Mixed membership stochastic blockmodels

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.Comment: 46 pages, 14 figures, 3 table

A reaction network scheme which implements inference and learning for Hidden Markov Models

With a view towards molecular communication systems and molecular multi-agent systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in our scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our reaction network scheme, and every positive fixed point of our scheme is a fixed point of the Baum-Welch algorithm. We prove that the "Expectation" step and the "Maximization" step of our reaction network separately converge exponentially fast. We simulate mass-action kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the Baum-Welch algorithm.Comment: Accepted at 25th International Conference on DNA Computing and Molecular Programmin

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

Inferential stability in systems biology

The modern biological sciences are fraught with statistical difficulties. Biomolecular stochasticity, experimental noise, and the “large p, small n” problem all contribute to the challenge of data analysis. Nevertheless, we routinely seek to draw robust, meaningful conclusions from observations. In this thesis, we explore methods for assessing the effects of data variability upon downstream inference, in an attempt to quantify and promote the stability of the inferences we make. We start with a review of existing methods for addressing this problem, focusing upon the bootstrap and similar methods. The key requirement for all such approaches is a statistical model that approximates the data generating process. We move on to consider biomarker discovery problems. We present a novel algorithm for proposing putative biomarkers on the strength of both their predictive ability and the stability with which they are selected. In a simulation study, we find our approach to perform favourably in comparison to strategies that select on the basis of predictive performance alone. We then consider the real problem of identifying protein peak biomarkers for HAM/TSP, an inflammatory condition of the central nervous system caused by HTLV-1 infection. We apply our algorithm to a set of SELDI mass spectral data, and identify a number of putative biomarkers. Additional experimental work, together with known results from the literature, provides corroborating evidence for the validity of these putative biomarkers. Having focused on static observations, we then make the natural progression to time course data sets. We propose a (Bayesian) bootstrap approach for such data, and then apply our method in the context of gene network inference and the estimation of parameters in ordinary differential equation models. We find that the inferred gene networks are relatively unstable, and demonstrate the importance of finding distributions of ODE parameter estimates, rather than single point estimates

A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell

Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio