Continuous Dynamic Modeling of Regulated Cell Adhesion: Sorting, Intercalation, and Involution

Mechanistic regulation of planarian shape during growth and degrowth

Adult planarians can grow when fed and degrow (shrink) when starved while maintaining their whole-body shape. It is unknown how the morphogens patterning the planarian axes are coordinated during feeding and starvation or how they modulate the necessary differential tissue growth or degrowth. Here, we investigate the dynamics of planarian shape together with a theoretical study of the mechanisms regulating whole-body proportions and shape. We found that the planarian body proportions scale isometrically following similar linear rates during growth and degrowth, but that fed worms are significantly wider than starved worms. By combining a descriptive model of planarian shape and size with a mechanistic model of anterior-posterior and medio-lateral signaling calibrated with a novel parameter optimization methodology, we theoretically demonstrate that the feedback loop between these positional information signals and the shape they control can regulate the planarian whole-body shape during growth. Furthermore, the computational model produced the correct shape and size dynamics during degrowth as a result of a predicted increase in apoptosis rate and pole signal during starvation. These results offer mechanistic insights into the dynamic regulation of whole-body morphologies.

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms-including the number of genes necessary for the formation of the target spatial pattern-we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1's contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration.

mergem: merging, comparing, and translating genome-scale metabolic models using universal identifiers

Numerous methods exist to produce and refine genome-scale metabolic models. However, due to the use of incompatible identifier systems for metabolites and reactions, computing and visualizing the metabolic differences and similarities of such models is a current challenge. Furthermore, there is a lack of automated tools that can combine the strengths of multiple reconstruction pipelines into a curated single comprehensive model by merging different drafts, which possibly use incompatible namespaces. Here we present mergem, a novel method to compare, merge, and translate two or more metabolic models. Using a universal metabolic identifier mapping system constructed from multiple metabolic databases, mergem robustly can compare models from different pipelines, merge their common elements, and translate their identifiers to other database systems. mergem is implemented as a command line tool, a Python package, and on the web-application Fluxer, which allows simulating and visually comparing multiple models with different interactive flux graphs. The ability to merge, compare, and translate diverse genome scale metabolic models can facilitate the curation of comprehensive reconstructions and the discovery of unique and common metabolic features among different organisms.

Automatic design of gene regulatory mechanisms for spatial pattern formation

Synthetic developmental biology aims to engineer gene regulatory mechanisms (GRMs) for understanding and producing desired multicellular patterns and shapes. However, designing GRMs for spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms-including the number of genes necessary for the formation of the target pattern-we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover pattern-producing genetic circuits.

Cell sorting in vitro and in vivo: How are cadherins involved?

Animal tissues are composed of heterogenous cells, and their sorting into different compartments of the tissue is a pivotal process for organogenesis. Cells accomplish sorting by themselves-it is well known that singly dispersed cells can self-organize into tissue-like structures in vitro. Cell sorting is regulated by both biochemical and physical mechanisms. Adhesive proteins connect cells together, selecting particular partners through their specific binding properties, while physical forces, such as cell-cortical tension, control the cohesiveness between cells and in turn cell assembly patterns in mechanical ways. These processes cooperate in determining the overall cell sorting behavior. This article focuses on the 'cadherin' family of adhesion molecules as a biochemical component of cell-cell interactions, addressing how they regulate cell sorting by themselves or by cooperating with other factors. New ideas beyond the classical models of cell sorting are also discussed.

Computational Systems Biology of Morphogenesis

Extracting mechanistic knowledge from the spatial and temporal phenotypes of morphogenesis is a current challenge due to the complexity of biological regulation and their feedback loops. Furthermore, these regulatory interactions are also linked to the biophysical forces that shape a developing tissue, creating complex interactions responsible for emergent patterns and forms. Here we show how a computational systems biology approach can aid in the understanding of morphogenesis from a mechanistic perspective. This methodology integrates the modeling of tissues and whole-embryos with dynamical systems, the reverse engineering of parameters or even whole equations with machine learning, and the generation of precise computational predictions that can be tested at the bench. To implement and perform the computational steps in the methodology, we present user-friendly tools, computer code, and guidelines. The principles of this methodology are general and can be adapted to other model organisms to extract mechanistic knowledge of their morphogenesis.

