Self-consistent field equations in the distribution function theory of polymeric liquids

In the distribution function approach to the conformational and thermodynamic properties of polymeric liquids site-site (pair) distribution functions are essential components of the theory. These site-site pair distribution functions are basically mean fields obeying integral equations. In our recent works, a set of self-consistent field equations has been proposed for site-site pair correlation functions which allow us to study conformational and thermodynamic properties of polymeric liquids. In this article, we present a short review of the theory and its applications to a number of aspects of polymeric liquids we have made until now. We also present a self-consistent version of the polymer reference interaction site model where the integral equations for the intramolecular site-site correlation functions are obtained from the Kirkwood hierarchy on the basis of the present theory. The present theory is shown to predict correctly the scaling properties associated with swollen and collapsed polymers in good and poor solvents, respectively. At finite densities, self-consistent solutions of the intra- and intermolecular equations yield the structures and thermodynamics of polymer melts which are favorably compared with Monte Carlo simulation results. Self-consistent theory results are found to be more accurate than the non-self-consistent approaches that use an ideal Gaussian chain conformation distribution function. © 1995 John Wiley & Sons, Inc.     

Protein dynamics from a NMR perspective: networks of coupled rotators and fractional Brownian dynamics

Nuclear magnetic resonance (NMR) has proven to be the most valuable tool for investigating internal dynamics of proteins. In this perspective, the interpretation of NMR relaxation data eventually relies on a model of the motions. In this article, we propose to compare two radically different approaches that aim at describing internal dynamics in proteins. It is shown that the correlation functions predicted by a network of coupled rotators can be interpreted in terms of a heuristic approach based on fractional Brownian dynamics for each of the vectors in the network. Our results are interpreted in terms of the probability distributions of relaxation modes in both processes, the median of which turns out to be the relevant quantity for the comparison of both models.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

Efficient use of pure component and interferent spectra in multivariate calibration

Partial Least Squares (PLS) is by far the most popular regression method for building multivariate calibration models for spectroscopic data. However, the success of the conventional PLS approach depends on the availability of a ‘representative data set’ as the model needs to be trained for all expected variation at the prediction stage. When the concentration of the known interferents and their correlation with the analyte of interest change in a fashion which is not covered in the calibration set, the predictive performance of inverse calibration approaches such as conventional PLS can deteriorate. This underscores the need for calibration methods that are capable of building multivariate calibration models which can be robustified against the unexpected variation in the concentrations and the correlations of the known interferents in the test set. Several methods incorporating ‘a priori’ information such as pure component spectra of the analyte of interest and/or the known interferents have been proposed to build more robust calibration models. In the present study, four such calibration techniques have been benchmarked on two data sets with respect to their predictive ability and robustness: Net Analyte Preprocessing (NAP), Improved Direct Calibration (IDC), Science Based Calibration (SBC) and Augmented Classical Least Squares (ACLS) Calibration. For both data sets, the alternative calibration techniques were found to give good prediction performance even when the interferent structure in the test set was different from the one in the calibration set. The best results were obtained by the ACLS model incorporating both the pure component spectra of the analyte of interest and the interferents, resulting in a reduction of the RMSEP by a factor 3 compared to conventional PLS for the situation when the test set had a different interferent structure than the one in the calibration set.     

Evaluation of several two-step scoring functions based on linear interaction energy, effective ligand size, and empirical pair potentials for prediction of protein-ligand binding geometry and free energy

