Discovering regulatory networks that explain experimental morphological data.

<p>(<i>A</i>) Surgical, genetic, and pharmacological experiments result in a set of patterning phenotypes. (<i>B</i>) Using a mathematical functional ontology, the experimental manipulations and the resultant phenotypes are formalized in a database. (<i>C</i>) Without any further knowledge beyond that dataset, the algorithm automatically infers a regulatory network that, when quantitatively modeled in a simulator, explains all the resultant phenotypes in the experiments. Discovered regulatory networks comprise specific genetic products (<i>β-catenin</i>, <i>notum</i>, <i>wnt1</i>), phenotypic products (head, trunk, tail, wound signal), and yet-unidentified products (labeled with single letters, e.g. ‘a’). Products can travel intercellularly (dashed border) or be intracellularly confined (solid border). Regulatory interactions can activate (blue lines) or repress (red lines) a product and these can be combined in a necessary (dashed lines) or sufficient (solid lines) fashion.</p

Inferring Regulatory Networks from Experimental Morphological Phenotypes: A Computational Method Reverse-Engineers Planarian Regeneration

<div><p>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 <i>in silico</i> 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.</p></div

Inferred comprehensive model of planarian head-versus-tail regeneration.

<p>(<i>A</i>) Regulatory network found by the automated system, which explains the combined phenotypic experimental data of the key publications of head-trunk-tail planarian regeneration. (<i>B</i>) Simulation of the 16 experiments comprising the dataset, resulting in the same reported experimental phenotypes. (<i>C</i>) Evolution of the error and complexity (number of products and regulations) of the best regulatory network in the population over time during the algorithm search.</p

Supporting Information S1 from Bioelectric gene and reaction networks: computational modelling of genetic, biochemical and bioelectrical dynamics in pattern regulation

Theoretical details relating to model details, ion channel, ion pump and transporter dynamics, and BIGR network models that are presented in the main text

Method to infer regulatory networks from phenotype-based experiments.

<p>Taking a dataset of formalized experiments as input, the algorithm cyclically generates candidate regulatory networks, simulates the experimental manipulations, and discards the networks with the highest errors (lowest predictive power); this process is repeated until a network with zero error is found.</p

Regulatory networks inferred from experimental data formalized from the key papers of head-versus-tail planarian regeneration.

<p>The algorithm infers both the parameters and topology of the regulatory networks containing specific experimentally-perturbed products when available and unknown products when necessary, and explaining the regeneration dynamics of the correct position, shape, and proportions of the head, trunk, and tail regions of the worm for all the experiments in each dataset. (<i>A</i>) <i>β-catenin</i>/<i>APC</i> knock-down experiments. (<i>B</i>) <i>wnt1</i>/<i>wnt11-5</i> knock-down experiments [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.ref075" target="_blank">75</a>]. (<i>C) β-catenin</i>/<i>notum</i>/<i>wnt1</i> knock-down experiments [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.ref076" target="_blank">76</a>]; (<i>D</i>) <i>β-catenin</i>/<i>hh</i>/<i>wnt1</i>/<i>ptc</i> knock-down experiments [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.ref077" target="_blank">77</a>]; (<i>E</i>) Gap junction communication blockage with octanol [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.ref078" target="_blank">78</a>]; (<i>F</i>) Classical trunk/anterior/posterior fragment cuts [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.ref079" target="_blank">79</a>].</p

Simulation of phenotypic experiments <i>in silico</i>.

<p>(<i>A</i>) Regulatory network used in the experiment, corresponding to the inferred network shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.g003" target="_blank">Fig 3A</a>. (<i>B</i>) An experiment is performed by loading and initializing the product concentrations according to the wild-type morphology, integrating the network equations, performing the manipulation specified in the experiment, and integrating for a second time the network equations. The product concentrations over time from a selection of locations in the worm are shown. Graph colors correspond to product colors in panel A. (<i>C</i>) Knock-down of <i>β-catenin</i> (RNAi) is simulated by setting its production constant to zero, which alters the dynamics of the network and results in the regeneration of a double-head morphology.</p

A subtraction control experiment with the automated method results in a regulatory network that can correctly predict three novel experiments not included during the search.

<p>(<i>A</i>) Regulatory network found by the automated system from a reduced comprehensive dataset excluding three experiments. (<i>B</i>) Simulations of the reduced dataset of experiments used during the search with the found network result in the regeneration of the correct phenotypes. (<i>C</i>) Simulations of the three novel experiments not included during the search with the found network result in the exact correct phenotypes obtained <i>in vivo</i>.</p

Selection of candidate networks evaluated during a search.

<p>Networks early in the search have low complexity and a limited capacity to explain the experiments in the dataset. The algorithm produces new networks by adding, deleting, and modifying products and regulations, until a network perfectly explaining all the experiments is found. The networks shown are a selection from the search of the model presented in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004295#pcbi.1004295.g003" target="_blank">Fig 3C</a>.</p

Additional file 1: of Bioelectric memory: modeling resting potential bistability in amphibian embryos and mammalian cells

Supplementary Materials. (PDF 261 kb