Computer-based technologies are becoming one of the most promising novel approaches due to continuously accelerated growth of both hardware processing power and software algorithm efficiency. One recent example includes machine learning algorithms that revolutionised data analysis in computer science, and lead to new computer games, visual recognition, and other applications that overtake human performance in many cases. Here, we propose to perform atomistic molecular simulations using novel enhanced sampling algorithms. Most biologically important processes take place on significantly longer timescales than those accessible to current computer simulations. Therefore, to obtain meaningful and accurate results regarding the kinetics and conformational dynamics of complex molecular systems, we use algorithms that enhance the sampling using parallel calculations with different biases. Developing more optimal biasing algorithms will allow us to model faster and more accurately the key biological processes of interest, including ligand binding, protein conformations, etc. Here we aim to use statistical algorithms inspired by machine learning to develop novel enhanced sampling methods for molecular simulations. Novel algorithms can be applied to a wide range of molecular modeling problems. We will focus on phosphate catalytic enzymes, and study key DNA processing enzymes to reveal the catalytic mechanism in these systems. Due to the essential nature of phosphate catalytic enzymes in most biological processes, a large number of drugs in current clinical practice also target phosphate-processing enzymes treating a wide range of diseases. Examples include reverse transcriptase and integrase inhibitors used against HIV and hepatitis B, proton pump inhibitors used in gastric diseases, kinase, PARP and topoisomerase inhibitors used against a large number of cancers. Studying phosphate catalytic systems with modern molecular modeling methods will enable fundamental advances in our current knowledge of the molecular basis of life. It will also create opportunities for rational development of better drugs to fight diseases.