Pairwise Potential Functions Research Articles

Evaluation of the Key Structural Features of Various Butyrylcholinesterase Inhibitors Using Simple Molecular Descriptors.

In this study, we developed several QSAR models based on simple descriptors (such as topological and constitutional) to estimate butyrylcholinesterase (BChE) inhibition potency, pKi (or pIC50), of a set of 297 (289 after exclusion of outliers) structurally different compounds. The models were similar to the best model that we obtained previously for acetylcholinesterase AChE and were based on the valence molecular connectivity indices of second and third order (2χv and 3χv), the number of aliphatic hydroxyl groups (nOH), AlogP Ghose–Crippen octanol–water partition coeff. (logP), and O-060–atom-centred fragments (Al-O-Ar, Ar-O-Ar, R..O..R and R-O-C=X). The best models with two and three descriptors yielded r = 0.787 and S.E. = 0.89, and r = 0.827 and S.E. = 0.81, respectively. We also correlated nine scoring functions, calculated for 20 ligands whose complexes with BChE we found in the Protein Data Bank as crystal structures to pKi (or pIC50). The best correlations yielded PLP1 and PLP2 (Piecewise Linear Pairwise potential functions) with r = 0.619 and 0.689, respectively. Correlation with certain simple topological and constitutional descriptors yielded better results, e.g., 3χv (r = 0.730), on the same set of compounds (N = 20).

Accuracy of Alternate Nonpolarizable Force Fields for the Determination of Protein-Ligand Binding Affinities Dominated by Cation-π Interactions.

Modifying pair-specific Lennard-Jones parameters through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field has proven cost-effective for improving the description of cation-π interactions in biological objects by means of pairwise additive potential energy functions. Here, two sets of newly optimized CHARMM36 force-field parameters including NBFIX corrections, coined CHARMM36m-NBF and CHARMM36-WYF, and the original force fields, namely CHARMM36m and Amber ff14SB, are used to determine the standard binding free energies of seven protein-ligand complexes containing cation-π interactions. Compared with precise experimental measurements, our results indicate that the uncorrected, original force fields significantly underestimate the binding free energies, with a mean error of 5.3 kcal/mol, while the mean errors of CHARMM36m-NBF and CHARMM36-WYF amount to 0.8 and 2.1 kcal/mol, respectively. The present study cogently demonstrates that the use of modified parameters jointly with NBFIX corrections dramatically increases the accuracy of the standard binding free energy of protein-ligand complexes dominated by cation-π interactions, most notably with CHARMM36m-NBF.

Pair Potentials as Machine Learning Features.

Atom pairwise potential functions make up an essential part of many scoring functions for protein decoy detection. With the development of machine learning (ML) tools, there are multiple ways to combine potential functions to create novel ML models and methods. Potential function parameters can be easily extracted; however, it is usually hard to directly obtain the calculated atom pairwise energies from scoring functions. Amber, as one of the most popular suites of modeling programs, has an extensive history and library of force field potential functions. In this work, we directly used the force field parameters in ff94 and ff14SB from Amber and encoded them to calculate atom pairwise energies for different interactions. Two sets of structures (single amino acid set and a dipeptide set) were used to evaluate the performance of our encoded Amber potentials. From the comparison results between energy terms obtained from our encoding and Amber, we find energy difference within ±0.06 kcal/mol for all tested structures. Previously we have shown that the Random Forest (RF) model can help to emphasize more important atom pairwise interactions and ignore insignificant ones [Pei, J.; Zheng, Z.; Merz, K. M. J. Chem. Inf. Model. 2019, 59, 1919-1929]. Here, as an example of combining ML methods with traditional potential functions, we followed the same work flow to combine the RF models with force field potential functions from Amber. To determine the performance of our RF models with force field potential functions, 224 different protein native-decoy systems were used as our training and testing sets We find that the RF models with ff94 and ff14SB force field parameters outperformed all other scoring functions (RF models with KECSA2, RWplus, DFIRE, dDFIRE, and GOAP) considered in this work for native structure detection, and they performed similarly in detecting the best decoy. Through inclusion of best decoy to decoy comparisons in building our RF models, we were able to generate models that outperformed the score functions tested herein both on accuracy and best decoy detection, again showing the performance and flexibility of our RF models to tackle this problem. Finally, the importance of the RF algorithm and force field parameters were also tested and the comparison results suggest that both the RF algorithm and force field potentials are important with the ML scoring function achieving its best performance only by combining them together. All code and data used in this work are available at https://github.com/JunPei000/FFENCODER_for_Protein_Folding_Pose_Selection.

