Development of an Advanced Force Field for Water using Variational Energy Decomposition Analysis

Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parameterize since they are fit to data like total energies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demonstrate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices that reduce the computational expense of the MB-UCB potential while remaining accurate. We optimize parameters using only single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties. We conclude that MB-UCB is comparable in performance to MB-Pol, but is less expensive and more transferable by eliminating the need to represent short-ranged interactions through large parameter fits to high order polynomials

Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom

Assessment of atomic charge models for gas-phase computations on polypeptides

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q0, that is suitable to describe biological systems bearing many locally charged functional groups

An Effective Fragment Method for Modeling Solvent Effects in Quantum Mechanical Calculations

An effective fragment model is developed to treat solvent effects on chemical properties andreactions. The solvent, which might consist of discrete water molecules, protein, or othermaterial, is treated explicitly using a model potential that incorporates electrostatics,polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water‐formamide are in good agreement with fully abinitio calculations

Novel Numerical Models of Electrostatic Interactions and Their Application to S-Nitrosothiol Simulations

Atom-centered point charge model of the molecular electrostatics remains a major workhorse in the atomistic biomolecular simulations. However, this approximation fails to reproduce anisotropic features of the molecular electrostatic potential (MEP), and the existing methods of the charge derivation are often associated with the numerical instabilities. This work provides an in-depth analysis of these limitations and offers a novel approach to describe electrostatic interactions that paves the way toward efficient next-generation force fields. By analyzing the charge fitting problem from first principles, as an example of the mathematical inverse problem, we show that the numerical instabilities of the charge-fitting problem arise due to the decreasing contribution from the higher multipole moments to the overall MEP. This insight suggests that if the point charges are arranged over the sphere using Lebedev quadrature, the resulting point charge model is able to exactly reproduce multipoles up to a given rank. At the same time, point charge values can be derived without fitting to the MEP, avoiding numerically unstable method of the charge derivation. This approach provides a systematic way to reproduce multipole moments up to any rank within the point charge approximation, which makes this model a computationally efficient analog of the multipolar expansion. Moreover, the proposed charged sphere model can be also used in the multi-site expansions with the expansion centers located at each atom in a molecule. This provides a natural approach to expand the traditional atom-centered point charge approximation to include higher-rank atomic multipoles and to account for the anisotropy of the MEP. We applied the proposed charged sphere model to S-nitrosothiols (RSNOs)—a class of biomolecules that serves to store and transmit nitric oxide, a biologically important signaling molecule. We showed that when the atom-centered charged spheres are optimized together with the Lennard-Jones parameters, the resulting force field can accurately reproduce the anisotropic features of the intermolecular interactions that play a crucial role in the biological regulation of RSNO chemistry. Overall, the developed charge model is a promising approach that can be used in the biomolecular simulations and beyond, e.g. in the multipolar force fields for atomistic and coarse-grained simulations

