On Networks and their Applications: Stability of Gene Regulatory Networks and Gene Function Prediction using Autoencoders

Abstract

We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any activity ratio and we determine the functional form of this boundary which has a nontrivial fractal structure. We further observe that the majority of the gene regulatory functions found in known biological networks (submitted to the Cell Collective database) lie on the line of minimum sensitivity which paradoxically remains largely in the unstable regime. Our results provide a quantitative basis for the argument that an evolutionary preference for nested canalizing functions in gene regulation (e.g., for higher robustness) and for elasticity of gene activity are sufficient for concentration of such systems near the "edge of chaos." The original structure of gene regulatory networks is unknown due to the undiscovered functions of some genes. Most gene function discovery approaches make use of unsupervised clustering or classification methods that discover and exploit patterns in gene expression profiles. However, existing knowledge in the field derives from multiple and diverse sources. Incorporating this know-how for novel gene function prediction can, therefore, be expected to improve such predictions. We here propose a function-specific novel gene discovery tool that uses a semi-supervised autoencoder. Our method is thus able to address the needs of a modern researcher whose expertise is typically confined to a specific functional domain. Lastly, the dynamics of unorthodox learning approaches like biologically plausible learning algorithms are investigated and found to exhibit a general form of Einstein relation.