Multiple copy sampling in protein loop modeling: computational efficiency and sensitivity to dihedral angle perturbations

Inverse Kinematics in Biology: The Protein Loop Closure Problem

Assembling fragments from known protein structures is a widely used approach to construct structural models for new proteins. We describe an application of this idea to an important inverse kinematics problem in structural biology: the loop closure problem. We have developed an algorithm for generating the conformations of candidate loops that fit in a gap of given length in a protein structure framework. Our method proceeds by concatenating small fragments of protein chosen from small libraries of representative fragments. Our approach has the advantages of ab initio methods since we are able to enumerate all candidate loops in the discrete approximation of the conformational space accessible to the loop, as well as the advantages of database search approach since the use of fragments of known protein structures guarantees that the backbone conformations are physically reasonable. We test our approach on a set of 427 loops, varying in length from four residues to 14 residues. The quality of the candidate loops is evaluated in terms of global coordinate root mean square (cRMS). The top predictions vary between 0.3 and 4.2 Å for four-residue loops and between 1.5 and 3.1 Å for 14-residue loops, respectively.

Protein structure modeling in the proteomics era

Structural proteomics aims to understand the structural basis of protein interactions and functions. A prerequisite for this is the availability of 3D protein structures that mediate the biochemical interactions. The explosion in the number of available gene sequences set the stage for the next step in genome-scale projects -- to obtain 3D structures for each protein. To achieve this ambitious goal, the slow and costly structure determination experiments are supplemented with theoretical approaches. The current state and recent advances in structure modeling approaches are reviewed here, with special emphasis on comparative protein structure modeling techniques.

Simulated mutagenesis of the hypervariable loops of a llama VHH domain for the recovery of canonical conformations

In this work, wildtype and mutated hypervariable regions of an anti-hCG llama VHH antibody were simulated via a molecular dynamics replica exchange method (REM). Seven mutants were simulated with the goal of identifying structural determinants that return the noncanonical H1 loop of the wildtype antibody to the type 1 canonical structure predicted by database methods formulated for conventional antibodies. Two cases with three point mutations yielded a stable type 1 H1 structure. In addition, other mutants with fewer mutations showed evidence of such conformations. Overall, the mutagenesis results suggest a marked influence of interloop interactions on the attainment of canonical conformations for this antibody. On the methodological front, a novel REM scheme was developed to quickly screen diverse mutants based on their relative propensities for attaining favorable structures. This multimutant REM (MMREM) was used to successfully identify mutations that stabilize a canonical H1 loop grafted on the llama antibody scaffold. The use of MMREM and REM for screening mutants and assessing structural stability may be useful in the rational design of antibody hypervariable loops.

Dihedral-angle information entropy as a gauge of secondary structure propensity

Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set--a sublibrary of the Protein Data Bank at the 90% sequence redundancy level--appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, (http://www.d2check.gatech.edu). Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation-namely, PROCHECK and WHAT_CHECK--is also provided.

Modeling protein conformational ensembles: From missing loops to equilibrium fluctuations

Characterizing protein flexibility is an important goal for understanding the physical-chemical principles governing biological function. This paper presents a Fragment Ensemble Method to capture the mobility of a protein fragment such as a missing loop and its extension into a Protein Ensemble Method to characterize the mobility of an entire protein at equilibrium. The underlying approach in both methods is to combine a geometric exploration of conformational space with a statistical mechanics formulation to generate an ensemble of physical conformations on which thermodynamic quantities can be measured as ensemble averages. The Fragment Ensemble Method is validated by applying it to characterize loop mobility in both instances of strongly stable and disordered loop fragments. In each instance, fluctuations measured over generated ensembles are consistent with data from experiment and simulation. The Protein Ensemble Method captures the mobility of an entire protein by generating and combining ensembles of conformations for consecutive overlapping fragments defined over the protein sequence. This method is validated by applying it to characterize flexibility in ubiquitin and protein G. Thermodynamic quantities measured over the ensembles generated for both proteins are fully consistent with available experimental data. On these proteins, the method recovers nontrivial data such as order parameters, residual dipolar couplings, and scalar couplings. Results presented in this work suggest that the proposed methods can provide insight into the interplay between protein flexibility and function.