Deep learning and conditional random fields-based depth estimation and topographical reconstruction from conventional endoscopy

Colorectal cancer is the fourth leading cause of cancer deaths worldwide and the second leading cause in the United States. The risk of colorectal cancer can be mitigated by the identification and removal of premalignant lesions through optical colonoscopy. Unfortunately, conventional colonoscopy misses more than 20% of the polyps that should be removed, due in part to poor contrast of lesion topography. Imaging depth and tissue topography during a colonoscopy is difficult because of the size constraints of the endoscope and the deforming mucosa. Most existing methods make unrealistic assumptions which limits accuracy and sensitivity. In this paper, we present a method that avoids these restrictions, using a joint deep convolutional neural network-conditional random field (CNN-CRF) framework for monocular endoscopy depth estimation. Estimated depth is used to reconstruct the topography of the surface of the colon from a single image. We train the unary and pairwise potential functions of a CRF in a CNN on synthetic data, generated by developing an endoscope camera model and rendering over 200,000 images of an anatomically-realistic colon.We validate our approach with real endoscopy images from a porcine colon, transferred to a synthetic-like domain via adversarial training, with ground truth from registered computed tomography measurements. The CNN-CRF approach estimates depths with a relative error of 0.152 for synthetic endoscopy images and 0.242 for real endoscopy images. We show that the estimated depth maps can be used for reconstructing the topography of the mucosa from conventional colonoscopy images. This approach can easily be integrated into existing endoscopy systems and provides a foundation for improving computer-aided detection algorithms for detection, segmentation and classification of lesions.

Conditional Random Field and Deep Feature Learning for Hyperspectral Image Classification

Image classification is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, a convolutional neural network (CNN) has established itself as a powerful model in classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the classification performance. In this paper, we propose a method to classify hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral band groups to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of 3-D data cubes. Furthermore, we introduce a deep deconvolution network that improves the final classification performance. We also introduced a new data set and experimented our proposed method on it along with several widely adopted benchmark data sets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.

Exploring Context with Deep Structured Models for Semantic Segmentation.

We propose an approach for exploiting contextual information in semantic image segmentation, and particularly investigate the use of patch-patch context and patch-background context in deep CNNs. We formulate deep structured models by combining CNNs and Conditional Random Fields (CRFs) for learning the patch-patch context between image regions. Specifically, we formulate CNN-based pairwise potential functions to capture semantic correlations between neighboring patches. Efficient piecewise training of the proposed deep structured model is then applied in order to avoid repeated expensive CRF inference during the course of back propagation. For capturing the patch-background context, we show that a network design with traditional multi-scale image inputs and sliding pyramid pooling is very effective for improving performance. We perform comprehensive evaluation of the proposed method. We achieve new state-of-the-art performance on a number of challenging semantic segmentation datasets.

Discriminative Training of Deep Fully Connected Continuous CRFs With Task-Specific Loss.

