PyBindE: Development of a Simple Python MM-PBSA Implementation for Estimating Protein-Protein and Protein-Ligand Binding Energies

Tese de mestrado, Bioquímica (Bioquímica), Universidade de Lisboa, Faculdade de Ciências, 2022Given the importance of proteins, the study of their interactions and binding affinities has been one of the most broadly populated fields of research for many years. Many approaches exist to calculate protein-protein and protein-ligand binding free energies, with single-trajectory MM-PBSA being a pop ular choice due to its more rigorous theoretical framework, when compared with methods, such as molec ular docking, while still possessing reasonable speed. MM-PBSA is particularly useful when the relative energy differences between system configurations are concerned, being able to provide insights about the forces involved in the binding process and their energetic contribution. In the present work, we describe a newly developed, DelPhi-based, single-trajectory MM-PBSA im plementation (PyBindE) written in Python, designed to be compatible with GROMOS force fields. A validation of this method was performed using a set of 37 HIV-1 protease-inhibitor complexes with experimentally-determined inhibition constants. These systems were also used as a validation set for g_mmpbsa, one widely used MM-PBSA implementation, originally validated using AMBER, thus com parisons with this method can be drawn. Molecular dynamics (MD) simulations of 150 ns were run in triplicate for every system, and MM-PBSA calculations were performed on the full trajectories, in 1500 snapshots per replicate. For 9 of the systems used for validation, the ligands of these systems con tained amine groups with pKa values ( 9) above physiological pH, and as such, different protonation scenarios for the ligands and the catalytic aspartate residues (Asp-25) were also explored. Furthermore, the impact of different values of the solute dielectric constant, on the correlation with experimental data, was studied for all different protonation cases. A practical application of PyBindE is also presented for the case of β-2 Microglobulin (β2M) D76N mutants, the causing-agents of a fatal form of amyloidosis. MM-PBSA was used to study the binding of 212 dimers derived from a Monte-Carlo Ensemble Docking protocol, determining the forces responsible for their binding and aggregation, and ranking the most stable binding modes. MM-PBSA calculations were run on 100 ns of MD trajectory for each dimer. Results of the comparison with g_mmpbsa are also analysed. Our validation results show an adequate correlation, 0.56, with experimental data when the correct ligand and catalytic aspartate residue protonations are employed, with a dielectric constant of 8. We found that underestimating the polar solvation contribution to the binding free energy resulted in an improvement of the correlations with our method, suggesting the need to optimize our parameterization and/or polar solvation calculation procedures. Regardless, our correlation results are higher than those reported for many standard MM-PBSA methods, with minimal parameter tweaking. The usefulness of PybindE was also highlighted in the calculation of binding free energies for β2M dimers. This method allowed the distinction of several binding modes from which different oligomerization patterns were then predicted. Overall, the results using PyBindE for the study of protein-protein binding affinities revealed a higher accuracy than g_mmpbsa, that often predicted positive binding energies suggesting unbinding events, which were not observed in the MD simulations

Accurate variational electronic structure calculations with the density matrix renormalization group

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS controls the size of the corner of the many-body Hilbert space that can be reached. Whereas the MPS ansatz will only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for other finite-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. DMRG and Hartree-Fock theory have an analogous structure. The former can be interpreted as a self-consistent mean-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-DMRG methods. Based on an approximate MPS, these methods provide improved ans\"atze for the ground state, as well as for excitations. Exponentiation of the single-particle (single-site) excitations for a Slater determinant (an MPS with open boundary conditions) leads to the Thouless theorem for Hartree-Fock theory (DMRG), an explicit nonredundant parameterization of the entire manifold of Slater determinants (MPS wavefunctions). This gives rise to the configuration interaction expansion for DMRG. The Hubbard-Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-lattice Hamiltonians allows to formulate a promising variant for MPSs.Comment: PhD thesis (225 pages). PhD thesis, Ghent University (2014), ISBN 978946197194

Tunneling and Zero-Point Energy Effects in Multidimensional Hydrogen Transfer Reactions: From Gas Phase to Adsorption on Metal Surfaces

Hydrogen transfer reactions play a significant role in many technological applications and fundamental processes in nature. Despite appearing to be simple reactions, they constitute complex processes where nuclear quantum effects (NQE) such as zero-point energy and nuclear tunneling play a decisive role even at ambient temperature. Moreover, the anharmonic coupling between different degrees of freedom that take place in realistic systems leads to hydrogen dynamics that, in many cases, are hard to interpret and understand. Systematic and quantitative ab initio studies of hydrogen dynamics were performed in systems ranging from gas phase molecules to adsorbates on metallic surfaces using state-of-the-art methodologies based on the path integral formulation of quantum mechanics in combination with the density functional approximation. In order to achieve this task, the construction of a general infrastructure that made the required ring polymer instanton simulations feasible was created, and a new approximation which considerably reduces the computational cost of including NQE on weakly bound systems was proposed and tested in the study of water dissociation at Pt(221) surface. Practical guidelines and limitations were also discussed to help the adoption of such methodologies by the community. The system of choice for most of the studies presented in this thesis was the porphycene molecule, a paradigmatic example of a molecular switch. The are a large number of experimental results in well-controlled environments available in the literature which have demonstrated the importance of NQE and multidimensional coupling for this molecule. Therefore, the porphycene molecule provides the unique possibility to theoretically address these effects and compare the theoretical predictions with experimental results in different environments. A portion of this thesis focuses on the study of porphycene molecule in the gas phase. For this purpose, the intramolecular double hydrogen transfer (DHT) rates and vibrational spectrum were calculated. The theoretical results showed a remarkable agreement with the experiments, and enabled the explanation of the unusual infrared spectra, the elucidation of the dominant DHT mechanism, and the understanding of their temperature dependence. In all the cases, the coupling between low- and high-frequency modes proved to be essential to get qualitatively correct trends. Another portion of this thesis examines molecules adsorbed on surfaces. Studies of porphycene molecules adsorbed on (111) and (110) metal surfaces showed that the stronger the surface-molecule interaction is, the more the molecule buckles upon adsorption, leading to an overall decrease of the DHT rates. The simulations identified different temperature regimes of the DHT mechanism, which was not possible by experimental measurements, and evidenced the importance of surface fluctuations on the DHT rates. In conclusion, this thesis provides a stepping stone towards the understanding of the impact of NQE, anharmonic effects, and multidimensional mode coupling on hydrogen dynamics, and also describes novel computational tools to approach their study by using first-principle calculations

Computational Chemistry Methods for Nanoporous Materials

International audienceWe present here the computational chemistry methods our group uses to investigate the physical and chemical properties of nanoporous materials and adsorbed fluids. We highlight the multiple time and length scales at which these properties can be examined and discuss the computational tools relevant to each scale. Furthermore, we include the key points to consider—upsides, downsides, and possible pitfalls—for these methods