# Browsing by Subject "Force field"

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Item Computational studies of protein-ligand recognition(2018-11-28) Qi, Rui, Ph. D.; Ren, Pengyu; Dalby, Kevin; Elber, Ron; Yeh, Hsin-ChihShow more Molecular recognition between biomolecules and ligands is very specific in living cells. The functions of all biochemical processes and cell mechanisms are dependent upon complex but specific non-covalent intermolecular interactions. As essential building blocks in protein and nucleic acid, phosphate groups are commonly found in nucleic acids, proteins, and lipids. Nearly half of known proteins have been shown to interact with ligands containing a phosphate group. Binding of a phosphoryl group is fundamental to a range of biological processes including metabolism, biosynthesis, gene regulation, signal transduction, muscle contraction, and antibiotic resistance. Phosphorylation is one of the most common forms of reversible posttranslational modification of protein and, nearly 30% of all proteins are phosphorylated on at least one residue in cells. However, phosphate binding sites are less well defined and fundamental principles of why and how proteins recognize phosphate groups are not yet fully understood. Molecular modeling is a common tool for studying biomolecular structure, dynamics, interaction and function. Due to the complex electrostatics, high concentration of ions and intricate interactions with environment, however, the modeling and designing of highly charged drug-like molecules and nucleic acid derivatives are extremely difficult. This thesis will focus on the highly charged phosphate, including its different protonation states, and energetic and thermodynamic driving forces behind protein-phosphate recognition. This thesis work will also discuss the development of more sophisticated computational models, AMOEBA+, that are necessary for a better understanding and prediction of the physical properties of small organic molecules. Four projects will be discussed in this dissertation: two projects on force field development, and two on applying molecular dynamic simulations to understand biological processes. These projects have led to new insights into understanding of physical and chemical principles and mechanisms underlying highly protein-phosphate binding and nucleic acid stability. In addition, this thesis work will enhance the capability to develop and apply computational and theoretical frameworks to model, predict and design proteins, therapeutics, and diagnostic strategies targeting phosphates, phosphate-containing biomoleculesShow more Item From basis sets to force fields : improving methods for high-accuracy quantum chemical calculations of small molecules(2016-12) McCaslin, Laura Marie; Stanton, John (John F.); Ellison, Barney; Anslyn, Eric; Makarov, Dmitrii; Henkelman, GraemeShow more The first section of this work details a force field modeled on VSEPR theory. Previous studies¹ from Bartell et al. have validated the use of the following function to describe repulsion between outer atoms, X [subscript i], bonded to a shared center, A, in binary compounds of the form AX [subscript n]: V=K/r [superscript n above subscript ij]. Here, K and n are parameters and r [subscript ij] is the distance between repelled atoms. Bartell et al. fixed the bond distances A-X [subscript i] so that the atoms X [subscript i] are “points-on-a-sphere” around the central atom A. Our current work extends this POS force field to include flexibility in the bond distances A-X [subscript i]. The functional form for the energy of the bonds is that of the Morse oscillator: V [subscript m, sub-subscript i] = D [subscript e](1 -- exp[ -- α(r [subscript i] -- Re)])². Here, D [subscript e], α, and R [subscript e] are parameters of the force field and r [subscript i] is the distance between atoms A and X [subscript i]. This extended VSEPR force field is applied to PF₅. Parameters were optimized to minimize differences between the VSEPR and MP2/cc-pVTZ PF₅ diagonal quadratic force constants. Quadratic and cubic bending and stretching force constants are presented and compared between Morse-POS and MP2/cc-pVTZ methods. The second section of this dissertation focuses on the analytical transformation of force constants and molecular properties between isotopologues. Within the Born-Oppenheimer approximation, potential energy surfaces of isotopologues are identical. When beginning an exploration of a Born-Oppenheimer potential energy surface, a molecular geometry is chosen and the energy and derivatives are calculated. The most efficient choice of coordinates for these derivatives is normal coordinates, which are mass dependent. This thesis details the transformation of force constants, dipole moments, derivatives of dipole moments, rotational constants, and Coriolis constants from one isotopologue to another. Two alternative systems of coordinates for use in quantum chemical calculations are rectilinear and curvilinear internal coordinates. Rectilinear internal coordinates express the displacement of atoms in a molecule as changes in bond length, bond angle, and dihedral angle as linear