Alignment-free molecular shape comparison using spectral geometry: the framework

A framework is presented for the calculation of novel alignment-free descriptors of molecular shape. The methods are based on the technique of spectral geometry which has been developed in the field of computer vision where it has shown impressive performance for the comparison of deformable objects such as people and animals. Spectral geometry techniques encode shape by capturing the curvature of the surface of an object into a compact, information-rich representation that is alignment-free while also being invariant to isometric deformations, that is, changes that do not distort distances over the surface. Here, we adapt the technique to the new domain of molecular shape representation. We describe a series of parametrization steps aimed at optimizing the method for this new domain. Our focus here is on demonstrating that the basic approach is able to capture a molecular shape into a compact and information-rich descriptor. We demonstrate improved performance in virtual screening over a more established alignment-free method and impressive performance compared to a more accurate, but much more computationally demanding, alignment-based approach

Molecular Surface Walk

A new algorithm to compute a solvent accessible molecular surface (MS) and a graphical computer program for a molecular surface walk have been designed. The surface is generated by rolling a spherical probe representing a solvent molecule over the atoms of the investigated molecule. This surface representation is used in the graphical computer program MS walk to achieve a new way of viewing the molecules. The advantage of the MS walk approach is that the molecular cavities, only partially visible by other methods, can be inspected. The new algorithm’s performance is comparable to that of similar existing algorithms and its time complexity is linear with respect to the number of atoms. The MS algorithm and the MS walk program can be accessed on the Web (http://www.cmm.ki.si/konc/ms_walk)

Multiscale Geometric Modeling of Macromolecules I: Cartesian Representation

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites

Modeling Electronic Structure And Dynamics Of Molecules On Metal Surfaces

Molecular dynamics near metal surfaces underlie a number of fields in chemistry, including chemisorption, electrochemistry, heterogeneous catalysis, and many others. Due to the continuum of electronic states possessed by metals, electron-hole pairs can be easily excited by moving molecules near metals. Consequently, molecular dynamics near metal surfaces often go beyond the Born-Oppenheimer approximation by demanding, e.g., a friction and its accompanied random force, or a surface hopping approach. In this thesis, we first propose an efficient and accurate interpolation method for computing the electronic friction tensor as appropriate for molecular dynamics. Unlike traditional methods based on broadening, our interpolation method relies only on orbital energy gradients (rather than derivative couplings), and does not involve any user-identified parameters. Next, we develop several configuration interaction approaches for characterizing the electronic structure of model molecule-metal system. Based on these approaches, we introduce an efficient reduced representation with a special focus on the molecular charge character. Thereafter, we modify the fewest switches surface hopping (FSSH) method to accommodate this reduced representation by including electronic relaxation (ER). The reduced representation and the FSSH-ER together form a new surface hopping scheme for modeling molecular nonadiabatic dynamics. This scheme is valid across a wide range of coupling strength as supported by tests applied to the Anderson-Holstein model for electron transfer

Modeling Electronic Structure And Dynamics Of Molecules On Metal Surfaces

Molecular dynamics near metal surfaces underlie a number of fields in chemistry, including chemisorption, electrochemistry, heterogeneous catalysis, and many others. Due to the continuum of electronic states possessed by metals, electron-hole pairs can be easily excited by moving molecules near metals. Consequently, molecular dynamics near metal surfaces often go beyond the Born-Oppenheimer approximation by demanding, e.g., a friction and its accompanied random force, or a surface hopping approach. In this thesis, we first propose an efficient and accurate interpolation method for computing the electronic friction tensor as appropriate for molecular dynamics. Unlike traditional methods based on broadening, our interpolation method relies only on orbital energy gradients (rather than derivative couplings), and does not involve any user-identified parameters. Next, we develop several configuration interaction approaches for characterizing the electronic structure of model molecule-metal system. Based on these approaches, we introduce an efficient reduced representation with a special focus on the molecular charge character. Thereafter, we modify the fewest switches surface hopping (FSSH) method to accommodate this reduced representation by including electronic relaxation (ER). The reduced representation and the FSSH-ER together form a new surface hopping scheme for modeling molecular nonadiabatic dynamics. This scheme is valid across a wide range of coupling strength as supported by tests applied to the Anderson-Holstein model for electron transfer

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package.Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perde

Photoexcited electron and hole dynamics in semiconductor quantum dots: phonon-induced relaxation, dephasing, multiple exciton generation and recombination.

Photoexcited dynamics of electrons and holes in semiconductor quantum dots (QD), including phonon-induced relaxation, multiple exciton generation, fission and recombination (MEG, MEF and MER), were simulated by combining ab initio time-dependent density functional theory and non-adiabatic molecular dynamics. These nonequilibrium phenomena govern the optical properties and photoexcited dynamics of QDs, determining the branching between electronic processes and thermal energy losses. Our approach accounts for QD size and shape as well as defects, core-shell distribution, surface ligands and charge trapping, which significantly influence the properties of photoexcited QDs. The method creates an explicit time-domain representation of photoinduced processes and describes various kinetic regimes owing to the non-perturbative treatment of quantum dynamics. QDs of different sizes and materials, with and without ligands, are considered. The simulations provide direct evidence that the high-frequency ligand modes on the QD surface play a pivotal role in the electron-phonon relaxation, MEG, MEF and MER. The insights reported here suggest novel routes for controlling the photoinduced processes in semiconductor QDs and lead to new design principles for increasing the efficiencies of photovoltaic devices

PL-PatchSurfer: A Novel Molecular Local Surface-Based Method for Exploring Protein-Ligand Interactions

Structure-based computational methods have been widely used in exploring protein-ligand interactions, including predicting the binding ligands of a given protein based on their structural complementarity. Compared to other protein and ligand representations, the advantages of a surface representation include reduced sensitivity to subtle changes in the pocket and ligand conformation and fast search speed. Here we developed a novel method named PL-PatchSurfer (Protein-Ligand PatchSurfer). PL-PatchSurfer represents the protein binding pocket and the ligand molecular surface as a combination of segmented surface patches. Each patch is characterized by its geometrical shape and the electrostatic potential, which are represented using the 3D Zernike descriptor (3DZD). We first tested PL-PatchSurfer on binding ligand prediction and found it outperformed the pocket-similarity based ligand prediction program. We then optimized the search algorithm of PL-PatchSurfer using the PDBbind dataset. Finally, we explored the utility of applying PL-PatchSurfer to a larger and more diverse dataset and showed that PL-PatchSurfer was able to provide a high early enrichment for most of the targets. To the best of our knowledge, PL-PatchSurfer is the first surface patch-based method that treats ligand complementarity at protein binding sites. We believe that using a surface patch approach to better understand protein-ligand interactions has the potential to significantly enhance the design of new ligands for a wide array of drug-targets