The performances of several two-step scoring approaches for molecular docking were assessed for their ability to predict binding geometries and free energies. Two new scoring functions designed for "step 2 discrimination" were proposed and compared to our CHARMM implementation of the linear interaction energy (LIE) approach using the Generalized-Born with Molecular Volume (GBMV) implicit solvation model. A scoring function S1 was proposed by considering only "interacting" ligand atoms as the "effective size" of the ligand and extended to an empirical regression-based pair potential S2. The S1 and S2 scoring schemes were trained and 5-fold cross-validated on a diverse set of 259 protein-ligand complexes from the Ligand Protein Database (LPDB). The regression-based parameters for S1 and S2 also demonstrated reasonable transferability in the CSARdock 2010 benchmark using a new data set (NRC HiQ) of diverse protein-ligand complexes. The ability of the scoring functions to accurately predict ligand geometry was evaluated by calculating the discriminative power (DP) of the scoring functions to identify native poses. The parameters for the LIE scoring function with the optimal discriminative power (DP) for geometry (step 1 discrimination) were found to be very similar to the best-fit parameters for binding free energy over a large number of protein-ligand complexes (step 2 discrimination). Reasonable performance of the scoring functions in enrichment of active compounds in four different protein target classes established that the parameters for S1 and S2 provided reasonable accuracy and transferability. Additional analysis was performed to definitively separate scoring function performance from molecular weight effects. This analysis included the prediction of ligand binding efficiencies for a subset of the CSARdock NRC HiQ data set where the number of ligand heavy atoms ranged from 17 to 35. This range of ligand heavy atoms is where improved accuracy of predicted ligand efficiencies is most relevant to real-world drug design efforts.     

PLS-DA - Docking Optimized Combined Energetic Terms (PLSDA-DOCET) protocol: a brief evaluation

Docking studies have become popular approaches in drug design, where the binding energy of the ligand in the active site of the protein is estimated by a scoring function. Many promising techniques were developed to enhance the performance of scoring functions including the fusion of multiple scoring functions outcomes into a so-called consensus scoring function. Hereby, we evaluated the target oriented consensus technique using the energetic terms of several scoring functions. The approach was denoted PLSDA-DOCET. Optimization strategies for consensus energetic terms and scoring functions based on ROC metric were compared to classical rigid docking and to ligand-based similarity search methods comprising 2D fingerprints and ROCS. The ROCS results indicate large performance variations depending on the biological target. The AUC-based strategy of PLSDA-DOCET outperformed the other docking approaches regarding simple retrieval and scaffold-hopping. The superior performance of PLSDA-DOCET protocol relative to single and combined scoring functions was validated on an external test set. We found a relative low mean correlation of the ranks of the chemotypes retrieved by the PLSDA-DOCET protocol and all the other methods employed here.     

Prediction of total green tea antioxidant capacity from chromatograms by multivariate modeling

In this paper, a fast strategy for determining the total antioxidant capacity of Chinese green tea extracts is developed. This strategy includes the use of experimental techniques, such as fast high-performance liquid chromatography (HPLC) on monolithic columns and a spectrophotometric approach to determine the total antioxidant capacity of the extracts. To extract the chemically relevant information from the obtained data, chemometrical approaches are used. Among them there are correlation optimized warping (COW) to align the chromatograms, robust principal component analysis (robust PCA) to detect outliers, and partial least squares (PLS) and uninformative variable elimination partial least squares (UVE-PLS) to construct a reliable multivariate regression model to predict the total antioxidant capacity from the fast chromatograms.     

No-alignment-strategies for exploring a set of two-way data tables obtained from capillary electrophoresis-mass spectrometry

Hyphenated techniques such as capillary electrophoresis-mass spectrometry (CE-MS) or high-performance liquid chromatography with diode array detection (HPLC-DAD), etc., are known to produce a huge amount of data since each sample is characterized by a two-way data table. In this paper different ways of obtaining sample-related information from a set of such tables are discussed. Working with original data requires alignment techniques due to time shifts caused by unavoidable variations in separation conditions. Other pre-processing techniques have been suggested to facilitate comparison among samples without prior peak alignment, for example, 'binning' and/or 'blurring' the data along the time dimension. All these techniques, however, require optimization of some parameters, and in this paper an alternative parameter-free method is proposed. The individual data tables (X) are represented as Gram matrices (XXT), where the summation is taken over the time dimension. Hence the possible variations in time scale are eliminated, while the time information is at least partly preserved by the correlation structure between the detection channels. For comparison among samples, a similarity matrix is constructed and explored by principal component analysis and hierarchical clustering. The Gram matrix approach was tested and compared to some other methods using 'binned' and 'blurred' data for a data set with CE-MS runs on urine samples. In addition to data exploration by principal component analysis and hierarchical clustering, a discriminant partial least squares model was constructed to discriminate between the samples that were taken with and without the prior intake of a drug. The result showed that the proposed method is at least as good as the others with respect to cluster identification and class prediction. A distinct advantage is that there is no need for parameter optimization, while a potential drawback is the large size of the Gram matrices for data with high mass resolution.     

