Continuum percolation theory of epimorphic regeneration

A biophysical model of epimorphic regeneration based on a continuum percolation process of fully penetrable disks in two dimensions is proposed. All cells within a randomly chosen disk of the regenerating organism are assumed to receive a signal in the form of a circular wave as a result of the action/reconfiguration of neoblasts and neoblast-derived mesenchymal cells in the blastema. These signals trigger the growth of the organism, whose cells read, on a faster time scale, the electric polarization state responsible for their differentiation and the resulting morphology. In the long time limit, the process leads to a morphological attractor that depends on experimentally accessible control parameters governing the blockage of cellular gap junctions and, therefore, the connectivity of the multicellular ensemble. When this connectivity is weakened, positional information is degraded leading to more symmetrical structures. This general theory is applied to the specifics of planaria regeneration. Computations and asymptotic analyses made with the model show that it correctly describes a significant subset of the most prominent experimental observations, notably anterior-posterior polarization (and its loss) or the formation of four-headed planaria.Comment: This author wish to retract the paper arXiv:1705.06720 because it began as part of a collaboration that later fell apart and it was published without the consent from the collaborators. Furthermore, the collaborators have managed to provide a better solution to this proble

Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.Comment: 20 pages, 6 figures, accepted for publication in PLoS On

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

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

A comprehensive conceptual and computational dynamics framework for autonomous regeneration systems

This paper presents a new conceptual and computational dynamics framework for damage detection and regeneration in multicellular structures similar to living animals. The model uniquely achieves complete and accurate regeneration from any damage anywhere in the system. We demonstrated the efficacy of the proposed framework on an artificial organism consisting of three tissue structures corresponding to the head, body and tail of a worm. Each structure consists of a stem cell surrounded by a tissue of differentiated cells. We represent a tissue as an Auto-Associative Neural Network (AANN) with local interactions and stem cells as a self-repair network with long-range interactions. We also propose another new concept, Information Field which is a mathematical abstraction over traditional components of tissues, to keep minimum pattern information of the tissue structures to be accessed by stem cells in extreme cases of damage. Through entropy, a measure of communication between a stem cell and differentiated cells, stem cells monitor the tissue pattern integrity, violation of which triggers damage detection and tissue repair. Stem cell network monitors its state and invokes stem cell repair in the case of stem cell damage. The model accomplishes regeneration at two levels: In the first level, damaged tissues with intact stem cells regenerate themselves. Here, stem cell identifies entropy change and finds the damage and regenerates the tissue in collaboration with the AANN. In the second level, involving missing whole tissues and stem cells, the remaining stem cell(s) access the information field to restore the stem cell network and regenerate missing tissues. In the case of partial tissue damage with missing stem cells, the two levels collaborate to accurately restore the stem cell network and tissues. This comprehensive hypothetical framework offers a new way to conceptualise regeneration for better understanding the regeneration processes in living systems. It could also be useful in biology for regenerative medicine and in engineering for building self-repairing biobots

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781

Functional analysis of Girardia tigrina transcriptome seeds pipeline for anthelmintic target discovery

Background Neglected diseases caused by helminth infections impose a massive hindrance to progress in the developing world. While basic research on parasitic flatworms (platyhelminths) continues to expand, researchers have yet to broadly adopt a free-living model to complement the study of these important parasites. Methods We report the high-coverage sequencing (RNA-Seq) and assembly of the transcriptome of the planarian Girardia tigrina across a set of dynamic conditions. The assembly was annotated and extensive orthology analysis was used to seed a pipeline for the rational prioritization and validation of putative anthelmintic targets. A small number of targets conserved between parasitic and free-living flatworms were comparatively interrogated. Results 240 million paired-end reads were assembled de novo to produce a strictly filtered predicted proteome consisting of over 22,000 proteins. Gene Ontology annotations were extended to 16,467 proteins. 2,693 sequences were identified in orthology groups spanning flukes, tapeworms and planaria, with 441 highlighted as belonging to druggable protein families. Chemical inhibitors were used on three targets in pharmacological screens using both planaria and schistosomula, revealing distinct motility phenotypes that were shown to correlate with planarian RNAi phenotypes. Conclusions This work provides the first comprehensive and annotated sequence resource for the model planarian G. tigrina, alongside a prioritized list of candidate drug targets conserved among parasitic and free-living flatworms. As proof of principle, we show that a simple RNAi and pharmacology pipeline in the more convenient planarian model system can inform parasite biology and serve as an efficient screening tool for the identification of lucrative anthelmintic targets

A comprehensive conceptual and computational dynamics framework for autonomous regeneration of form and function in biological organisms

In biology, regeneration is a mysterious phenomenon that has inspired self-repairing systems, robots, and biobots. It is a collective computational process whereby cells communicate to achieve an anatomical set point and restore original function in regenerated tissue or the whole organism. Despite decades of research, the mechanisms involved in this process are still poorly understood. Likewise, the current algorithms are insufficient to overcome this knowledge barrier and enable advances in regenerative medicine, synthetic biology, and living machines/biobots. We propose a comprehensive conceptual framework for the engine of regeneration with hypotheses for the mechanisms and algorithms of stem cell-mediated regeneration that enables a system like the planarian flatworm to fully restore anatomical (form) and bioelectric (function) homeostasis from any small- or large-scale damage. The framework extends the available regeneration knowledge with novel hypotheses to propose collective intelligent self-repair machines, with multi-level feedback neural control systems, driven by somatic and stem cells. We computationally implemented the framework to demonstrate the robust recovery of both anatomical and bioelectric homeostasis in an worm that, in a simple way, resembles the planarian. In the absence of complete regeneration knowledge, the framework contributes to understanding and generating hypotheses for stem cell mediated form and function regeneration which may help advance regenerative medicine and synthetic biology. Further, as our framework is a bio-inspired and bio-computing self-repair machine, it may be useful for building self-repair robots/biobots and artificial self-repair systems