Cross-inhibition of Turing patterns explains the self-organized regulatory mechanism of planarian fission

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.

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.

Transplantation of fragments from different planaria: A bioelectrical model for head regeneration

Head-tail planaria morphologies are influenced by the electric potential differences across the animal's primary axis, as evidenced e.g. by voltage-sensitive dyes and functional experiments that create permanent lines of 2-headed but genetically wild-type animals. However, bioelectrical and biochemical models that make predictions on what would happen in the case of spatial chimeras made by tissue transplantation from different planaria (different species and head shapes) are lacking. Here, we use a bioelectrical model to qualitatively describe the effects of tissue transplantation on the shape of the regenerated head. To this end, we assume that the cells may have distinct sets of ion channels and ascribe the system outcome to the axial distributions of average cell potentials over morphologically relevant regions. Our rationale is that the distributions of signaling ions and molecules are spatially coupled with multicellular electric potentials. Thus, long-time downstream transcriptional events should be triggered by short-time bioelectrical processes. We show that relatively small differences between the ion channel characteristics of the cells could eventually give noticeable changes in the electric potential profiles and the expected morphological deviations, which suggests that small but timely bioelectrical actions may have significant morphological effects. Our approach is based on the observed relationships between bioelectrical regionalization and biochemical gradients in body-plan studies. Such models are relevant to regenerative, developmental, and cancer biology in which cells with distinct properties and morphogenetic target states confront each other in the same tissue.

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.

Let it rip: the mechanics of self-bisection in asexual planarians determines their population reproductive strategies

Asexual freshwater planarians reproduce by transverse bisection (binary fission) into two pieces. This process produces a head and a tail, which fully regenerate within 1-2 weeks. How planarians split into two offspring-using only their musculature and substrate traction-is a challenging biomechanics problem. We found that three different species,Dugesia japonica,Girardia tigrinaandSchmidtea mediterranea, have evolved three different mechanical solutions to self-bisect. Using time lapse imaging of the fission process, we quantitatively characterize the main steps of division in the three species and extract the distinct and shared key features. Across the three species, planarians actively alter their body shape, regulate substrate traction, and use their muscles to generate tensile stresses large enough to overcome the ultimate tensile strength of the tissue. Moreover, we show thathoweach planarian species divides dictates how resources are split among its offspring. This ultimately determines offspring survival and reproductive success. Thus, heterospecific differences in the mechanics of self-bisection of individual worms explain the observed differences in the population reproductive strategies of different planarian species.

Morphology changes induced by intercellular gap junction blocking: A reaction-diffusion mechanism

Complex anatomical form is regulated in part by endogenous physiological communication between cells; however, the dynamics by which gap junctional (GJ) states across tissues regulate morphology are still poorly understood. We employed a biophysical modeling approach combining different signaling molecules (morphogens) to qualitatively describe the anteroposterior and lateral morphology changes in model multicellular systems due to intercellular GJ blockade. The model is based on two assumptions for blocking-induced patterning: (i) the local concentrations of two small antagonistic morphogens diffusing through the GJs along the axial direction, together with that of an independent, uncoupled morphogen concentration along an orthogonal direction, constitute the instructive patterns that modulate the morphological outcomes, and (ii) the addition of an external agent partially blocks the intercellular GJs between neighboring cells and modifies thus the establishment of these patterns. As an illustrative example, we study how the different connectivity and morphogen patterns obtained in presence of a GJ blocker can give rise to novel head morphologies in regenerating planaria. We note that the ability of GJs to regulate the permeability of morphogens post-translationally suggests a mechanism by which different anatomies can be produced from the same genome without the modification of gene-regulatory networks. Conceptually, our model biosystem constitutes a reaction-diffusion information processing mechanism that allows reprogramming of biological morphologies through the external manipulation of the intercellular GJs and the resulting changes in instructive biochemical signals.

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.

Extreme Environmental Stress-Induced Biological Responses in the Planarian

Planarians are bilaterally symmetric metazoans of the phylum Platyhelminthes. They have well-defined anteroposterior and dorsoventral axes and have a highly structured true brain which consists of all neural cell types and neuropeptides found in a vertebrate. Planarian flatworms are famous for their strong regenerative ability; they can easily regenerate any part of the body including the complete neoformation of a functional brain within a few days and can survive a series of extreme environmental stress. Nowadays, they are an emerging model system in the field of developmental, regenerative, and stem cell biology and have offered lots of helpful information for these realms. In this review, we will summarize the response of planarians to some typical environmental stress and hope to shed light on basic mechanisms of how organisms interact with extreme environmental stress and survive it, such as altered gravity, temperature, and oxygen, and this information will help researchers improve the design in future studies.

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.

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

Cell-cell adhesion is essential for tissue growth and multicellular pattern formation and crucial for the cellular dynamics during embryogenesis and cancer progression. Understanding the dynamical gene regulation of cell adhesion molecules (CAMs) responsible for the emerging spatial tissue behaviors is a current challenge because of the complexity of these nonlinear interactions and feedback loops at different levels of abstraction-from genetic regulation to whole-organism shape formation. To extend our understanding of cell and tissue behaviors due to the regulation of adhesion molecules, here we present a novel, to our knowledge, model for the spatial dynamics of cellular patterning, growth, and shape formation due to the differential expression of CAMs and their regulation. Capturing the dynamic interplay between genetic regulation, CAM expression, and differential cell adhesion, the proposed continuous model can explain the complex and emergent spatial behaviors of cell populations that change their adhesion properties dynamically because of inter- and intracellular genetic regulation. This approach can demonstrate the mechanisms responsible for classical cell-sorting behaviors, cell intercalation in proliferating populations, and the involution of germ layer cells induced by a diffusing morphogen during gastrulation. The model makes predictions on the physical parameters controlling the amplitude and wavelength of a cellular intercalation interface, as well as the crucial role of N-cadherin regulation for the involution and migration of cells beyond the gradient of the morphogen Nodal during zebrafish gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way toward understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.