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.

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.

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.

Kinetic modeling of microbial growth, enzyme activity, and gene deletions: An integrated model of ß-glucosidase function in Cellvibrio japonicus.

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in ß-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different ß-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.

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

Planarian worms reproduce asexually by fission, resulting in two separated pieces each repatterning and regenerating a complete animal. The induction of this process is known to be dependent on the size of the worm as well as on environmental factors such as population density, temperature, and light intensity. However, despite much progress in understanding the signaling mechanisms of planarian regeneration and the biomechanics of fissioning, no induction mechanism has been proposed for the signaling of fission. Here, we propose and analyze a cross-inhibited Turing system in a growing domain for the signaling of fission in planaria and the regeneration of the anterior-posterior opposite head and tail gene expression gradient patterns. This self-regulated mechanism explains when and where growing planaria fission, and its dependence on the worm length. Furthermore, we show how a delayed control mechanism of the cross-inhibited Turing system explains the asymmetry of the resulting fragments, the induction of fission with an anterior amputation even in a short worm, the consecutive multiple fissions called fragmentation, and the effects of environmental factors in the signaling of fission. We discuss the possible molecular and biophysical implementations of the proposed model and suggest specific experiments to elucidate them. In summary, the proposed controlled cross-inhibited Turing system represents a completely self-regulated model of the fission and regeneration signaling in planaria.

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.

Computational discovery and in vivo validation of hnf4 as a regulatory gene in planarian regeneration.

MOTIVATION: Automated computational methods can infer dynamic regulatory network models directly from temporal and spatial experimental data, such as genetic perturbations and their resultant morphologies. Recently, a computational method was able to reverse-engineer the first mechanistic model of planarian regeneration that can recapitulate the main anterior-posterior patterning experiments published in the literature. Validating this comprehensive regulatory model via novel experiments that had not yet been performed would add in our understanding of the remarkable regeneration capacity of planarian worms and demonstrate the power of this automated methodology. RESULTS: Using the Michigan Molecular Interactions and STRING databases and the MoCha software tool, we characterized as hnf4 an unknown regulatory gene predicted to exist by the reverse-engineered dynamic model of planarian regeneration. Then, we used the dynamic model to predict the morphological outcomes under different single and multiple knock-downs (RNA interference) of hnf4 and its predicted gene pathway interactors ß-catenin and hh Interestingly, the model predicted that RNAi of hnf4 would rescue the abnormal regenerated phenotype (tailless) of RNAi of hh in amputated trunk fragments. Finally, we validated these predictions in vivo by performing the same surgical and genetic experiments with planarian worms, obtaining the same phenotypic outcomes predicted by the reverse-engineered model. CONCLUSION: These results suggest that hnf4 is a regulatory gene in planarian regeneration, validate the computational predictions of the reverse-engineered dynamic model, and demonstrate the automated methodology for the discovery of novel genes, pathways and experimental phenotypes. CONTACT: michael.levin@tufts.edu.

Thiamine Deficiency Increases Ca2+ Current and CaV1.2 L-type Ca2+ Channel Levels in Cerebellum Granular Neurons.

Thiamine (vitamin B1) is co-factor for three pivotal enzymes for glycolytic metabolism: pyruvate dehydrogenase, α-ketoglutarate dehydrogenase, and transketolase. Thiamine deficiency leads to neurodegeneration of several brain regions, especially the cerebellum. In addition, several neurodegenerative diseases are associated with impairments of glycolytic metabolism, including Alzheimer's disease. Therefore, understanding the link between dysfunction of the glycolytic pathway and neuronal death will be an important step to comprehend the mechanism and progression of neuronal degeneration as well as the development of new treatment for neurodegenerative states. Here, using an in vitro model to study the effects of thiamine deficiency on cerebellum granule neurons, we show an increase in Ca2+ current density and CaV1.2 expression. These results indicate a link between alterations in glycolytic metabolism and changes to Ca2+ dynamics, two factors that have been implicated in neurodegeneration.

Inferring regulatory networks from experimental morphological phenotypes: a computational method reverse-engineers planarian regeneration.

