Theory Of Local Free Energy Landscape And Its Application In Protein Structure Refinement

The computation of free energy of proteins has always been a top priority in computational biology,and it has direct guiding significance for protein structure prediction,design,docking and refinement.Many of the functions of organisms are realized by conformational changes of proteins,such as allosteric effect and so on.Traditional protein free energy calculation methods require adequate conformational sampling of the local and global protein structure,which consumes a lot of computing resources and time.This paper proposes a local free energy landscape(LFEL)theory for local repeated sampling calculations that have not received attention in the traditional calculation framework,and develops a new free energy refinement method based on the generalized solvation free energy(GSFE)theory.This method combines coordinate transformation,automatic differentiation,and a neural network that trains and saves local free energy landscape to construct a computational graph,and achieves end-to-end optimization(free energy of protein molecules to atomic coordinates in proteins)in an iterative manner.Compared with the current mainstream protein structure refinement methods,this method demonstrated competitive accuracy in the14 of Critical Assessment of Techniques for Protein Structure Prediction(CASP14)structure refinement competition,and achieved a huge improvement in efficiency of more than three orders of magnitude.In the paper,the main contributions are divided into the following aspects:Firstly,rapid free energy assessment of protein structure.At the amino acid scale,the information of the protein backbone(,,)andatoms,including the identity of amino acid,pair distance,and the Angle information of the backbone atom were input into the neural network as features,and the local free energy landscape(LFEL)was fitted to evaluate the free energy of the local environment of the protein.Then the global protein free energy can be obtained by local dynamic splicing to obtain the free energy of native protein structure and decoys.This part is mainly to fit the free energy landscape through the neural network,construct a function for rapid evaluation of protein free energy,and pave the way for the optimization of protein structure.Secondly,optimize and update the coordinates of the protein backbone through the trained neural network.We convert the input cartesian coordinates of the protein backbone andatoms into internal coordinates,set the gradients for the backbone dihedral angles?and?,and then convert them into cartesian coordinates and extract the features and input them into the trained neural network to calculate free energy.The whole process is kept in the calculation diagram,and then the inverse derivation and minimum free energy are used to optimize the protein backbone structure.Thirdly,A program was developed to rearrange protein side chains,that is,to optimize the structure of protein side chains with atomic scale.There are mainly two modes:one is in the random assembly mode,using the sequence Monte Carlo method to assemble,that is,randomly obtaining amino acid conformations from the protein rotamer library.And it is satisfied that there is no strong collision with the backbone atoms and the installed side chain atoms Another mode is to predict the dihedral angle₁ of the side chain through a neural network,and select an appropriate conformation for assembly based on the predicted dihedral angle of the side chain.As a result,the dihedral angle of the side chain assembled in the second mode is closer to the natural structure.In summary,this article uses neural networks and computational graphs and other tools based on the generalized solvation free energy theory,developed a fast computational free energy method on the amino acid scale to avoid repeated local sampling.And greatly speed up the free energy evaluation of protein structure.In addition,the protein structure was optimized on the atomic scale by rearranging the side chains of amino acids.