combinations of Cartesian coordinates. Though other internal coordinates exist, the previously mentioned are the most commonly used. There are immediate problems with the general use of rectilinear internal coordinates. When one calculates the displacement in Cartesian coordinates needed to increase a bond angle, the bond angle does not scale linearly with the Cartesian coordinates. The following thesis provides the derivation of equations that allow for the analytical transformation from rectilinear to curvilinear coordinates of first through fourth derivatives of the energy. As shown here, these transformations may also be used in converting between the force fields of isotopologues. Additionally, the transformations used between force fields of isotopologues are generalized to the transformation of derivatives of the dipole moment vector. Because the dipole moment vector is rotationally variant, the transformation is extended to include rotational parameters that can successfully transform derivatives of vector quantities between isotopologues. Third, a benchmark comparison of atomic natural orbital (ANO) and Dunning's correlation consistent basis sets is presented²⁻⁴. ANO basis sets, made up of atomic natural orbitals of the CISD wavefunction, are used far less frequently than the correlation consistent basis sets of Dunning and coworkers. However, ANO basis sets, especially smaller truncations (like ANO0) are powerful tools in calculations that require a high-accuracy description of correlation energy as is necessary in second order vibrational perturbation theory (VPT2) calculations. A benchmark study comparing the ANOX (X=0,1,2) and cc-pVNZ (N=D,T,Q) families of basis sets is detailed here. Using VPT2, fundamental frequencies of a set of small molecules were calculated with each of these six basis sets and compared. Of the comparisons, ANO0 outperforms cc-pVDZ in this work, validating more development and interest in ANO-type basis sets. This thesis also details the construction and benchmarking of new ANO-type basis sets using atomic natural orbitals from coupled cluster wavefunctions with single and double excitations (CCSD) and single, double, and triple excitations (CCSDT). These are used to calculate the fundamental frequencies of a set of small molecules and are compared to the original ANO basis sets, which are constructed from the configuration interaction wavefunction with single and double excitations (CISD). The three ANO-type basis sets are comparable in error, though small systematic trends arise that validate the use of the original ANO-type basis sets over those constructed with CCSD or CCSDT wavefunctions. The final section discusses experimental and theoretical collaboration to characterize the rotational and vibrational spectra of isomers of dihydroxycarbene⁵⁻⁶. The first publication discussed here⁵ details measured rotational spectra of isotopomers of cis,trans-dihydroxycarbene. Using ab initio parameters and a fitting procedure, a high-accuracy semi-experimental equilibrium structure of cis,trans-dihydroxycarbene was determined. The semi-experimental equilibrium structure agrees with high-level ab initio calculations to two significant figures in the bond lengths and three significant figure in bond angles. This section also details a recent publication⁶ that uses ab initio calculations to aid in the characterization of vibrational spectra of cis,transand trans,trans-dihydroxycarbene in ⁴He nanodroplets. VPT2 fundamental frequencies are compared to experimental values, all matching to ~7 cm⁻¹. State-specific dipole moments and components of the dipole moment vector along inertial axes determined from ab initio calculations are also compared with experimental results.Show more Item Optimization of force fields for molecular dynamics(2014-12) Di Pierro, Michele; Elber, RonShow more A technology for optimization of potential parameters from condensed phase simulations (POP) is discussed and illustrated. It is based on direct calculations of the derivatives of macroscopic observables with respect to the potential parameters. The derivatives are used in a local minimization scheme, comparing simulated and experimental data. In particular, we show that the Newton Trust-Region protocol allows for accurate and robust optimization. POP is illustrated for a toy problem of alanine dipeptide and is applied to folding of the peptide WAAAH. The helix fraction is highly sensitive to the potential parameters while the slope of the melting curve is not. The sensitivity variations make it difficult to satisfy both observations simultaneously. We conjecture that there is no set of parameters that reproduces experimental melting curves of short peptides that are modeled with the usual functional form of a force field. We then apply the newly developed technology to study the liquid mixture of tert-butanol and water. We are able to obtain, after 4 iterations, the correct phase behavior and accurately predict the value of the Kirkwood Buff (KB) integrals. We further illustrate that a potential that is determined solely by KB information, or the pair correlation function, is not necessarily unique.Show more