Transformative applications in biomedicine require the discovery of complex regulatory networks that explain the development and regeneration of anatomical structures, and reveal what external signals will trigger desired changes of large-scale pattern. Despite recent advances in bioinformatics, extracting mechanistic pathway models from experimental morphological data is a key open challenge that has resisted automation. The fundamental difficulty of manually predicting emergent behavior of even simple networks has limited the models invented by human scientists to pathway diagrams that show necessary subunit interactions but do not reveal the dynamics that are sufficient for complex, self-regulating pattern to emerge. To finally bridge the gap between high-resolution genetic data and the ability to understand and control patterning, it is critical to develop computational tools to efficiently extract regulatory pathways from the resultant experimental shape phenotypes. For example, planarian regeneration has been studied for over a century, but despite increasing insight into the pathways that control its stem cells, no constructive, mechanistic model has yet been found by human scientists that explains more than one or two key features of its remarkable ability to regenerate its correct anatomical pattern after drastic perturbations. We present a method to infer the molecular products, topology, and spatial and temporal non-linear dynamics of regulatory networks recapitulating in silico the rich dataset of morphological phenotypes resulting from genetic, surgical, and pharmacological experiments. We demonstrated our approach by inferring complete regulatory networks explaining the outcomes of the main functional regeneration experiments in the planarian literature; By analyzing all the datasets together, our system inferred the first systems-biology comprehensive dynamical model explaining patterning in planarian regeneration. This method provides an automated, highly generalizable framework for identifying the underlying control mechanisms responsible for the dynamic regulation of growth and form.

Limbform: a functional ontology-based database of limb regeneration experiments.

SUMMARY: The ability of certain organisms to completely regenerate lost limbs is a fascinating process, far from solved. Despite the extraordinary published efforts during the past centuries of scientists performing amputations, transplantations and molecular experiments, no mechanistic model exists yet that can completely explain patterning during the limb regeneration process. The lack of a centralized repository to enable the efficient mining of this huge dataset is hindering the discovery of comprehensive models of limb regeneration. Here, we introduce Limbform (Limb formalization), a centralized database of published limb regeneration experiments. In contrast to natural language or text-based ontologies, Limbform is based on a functional ontology using mathematical graphs to represent unambiguously limb phenotypes and manipulation procedures. The centralized database currently contains >800 published limb regeneration experiments comprising many model organisms, including salamanders, frogs, insects, crustaceans and arachnids. The database represents an extraordinary resource for mining the existing knowledge of functional data in this field; furthermore, its mathematical nature based on a functional ontology will pave the way for artificial intelligence tools applied to the discovery of the sought-after comprehensive limb regeneration models.

Gap Junctional Blockade Stochastically Induces Different Species-Specific Head Anatomies in Genetically Wild-Type Girardia dorotocephala Flatworms.

The shape of an animal body plan is constructed from protein components encoded by the genome. However, bioelectric networks composed of many cell types have their own intrinsic dynamics, and can drive distinct morphological outcomes during embryogenesis and regeneration. Planarian flatworms are a popular system for exploring body plan patterning due to their regenerative capacity, but despite considerable molecular information regarding stem cell differentiation and basic axial patterning, very little is known about how distinct head shapes are produced. Here, we show that after decapitation in G. dorotocephala, a transient perturbation of physiological connectivity among cells (using the gap junction blocker octanol) can result in regenerated heads with quite different shapes, stochastically matching other known species of planaria (S. mediterranea, D. japonica, and P. felina). We use morphometric analysis to quantify the ability of physiological network perturbations to induce different species-specific head shapes from the same genome. Moreover, we present a computational agent-based model of cell and physical dynamics during regeneration that quantitatively reproduces the observed shape changes. Morphological alterations induced in a genomically wild-type G. dorotocephala during regeneration include not only the shape of the head but also the morphology of the brain, the characteristic distribution of adult stem cells (neoblasts), and the bioelectric gradients of resting potential within the anterior tissues. Interestingly, the shape change is not permanent; after regeneration is complete, intact animals remodel back to G. dorotocephala-appropriate head shape within several weeks in a secondary phase of remodeling following initial complete regeneration. We present a conceptual model to guide future work to delineate the molecular mechanisms by which bioelectric networks stochastically select among a small set of discrete head morphologies. Taken together, these data and analyses shed light on important physiological modifiers of morphological information in dictating species-specific shape, and reveal them to be a novel instructive input into head patterning in regenerating planaria.

