The effects of solvent screening in quantum mechanical calculations in protein systems

We report on an implementation of quantum mechanical density functional calculations carried out in a dielectric medium. The dielectric medium is introduced by integrating the solution of the Poisson-Boltzmann equations into the density functional calculation. The calculations are carried out for a simple amide in vacuum, in the field of an ion, and in the ion field in several dielectric environments. The environment was constructed to include a low dielectric interior embedded in a high dielectric continuum of dielectric 80 (corresponding to aqueous solution). The energies and electron densities of formamide in the ion field were calculated at various configurations in this system, including at the low dielectric–high dielectric interface. The systems were designed to simulate situations which are similar to those that occur in proteins (i.e., the protein constitutes the low dielectric medium surrounded by aqueous solution). The system mimics situations in which charges in such proteins located in various regions interact with other parts of the protein and with ligands which mainly bind to the surface. © 1994 by John Wiley & Sons, Inc.     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments. © 1994 by John Wiley & Sons, Inc.     

Sampling, sample preparation, and analytical variability associated with testing wheat for deoxynivalenol

The variability associated with testing wheat for deoxynivalenol (DON) was measured using a 0.454 kg sample, Romer mill, 25 g comminuted subsample, and the Romer Fluoroquant analytical method. The total variability was partitioned into sampling, sample preparation, and analytical variability components. Each variance component was a function of the DON concentration and equations were developed to predict each variance component using regression techniques. The effect of sample size, subsample size, and number of aliquots on reducing the variability of the DON test procedure was also determined. For the test procedure, the coefficient of variation (CV) associated with testing wheat at 5 ppm was 13.4%. The CVs associated with sampling, sample preparation, and analysis were 6.3, 10.0, and 6.3%, respectively. For the sample variation, a 0.454 kg sample was used; for the sample preparation variation, a Romer mill and a 25 g subsample were used; for the analytical variation, the Romer Fluoroquant method was used. The CVs associated with testing wheat are relatively small compared to the CV associated with testing other commodities for other mycotoxins, such as aflatoxin in peanuts. Even when the small sample size of 0.454 kg was used, the sampling variation was not the largest source of error as found in other mycotoxin test procedures.     

Testing shelled corn for aflatoxin, Part II: modeling the observed distribution of aflatoxin test results

The suitability of several theoretical distributions to predict the observed distribution of aflatoxin test results in shelled corn was investigated. Fifteen positively skewed theoretical distributions were each fitted to 18 empirical distributions of aflatoxin test results for shelled corn. The compound gamma distribution was selected to model aflatoxin test results for shelled corn. The method of moments technique was chosen to estimate the parameters of the compound gamma distribution. Mathematical expressions were developed to calculate the parameters of the compound gamma distribution for any lot aflatoxin concentration and test procedure. Observed acceptance probabilities were compared to operating characteristic curves predicted from the compound gamma distribution, and all 18 observed acceptance probabilities were found to lie within a 95% confidence band. The parameters of compound gamma were used to calculate the fraction of aflatoxin-contaminated kernels in contaminated lots. At 20 ppb, it was estimated that about 6 in 10,000 kernels are contaminated.     

Force field studies of cholesterol and cholesteryl acetate crystals and cholesterol–cholesterol intermolecular interactions

To model the physical properties of sterols and related species, an all-atom Class II force field has been derived based on the recently reported CFF93 force field for hydrocarbons. It has been tested using both energy minimization and molecular dynamics (MD) simulations of the low-temperature neutron-diffraction structure of cholesteryl acetate crystals and the X-ray diffraction crystal structure of cholesterol. Thus these studies test the techniques and limitations of high-accuracy crystal simulations as well. Employing energy minimization, all cell vectors and volumes were reproduced to within 2.4% of experimental values. For cholesteryl acetate, the root mean square (rms) deviations between the calculated and experimental bond lengths, angles, and torsions of nonhydrogen atoms are 0.013 Å, 1.2°, and 2.4°, respectively. The corresponding maximum deviations are also very small: 0.027 Å for bond length, 3.2° for angle, and 7.6° for torsion. For cholesterol, good agreement between the calculated and experimental structures was found only when the comparison was limited to atoms with relatively small thermal factors (B_eq < 15 Ų). It was found that for both systems, the MD averaged structures were in better agreement with the experimental ones than the energy minimized structures, since the rms deviations in atom positions are smaller for the MD-averaged structures (0.064 Å for cholesteryl acetate and 0.152 Å for cholesterol) than those for the minimized structures (0.178 Å for cholesteryl acetate and 0.189 Å for cholesterol). The force field was then applied to isolated molecules focusing on the rigidity of the cholesteryl ring and cholesterol–cholesterol interaction energies. It is concluded that the cholesteryl ring is fairly rigid since no major conformational change was observed during an MD simulation of a single cholesterol molecule in vacuo at 500 K, in agreement with condensed phase experiments. Calculations of cholesterol–cholesterol pairs suggest that there are only four low-energy configurations and that it is more useful to describe each molecule as having a plane (flat face) and two grooves rather than as having two (one flat and one rough) faces. This provides some insight into the equilibrium crystal structures. Limited results from a modified Class I (CVFF) force field are presented for comparison. © 1995 by John Wiley & Sons, Inc.     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

Optimizing lactose hydrolysis by computer-guided modification of the catalytic site of a wild-type enzyme

Lactose intolerance is a serious global health problem. A lactose hydrolysis enzyme, thermostable $\upbeta $ -galactosidase, BgaB (from Geobacillus stearothermophilus) has attracted the attention of industrial biologists because of its potential application in processing lactose-containing products. However, this enzyme experiences galactose product inhibition. Through homology modeling and molecular dynamics (MD) simulation, we have identified the galactose binding sites in the thermostable $\upbeta $ -galactosidase BgaB (BgaB). The binding sites are formed from Glu303, Asn310, Trp311, His354, Arg109, Phe341, Try272, Asn147, Glu148, and H354; these residues are all important for enzyme catalysis. A ligand–receptor binding model has been proposed to guide site-directed BgaB mutagenesis experiments. Based upon the model and the MD simulations, we recommend mutating Arg109, Phe341, Trp311, Asn147, Asn310, Try272, and His354 to reduce galactose product inhibition. In vitro site-directed mutagenesis experiments confirmed our predictions. The success rate for mutagenesis was 66.7 %. The best BgaB mutant, F341T, can hydrolyze lactose completely, and is the most promising enzyme for use by the dairy industry. Thus, our study is a successful example of optimizing enzyme catalytic chemical reaction by computer-guided modifying the catalytic site of a wild-type enzyme.     

Anchoring and steering gaussian quadrature for positive definite strong moment functionals

Algorithms for the construction of block-formed orthogonal Laurent polynomial sequences and corresponding Gaussian quadratures associated with positive definite strong moment functionals are introduced and compared. Cost estimates and numerical examples are included.