Recent works on deep conditional random fields (CRFs) have set new records on many vision tasks involving structured predictions. Here, we propose a fully connected deep continuous CRF model with task-specific losses for both discrete and continuous labeling problems. We exemplify the usefulness of the proposed model on multi-class semantic labeling (discrete) and the robust depth estimation (continuous) problems. In our framework, we model both the unary and the pairwise potential functions as deep convolutional neural networks (CNNs), which are jointly learned in an end-to-end fashion. The proposed method possesses the main advantage of continuously valued CRFs, which is a closed-form solution for the maximum a posteriori (MAP) inference. To better take into account the quality of the predicted estimates during the cause of learning, instead of using the commonly employed maximum likelihood CRF parameter learning protocol, we propose task-specific loss functions for learning the CRF parameters. It enables direct optimization of the quality of the MAP estimates during the learning process. Specifically, we optimize the multi-class classification loss for the semantic labeling task and the Tukey's biweight loss for the robust depth estimation problem. Experimental results on the semantic labeling and robust depth estimation tasks demonstrate that the proposed method compare favorably against both baseline and state-of-the-art methods. In particular, we show that although the proposed deep CRF model is continuously valued, with the equipment of task-specific loss, it achieves impressive results even on discrete labeling tasks.

3D Pictorial Structures Revisited: Multiple Human Pose Estimation.

We address the problem of 3D pose estimation of multiple humans from multiple views. The transition from single to multiple human pose estimation and from the 2D to 3D space is challenging due to a much larger state space, occlusions and across-view ambiguities when not knowing the identity of the humans in advance. To address these problems, we first create a reduced state space by triangulation of corresponding pairs of body parts obtained by part detectors for each camera view. In order to resolve ambiguities of wrong and mixed parts of multiple humans after triangulation and also those coming from false positive detections, we introduce a 3D pictorial structures (3DPS) model. Our model builds on multi-view unary potentials, while a prior model is integrated into pairwise and ternary potential functions. To balance the potentials' influence, the model parameters are learnt using a Structured SVM (SSVM). The model is generic and applicable to both single and multiple human pose estimation. To evaluate our model on single and multiple human pose estimation, we rely on four different datasets. We first analyse the contribution of the potentials and then compare our results with related work where we demonstrate superior performance.

MULTI-QUADRATIC DYNAMIC PROGRAMMING PROCEDURE OF EDGE– PRESERVING DENOISING FOR MEDICAL IMAGES

Abstract. In this paper, we present a computationally efficient technique for edge preserving in medical image smoothing, which is developed on the basis of dynamic programming multi-quadratic procedure. Additionally, we propose a new non-convex type of pair-wise potential functions, allow more flexibility to set a priori preferences, using different penalties for various ranges of differences between the values of adjacent image elements. The procedure of image analysis, based on the new data models, significantly expands the class of applied problems, and can take into account the presence of heterogeneities and discontinuities in the source data, while retaining high computational efficiency of the dynamic programming procedure and Kalman filterinterpolator. Comparative study shows, that our algorithm has high accuracy to speed ratio, especially in the case of high-resolution medical images.

A generalization of improved susceptibility propagation

Recently, an effective susceptibility propagation method for binary Markov random fields based on a concept of diagonal consistency was proposed. This improved susceptibility propagation is a powerful method and exhibits a robust performance for various types of network structures. In this paper, a generalization of the improved susceptibility propagation using an orthonormal function expansion is proposed in which any pairwise potential functions and multivalued random variables are acceptable. In the latter part of this paper, the proposed method is applied to a direct problem and an inverse problem on a generalized sparse prior, which is a recently proposed prior model for natural images.

Atomistic Modeling and Ab Initio Calculations of Yttria-Stabilized Zirconia

Though a number of atomistic-model studies of yttria-stabilized zirconia (YSZ) have been reported to elucidate its properties, most of them have employed simple pairwise potential functions to express interactions between atoms, which limits the transferability of the models. We have developed a Tangney-Scandolo dipole model potential for YSZ. Energy, stress and forces on atoms calculated by the ab initio (first-principles) density functional theory are provided as reference data for potential fitting. The developed potential successfully reproduces cubic-tetragonal phase transition at a range of yttria concentration relevant with SOFC application. The potential can well reproduce the barrier energy of oxygen vacancy migration. Molecular dynamics simulations of oxygen diffusion in bulk and at grain boundaries are demonstrated.

