A kinematic view of loop closure

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.     

Visualisation of inter loop tertiary base pairing and stacking interactions in an unusual slipped loop DNA structure

The conformation of an unusual slipped loop DNA structure exhibited by the sequence d(GAATTCCCGAATTC)₂ is determined using a combination of geometrical and molecular mechanics methods. This sequence is known to form a B-DNA-like duplex with the central non-complementary cytosines extruded into single stranded loop regions. The unusual feature is that the interior guanine does not pair with the cytosine across, instead, it pairs with the cytosine upstream by skipping two cytosines, leading to a slipped loop DNA structure with the loops staggered by two base pairs. The two loops, despite being very small, can fold across minor or major groove symmetrically or asymmetrically disposed, with one of the loop bases partially blocking the major or minor groove. Most interestingly, for certain conformations, the loop bases approach one another at close proximity so as to engage even in base pairing as well as base stacking interactions across the major groove. While such pairing and stacking are common in the tertiary folds of RNA, this is the first time that such an interaction is visualized in a DNA. This observation demonstrates that a W-C pair can readily be accomplished in a typical slipped loop structure postulated for DNA. Such tertiary loop interaction may prevent access to regulatory proteins across the major groove of the duplex DNA, thus providing a structure-function relation for the occurrence of slipped loop structure in DNA. Contribution no. 839 from this department     

Key issues in the computational simulation of GPCR function: representation of loop domains

Some key concerns raised by molecular modeling and computational simulation of functional mechanisms for membrane proteins are discussed and illustrated for members of the family of G protein coupled receptors (GPCRs). Of particular importance are issues related to the modeling and computational treatment of loop regions. These are demonstrated here with results from different levels of computational simulations applied to the structures of rhodopsin and a model of the 5-HT2A serotonin receptor, 5-HT2AR. First, comparative Molecular Dynamics (MD) simulations are reported for rhodopsin in vacuum and embedded in an explicit representation of the membrane and water environment. It is shown that in spite of a partial accounting of solvent screening effects by neutralization of charged side chains, vacuum MD simulations can lead to severe distortions of the loop structures. The primary source of the distortion appears to be formation of artifactual H-bonds, as has been repeatedly observed in vacuum simulations. To address such shortcomings, a recently proposed approach that has been developed for calculating the structure of segments that connect elements of secondary structure with known coordinates, is applied to 5-HT2AR to obtain an initial representation of the loops connecting the transmembrane (TM) helices. The approach consists of a simulated annealing combined with biased scaled collective variables Monte Carlo technique, and is applied to loops connecting the TM segments on both the extra-cellular and the cytoplasmic sides of the receptor. Although this initial calculation treats the loops as independent structural entities, the final structure exhibits a number of interloop interactions that may have functional significance. Finally, it is shown here that in the case where a given loop from two different GPCRs (here rhodopsin and 5-HT2AR) has approximately the same length and some degree of sequence identity, the fold adopted by the loops can be similar. Thus, in such special cases homology modeling might be used to obtain initial structures of these loops. Notably, however, all other loops in these two receptors appear to be very different in sequence and structure, so that their conformations can be found reliably only by ab initio, energy based methods and not by homology modeling.     

Sampling multiple scoring functions can improve protein loop structure prediction accuracy

Accurately predicting loop structures is important for understanding functions of many proteins. In order to obtain loop models with high accuracy, efficiently sampling the loop conformation space to discover reasonable structures is a critical step. In loop conformation sampling, coarse-grain energy (scoring) functions coupling with reduced protein representations are often used to reduce the number of degrees of freedom as well as sampling computational time. However, due to implicitly considering many factors by reduced representations, the coarse-grain scoring functions may have potential insensitivity and inaccuracy, which can mislead the sampling process and consequently ignore important loop conformations. In this paper, we present a new computational sampling approach to obtain reasonable loop backbone models, so-called the Pareto optimal sampling (POS) method. The rationale of the POS method is to sample the function space of multiple, carefully selected scoring functions to discover an ensemble of diversified structures yielding Pareto optimality to all sampled conformations. The POS method can efficiently tolerate insensitivity and inaccuracy in individual scoring functions and thereby lead to significant accuracy improvement in loop structure prediction. We apply the POS method to a set of 4-12-residue loop targets using a function space composed of backbone-only Rosetta and distance-scale finite ideal-gas reference (DFIRE) and a triplet backbone dihedral potential developed in our lab. Our computational results show that in 501 out of 502 targets, the model sets generated by POS contain structure models are within subangstrom resolution. Moreover, the top-ranked models have a root mean square deviation (rmsd) less than 1 A in 96.8, 84.1, and 72.2% of the short (4-6 residues), medium (7-9 residues), and long (10-12 residues) targets, respectively, when the all-atom models are generated by local optimization from the backbone models and are ranked by our recently developed Pareto optimal consensus (POC) method. Similar sampling effectiveness can also be found in a set of 13-residue loop targets.     

蛋白质分子与配体结合过程构象变化的研究

蛋白质分子与配体的作用模式主要有直接的环区结合及铰链式结合两种方式。针对这两种不同的作用方式,我们提出采用不同的策略进行结合过程的构象研究。对于直接的环区结合模式,通过建立环区主链构象库,来实现蛋白质环区与配体的准柔性对接,并以链霉抗生物素蛋白体系为例对构象库建立的可行性进行了验证计算。对铰链结合方式,采用分步对接的方法进行计算,并具体应用于HIV蛋白酶与其小分子配体的结合过程。计算结果表明,这两种处理方法分别能较好地模拟不同类型的蛋白质与配体结合的的构象变化。     

Parallel implementation of a protein structure refinement algorithm

An algorithm is presented for the refinement of reduced-model structures of proteins. A simulated annealing minimization is carried out in which the trial moves consist of the replacement of three-residue segments from a presorted library. The segments in the library are screened independently by their net end-to-end rotations so as to reproduce a distribution of conformations in the library similar to those in the ensemble. A general form of a look-up table contact potential is used to evaluate the free energy. This algorithm has been implemented on a parallel connection machine, on which a large number of molecules can be simultaneously simulated. The calculation of the pairwise distance matrix is distributed across the nodes of the machine to achieve an increase in performance and a reduction in the memory required on each node to store the potential table. The results of the refinement are shown for the test case of myoglobin, and the parallel performance is compared to that of a serial version of the algorithm. © 1996 by John Wiley & Sons, Inc.     

Effect of loop on the stability of intramolecular triplex DNA

Conformation stabilities of intramolecular triple-helical DNAs (intra-tnplex DNAs: 5-d(TC)6-d(T)m-d(CT)6-d(C)n-d(AG)6-3',where m and n are chosen to be 4 and 3) have been examined by molecular mechanics.The four intra-triplexes (H-DNAs) are compared with the mtermolecular triplexes d(TC)6 * d ( AG)6 d(CT)6.The results revealed that loops do not significantly influence the mtratriplex conformations,loop conformations,however,depend partly on its length.Loop also makes strand Ⅱ of every intra-triplex DNA longer than that of the inter-triplex DNA.Most of residue sugar conformations of triple-helical DNAs are S-type,there aiso exist,however,N-type conformation and the conformations between S-type and N-type Possible models of the five triplex DNAs are presented.     

Coexistence of hydrogen-bonded loop and extended tetrapeptide conformations

The conformations of a protected tetrathiopeptide have been analysed by isotope labelling and two-dimensional infrared spectroscopy (2D-IR). It has been found that Boc-Ala-Gly(=S)-Ala-Aib-OMe in acetonitrile, as well as its oxopeptide analogue, can adopt a hydrogen-bonded loop conformation in coexistence with less restricted structures. The two types of conformations interconvert too quickly to be resolved on the nuclear magnetic resonance (NMR) timescale, but give rise to different cross peaks in two-dimensional infrared spectra. The hydrogen bond between the Boc terminal group and the amide proton of Aib can be broken by photoisomerisation of the thioamide bond.     

Mean‐field and fluctuation correction analyses for a diblock copolymer melt exhibiting an immiscibility loop

A study on a diblock copolymer melt that can form certain specific interactions between dissimilar monomers is performed first with a mean‐field approach and then with a fluctuation correction approach. Flory's interaction parameter χ possesses both enthalpic and entropic contributions because of the specific interactions. It is found that not only a lower critical ordering transition but also an immiscibility loop with an upper critical ordering transition can be developed in the copolymer by the presence of the specific interactions and the entropic component in χ. The mean‐field loop phase diagram is shown to feature a typical sequence of microphase transitions upon both heating and cooling with two continuous transition points at a symmetric composition. It is revealed that the fluctuation effects remove both continuous transition points to significantly shrink the loop. The pressure effects on the phase behavior of the copolymer are also discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1889–1896, 2003     

End-to-end vs interior loop formation kinetics in unfolded polypeptide chains

The conformational search for favorable intramolecular interactions during protein folding is limited by intrachain diffusion processes. Recent studies on the dynamics of loop formation in unfolded polypeptide chains have focused on loops involving residues near the chain ends. During protein folding, however, most contacts are formed between residues in the interior of the chain. We compared the kinetics of end-to-end loop formation (type I loops) to the formation of end-to-interior (type II loops) and interior-to-interior loops (type III loops) using triplet-triplet energy transfer from xanthone to naphthylalanine. The results show that formation of type II and type III loops is slower compared to type I loops of the same size and amino acid sequence. The rate constant for type II loop formation decreases with increasing overall chain dimensions up to a limiting value, at which loop formation is about 2.5-fold slower for type II loops compared to type I loops. Comparing type II loops of different loop size and amino acid sequence shows that the ratio of loop dimension over total chain dimension determines the rate constant for loop formation. Formation of type III loops is 1.7-fold slower than formation of type II loops, indicating that local chain motions are strongly coupled to motions of other chain segments which leads to faster dynamics toward the chain ends. Our results show that differences in the kinetics of formation of type I, type II, and type III loops are mainly caused by differences in internal flexibility at the different positions in the polypeptide chain. Interactions of the polypeptide chain with the solvent contribute to the kinetics of loop formation, which are strongly viscosity-dependent. However, the observed differences in the kinetics of formation of type I, type II, and type III loops are not due to the increased number of peptide-solvent interactions in type II and type III loops compared to type I loops as indicated by identical viscosity dependencies for the kinetics of formation of the different types of loops.     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Exact analytical loop closure in proteins using polynomial equations

Loop closure in proteins has been studied actively for over 25 years. Using spherical geometry and polynomial equations, several loop-closure problems in proteins are solved exactly by reducing them to the determination of the real roots of a polynomial. Loops of seven, eight, and nine atoms are treated explicitly, including the tripeptide and disulfide-bonded loop-closure problems. The number of valid loop closures can be evaluated by the method of Sturm chains, which counts the number of real roots of a polynomial. Longer loops can be treated by three methods: by sampling enough dihedral angles to reduce the problem to a soluble loop-closure problem; by applying the loop-closure algorithm hierarchically; or by decimating the chain into independently moving rigid elements that can be reconnected using loop-closure algorithms. Applications of the methods to docking, homology modeling and NMR problems are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 819–844, 1999     

Effect of loop orientation on quadruplex-TMPyP4 interaction

G-quadruplexes are believed to be potential targets for therapeutic intervention and this has resulted in designing of various quadruplex interacting ligands. Moreover, reports about existence of quadruplex forming sequences across the genome have propelled greater interest in understanding their interaction with small molecules. An intramolecular quadruplex sequence can adopt different conformations, owing to different orientation of loops in the structure. The differences in the loop orientation can affect their molecular recognition. Herein, we have studied the interaction of 5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21H, 23H-porphine (TMPyP4), a well-known G quadruplex binding ligand with three DNA quadruplexes differing in loop orientations. Results obtained from UV, ITC, and SPR studies have coherently revealed that the TMPyP4 molecule shows preferential binding to parallel G-quadruplex ( c-myc and c-kit) over its antiparallel counterpart (human telomeric). The binding affinity for parallel quadruplex was (10(7)) 1 order of magnitude higher than that for antiparallel DNA quadruplex (10 ). The study shows two binding modes, stronger binding (10(7)) of TMPyP4 involving end stacking and a weaker external binding (10 ), while TMPyP4 shows only one binding mode with duplex with a binding affinity of the order of 10(6). Overall, the study emphasizes that differences in the loop orientation give rise to different conformations of quadruplex, which in turn govern its binding to small molecules, and thereby play a pivotal role in molecular recognition.     

Complete maps of molecular-loop conformational spaces

This paper presents a numerical method to compute all possible conformations of distance-constrained molecular loops, i.e., loops where some interatomic distances are held fixed, while others can vary. The method is general (it can be applied to single or multiple intermingled loops of arbitrary topology) and complete (it isolates all solutions, even if they form positive-dimensional sets). Generality is achieved by reducing the problem to finding all embeddings of a set of points constrained by pairwise distances, which can be formulated as computing the roots of a system of Cayley-Menger determinants. Completeness is achieved by expressing these determinants in Bernstein form and using a numerical algorithm that exploits such form to bound all root locations at any desired precision. The method is readily parallelizable, and the current implementation can be run on single- or multiprocessor machines. Experiments are included that show the method's performance on rigid loops, mobile loops, and multiloop molecules. In all cases, complete maps including all possible conformations are obtained, thus allowing an exhaustive analysis and visualization of all pseudo-rotation paths between different conformations satisfying loop closure.     

Closing the side-chain gap in protein loop modeling

The success of structure-based drug design relies on accurate protein modeling where one of the key issues is the modeling and refinement of loops. This study takes a critical look at modeled loops, determining the effect of re-sampling side-chains after the loop conformation has been generated. The results are evaluated in terms of backbone and side-chain conformations with respect to the native loop. While models can contain loops with high quality backbone conformations, the side-chain orientations could be poor, and therefore unsuitable for ligand docking and structure-based design. In this study, we report on the ability to model loop side-chains accurately using a variety of commercially available algorithms that include rotamer libraries, systematic torsion scans and knowledge-based methods. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Design of a peptide hairpin containing a central three-residue loop

The construction of a designed beta-hairpin structure, containing a central three-residue loop has been successfully achieved in the synthetic nonapeptide Boc-Leu-Phe-Val-(D)Pro-(L)Pro-(D)Ala-Leu-Phe-Val-OMe (2). The design is based on expanding the two-residue loop established in the peptide beta-hairpin Boc-Leu-Phe-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (1). Characterization of the registered beta-hairpins in peptides 1 and 2 is based on the observation of key nuclear Overhauser effects (NOEs) in CDCl(3) and CD(3)OH. Solvent titration and temperature dependence of NH chemical shifts establish the identity of NH groups involved in interstrand hydrogen bonding. In peptide 2, the antiparallel registry is maintained, with the formation of a (D)Pro-(L)Pro-(D)Ala loop, stabilized by a 5-->1 hydrogen bond between Val3 CO and Leu7 NH groups (C(13), alpha-turn) and a 3-->1 hydrogen bond between (D)Pro4 CO and (d)Ala6 NH groups (C(7), gamma-turn). NMR derived structures suggest that in peptide 2, (d)Ala(6) adopts an alpha(L) conformation. In peptide 1, the (D)Pro-(L)Pro segment adopts a type II' beta-turn. Replacement of (D)Ala (6) in peptide 2 by (L)Ala in peptide 3 yields a beta-hairpin conformation, with a central (D)Pro-(L)Pro two-residue loop. Strand slippage at the C-terminus results in altered registry of the antiparallel strands.     

Ab initio computational modeling of long loops in G-protein coupled receptors

A newly developed approach for predicting the structure of segments that connect known elements of secondary structure in proteins has been applied to some of the longer loops in the G-protein coupled receptors (GPCRs) rhodopsin and the dopamine receptor D2R. The algorithm uses Monte Carlo (MC) simulation in a temperature annealing protocol combined with a scaled collective variables (SCV) technique to search conformation space for loop structures that could belong to the native ensemble. Except for rhodopsin, structural information is only available for the transmembrane helices (TMHs), and therefore the usual approach of finding a single conformation of lowest energy has to be abandoned. Instead the MC search aims to find the ensemble located at the absolute minimum free energy, i.e., the native ensemble. It is assumed that structures in the native ensemble can be found by an MC search starting from any conformation in the native funnel. The hypothesis is that native structures are trapped in this part of conformational space because of the high-energy barriers that surround the native funnel. In this work it is shown that the crystal structure of the second extracellular loop (e2) of rhodopsin is a member of this loop’s native ensemble. In contrast, the crystal structure of the third intracellular loop is quite different in the different crystal structures that have been reported. Our calculations indicate, that of three crystal structures examined, two show features characteristic of native ensembles while the other one does not. Finally the protocol is used to calculate the structure of the e2 loop in D2R. Here, the crystal structure is not known, but it is shown that several side chains that are involved in interaction with a class of substituted benzamides assume conformations that point into the active site. Thus, they are poised to interact with the incoming ligand.     

LEAP: Highly accurate prediction of protein loop conformations by integrating coarse‐grained sampling and optimized energy scores with all‐atom refinement of backbone and side chains

Prediction of protein loop conformations without any prior knowledge (ab initio prediction) is an unsolved problem. Its solution will significantly impact protein homology and template‐based modeling as well as ab initio protein‐structure prediction. Here, we developed a coarse‐grained, optimized scoring function for initial sampling and ranking of loop decoys. The resulting decoys are then further optimized in backbone and side‐chain conformations and ranked by all‐atom energy scoring functions. The final integrated technique called loop prediction by energy‐assisted protocol achieved a median value of 2.1 Å root mean square deviation (RMSD) for 325 12‐residue test loops and 2.0 Å RMSD for 45 12‐residue loops from critical assessment of structure‐prediction techniques (CASP) 10 target proteins with native core structures (backbone and side chains). If all side‐chain conformations in protein cores were predicted in the absence of the target loop, loop‐prediction accuracy only reduces slightly (0.2 Å difference in RMSD for 12‐residue loops in the CASP target proteins). The accuracy obtained is about 1 Å RMSD or more improvement over other methods we tested. The executable file for a Linux system is freely available for academic users at http://sparks‐lab.org . © 2013 Wiley Periodicals, Inc.