Accounting for loop flexibility during protein-protein docking

Although reliable docking can now be achieved for systems that do not undergo important induced conformational change upon association, the presence of flexible surface loops, which must adapt to the steric and electrostatic properties of a partner, generally presents a major obstacle. We report here the first docking method that allows large loop movements during a systematic exploration of the possible arrangements of the two partners in terms of position and rotation. Our strategy consists in taking into account an ensemble of possible loop conformations by a multi-copy representation within a reduced protein model. The docking process starts from regularly distributed positions and orientations of the ligand around the whole receptor. Each starting configuration is submitted to energy minimization during which the best-fitting loop conformation is selected based on the mean-field theory. Trials were carried out on proteins with significant differences in the main-chain conformation of the binding loop between isolated form and complexed form, which were docked to their partner considered in their bound form. The method is able to predict complexes very close to the crystal complex both in terms of relative position of the two partners and of the geometry of the flexible loop. We also show that introducing loop flexibility on the isolated protein form during systematic docking largely improves the predictions of relative position of the partners in comparison with rigid-body docking.

Modified replica exchange simulation methods for local structure refinement

Parallel tempering, also known as replica exchange molecular dynamics (REMD), has recently been successfully used to study the structure and thermodynamic properties of biomolecules such as peptides and small proteins. For large systems, however, applying REMD can be costly since the number of replicas needed increases as the square root of the number of degrees of freedom in the system. Often, enhanced sampling is only needed for a subset of atoms, such as a loop region of a large protein or a small ligand binding to a receptor. In such applications, it is often reasonable to assume a weak dependence of the structure of the larger region on the instantaneous conformation of the smaller region of interest. For these cases, we derived two variant replica exchange methods, partial replica exchange molecular dynamics (PREMD) and local replica exchange molecular dynamics (LREMD). The Hamiltonian for the system is separated, with replica exchange carried out only for terms involving the subsystem of interest while the remainder of the system is maintained at a single temperature. The number of replicas required for efficient exchange thus depends on the number of degrees of freedom in the fragment needing refinement rather than on the size of the full system. The method can be applied to much larger systems than was previously practical. This also provides a means to preserve the integrity of the structure outside the refinement region without introduction of restraints. LREMD takes this weak coupling approximation a step further, employing only a single representation of the large fragment that simultaneously interacts with all of the replicas of the subsystem of interest. This is obtained by combining replica exchange with the locally enhanced sampling approximation (LES), reducing the computational expense of replica exchange simulations to near that of a single standard molecular dynamics (MD) simulation. Use of LREMD also permits the use of LES without requiring the specification of a single temperature, a known difficulty for standard LES simulations. We tested these two methods on the loop region of an RNA hairpin model system and find significant advantages over standard MD and REMD simulations.

Docking macromolecules with flexible segments

We address a major obstacle to macromolecular docking algorithms by presenting a new method that takes into account the induced conformational adjustment of flexible loops situated at a protein/macromolecule interface. The method, MC2, is based on a multiple copy representation of the loops, coupled with a Monte Carlo conformational search of the relative position of the macromolecules and their side chain conformations. The selection of optimal loop conformations takes place during Monte Carlo cycling by the iterative adjustment of the weight of each copy. We describe here the parameterization of the method and trials on a protein-DNA complex of known 3-D structure, involving the Drosophila prd paired domain protein and its target oligonucleotide Wenqing, X. et al., Cell 1995, 80, 639. We demonstrate that our algorithm can correctly configure and position this protein, despite its relatively complex interactions with both grooves of DNA.

Hybrid Monte Carlo with multidimensional replica exchanges: conformational equilibria of the hypervariable regions of a llama VHH antibody domain

Since the structural repertoire of the hypervariable regions of human antibodies is known to be more restricted than what is implied by sequence variability, a common approach to structural prediction is to use a knowledge-based (KB) method, such as the canonical structure model (C. Chothia and A. M. Lesk, Journal of Molecular Biology, 1987, Vol. 196, pp. 901-917). However, this model is less successful when applied to camelid heavy chain antibodies. In this study, molecular simulations were used to examine the conformational equilibria of the hypervariable regions (H1, H2, and H3) of a llama heavy chain variable domain, for which KB predictions are poor. Simulations were carried out using both conventional molecular dynamics (MD) and hybrid Monte Carlo with multidimensional replica exchanges (HYMREX). The advantage of the latter method is its ability to selectively target parts of the Hamiltonian that can most readily improve sampling. A novel variant of HYMREX was implemented in which, besides the temperature, torsional interactions and the range of nonbonded interactions were varied. To compare the sampling abilities of MD and this HYMREX scheme, simulations were started from a misfolded conformational state. Overall, MD yielded final conformations more similar to the initial state, implying quasi-ergodic sampling. In contrast, HYMREX achieved more ergodic sampling, and the majority of conformations that it sampled agreed well with the known crystal structure. The HYMREX simulation results were used to help identify the chief interactions governing the conformational equilibria and to reexamine the key assumptions underlying the KB predictions. The data show that the H1 region exhibited significant conformational freedom, in support of the hypothesis that main-chain structural variability in this region could play a greater role in antigen binding in camelid antibodies than it does in normal antibodies. Key H1 residues and associated inter-loop interactions are conjectured to account for the poor KB predictions.