Formalizing Phenotypes of Regeneration

Regeneration experiments can produce complex phenotypes including morphological outcomes and gene expression patterns that are crucial for the understanding of the mechanisms of regeneration. However, due to their inherent complexity, variability between individuals, and heterogeneous data spreading across the literature, extracting mechanistic knowledge from them is a current challenge. Toward this goal, here we present protocols to unambiguously formalize the phenotypes of regeneration and their experimental procedures using precise mathematical morphological descriptions and standardized gene expression patterns. We illustrate the application of the methodology with step-by-step protocols for planaria and limb regeneration phenotypes. The curated datasets with these methods are not only helpful for human scientists, but they represent a key formalized resource that can be easily integrated into downstream reverse engineering methodologies for the automatic extraction of mechanistic knowledge. This approach can pave the way for discovering comprehensive systems-level models of regeneration.

Model-Based Prediction of an Effective Adhesion Parameter Guiding Multi-Type Cell Segregation

The process of cell-sorting is essential for development and maintenance of tissues. Mathematical modeling can provide the means to analyze the consequences of different hypotheses about the underlying mechanisms. With the Differential Adhesion Hypothesis, Steinberg proposed that cell-sorting is determined by quantitative differences in cell-type-specific intercellular adhesion strengths. An implementation of the Differential Adhesion Hypothesis is the Differential Migration Model by Voss-Böhme and Deutsch. There, an effective adhesion parameter was derived analytically for systems with two cell types, which predicts the asymptotic sorting pattern. However, the existence and form of such a parameter for more than two cell types is unclear. Here, we generalize analytically the concept of an effective adhesion parameter to three and more cell types and demonstrate its existence numerically for three cell types based on in silico time-series data that is produced by a cellular-automaton implementation of the Differential Migration Model. Additionally, we classify the segregation behavior using statistical learning methods and show that the estimated effective adhesion parameter for three cell types matches our analytical prediction. Finally, we demonstrate that the effective adhesion parameter can resolve a recent dispute about the impact of interfacial adhesion, cortical tension and heterotypic repulsion on cell segregation.

SysMod: the ISCB community for data-driven computational modelling and multi-scale analysis of biological systems

Computational models of biological systems can exploit a broad range of rapidly developing approaches, including novel experimental approaches, bioinformatics data analysis, emerging modelling paradigms, data standards and algorithms. A discussion about the most recent advances among experts from various domains is crucial to foster data-driven computational modelling and its growing use in assessing and predicting the behaviour of biological systems. Intending to encourage the development of tools, approaches and predictive models, and to deepen our understanding of biological systems, the Community of Special Interest (COSI) was launched in Computational Modelling of Biological Systems (SysMod) in 2016. SysMod’s main activity is an annual meeting at the Intelligent Systems for Molecular Biology (ISMB) conference, which brings together computer scientists, biologists, mathematicians, engineers, computational and systems biologists. In the five years since its inception, SysMod has evolved into a dynamic and expanding community, as the increasing number of contributions and participants illustrate. SysMod maintains several online resources to facilitate interaction among the community members, including an online forum, a calendar of relevant meetings and a YouTube channel with talks and lectures of interest for the modelling community. For more than half a decade, the growing interest in computational systems modelling and multi-scale data integration has inspired and supported the SysMod community. Its members get progressively more involved and actively contribute to the annual COSI meeting and several related community workshops and meetings, focusing on specific topics, including particular techniques for computational modelling or standardisation efforts.

