Minimal Developmental Computation: A Causal Network Approach to Understand Morphogenetic Pattern Formation

What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal 'genetic' networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions-a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel "causal network" analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns-an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization.

Antifragility Predicts the Robustness and Evolvability of Biological Networks through Multi-Class Classification with a Convolutional Neural Network

Robustness and evolvability are essential properties to the evolution of biological networks. To determine if a biological network is robust and/or evolvable, it is required to compare its functions before and after mutations. However, this sometimes takes a high computational cost as the network size grows. Here, we develop a predictive method to estimate the robustness and evolvability of biological networks without an explicit comparison of functions. We measure antifragility in Boolean network models of biological systems and use this as the predictor. Antifragility occurs when a system benefits from external perturbations. By means of the differences of antifragility between the original and mutated biological networks, we train a convolutional neural network (CNN) and test it to classify the properties of robustness and evolvability. We found that our CNN model successfully classified the properties. Thus, we conclude that our antifragility measure can be used as a predictor of the robustness and evolvability of biological networks.