Quantenklassische Hybridbeschreibung von Solvatisierungseffekten

Eine aussagekräftige theoretische Beschreibung des Infrarot (IR)-Schwingungsspektrums eines Biomoleküls in seiner nativen Umgebung durch Molekulardynamik (MD)-Simulationen benötigt hinreichend genaue Modelle sowohl für das Biomolekül, als auch für das umgebende Lösungsmittel. Die quantenmechanische Dichtefunktionaltheorie (DFT) stellt solche genauen Modelle zur Verfügung, zieht aber hohen Rechenaufwand nach sich. Daher ist dieser Ansatz nicht zur Simulation der MD ausgedehnter Biomolekül-Lösungsmittel-Komplexe einsetzbar. Solche Systeme können effizient mit polarisierbaren molekülmechanischen (PMM) Kraftfeldern behandelt werden, die jedoch nicht die zur Berechnung von IR-Spektren nötige Genauigkeit liefern. Einen Ausweg aus dem skizzierten Dilemma bieten Hybridverfahren, die einen relevanten Teil eines Simulationssystems mit DFT, und die ausgedehnte Lösungsmittelumgebung mit einem (P)MM-Kraftfeld beschreiben. Im Rahmen dieser Arbeit wird, ausgehend von einer DFT/MM-Hybridmethode [Eichinger et al., J. Chem. Phys. 110, 10452-10467 (1999)], ein genaues und hocheffizientes DFT/PMM-Rechenverfahren entwickelt, das der wissenschaftlichen Ọ̈ffentlichkeit nun in Form des auf Großrechnern einsetzbaren Programmpakets IPHIGENIE/CPMD zur Verfügung steht. Die neue DFT/PMM-Methode fußt auf der optimalen Integration des DFT-Fragments in die "schnelle strukturadaptierte Multipolmethode" (SAMM) zur effizienten approximativen Berechnung der Wechselwirkungen zwischen den mit gitterbasierter DFT bzw. mit PMM beschriebenen Subsystemen. Dies erlaubt stabile Hamilton'sche MD-Simulationen sowie die Steigerung der Performanz (d.h. dem Produkt aus Genauigkeit und Recheneffizienz) um mehr als eine Größenordnung. Die eingeführte explizite Modellierung der elektronischen Polarisierbarkeit im PMM-Subsystem durch induzierbare Gauß'sche Dipole ermöglicht die Verwendung wesentlich genauerer PMM-Lösungsmittelmodelle. Ein effizientes Abtastens von Peptidkonformationen mit DFT/ PMM-MD kann mit einer generalisierten Ensemblemethode erfolgen. Durch die Entwicklung eines Gauß'schen polarisierbaren Sechspunktmodells (GP6P) für Wasser und die Parametrisierung der Modellpotentiale für van der Waals-Wechselwirkungen zwischen GP6P-Molekülen und der Amidgruppe (AG) von N-Methyl-Acetamid (NMA) wird ein DFT/PMM-Modell für (Poly-)Peptide und Proteine in wässriger Lösung konstruiert. Das neue GP6P-Modell kann die Eigenschaften von flüssigem Wasser mit guter Qualität beschreiben. Ferner können die mit DFT/PMM-MD berechneten IR-Spektren eines in GP6P gelösten DFT-Modells von NMA die experimentelle Evidenz mit hervorragender Genauigkeit reproduzieren. Somit ist nun ein hocheffizientes und ausgereiftes DFT/PMM-MD-Verfahren zur genauen Berechnung der Konformationslandschaften und IR-Schwingungsspektren von in Wasser gelösten Proteinen verfügbar.A meaningful theoretical description of the infrared (IR) spectrum of a biomolecule in its native environment by molecular dynamics (MD) simulations requires adequately accurate models both for the biomolecule and for its solvent environment. The quantum mechanical density functional theory (DFT) provides such accurate models, but entails high computational effort. Therefore, this approach is not suited for the simulation of the MD of extended biomolecule-solvent-complexes. Such systems can be handled efficiently by polarizable molecular mechanics (PMM) force fields, which, however, do not provide the accuracy required for the computation of IR spectra. The sketched dilemma is resolved by hybrid approaches, which describe a relevant part of a simulation system by DFT, and the extended solvent environment by a (P)MM force field. Based on a DFT/MM hybrid method [Eichinger et al., J. Chem. Phys. 110, 10452-10467 (1999)], an accurate and highly efficient DFT/PMM approach is developed in this thesis. Its implementation in the program package IPHIGENIE/CPMD is suitable for high-performance computing applications and available to the scientific community. The new DFT/PMM method is based on the optimal integration of the DFT fragment into the "structure-adapted fast multipole method" (SAMM) for the efficient approximative computation of interactions between the subsystems described by grid-based DFT and PMM, respectively. It enables stable, Hamiltonian MD simulations, and increases the performance (i.e. accuracy times efficiency) by more than one order of magnitude. The explicit modeling of electronic polarizability in the PMM subsystem by induced Gaussian dipoles allows the use of much more accurate PMM solvent models. The efficiency of peptide conformational sampling with DFT/PMM-MD is increased by applying a generalized ensemble method. By constructing a Gaussian polarizable six-point (GP6P) model for water and by parametrizing the model potentials for van der Waals interactions between GP6P molecules and the amide group (AG) of N-Methyl-Acetamide (NMA), a DFT/PMM model for (poly-)peptides and proteins in aqueous solution is developed. The new GP6P model can describe the properties of liquid water with good quality. Furthermore, the IR spectra of a DFT model of NMA solvated in GP6P, which were calculated by DFT/PMM-MD, can reproduce the experimental evidence with excellent quality. Thus, a highly efficient and mature DFT/PMM-MD approach for the accurate computation of conformational landscapes and IR spectra of proteins in aqueous solution is now available

Development and analysis of Tinker-OpenMM as a GPU-based free energy perturbation engine

The utilization of computational technologies for the lead optimization process is one of the biggest challenges in the computational chemistry field. In this dissertation, I describe the addition of GPU-based absolute and relative free energy calculation methods using polarizable force field AMOEBA to Tinker-OpenMM. I then proceed to test the capabilities of this platform by studying the binding free energy and binding structures of derivatives of the MELK inhibitor IN17. Also, I present the implementation of virial-based pressure control to the Tinker-OpenMM platform that is needed for performing isobaric simulations.Cellular and Molecular Biolog