The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 310- and α-helix of acetyl(alanine)nNH2 (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm(-1) is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine)20 and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.

Accurate prediction of energetic properties of ionic liquid clusters using a fragment-based quantum mechanical method

Accurate prediction of physicochemical properties of ionic liquids (ILs) is of great significance to understand and design novel ILs with unique properties.

Quantum mechanical calculation of electric fields and vibrational Stark shifts at active site of human aldose reductase

Recent advance in biophysics has made it possible to directly measure site-specific electric field at internal sites of proteins using molecular probes with C = O or C≡N groups in the context of vibrational Stark effect. These measurements directly probe changes of electric field at specific protein sites due to, e.g., mutation and are very useful in protein design. Computational simulation of the Stark effect based on force fields such as AMBER and OPLS, while providing good insight, shows large errors in comparison to experimental measurement due to inherent difficulties associated with point charge based representation of force fields. In this study, quantum mechanical calculation of protein's internal electrostatic properties and vibrational Stark shifts was carried out by using electrostatically embedded generalized molecular fractionation with conjugate caps method. Quantum calculated change of mutation-induced electric field and vibrational Stark shift is reported at the internal probing site of enzyme human aldose reductase. The quantum result is in much better agreement with experimental data than those predicted by force fields, underscoring the deficiency of traditional point charge models describing intra-protein electrostatic properties.

Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

Quantum chemical studies on nucleophilic sites in calcium ion bound zwitterionic calmodulin loops

Quantum chemical calculation on Ca²⁺ bound zwitterionic calmodulin-loops shows terminal capping contributions localized near HOMO and LUMO, which decay exponentially and presence of nucleophilic site at the phenyl-ring O_h of Y99.

Fragment quantum chemical approach to geometry optimization and vibrational spectrum calculation of proteins

Geometry optimization and vibrational spectra (infrared and Raman spectra) calculations of proteins are carried out by a quantum chemical approach using the EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) method (J. Phys. Chem. A, 2013, 117, 7149).

Quantum Fragment Based ab Initio Molecular Dynamics for Proteins

Developing ab initio molecular dynamics (AIMD) methods for practical application in protein dynamics is of significant interest. Due to the large size of biomolecules, applying standard quantum chemical methods to compute energies for dynamic simulation is computationally prohibitive. In this work, a fragment based ab initio molecular dynamics approach is presented for practical application in protein dynamics study. In this approach, the energy and forces of the protein are calculated by a recently developed electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. For simulation in explicit solvent, mechanical embedding is introduced to treat protein interaction with explicit water molecules. This AIMD approach has been applied to MD simulations of a small benchmark protein Trpcage (with 20 residues and 304 atoms) in both the gas phase and in solution. Comparison to the simulation result using the AMBER force field shows that the AIMD gives a more stable protein structure in the simulation, indicating that quantum chemical energy is more reliable. Importantly, the present fragment-based AIMD simulation captures quantum effects including electrostatic polarization and charge transfer that are missing in standard classical MD simulations. The current approach is linear-scaling, trivially parallel, and applicable to performing the AIMD simulation of proteins with a large size.

Quantum Chemical Studies on Stability and Chemical Activities in Calcium Ion Bound Calmodulin Loops

Quantum chemical (QC) calculations for macromolecules require truncation of the molecule, highlighting the portion of interest due to heavy computation cost. As a result, an estimation of the effects of truncation is important to interpret the energy spectrum of such calculations. We perform density functional theory based QC calculations on calcium ion bound EF-hand loops of Calmodulin isolated from the crystal structure in an implicit solvent. We find that the terminal contributions of neutral capping are negligible across the entire ground-state energy spectrum. The coordination energy range and the nature of hybridization of the coordination state molecular orbitals remain qualitatively similar across these loops. While the HOMO and LUMO of loops in the N-terminal domain are dominated by the acidic aspartates, and the polar/hydrophobic residues, respectively, these levels of the C-terminal domain loops show strong localized electron density on the phenyl rings of the tyrosines. The Fukui index calculation identifies the hydroxyl oxygen in the phenyl ring of Y99 as a potent nucleophile. Our analysis indicates a general way of interpreting the electronic energy spectra to understand stability and functions of large biomolecules where the truncation of the molecule and, hence, the terminal capping effects are inevitable.

Calculation of protein–ligand binding affinities based on a fragment quantum mechanical method

An efficient fragment-based quantum mechanical method has been successfully applied for reliable prediction of protein–ligand binding affinities.

