In this paper we propose a computational framework 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 in SBML that are currently stored in public databases. With the proposed framework, existing SBML mechanistic models may be upgraded to 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 stored back in model databases, where they can be further analyzed as regular SBML models. The application of this approach is illustrated with three well-known case studies: the threonine synthesis model in Escherichia coli, 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.
