A General Hybrid Modeling Framework for Systems Biology Applications: Combining Mechanistic Knowledge with Deep Neural Networks under the SBML Standard

In this paper, a computational framework is proposed that merges mechanistic modeling with deep neural networks obeying the Systems Biology Markup Language (SBML) standard. Over the last 20 years, the systems biology community has developed a large number of mechanistic models that are currently stored in public databases in SBML. With the proposed framework, existing SBML models may be redesigned into hybrid systems through the incorporation of deep neural networks into the model core, using a freely available python tool. The so-formed hybrid mechanistic/neural network models are trained with a deep learning algorithm based on the adaptive moment estimation method (ADAM), stochastic regularization and semidirect sensitivity equations. The trained hybrid models are encoded in SBML and uploaded in model databases, where they may be further analyzed as regular SBML models. This approach is illustrated with three well-known case studies: the Escherichia coli threonine synthesis model, the P58IPK signal transduction model, and the Yeast glycolytic oscillations model. The proposed framework is expected to greatly facilitate the widespread use of hybrid modeling techniques for systems biology applications.