Computer simulations using molecular dynamics (MD) and the combined quantum mechanical/molecular mechanical (QM/MM) approach are capable of describing structures and dynamics of proteins and chemical reactions catalyzed by enzymes. An accurate and computationally efficient energy function is necessary. However, challenges remain: the accuracy of QM method, the compatibility between the electron density of the QM subsystem and classical force fields for the MM subsystem, and the cost of ab initio QM/MM methods capitalizing on the accuracy and reliability of the associated QM approaches. To address these challenges, we have developed a series of ab initio QM/MM approaches on reaction path optimizations and free energy calculations, the QM/MM minimum free-energy path (QM/MM-MFEP) and the QM/MM neural network (QM/MM-NN) methods. This proposal aims to develop further the ab initio QM/MM methodology and its applications to the studies of redox processes in important enzymes, and the construction of ab initio force fields combined with neural network representations. Our long-term goals are to develop and establish accurate first-principles based and density functional theory (DFT) based MD and QM/MM simulation as an equal partner with experiments for the study of enzymes and proteins and to provide insight into chemical and redox processes in biological systems. Our aims are as follows: (1) We aim to make ab initio QM/MM models for much more accurate QM/MM energies, for the QM description and for the electrostatic and vdW interactions between the QM and MM subsystems. (2) We aim to develop a combined computational model to explore the key molecular determinants of the reduction potential variability in metalloproteins. We will provide detailed insight into chemical and redox reaction mechanisms in biological systems, in particular laccases. (3) We aim at the development of accurate force fields of water, and proteins for simulations in biological applications, going beyond the traditional force field forms and limitation in accuracy. The proposed developments will capitalize on the theoretical developments in quantum electronic theory, such as the linear response theory and accurate many-electron approach for non-covalent interactions, and leverage machine-learning methods in data science for biological system simulations. The proposed work will lead to the major advancement of the ab initio QM/MM method and force fields, and insights into the structure-function paradigm for proteins and important redox process and reaction mechanisms in enzymes. In addition, it will also lead to methodology development for design of new drugs and enzyme inhibitors.