Interventional Tool Tracking Using Discrete Optimization

This work presents a novel scheme for tracking of motion and deformation of interventional tools such as guide-wires and catheters in fluoroscopic X-ray sequences. Being able to track and thus to estimate the correct positions of these tools is crucial in order to offer guidance enhancement during interventions. The task of estimating the apparent motion is particularly challenging due to the low signal-to-noise ratio (SNR) of fluoroscopic images and due to combined motion components originating from patient breathing and tool interactions performed by the physician. The presented approach is based on modeling interventional tools with B-splines whose optimal configuration of control points is determined through efficient discrete optimization. Each control point corresponds to a discrete random variable in a Markov random field (MRF) formulation where a set of labels represents the deformation space. In this context, the optimal curve corresponds to the maximum a posteriori (MAP) estimate of the MRF energy. The main motivation for employing a discrete approach is the possibility to incorporate a multi-directional search space which is robust to local minima. This is of particular interest for curve tracking under large deformation. This work analyzes feasibility of employing efficient first-order MRFs for tracking. In particular it shows how to achieve a good compromise between energy approximations and computational efficiency. Experimental results suggest to define both the external and internal energy in terms of pairwise potential functions. The method was successfully applied to the tracking of guide-wires in fluoroscopic X-ray sequences of several hundred frames which requires extremely robust techniques. Comparisons with state-of-the-art guide-wire tracking algorithms confirm the effectiveness of the proposed method.

Flocking for Multiple Ellipsoidal Agents with Limited Communication Ranges

This paper contributes a design of distributed controllers for flocking of mobile agents with an ellipsoidal shape and a limited communication range. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise potential functions to design flocking control algorithms. The proposed flocking design results in (1) smooth controllers despite of the agents’ limited communication ranges, (2) no collisions between any agents, (3) asymptotic convergence of each agent’s generalized velocity to a desired velocity, and (4) boundedness of the flock size, defined as the sum of all distances between the agents, by a constant.

A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction.

BackgroundAn accurate potential function is essential to attack protein folding and structure prediction problems. The key to developing efficient knowledge-based potential functions is to design reference states that can appropriately counteract generic interactions. The reference states of many knowledge-based distance-dependent atomic potential functions were derived from non-interacting particles such as ideal gas, however, which ignored the inherent sequence connectivity and entropic elasticity of proteins.MethodologyWe developed a new pair-wise distance-dependent, atomic statistical potential function (RW), using an ideal random-walk chain as reference state, which was optimized on CASP models and then benchmarked on nine structural decoy sets. Second, we incorporated a new side-chain orientation-dependent energy term into RW (RWplus) and found that the side-chain packing orientation specificity can further improve the decoy recognition ability of the statistical potential.SignificanceRW and RWplus demonstrate a significantly better ability than the best performing pair-wise distance-dependent atomic potential functions in both native and near-native model selections. It has higher energy-RMSD and energy-TM-score correlations compared with other potentials of the same type in real-life structure assembly decoys. When benchmarked with a comprehensive list of publicly available potentials, RW and RWplus shows comparable performance to the state-of-the-art scoring functions, including those combining terms from multiple resources. These data demonstrate the usefulness of random-walk chain as reference states which correctly account for sequence connectivity and entropic elasticity of proteins. It shows potential usefulness in structure recognition and protein folding simulations. The RW and RWplus potentials, as well as the newly generated I-TASSER decoys, are freely available in http://zhanglab.ccmb.med.umich.edu/RW.

Using piecewise polynomials for faster potential function evaluation

In many molecular dynamics simulation software packages and hardware implementations, piecewise polynomials are used to represent and compute pairwise potential functions efficiently. In this paper, we present three modifications applicable to most interpolations to increase their accuracy. The increased accuracy reduces the amount of data that needs to be stored for each interaction potential, making such interpolations more suitable for architectures with limited memory and/or cache or hardware implementations.

Performance vs computational efficiency for optimizing single and dynamic MRFs: Setting the state of the art with primal-dual strategies

In this paper we introduce a novel method to address minimization of static and dynamic MRFs. Our approach is based on principles from linear programming and, in particular, on primal-dual strategies. It generalizes prior state-of-the-art methods such as α-expansion, while it can also be used for efficiently minimizing NP-hard problems with complex pair-wise potential functions. Furthermore, it offers a substantial speedup – of a magnitude 10 – over existing techniques, due to the fact that it exploits information coming not only from the original MRF problem, but also from a dual one. The proposed technique consists of recovering pair of solutions for the primal and the dual such that the gap between them is minimized. Therefore, it can also boost performance of dynamic MRFs, where one should expect that the new pair of primal-dual solutions is closed to the previous one. Promising results in a number of applications, and theoretical, as well as numerical comparisons with the state of the art demonstrate the extreme potentials of this approach. 2 A version of our MRF optimization code will become publicly available from: http://www.csd.uoc.gr/komod/FastPD. 2

A comparison of interatomic potentials for rare gas nanoaggregates

Rare-gas clusters are usually modeled by Lennard–Jones pairwise potential energy functions. A more realistic representation of the rare-gas pair interaction is given by the benchmark Aziz HFD type potentials, of high computational cost for large scale molecular simulations. Here we compare Lennard–Jones and HFD potentials with that obtained from a generalization of the Lennard–Jones potential, recently presented by Pirani et al. Parameters are given for the two-body interaction for all dimers and structural properties of Ar 5 and Ar 6 are discussed through a comparison of the Pirani et al. potentials with those of Lennard–Jones.

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.

Studies of protein-protein interfaces: a statistical analysis of the hydrophobic effect.

Data sets of 362 structurally nonredundant protein-protein interfaces and of 57 symmetry-related oligomeric interfaces have been used to explore whether the hydrophobic effect that guides protein folding is also the main driving force for protein-protein associations. The buried nonpolar surface area has been used to measure the hydrophobic effect. Our analysis indicates that, although the hydrophobic effect plays a dominant role in protein-protein binding, it is not as strong as that observed in the interior of protein monomers. Comparison of interiors of the monomers with those of the interfaces reveals that, in general, the hydrophobic amino acids are more frequent in the interior of the monomers than in the interior of the protein-protein interfaces. On the other hand, a higher proportion of charged and polar residues are buried at the interfaces, suggesting that hydrogen bonds and ion pairs contribute more to the stability of protein binding than to that of protein folding. Moreover, comparison of the interior of the interfaces to protein surfaces indicates that the interfaces are poorer in polar/charged than the surfaces and are richer in hydrophobic residues. The interior of the interfaces appears to constitute a compromise between the stabilization contributed by the hydrophobic effect on the one hand and avoiding patches on the protein surfaces that are too hydrophobic on the other. Such patches would be unfavorable for the unassociated monomers in solution. We conclude that, although the types of interactions are similar between protein-protein interfaces and single-chain proteins overall, the contribution of the hydrophobic effect to protein-protein associations is not as strong as to protein folding. This implies that packing patterns and interatom, or interresidue, pairwise potential functions, derived from monomers, are not ideally suited to predicting and assessing ligand associations or design. These would perform adequately only in cases where the hydrophobic effect at the binding site is substantial.

Effective potentials for liquid water using polarizable and nonpolarizable models

Two three-site potentials for use in liquid water simulations are constructed using effective interactions. The rigid molecule has interaction centers located at atomic sites coinciding with the gas-phase monomer geometry. One potential uses solely pairwise additive potential functions whereas the other includes polarization contributions. These functions and parameters are adjusted to give simulated liquid properties at room temperature that resemble the experimental values for structure, energy, and pressure. The models presented correspond to a reduced effective representation of liquid water interactions and are labeled RER(pair) and RER(pol). Thus, the local structure of the liquid is reproduced based on the pair correlation functions for atom pain