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.

Molecular modelling in structural biology

Molecular modelling is a powerful methodology for analysing the three dimensional structure of biological macromolecules. There are many ways in which molecular modelling methods have been used to address problems in structural biology. It is not widely appreciated that modelling methods are often an integral component of structure determination by NMR spectroscopy and X-ray crystallography. In this review we consider some of the numerous ways in which modelling can be used to interpret and rationalise experimental data and in constructing hypotheses that can be tested by experiment. Genome sequencing projects are producing a vast wealth of data describing the protein coding regions of the genome under study. However, only a minority of the protein sequences thus identified will have a clear sequence homology to a known protein. In such cases valuable three-dimensional models of the protein coding sequence can be constructed by homology modelling methods. Threading methods, which used specialised schemes to relate protein sequences to a library of known structures, have been shown to be able to identify the likely protein fold even in cases where there is no clear sequence homology. The number of protein sequences that cannot be assigned to a structural class by homology or threading methods, simply because they belong to a previously unidentified protein folding class, will decrease in the future as collaborative efforts in systematic structure determination begin to develop. For this reason, modelling methods are likely to become increasingly useful in the near future. The role of the blind prediction contests, such as the Critical Assessment of techniques for protein Structure Prediction (CASP), will be briefly discussed. Methods for modelling protein-ligand and protein-protein complexes are also described and examples of their applications given.

A divide and conquer approach to fast loop modeling

We describe a fast ab initio method for modeling local segments in protein structures. The algorithm is based on a divide and conquer approach and uses a database of precalculated look-up tables, which represent a large set of possible conformations for loop segments of variable length. The target loop is recursively decomposed until the resulting conformations are small enough to be compiled analytically. The algorithm, which is not restricted to any specific loop length, generates a ranked set of loop conformations in 20-180 s on a desktop PC. The prediction quality is evaluated in terms of global RMSD. Depending on loop length the top prediction varies between 1.06 A RMSD for three-residue loops and 3.72 A RMSD for eight-residue loops. Due to its speed the method may also be useful to generate alternative starting conformations for complex simulations.

ADAPT: a molecular mechanics approach for studying the structural properties of long DNA sequences

We describe an original approach to determining sequence-structure relationships for DNA. This approach, termed ADAPT, combines all-atom molecular mechanics with a multicopy algorithm to build nucleotides that contain all four standard bases in variable proportions. These nucleotides enable us to search very rapidly for base sequences that energetically favor chosen types of DNA deformation or chosen DNA-protein or DNA-ligand interactions. Sequences satisfying the chosen criteria can be found by energy minimization, combinatorial sequence searching, or genome scanning, in a manner similar to the threading approaches developed for protein structure prediction. In the latter case, we are able to analyze roughly 2000 base pairs per second. Applications of the method to DNA allomorphic transitions, DNA deformation, and specific DNA interactions are presented.

Ab initio modeling of small, medium, and large loops in proteins

This study presents different procedures for ab initio modeling of peptide loops of different sizes in proteins. Small loops (up to 8--12 residues) were generated by a straightforward procedure with subsequent "averaging" over all the low-energy conformers obtained. The averaged conformer fairly represents the entire set of low-energy conformers, root mean square deviation (RMSD) values being from 1.01 A for a 4-residue loop to 1.94 A for an 8-residue loop. Three-dimensional (3D) structures for several medium loops (20--30 residues) and for two large loops (54 and 61 residues) were predicted using residue-residue contact matrices divided into variable parts corresponding to the loops, and into a constant part corresponding to the known core of the protein. For each medium loop, a very limited number of sterically reasonable C(alpha) traces (from 1 to 3) was found; RMSD values ranged from 2.4 to 5.9 A. Single C(alpha) traces predicted for each of the large loops possessed RMSD values of 4.5 A. Generally, ab initio loop modeling presented in this work combines elements of computational procedures developed both for protein folding and for peptide conformational analysis.

