine CO2 and O2 variations in media fill headspaces as related to metabolic activity of growing microorganisms. The study results demonstrated that TDLAS can automate the visual media fill inspection reliably (inspection rate of 100 containers per minute) allowing a roughly 90% faster inspection than achieved by the manual visual inspection on turbidity. TDLAS was further assessed on its potential in simplifying conventional measurement techniques in the field of calorespirometry. Calorespirometry deals with the simultaneous analysis of O2 consumption, CO2 production and heat emission by living systems such as tissues or organism cultures. TDLAS is a well-performing and convenient way to evaluate non-invasively the rates of O2 consumption, CO2 production during mentioned studies. In aseptic manufacturing the sterility assessment is the last control of product sterility before an entire batch is released to the market. The assessment usually consists of a final visual inspection on turbidity 14 days after drug preparation. Isothermal microcalorimetry (IMC) is a methodology measuring small amounts of emitted heat and can thereby detect growing microorganisms. It is more sensitive than the visual inspection on turbidity and was therefore applied as alternative test for microbial growth to sterility assessments. IMC appears to have a large potential to improve the sterility assessment as all tested microorganisms were earlier detected by IMC as by the visual inspection. Performed projects demonstrate that IMC and TDLAS can improve quality control mechanism by designing those more efficiently. Therefore, ongoing IMC and TDLAS based research is recommended to exploit the full potential of the aforementioned technologies

Learning the dynamics of cell-cell interactions in confined cell migration

The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following and sliding past each other upon collision. Capitalizing on this large experimental data set of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting non-cancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and anti-friction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types

Chromosomes are predominantly located randomly with respect to each other in interphase human cells

To test quantitatively whether there are systematic chromosome–chromosome associations within human interphase nuclei, interchanges between all possible heterologous pairs of chromosomes were measured with 24-color whole-chromosome painting (multiplex FISH), after damage to interphase lymphocytes by sparsely ionizing radiation in vitro. An excess of interchanges for a specific chromosome pair would indicate spatial proximity between the chromosomes comprising that pair. The experimental design was such that quite small deviations from randomness (extra pairwise interchanges within a group of chromosomes) would be detectable. The only statistically significant chromosome cluster was a group of five chromosomes previously observed to be preferentially located near the center of the nucleus. However, quantitatively, the overall deviation from randomness within the whole genome was small. Thus, whereas some chromosome–chromosome associations are clearly present, at the whole-chromosomal level, the predominant overall pattern appears to be spatially random

Towards elucidating carnosic acid biosynthesis in Lamiaceae: Functional characterization of the three first steps of the pathway in Salvia fruticosa and Rosmarinus officinalis

Carnosic acid (CA) is a phenolic diterpene with anti-tumour, anti-diabetic, antibacterial and neuroprotective properties that is produced by a number of species from several genera of the Lamiaceae family, including Salvia fruticosa (Cretan sage) and Rosmarinus officinalis (Rosemary). To elucidate CA biosynthesis, glandular trichome transcriptome data of S. fruticosa were mined for terpene synthase genes. Two putative diterpene synthase genes, namely SfCPSand SfKSL, showing similarities to copalyl diphosphate synthase and kaurene synthase-like genes, respectively, were isolated and functionally characterized. Recombinant expression in Escherichia coli followed by in vitro enzyme activity assays confirmed that SfCPS is a copalyl diphosphate synthase. Coupling of SfCPS with SfKSL, both in vitro and in yeast, resulted in the synthesis miltiradiene, as confirmed by 1D and 2D NMR analyses (1H, 13C, DEPT, COSY H-H, HMQC and HMBC). Coupled transient in vivo assays of SfCPS and SfKSL in Nicotiana benthamiana further confirmed production of miltiradiene in planta. To elucidate the subsequent biosynthetic step, RNA-Seq data of S. fruticosa and R. officinalis were searched for cytochrome P450 (CYP) encoding genes potentially involved in the synthesis of the first phenolic compound in the CA pathway, ferruginol. Three candidate genes were selected, SfFS, RoFS1 and RoFS2. Using yeast and N. benthamiana expression systems, all three where confirmed to be coding for ferruginol synthases, thus revealing the enzymatic activities responsible for the first three steps leading to CA in two Lamiaceae genera