Semantically predicting protein functions based on protein functional connectivity

BackgroundThe current availability of public protein–protein interaction (PPI) databases which are usually modelled as PPI networks has led to the rapid development of protein function prediction approaches. The existing network-based prediction approaches mainly focus on the topological similarities between immediately interacting proteins, neglecting the protein functional connectivity which is the functional tightness between proteins. In this paper, we attempt to predict the functions of unannotated proteins based on PPI networks by incorporating the protein functional connectivity, as well as the similarity of protein functions, into the prediction procedure.ResultsAn approach named Semantic protein function Prediction based on protein Functional Connectivity (SPFC) is proposed to achieve a higher accuracy in predicting functions of unannotated protein. We define the functional connectivity and function addition for each protein, and incorporate them into the prediction. We evaluated the SPFC on real PPI datasets and the experiment results show that the SPFC method is more effective in function prediction than other network-based approaches.ConclusionIncorporating the functional connectivity of each protein into the function prediction can significantly improve the accuracy of protein prediction.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Chemical equilibria studies using multivariate analysis methods

Chemical multiequilibria systems can be monitored efficiently with the aid of spectroscopic techniques. Both hard- and soft-modeling are effective and powerful tools to extract chemical information from spectroscopic data. Recently, hybrid approaches that combine the flexibility of soft-modeling with the precise solutions provided by hard-modeling have been proposed. Here, we tested the performance of these three chemometric approaches for the analysis of several simulated data sets. In addition, experimental data recorded during the study of the acid–base equilibria of two DNA structures (G-quadruplex and i-motif) corresponding to two short sequences of the k-ras oncogene were studied. Finally, we also analyzed the interaction of the two DNA sequences with the model ligand TMPyP4. The results obtained from the analysis of these data sets may be useful to determine the most appropriate use of each approach. Whenever the presence of optically active interferences or unknown drifts can be neglected and a chemical model can easily be proposed and fitted, the hard-modeling method shows the best performance. If any of these conditions is not fulfilled, a hybrid-modeling approach may be a better option because all the contributions (chemical and unknown) can be modeled and the ambiguities inherent to soft-modeling methods show minor effects.     

A vibrational circular dichroism implementation within a Slater-type-orbital based density functional framework and its application to hexa- and hepta-helicenes

We describe the implementation of the rotational strengths for vibrational circular dichroism (VCD) in the Slater-type orbital based Amsterdam Density Functional (ADF) package. We show that our implementation, which makes use of analytical derivative techniques and London atomic orbitals, yields origin independent rotational strengths. The basis set dependence in the particular case of Slater-type basis functions is also discussed. It turns out that the triple zeta STO basis sets with one set of polarization functions (TZP) are adequate for VCD calculations. The origin- dependence of the atomic axial tensors is checked by a distributed origin gauge implementation. The distributed and common origin gauge implementations yield virtually identical atomic axial tensors with the Slater-type basis sets employed here, proving that our implementation yields origin independent rotational strengths. We verify the implementation for a set of benchmark molecules, for which the dependence of the VCD spectra on the particular choice of the exchange–correlation functional is studied. The pure functionals BP86 and OLYP show a particularly good performance. Then, we apply this approach to study the VCD spectra of hexa- and hepta- helicenes. In particular we focus on relationships between the sign of the rotational strengths of the two helicenes. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.