An information-theoretic measure for patterning in epithelial tissues

We present path entropy, an information-theoretic measure that captures the notion of patterning due to phase separation in organic tissues. Recent work has demonstrated, both in silico and in vitro, that phase separation in epithelia can arise simply from the forces at play between cells with differing mechanical properties. These qualitative results give rise to numerous questions about how the degree of patterning relates to model parameters or underlying biophysical properties. Answering these questions requires a consistent and meaningful way of quantifying degree of patterning that we observe. We define a resolution-independent measure that is better suited than image-processing techniques for comparing cellular structures. We show how this measure can be usefully applied in a selection of scenarios from biological experiment and computer simulation, and argue for the establishment of a tissue-graph library to assist with parameter estimation for synthetic morphology

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.Comment: paper + supporting information, total 35 pages, 15 figure

Emergence of structure in mouse embryos: Structural Entropy morphometry applied to digital models of embryonic anatomy

We apply an information-theoretic measure to anatomical models of the Edinburgh Mouse Atlas Project. Our goal is to quantify the anatomical complexity of the embryo and to understand how this quantity changes as the organism develops through time. Our measure, Structural Entropy, takes into account the geometrical character of the intermingling of tissue types in the embryo. It does this by a mathematical process that effectively imagines a point-like explorer that starts at an arbitrary place in the 3D structure of the embryo and takes a random path through the embryo, recording the sequence of tissues through which it passes. Consideration of a large number of such paths yields a probability distribution of paths making connections between specific tissue types, and Structural Entropy is calculated from this (mathematical details are given in the main text). We find that Structural Entropy generally decreases (order increases) almost linearly throughout developmental time (4–18 days). There is one `blip’ of increased Structural Entropy across days 7–8: this corresponds to gastrulation. Our results highlight the potential for mathematical techniques to provide insight into the development of anatomical structure, and also the need for further sources of accurate 3D anatomical data to support analyses of this kind

DIVERSE SOURCES OF NOISE IN BIOLOGICAL SYSTEMS

Variation is omnipresent in biological systems. Organisms must survive in fluctuating environments, genetic diversity drives evolution, and finite molecule counts challenge signal processing accuracy. However, in classic cellular biology, this variation is often ignored. While a dose-response curve may show error bars, these are often attributed to measurement error and not assumed to be true biological variation, or noise. Recently, however, sufficiently powerful technology has been developed to measure response of many cells at the single-cell level. These studies have raised significant questions in cellular and systems biology, requiring the development of new methods and revisiting of old models. In this manuscript, we first develop a novel method based on organism symmetry for differentiating between sources of noise. We apply this method to Drosophila early morphogenesis dorsal-ventral (D-V) cell differentiation. We identify significant position-dependent structure to the noise. Given commonality of organisms exhibiting bilateral symmetry, this method can find very wide applicability. Further, by leveraging information, we are able to demonstrate which components of the noise have a significant effect on Drosophila development. We then investigate noise in the context of a multicellular organism performing gradient detection. In contrast to previous studies, which have focused only on noise outside of the cell, we find that noise inside the cell contributes significantly to gradient detection accuracy. In particular, as a cell grows however, internal communication noise is also expected to grow, complicating comparison of concentrations. We discover this effect through a combination of using linear mathematics, nonlinear simulations, and in vivo experiments on multicellular organoids, we show that results obtained by ignoring internal system variation are incomplete. Finally, we consider noise in the context of a system which must detect signal duration despite variation in the signal amplitude. We show that the Incoherent Type 1 Feed Forward Loop (I1FFL), one of the most common network motifs, is capable of accurately performing this detection function. Taken together, these contributions provide new analytical tools, shed additional light on the importance of biological noise, and support an increasingly wide-held view that variation is a fundamental aspect of biology

Geometric signatures of tissue surface tension in a three-dimensional model of confluent tissue

In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic tension at the interface between two distinct cell types in a fully 3D Voronoi model for confluent tissues. We find that cells rapidly sort and self-organize to generate a tissue-scale interface between cell types, and cells adjacent to this interface exhibit signature geometric features including nematic-like ordering, bimodal facet areas, and registration, or alignment, of cell centers on either side of the two-tissue interface. The magnitude of these features scales directly with the magnitude of the imposed tension, suggesting that biologists can estimate the magnitude of tissue surface tension between two tissue types simply by segmenting a 3D tissue. To uncover the underlying physical mechanisms driving these geometric features, we develop two minimal, ordered models using two different underlying lattices that identify an energetic competition between bulk cell shapes and tissue interface area. When the interface area dominates, changes to neighbor topology are costly and occur less frequently, which generates the observed geometric features

Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

Tracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterizing cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a ‘maximum common subgraph’ to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as phototoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell–cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues

Universal Calcium fluctuations in Hydra morphogenesis

Morphogenesis in development involves significant morphological transitions toward the emerging body plan of a mature animal. Understanding how the collective physical processes drive robust morphological patterning requires the characterization of the underlying relevant fields. Calcium (Ca2+) is known to be such a field. Here we show that the Ca2+ spatial fluctuations, in whole-body Hydra regeneration, exhibit universal properties captured by a field-theoretic model describing fluctuations in a tilted double-well potential. We utilize an external electric field and Heptanol, a drug blocking gap junctions, as two separate controls affecting the Ca2+ activity and pausing the regeneration process in a reversible way. Subjecting the Hydra tissue to an electric field increases the calcium activity and its spatial correlations, while applying Heptanol inhibits the activity and weakens the spatial correlations. Statistical characteristics of the Ca2+ spatial fluctuations, i.e., the coefficient of variation and the skewness, exhibit universal shape distributions across tissue samples and conditions, demonstrating the existence of global constraints over this field. Our analysis shows that the Hydra's tissue resides near the onset of bistability. The controls modulate the dynamics near that onset in a way that preserves the tissue's ability to regenerate, which is reflected by the aforementioned universality

Algorithmic Information Theory Applications in Bright Field Microscopy and Epithelial Pattern Formation

Algorithmic Information Theory (AIT), also known as Kolmogorov complexity, is a quantitative approach to defining information. AIT is mainly used to measure the amount of information present in the observations of a given phenomenon. In this dissertation we explore the applications of AIT in two case studies. The first examines bright field cell image segmentation and the second examines the information complexity of multicellular patterns. In the first study we demonstrate that our proposed AIT-based algorithm provides an accurate and robust bright field cell segmentation. Cell segmentation is the process of detecting cells in microscopy images, which is usually a challenging task for bright field microscopy due to the low contrast of the images. In the second study, which is the primary contribution of this dissertation, we employ an AIT-based algorithm to quantify the complexity of information content that arises during the development of multicellular organisms. We simulate multicellular organism development by coupling the Gene Regulatory Networks (GRN) within an epithelial field. Our results show that the configuration of GRNs influences the information complexity in the resultant multicellular patterns

Investigating biocomplexity through the agent-based paradigm.

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex