Elongation cutoff technique: low-order scaling SCF method

The elongation cutoff technique at restricted Hartree-Fock (HF) level of theory in conventional type of calculations, i.e., with two electron integrals (TEI) stored on a disc, is presented for two model systems. It is demonstrated that the number of TEI in the elongation cutoff calculations increases linearly with the system size thus, allowing to extend the conventional type of calculations to bigger systems. The step CPU (central processing unit) time in the elongation cutoff calculations is much lower than in the HF reference calculations. Such behavior reduces significantly the prefactor in the quadratic scaling relation. The total CPU time in the elongation calculation is about 40% lower than in the conventional HF calculations or comparable to direct type of calculations with the quantum fast multipoles method employed. It is shown that by introducing the interaction radius one can obtain linear scaling in the SCF calculations. Figure: The structure of density matrix and total CPU timings for polyglycine clusters in the elongation cutoff calculations. The structure of density matrix and total CPU timings for polyglycine clusters in the elongation cutoff calculations     

Calculation and display of electrostatic potentials

A general methodology is developed for incorporating accurate electrostatic information from ab initio molecular orbital calculations into molecular mechanics calculations. Examples are given of the method applied to simple aromatic organic molecules. A program has been developed for displaying the results of the ab initio calculations on a Silicon Graphics workstation. The technique developed here provides an alternative method for including electrostatic interactions in molecular mechanics calculations and is compared with other methods for determining atomic charges.     

Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility.

A new method for including local conformational flexibility in calculations of the hydrogen ion titration of proteins using macroscopic electrostatic models is presented. Intrinsic pKa values and electrostatic interactions between titrating sites are calculated from an ensemble of conformers in which the positions of titrating side chains are systematically varied. The method is applied to the Asp, Glu, and Tyr residues of hen lysozyme. The effects of different minimization and/or sampling protocols for both single-conformer and multi-conformer calculations are studied. For single-conformer calculations it is found that the results are sensitive to the choice of all-hydrogen versus polar-hydrogen-only atomic models and to the minimization protocol chosen. The best overall agreement of single-conformer calculations with experiment is obtained with an all-hydrogen model and either a two-step minimization process or minimization using a high dielectric constant. Multi-conformational calculations give significantly improved agreement with experiment, slightly smaller shifts between model compound pKa values and calculated intrinsic pKa values, and reduced sensitivity of the intrinsic pKa calculations to the initial details of the structure compared to single-conformer calculations. The extent of these improvements depends on the type of minimization used during the generation of conformers, with more extensive minimization giving greater improvements. The ordering of the titrations of the active-site residues, Glu-35 and Asp-52, is particularly sensitive to the minimization and sampling protocols used. The balance of strong site-site interactions in the active site suggests a need for including site-site conformational correlations.     

Automation of conformational analysis and other molecular modeling calculations

A software system has been developed for facilitating modeling calculations on large numbers of molecules. Using the system, it is possible to subject one or more molecules to a series of calculations, each requiring use of a different computer program. No user intervention is required: where necessary, output from one program is used automatically as input to the next. Names are assigned to output files automatically and in a systematic manner. As an example, the system can be used to perform a succession of calculations aimed at identifying the major low-energy conformers of each of a set of molecules, starting only from their chemical connectivities. The reliability of the results has been tested by calculations on 40 molecules taken from the Cambridge Structural Database. The observed crystal structure geometry could be found for the majority of these molecules.     

Explicit Tracking of Uncertainty Increases the Power of Quantitative Rule-of-Thumb Reasoning in Cell Biology

Back-of-the-envelope or rule-of-thumb calculations involving rough estimates of quantities play a central scientific role in developing intuition about the structure and behavior of physical systems, for example in so-called Fermi problems in the physical sciences. Such calculations can be used to powerfully and quantitatively reason about biological systems, particularly at the interface between physics and biology. However, substantial uncertainties are often associated with values in cell biology, and performing calculations without taking this uncertainty into account may limit the extent to which results can be interpreted for a given problem. We present a means to facilitate such calculations where uncertainties are explicitly tracked through the line of reasoning, and introduce a probabilistic calculator called CALADIS, a free web tool, designed to perform this tracking. This approach allows users to perform more statistically robust calculations in cell biology despite having uncertain values, and to identify which quantities need to be measured more precisely to make confident statements, facilitating efficient experimental design. We illustrate the use of our tool for tracking uncertainty in several example biological calculations, showing that the results yield powerful and interpretable statistics on the quantities of interest. We also demonstrate that the outcomes of calculations may differ from point estimates when uncertainty is accurately tracked. An integral link between CALADIS and the BioNumbers repository of biological quantities further facilitates the straightforward location, selection, and use of a wealth of experimental data in cell biological calculations.     

Power calculations for a general class of family-based association tests: dichotomous traits

Using large-sample theory, we present a unified approach to power calculations for family-based association tests. Currently available methods for power calculations are restricted to special designs or require approximations or simulations. Our analytical approach to power calculations is broadly applicable in many settings. We discuss power calculations for two scenarios that have high practical relevance and in which power previously could only be assessed by simulation studies or by approximations: (1) studies using both affected and unaffected offspring and (2) studies with missing parental information. When the population prevalence is high, it can be worthwhile to genotype unaffected offspring. For many scenarios, high power can be achieved with reasonable sample sizes, even when no parental information is available.     

Continuum solvent model calculations of alamethicin-membrane interactions: thermodynamic aspects

Alamethicin is a 20-amino acid antibiotic peptide that forms voltage-gated ion channels in lipid bilayers. Here we report calculations of its association free energy with membranes. The calculations take into account the various free-energy terms that contribute to the transfer of the peptide from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the solvation free energy are calculated using continuum solvent models. The contributions from the lipid perturbation and membrane deformation effects and the entropy loss associated with peptide immobilization in the bilayer are estimated from a statistical thermodynamic model. The calculations were carried out using two classes of experimentally observed conformations, both of which are helical: the NMR and the x-ray crystal structures. Our calculations show that alamethicin is unlikely to partition into bilayers in any of the NMR conformations because they have uncompensated backbone hydrogen bonds and their association with the membrane involves a large electrostatic solvation free energy penalty. In contrast, the x-ray conformations provide enough backbone hydrogen bonds for the peptide to associate with bilayers. We tested numerous transmembrane and surface orientations of the peptide in bilayers, and our calculations indicate that the most favorable orientation is transmembrane, where the peptide protrudes approximately 4 A into the water-membrane interface, in very good agreement with electron paramagnetic resonance and oriented circular dichroism measurements. The calculations were carried out using two alamethicin isoforms: one with glutamine and the other with glutamate in the 18th position. The calculations indicate that the two isoforms have similar membrane orientations and that their insertion into the membrane is likely to involve a 2-A deformation of the bilayer, again, in good agreement with experimental data. The implications of the results for the biological function of alamethicin and its capacity to oligomerize and form ion channels are discussed.     

Vibrational analysis of peptides, polypeptides and proteins. XXVII. Structure of gramicidin S from normal mode analyses of low-energy conformations

Normal mode calculations have been carried out on three low-energy structures of gramicidin S obtained from conformational energy calculations. When the results on the amide modes are compared with observed bands in the infrared and Raman spectra of crystalline gramicidin S and its N-deuterated derivative, one of the structures is clearly disfavored. Of the other two, one is slightly favored, and it corresponds to the lowest-energy structure obtained from the energy calculations. Spectra from solutions in DMSO and CH3 OH suggest that the molecular conformation is essentially retained in these solvents.     

Phenylisoserine in the gas-phase and water: Ab initio studies on neutral and zwitterion conformers

The conformational landscape of phenylisoserine (PhIS) was studied. Trial structures were generated by allowing for all combinations of single-bond rotamers. Based on the B3LYP/aug-cc-pVDZ calculations 54 conformers were found to be stable in the gas phase. The six most stable conformers were further optimized at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVDZ levels for which characteristic intramolecular hydrogen bond types were classified. To estimate the influence of water on PhIS conformation, the IEF-PCM/B3LYP/aug-cc-pVDZ calculations were carried out and showed 51 neutral and six zwitterionic conformers to be stable in water solution. According to DFT calculations, the conformer equilibrium in the gas phase is dominated by one conformer, whereas the MP2 calculations suggest three PhIS structures to be significantly populated. Comparison of DFT and MP2 energies of all 57 structures stable in water indicates that, in practice, one zwitterionic and one neutral conformer determine the equilibrium in water. Based on the AIM calculations, we found that for the neutral conformers in vacuum and in water, d(H...B) is linearly correlated with Laplacian at the H-bond critical point.     

An electron spin resonance investigation and molecular orbital calculation of the anion radical intermediate in the enzymatic cis-trans isomerization of furylfuramide, a nitrofuran derivative of ethylene

The enzymatic cis-trans isomerization of nitrofuran derivatives has been proposed to occur via the formation of a radical anion intermediate. ESR investigations, in conjunction with intermediate neglect of differential overlap (INDO) molecular orbital calculations, support this concept by demonstrating the enzymatic generation of cis and trans radical anions of 3-(5-nitro-2-furyl)-2-(2-furyl) acrylamide. The INDO calculations further indicate that the rotational barrier between the cis and trans anion radicals of this compound is only 5--10 kcal/mol, whereas a 70 kcal/mol barrier exists for the parent geometric isomers. Hyperfine splitting constants for the cis-trans conformers have been assigned on the basis of INDO calculations. Surprisingly, only the nitrogen hyperfine splitting of the nitro group is distinguishably different in the two conformers, a result which is not inconsistent with the INDO calculations.     

New ultrasoft pseudopotentials for the study of silicates

New ultra-soft pseudopotentials (UPS's) for Si and O suitable for studies of silicate materials are reported. The performance of the new USP's in density functional calculations on a number of model systems is documented and compared both to observed properties and to those computed in highly converged all-electron calculations. The new USP's are significantly more reliable and accurate than thos previsouly developed and widely distributed. With the new USP's computed structural parameters follow well establised trends with regard to local and gradient corrected treatments of exchange and correlation. The correct order of stability of the α-quartz and sodalite structures is also reproduced although the energy difference is not in quantitative agreement with the all-electron calculations. A new Al USP is also generated and its performance in calculations on α-alumina documented. The importance of consistent treatments of exchange and correlation for core and valence electrons is established.     

Structure,energetics and properties of some molecules with potent anti-HIV activity: a theoretical study

Density functional theory (DFT; B3LYP) and Hartree–Fock (HF; 3-21G, 6-31G(d) and 6-311G(d,p)) calculations with complete geometry optimisations are carried out in the ground state on five 6-aminoquinolone derivatives, which have been proved to be highly effective in inhibiting HIV replication, to study their structures, energetics and HOMO–LUMO correlation with physiological action. The gas-phase calculations and single-point polarisable continuum model water-phase calculations show that the molecules are highly effective in inhibiting HIV replication, which is in excellent agreement with the experiment. Structural features, energies, charge densities and HOMO–LUMO correlation have been found to substantiate the experimental findings. Compound 4 (pyrazine) shows some special features in DFT calculations which are not found in HF calculations. In the present series, HF results are more reliable as expected.     

A Semiempirical Transition State Structure for the First Step in the Alkaline Hydrolysis of Cocaine. Comparison between the Transition State Structure,the Phosphonate Monoester Transition State Analog,and a Newly Designed Thiophosphonate Transition State Analog

Semiempirical molecular orbital calculations have been performed for the first step in the alkaline hydrolysis of the neutral benzoylester of cocaine. Successes, failures, and limitations of these calculations are reviewed. A PM3 calculated transition state structure is compared with the PM3 calculated structure for the hapten used to induce catalytic antibodies for the hydrolysis of cocaine. Implications of these calculations for the computer–aided design of transition state analogs for the induction of catalytic antibodies are discussed.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s0089460020062     

Do electrostatic interactions destabilize protein–nucleic acid binding?

The negatively charged phosphates of nucleic acids are often paired with positively charged residues upon binding proteins. It was thus counter-intuitive when previous Poisson-Boltzmann (PB) calculations gave positive energies from electrostatic interactions, meaning that they destabilize protein-nucleic acid binding. Our own PB calculations on protein-protein binding have shown that the sign and the magnitude of the electrostatic component are sensitive to the specification of the dielectric boundary in PB calculations. A popular choice for the boundary between the solute low dielectric and the solvent high dielectric is the molecular surface; an alternative is the van der Waals (vdW) surface. In line with results for protein-protein binding, in this article, we found that PB calculations with the molecular surface gave positive electrostatic interaction energies for two protein-RNA complexes, but the signs are reversed when the vdW surface was used. Therefore, whether destabilizing or stabilizing effects are predicted depends on the choice of the dielectric boundary. The two calculation protocols, however, yielded similar salt effects on the binding affinity. Effects of charge mutations differentiated the two calculation protocols; PB calculations with the vdW surface had smaller deviations overall from experimental data.     