Design of a flexible component gathering algorithm for converting cell-based models to graph representations for use in evolutionary search.

BACKGROUND: The ability of science to produce experimental data has outpaced the ability to effectively visualize and integrate the data into a conceptual framework that can further higher order understanding. Multidimensional and shape-based observational data of regenerative biology presents a particularly daunting challenge in this regard. Large amounts of data are available in regenerative biology, but little progress has been made in understanding how organisms such as planaria robustly achieve and maintain body form. An example of this kind of data can be found in a new repository (PlanformDB) that encodes descriptions of planaria experiments and morphological outcomes using a graph formalism. RESULTS: We are developing a model discovery framework that uses a cell-based modeling platform combined with evolutionary search to automatically search for and identify plausible mechanisms for the biological behavior described in PlanformDB. To automate the evolutionary search we developed a way to compare the output of the modeling platform to the morphological descriptions stored in PlanformDB. We used a flexible connected component algorithm to create a graph representation of the virtual worm from the robust, cell-based simulation data. These graphs can then be validated and compared with target data from PlanformDB using the well-known graph-edit distance calculation, which provides a quantitative metric of similarity between graphs. The graph edit distance calculation was integrated into a fitness function that was able to guide automated searches for unbiased models of planarian regeneration. We present a cell-based model of planarian that can regenerate anatomical regions following bisection of the organism, and show that the automated model discovery framework is capable of searching for and finding models of planarian regeneration that match experimental data stored in PlanformDB. CONCLUSION: The work presented here, including our algorithm for converting cell-based models into graphs for comparison with data stored in an external data repository, has made feasible the automated development, training, and validation of computational models using morphology-based data. This work is part of an ongoing project to automate the search process, which will greatly expand our ability to identify, consider, and test biological mechanisms in the field of regenerative biology.

Planform: an application and database of graph-encoded planarian regenerative experiments.

SUMMARY: Understanding the mechanisms governing the regeneration capabilities of many organisms is a fundamental interest in biology and medicine. An ever-increasing number of manipulation and molecular experiments are attempting to discover a comprehensive model for regeneration, with the planarian flatworm being one of the most important model species. Despite much effort, no comprehensive, constructive, mechanistic models exist yet, and it is now clear that computational tools are needed to mine this huge dataset. However, until now, there is no database of regenerative experiments, and the current genotype-phenotype ontologies and databases are based on textual descriptions, which are not understandable by computers. To overcome these difficulties, we present here Planform (Planarian formalization), a manually curated database and software tool for planarian regenerative experiments, based on a mathematical graph formalism. The database contains more than a thousand experiments from the main publications in the planarian literature. The software tool provides the user with a graphical interface to easily interact with and mine the database. The presented system is a valuable resource for the regeneration community and, more importantly, will pave the way for the application of novel artificial intelligence tools to extract knowledge from this dataset. AVAILABILITY: The database and software tool are freely available at http://planform.daniel-lobo.com.

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.

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.

Mitochondrial Variation of Bottlenose Dolphins (Tursiops truncatus) from the Canary Islands Suggests a Key Population for Conservation with High Connectivity within the North-East Atlantic Ocean.

In recent decades, worldwide cetacean species have been protected, but they are still threatened. The bottlenose dolphin (Tursiops truncatus) is a vulnerable keystone species and a useful bioindicator of the health and balance of marine ecosystems in oceans all over the world. The genetic structure of the species is shaped by their niche specialization (along with other factors), leading to the classification of two ecotypes: coastal and pelagic. In this study, the genetic diversity, population structure, and ecotypes of bottlenose dolphins from the Canary Islands were assessed through the analysis of 49 new samples from biopsies and from stranded animals using the 636 bp portion of the mitochondrial control region and 343 individuals from databases (n = 392). The results reveal high genetic diversity in Canarian bottlenose dolphins (Hd = 0.969 and π = 0.0165) and the apparent lack of population genetic structure within this archipelago. High genetic structure (Fst, Φst) was found between the Canary Islands and coastal populations, while little to no structure was found with the pelagic populations. These results suggest that Canarian bottlenose dolphins are part of pelagic ecotype populations in the North Atlantic. The studied Special Areas of Conservation in the Canary Islands may correspond to a hotspot of genetic diversity of the species and could be a strategic area for the conservation of the oceanic ecotype of bottlenose dolphins.

Modeling planarian regeneration: a primer for reverse-engineering the worm.

A mechanistic understanding of robust self-assembly and repair capabilities of complex systems would have enormous implications for basic evolutionary developmental biology as well as for transformative applications in regenerative biomedicine and the engineering of highly fault-tolerant cybernetic systems. Molecular biologists are working to identify the pathways underlying the remarkable regenerative abilities of model species that perfectly regenerate limbs, brains, and other complex body parts. However, a profound disconnect remains between the deluge of high-resolution genetic and protein data on pathways required for regeneration, and the desired spatial, algorithmic models that show how self-monitoring and growth control arise from the synthesis of cellular activities. This barrier to progress in the understanding of morphogenetic controls may be breached by powerful techniques from the computational sciences-using non-traditional modeling approaches to reverse-engineer systems such as planaria: flatworms with a complex bodyplan and nervous system that are able to regenerate any body part after traumatic injury. Currently, the involvement of experts from outside of molecular genetics is hampered by the specialist literature of molecular developmental biology: impactful collaborations across such different fields require that review literature be available that presents the key functional capabilities of important biological model systems while abstracting away from the often irrelevant and confusing details of specific genes and proteins. To facilitate modeling efforts by computer scientists, physicists, engineers, and mathematicians, we present a different kind of review of planarian regeneration. Focusing on the main patterning properties of this system, we review what is known about the signal exchanges that occur during regenerative repair in planaria and the cellular mechanisms that are thought to underlie them. By establishing an engineering-like style for reviews of the molecular developmental biology of biomedically important model systems, significant fresh insights and quantitative computational models will be developed by new collaborations between biology and the information sciences.

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.

Resting potential, oncogene-induced tumorigenesis, and metastasis: the bioelectric basis of cancer in vivo.

Cancer may result from localized failure of instructive cues that normally orchestrate cell behaviors toward the patterning needs of the organism. Steady-state gradients of transmembrane voltage (V(mem)) in non-neural cells are instructive, epigenetic signals that regulate pattern formation during embryogenesis and morphostatic repair. Here, we review molecular data on the role of bioelectric cues in cancer and present new findings in the Xenopus laevis model on how the microenvironment's biophysical properties contribute to cancer in vivo. First, we investigated the melanoma-like phenotype arising from serotonergic signaling by 'instructor' cells-a cell population that is able to induce a metastatic phenotype in normal melanocytes. We show that when these instructor cells are depolarized, blood vessel patterning is disrupted in addition to the metastatic phenotype induced in melanocytes. Surprisingly, very few instructor cells need to be depolarized for the hyperpigmentation phenotype to occur; we present a model of antagonistic signaling by serotonin receptors that explains the unusual all-or-none nature of this effect. In addition to the body-wide depolarization-induced metastatic phenotype, we investigated the bioelectrical properties of tumor-like structures induced by canonical oncogenes and cancer-causing compounds. Exposure to carcinogen 4-nitroquinoline 1-oxide (4NQO) induces localized tumors, but has a broad (and variable) effect on the bioelectric properties of the whole body. Tumors induced by oncogenes show aberrantly high sodium content, representing a non-invasive diagnostic modality. Importantly, depolarized transmembrane potential is not only a marker of cancer but is functionally instructive: susceptibility to oncogene-induced tumorigenesis is significantly reduced by forced prior expression of hyperpolarizing ion channels. Importantly, the same effect can be achieved by pharmacological manipulation of endogenous chloride channels, suggesting a strategy for cancer suppression that does not require gene therapy. Together, these data extend our understanding of the recently demonstrated role of transmembrane potential in tumor formation and metastatic cell behavior. V(mem) is an important non-genetic biophysical aspect of the microenvironment that regulates the balance between normally patterned growth and carcinogenesis.