Inference of dynamic spatial GRN models with multi-GPU evolutionary computation

Reverse engineering mechanistic gene regulatory network (GRN) models with a specific dynamic spatial behavior is an inverse problem without analytical solutions in general. Instead, heuristic machine learning algorithms have been proposed to infer the structure and parameters of a system of equations able to recapitulate a given gene expression pattern. However, these algorithms are computationally intensive as they need to simulate millions of candidate models, which limits their applicability and requires high computational resources. Graphics processing unit (GPU) computing is an affordable alternative for accelerating large-scale scientific computation, yet no method is currently available to exploit GPU technology for the reverse engineering of mechanistic GRNs from spatial phenotypes. Here we present an efficient methodology to parallelize evolutionary algorithms using GPU computing for the inference of mechanistic GRNs that can develop a given gene expression pattern in a multicellular tissue area or cell culture. The proposed approach is based on multi-CPU threads running the lightweight crossover, mutation and selection operators and launching GPU kernels asynchronously. Kernels can run in parallel in a single or multiple GPUs and each kernel simulates and scores the error of a model using the thread parallelism of the GPU. We tested this methodology for the inference of spatiotemporal mechanistic gene regulatory networks (GRNs)-including topology and parameters-that can develop a given 2D gene expression pattern. The results show a 700-fold speedup with respect to a single CPU implementation. This approach can streamline the extraction of knowledge from biological and medical datasets and accelerate the automatic design of GRNs for synthetic biology applications.

Fluxer: a web application to compute, analyze and visualize genome-scale metabolic flux networks

Next-generation sequencing has paved the way for the reconstruction of genome-scale metabolic networks as a powerful tool for understanding metabolic circuits in any organism. However, the visualization and extraction of knowledge from these large networks comprising thousands of reactions and metabolites is a current challenge in need of user-friendly tools. Here we present Fluxer (https://fluxer.umbc.edu), a free and open-access novel web application for the computation and visualization of genome-scale metabolic flux networks. Any genome-scale model based on the Systems Biology Markup Language can be uploaded to the tool, which automatically performs Flux Balance Analysis and computes different flux graphs for visualization and analysis. The major metabolic pathways for biomass growth or for biosynthesis of any metabolite can be interactively knocked-out, analyzed and visualized as a spanning tree, dendrogram or complete graph using different layouts. In addition, Fluxer can compute and visualize the k-shortest metabolic paths between any two metabolites or reactions to identify the main metabolic routes between two compounds of interest. The web application includes >80 whole-genome metabolic reconstructions of diverse organisms from bacteria to human, readily available for exploration. Fluxer enables the efficient analysis and visualization of genome-scale metabolic models toward the discovery of key metabolic pathways.

Mathematical models for cell migration: a non-local perspective

We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Engineering and modeling of multicellular morphologies and patterns

Synthetic multicellular (MC) systems have the capacity to increase our understanding of biofilms and higher organisms, and to serve as engineering platforms for developing complex products in the areas of medicine, biosynthesis and smart materials. Here we provide an interdisciplinary perspective and review on emerging approaches to engineer and model MC systems. We lay out definitions for key terms in the field and identify toolboxes of standardized parts which can be combined into various MC algorithms to achieve specific outcomes. Many essential parts and algorithms have been demonstrated in some form. As key next milestones for the field, we foresee the improvement of these parts and their adaptation to more biological systems, the demonstration of more complex algorithms, the advancement of quantitative modeling approaches and compilers to support rational MC engineering, and implementation of MC engineering for practical applications.

Curation and annotation of planarian gene expression patterns with segmented reference morphologies

Motivation

Morphological and genetic spatial data from functional experiments based on genetic, surgical and pharmacological perturbations are being produced at an extraordinary pace in developmental and regenerative biology. However, our ability to extract knowledge from these large datasets are hindered due to the lack of formalization methods and tools able to unambiguously describe, centralize and interpret them. Formalizing spatial phenotypes and gene expression patterns is especially challenging in organisms with highly variable morphologies such as planarian worms, which due to their extraordinary regenerative capability can experimentally result in phenotypes with almost any combination of body regions or parts.

Results

Here, we present a computational methodology and mathematical formalism to encode and curate the morphological outcomes and gene expression patterns in planaria. Worm morphologies are encoded with mathematical graphs based on anatomical ontology terms to automatically generate reference morphologies. Gene expression patterns are registered to these standard reference morphologies, which can then be annotated automatically with anatomical ontology terms by analyzing the spatial expression patterns and their textual descriptions. This methodology enables the curation and annotation of complex experimental morphologies together with their gene expression patterns in a centralized standardized dataset, paving the way for the extraction of knowledge and reverse-engineering of the much sought-after mechanistic models in planaria and other regenerative organisms.

Availability and implementation

We implemented this methodology in a user-friendly graphical software tool, PlanGexQ, freely available together with the data in the manuscript at https://lobolab.umbc.edu/plangexq.

Supplementary information

Supplementary data are available at Bioinformatics online.