Development Of Theoretical Methods For Studying Biological Macromolecules

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pKa prediction by machine learning Machine learning techniques are developing rapidly in recent years and have been applied to numerous scientific fields. Previously, we presented four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA. Error analyses were performed and showed that coupled ionizable residues are the most difficult ones in pKa prediction. To curate a more decent pKa database, we collected detailed information for the PDB structures (e.g., co-factors, whether it is membrane protein or not, etc.), which could be new features for our next version of pKa predictor. In addition, the calculated pKa's based on continuum electrostatic, will be added to the model. This feature will assure the inclusion of long-range electrostatics and the hydrophobic effect. Additional experimental pKa data were found in literatures and added to the new database. We also examined experimental conditions for both PDB structure measurements and pKa measurements to check if the structure-pKa pairs are compatible. Conceptual DFT for studying catalytic reactions in metalloproteins Metalloenzymes play a crucial role in maintaining human health by participating in essential biochemical processes that are vital for various physiological functions. These specialized enzymes require metal ions as cofactors to catalyze specific reactions with remarkable efficiency and specificity. Understanding the electronic structure of the active site helps reveal reaction mechanisms. In this project we use Conceptual DFT (CDFT) to study the electronic structure of metallic active sites in Photosystem II. CDFT uses quantum mechanical calculations for understanding and predicting the electronic structure and the inter-molecular and intra-molecular reactivity of molecules. It extends DFT by introducing the concept of quantum descriptors, which describe the tendency of a system to donate or accept electrons based on properties that include electronegativity, hardness, softness, the Fukui functions, and the dual descriptor. Furthermore, the local version of these descriptors is used to predict the reactive sites within the molecule. For example, the condensed Fukui functions and dual descriptors have been used to identify the atoms within the molecule that participate in nucleophilic/electrophilic attack. Our results show that metal cluster in Photosystem II divide the oxygen ligands into nucleophilic and electrophilic ligands to reduce the barrier of the O=O bond formation. Machine Learning models for predicting oxidation states of metals in proteins Imaging metalloenzymes with X-ray causes radiation damage, which changes the physical/chemical properties of the metal active site. However, the catalytic reactions in metalloproteins are usually coupled to the metal oxidation states. Thus, identifying the correct oxidation states of the metals is essential for understanding the reaction mechanisms. We built a huge data set of small coordination compounds collected from Cambridge Crystallographic Database (CCDC) for different metals (Fe, Mn, Cu, Co) at different oxidation states and used it to build a machine learning models (Decision Tree and Neural Networks classifiers) to predict the oxidation states of the metals in proteins structures imaged with X-ray and XFEL crystallography. Equivariant graph neural based electrostatic embedding in QM/MM simulations We present a novel methodology for efficiently and accurately integrating classical force fields with Quantum Mechanical (QM) theory in additive Quantum Mechanics/Molecular Mechanics (QM/MM) simulations. We design sparse E(3) equivariant neural networks, incorporating a sparse connection scheme that emulates the one-electron integrals in the ab-initio QM and MM regions of the calculations. Specifically, point charges from the MM engage in messaging solely with the QM region, eliminating direct interactions among themselves. To validate the effectiveness of our methodology, we conduct ablation studies and compare it to prominent alternatives, including High-Dimensional Neural Networks (HDNNs) and graph convolutional networks. Our findings demonstrate that our approach not only exhibits superior data efficiency but also outperforms HDNNs and graph convolutional networks by an order of magnitude in terms of computational efficiency. These advancements hold significant promise for diverse applications in areas such as materials science, chemistry, and drug discovery. bEDS for evaluation of free energies Free energies of binding and solvation are key quantities in modern drug-design, and being able to accurately and rapidly evaluate them remains an ongoing challenge. Taking inspiration from the Enveloping Distribution Sampling method (EDS), we developed the bridge-EDS (bEDS) method. EDS defines a smoothed potential energy function to overcome barriers on the potential energy surface. bridge-EDS applies this to all alchemical states typically used for solvation or ligand-binding processes. This samples a phase space with better overlap amongst alchemical states, freed from PES energy barriers, thus requiring shorter overall simulations. Thanks to our apoCHARMM code architecture and its multistate handling capability, energies of all different alchemical states are computed on the fly at no extra cost, and the post-processing effort becomes negligible, making bEDS a valuable asset for free energy prediction. Implementation of the Spherical Grids and Treecode Summation Algorithm Evaluating pair-wise electrostatic interactions is the most time consuming part when running molec- ular dynamics (MD) simulations, because of the slow decay of the Coulomb operator. The Spherical Grid and Treecode (SGT) summation algorithm speeds up the calculation by factoring the Coulomb operator into short and long ranged terms, where the short ranged term is handled by computing only the pair-wise interactions within a cutoff radius and the long ranged term is approximated using nu- merical cubature techniques. The SGT algorithms primary advantage over traditional methods is that it does not use the fast Fourier transform (FFT) which requires multiple all-to-all communications on multi-node systems. Avoiding the FFT makes the SGT algorithm well suited to be implemented for use on large CPU clusters and multi-GPU systems. In this work, we plan to develop a standalone library which implements the SGT algorithm. We have currently developed pilot code implementations and are in the process of developing high-performance versions for CPU and GPU based platforms. The CPU version is parallelized using a hybrid OpenMPI/OpenMP approach and the GPU version utilizes the CUDA API. We are currently in the process of optimizing the CPU and single GPU versions and plan to develop a multi-GPU version in the future. Other active projects: Rotatable Grids for Grid Inhomogeneous Solvation Theory Calculations Free energy calculation with Double Exponential Potential A spatial Self-Guided Molecular Simulation Method Free Energy Profile Decomposition Analysis Machine Learning Potentials (MLPs) for Reactive Systems Conceptual Density Functional Theory (DFT) Analysis for Enzyme Catalysis