Novel theoretically designed HIV-1 non-nucleoside reverse transcriptase inhibitors derived from nevirapine

A common problem with non-nucleoside reverse transcriptase inhibitors (NNRTIs) of HIV-1 is the emergence of mutations in the HIV-1 RT, in particular Lys103 → Asn (K103N) and Tyr181 → Cys (Y181C), which lead to resistance to this entire class of inhibitors. In this study, we theoretically designed two new non-nucleoside HIV-1 RT inhibitors, Mnev-1 and Mnev-2, derived from nevirapine, in order to reduce the resistance caused by those HIV-1 RT mutations. The binding modes of Mnev-1 and Mnev-2 with the wild-type HIV-1 RT and its mutants (K103N and Y181C) were suggested by molecular docking followed by 20-ns molecular dynamics (MD) simulations in explicit water of those binding complexes (HIV-1 RTs with the new inhibitors). A molecular mechanics/generalized Born surface area (MM/GBSA) calculation was carried out for multiple snapshots extracted from the MD trajectory to estimate the binding free energy. The results of the calculations show that each of the new inhibitors forms a stable hydrogen bond with His235 during the MD simulations, leading to tighter binding of the new inhibitors with their targets. In addition, the repulsive interaction with Cys181 in the Y181C-nevirapine complex is not present in the novel inhibitors. The binding affinities predicted using the MM/GBSA calculations indicate that the new inhibitors could be effective at bypassing the drug resistance of these HIV-1 RT mutants.

Fragment quantum mechanical calculation of proteins and its applications

Conspectus The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system. In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein-ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins. On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin-spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein-ligand complexes.

Density functional calculations of extended, periodic systems using Coulomb corrected molecular fractionation with conjugated caps method (CC-MFCC)

A consistent DFT based formulation of the order-N molecular fractionation with conjugated caps method in which a molecular system is calculated considering a set of finite fragments, is proposed. Here we apply the method and test its performance on a periodic metal–organic framework system.

Electrostatically embedded generalized molecular fractionation with conjugate caps method for full quantum mechanical calculation of protein energy

An electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is developed for efficient linear-scaling quantum mechanical (QM) calculation of protein energy. This approach is based on our previously proposed GMFCC/MM method (He; et al. J. Chem. Phys. 2006, 124, 184703), In this EE-GMFCC scheme, the total energy of protein is calculated by taking a linear combination of the QM energy of the neighboring residues and the two-body QM interaction energy between non-neighboring residues that are spatially in close contact. All the fragment calculations are embedded in a field of point charges representing the remaining protein environment, which is the major improvement over our previous GMFCC/MM approach. Numerical studies are carried out to calculate the total energies of 18 real three-dimensional proteins of up to 1142 atoms using the EE-GMFCC approach at the HF/6-31G* level. The overall mean unsigned error of EE-GMFCC for the 18 proteins is 2.39 kcal/mol with reference to the full system HF/6-31G* energies. The EE-GMFCC approach is also applied for proteins at the levels of the density functional theory (DFT) and second-order many-body perturbation theory (MP2), also showing only a few kcal/mol deviation from the corresponding full system result. The EE-GMFCC method is linear-scaling with a low prefactor, trivially parallel, and can be readily applied to routinely perform structural optimization of proteins and molecular dynamics simulation with high level ab initio electronic structure theories.

A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields

We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.

Electrostatic polarization is critical for the strong binding in streptavidin-biotin system

The origin of strong affinity of biotin and its analogs binding to (strept)avidin is still the subject of an ongoing controversy. In this work, thermodynamic integration is carried out to study of the difference of binding free energies between biotin and iminobiotin to streptavidin. Three atomic charge schemes are implemented and compared. One is the traditional AMBER charge, and the other two, termed the polarized protein-specific charge, are based on a linear scaling quantum mechanical method and a continuous solvation model and have polarization effect partially or fully included. The result indicates that when nonpolarized AMBER force field is applied, the result is much underestimated. When electronic polarization is gradually included, the difference of binding affinity increases along with it. Using the linear-response approximation to eliminate the error in self-charging process, the corrected binding affinity agrees well with the experimental observation. This study is direct evidence indicating that polarization effect is critical for the strong binding in streptavidin-biotin system.

Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies

The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.

Protein NMR chemical shift calculations based on the automated fragmentation QM/MM approach

An automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach has been developed to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field (SCF) calculations of the NMR chemical shieldings for the mini-protein Trp cage. The root-mean-square errors (RMSEs) for 1H, 13C, and 15N NMR chemical shieldings are equal to or less than 0.09, 0.32, and 0.78 ppm, respectively, for all Hartree-Fock (HF) and density functional theory (DFT) calculations reported in this work. The environmental electrostatic potential is necessary to accurately reproduce the NMR chemical shieldings using the AF-QM/MM approach. The point-charge models provided by AMBER, AM1/CM2, PM3/CM1, and PM3/CM2 all effectively model the electrostatic field. The latter three point-charge models are generated via semiempirical linear-scaling SCF calculations of the entire protein system. The correlations between experimental 1H NMR chemical shifts and theoretical predictions are >0.95 for AF-QM/MM calculations using B3LYP with the 6-31G**, 6-311G**, and 6-311++G** basis sets. Our study, not unexpectedly, finds that conformational changes within a protein structure play an important role in the accurate prediction of experimental NMR chemical shifts from theory.