A least-squares computer method for the determination of the molecular ratio of conjugates between two different proteins from the results of the amino acid analysis

A method for the determination of the composition of a conjugate between two different proteins by amino acid analysis followed by least-squares evaluation of the concentration ratio of the two components is presented. The method is based solely on calculations and avoids the use of labeled residues. A computer program, written in BASIC, is also presented to perform the calculations.     

Hydrogen Bonding and Stacking of DNA Bases: A Review of Quantum-chemical ab initio Studies

Abstract

Ab initio quantum-chemical calculations with inclusion of electron correlation made since 1994 (such reliable calculations were not feasible before) significantly modified our view on interactions of nucleic acid bases. These calculations allowed to perform the first reliable comparison of the strength of stacked and hydrogen bonded pairs of nucleic acid bases, and to characterize the nature of the base-base interactions. Although hydrogen-bonded complexes of nucleobases are primarily stabilized by the electrostatic interaction, the dispersion attraction is also important. The stacked pairs are stabilized by dispersion attraction, however, the mutual orientation of stacked bases is determined rather by the electrostatic energy. Some popular theories of stacking were ruled out: The theory based on attractive interactions of polar exocyclic groups of bases with delocalized electrons of the aromatic rings (Bugg et al., Biopolymers 10, 175 (1971).), and the II-II interactions model (C.A. Hunter, J. Mol. Biol. 230, 1025 (1993)). The calculations demonstrated that amino groups of nucleobases are very flexible and intrinsically nonplanar, allowing hydrogen-bond-like interactions which are oriented out of the plane of the nucleobase. Many H-bonded DNA base pairs are intrinsically nonplanar. Higher-level ab initio calculations provide a unique set of reliable and consistent data for parametrization and verification of empirical potentials. In this article, we present a short survey of the recent calculations, and discuss their significance and limitations. This summary is written for readers which are not experts in computational quantum chemistry.     

Conformational behaviour of the architectural units of peptides and proteins. Assessment of current understanding by ab initio quantum mechanical methods and refinement of the dipeptide energy surface.

The conformational energy surfaces of analogues of the dipeptide unit of polypeptides and proteins are calculated by ab initio methods using extended basis sets.The calculations are not particularly sensitive to the choice of (extended) basis set.The calculations are shown to support a particular empirical method parameterized with respect to crystal data. Non-hydrogen bonded conformations agree to within 3 kcal mol^?1, even for conformations in which quite considerable degrees of atomic overlap occur.Hydrogen bonded conformations, are, however, in less satisfactory agreement and it is the ab initio calculations which appear to be at fault.A simple correction is applied to the ab initio energy for hydrogen bonded conformations, and with the use of the empirical energy surface a full quantum mechanical conformational energy map is interpolated for the alanyl dipeptide.The effect of flexibility in the peptide backbone is taken into account, and supports recent empirical findings that distortions in valence angles must be considered in calculations of the conformational behaviour of peptides.     

Estimates of absolute cause-specific risk in cohort studies

In this paper we study methods for estimating the absolute risk of an event c1 in a time interval [t1, t2], given that the individual is at risk at t1 and given the presence of competing risks. We discuss some advantages of absolute risk for measuring the prognosis of an individual patient and some difficulties of interpretation for comparing two treatment groups. We also discuss the importance of the concept of absolute risk in evaluating public health measures to prevent disease. Variance calculations permit one to gauge the relative importance of random and systematic errors in estimating absolute risk. Efficiency calculations were also performed to determine how much precision is lost in estimating absolute risk with a nonparametric approach or with a flexible piecewise exponential model rather than a simple exponential model, and other calculations indicate the extent of bias that arises with the simple exponential model when that model is invalid. Such calculations suggest that the more flexible models will be useful in practice. Simulations confirm that asymptotic methods yield reliable variance estimates and confidence interval coverages in samples of practical size.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.