Rigorous classical-mechanical derivation of a multiple-copy algorithm for sampling statistical mechanical ensembles

We derive a rigorous, multiple-copy simulation algorithm that is formally equivalent to conventional classical molecular dynamics for an ensemble of systems, but may be used for rapid geometry optimizations. The derivation is accomplished by starting from an ensemble of copies of the entire system and applying a point coordinate transformation to a large subsystem defined as the bath. After the transformation, each atom of the bath is described by one "major" set of coordinates located at the average position of the ensemble of equivalent atoms and a set of "minor" coordinates that when combined with the "major" coordinates represent exact dynamics. Neglecting the "minor" set of coordinates results in a Hamiltonian and a probability density equivalent to those used in existing multiple-copy methods. Neglecting Hamilton's equations of motion for the minor variables gives the equations of motion for locally enhanced sampling. Numerical tests indicate that the algorithm can recover exact molecular dynamics of the ensemble, conventional multiple-copy dynamics, or results of intermediate accuracy. Thus, the algorithm provides a rigorous basis for multiple-copy dynamics, resolves many of the uncertainties associated with their current implementations, and offers the potential for calculating ensemble average properties in conjunction with finding a system's global minimum energy geometry.

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.

Pathways of ligand clearance in acetylcholinesterase by multiple copy sampling

The clearance of seven different ligands from the deeply buried active-site of Torpedo californica acetylcholinesterase is investigated by combining multiple copy sampling molecular dynamics simulations, with the analysis of protein-ligand interactions, protein motion and the electrostatic potential sampled by the ligand copies along their journey outwards. The considered ligands are the cations ammonium, methylammonium, and tetramethylammonium, the hydrophobic methane and neopentane, and the anionic product acetate and its neutral form, acetic acid. We find that the pathways explored by the different ligands vary with ligand size and chemical properties. Very small ligands, such as ammonium and methane, exit through several routes. One involves the main exit through the mouth of the enzyme gorge, another is through the so-called back door near Trp84, and a third uses a side door at a direction of approximately 45 degrees to the main exit. The larger polar ligands, methylammonium and acetic acid, leave through the main exit, but the bulkiest, tetramethylammonium and neopentane, as well as the smaller acetate ion, remain trapped in the enzyme gorge during the time of the simulations. The pattern of protein-ligand contacts during the diffusion process is highly non-random and differs for different ligands. A majority is made with aromatic side-chains, but classical H-bonds are also formed. In the case of acetate, but not acetic acid, the anionic and neutral form, respectively, of one of the reaction products, specific electrostatic interactions with protein groups, seem to slow ligand motion and interfere with protein flexibility; protonation of the acetate ion is therefore suggested to facilitate clearance. The Poisson-Boltzmann formalism is used to compute the electrostatic potential of the thermally fluctuating acetylcholinesterase protein at positions actually visited by the diffusing ligand copies. Ligands of different charge and size are shown to sample somewhat different electrostatic potentials during their migration, because they explore different microscopic routes. The potential along the clearance route of a cation such as methylammonium displays two clear minima at the active and peripheral anionic site. We find moreover that the electrostatic energy barrier that the cation needs to overcome when moving between these two sites is small in both directions, being of the order of the ligand kinetic energy. The peripheral site thus appears to play a role in trapping inbound cationic ligands as well as in cation clearance, and hence in product release.

New efficient statistical sequence-dependent structure prediction of short to medium-sized protein loops based on an exhaustive loop classification

A bank of 13,563 loops from three to eight amino acid residues long, representing motifs between two consecutive regular secondary structures, has been derived from protein structures presenting less than 95 % sequence identity. Statistical analyses of occurrences of conformations and residues revealed length-dependent over-representations of particular amino acids (glycine, proline, asparagine, serine, and aspartate) and conformations (alphaL, epsilon, betaPregions of the Ramachandran plot). A position-dependent distribution of these occurrences was observed for N and C-terminal residues, which are correlated to the nature of the flanking regions. Loops of the same length were clustered into statistically meaningful families on the basis of their backbone structures when placed in a common reference frame, independent of the flanks. These clusters present significantly different distributions of sequence, conformations, and endpoint residue Calphadistances. On the basis of the sequence-structure correlation of this clustering, an automatic loop modeling algorithm was developed. Based on the knowledge of its sequence and of its flank backbone structures each query loop is assigned to a family and target loop supports are selected in this family. The support backbones of these target loops are then adjusted on flanking structures by partial exploration of the conformational space. Loop closure is performed by energy minimization for each support and the final model is chosen among connected supports based upon energy criteria. The quality of the prediction is evaluated by the root-mean-square deviation (rmsd) between the final model and the native loops when the whole bank is re-attributed on itself with a Jackknife test. This average rmsd ranges from 1.1 A for three-residue loops to 3.8 A for eight-residue loops. A few poorly predicted loops are inescapable, considering the high level of diversity in loops and the lack of environment data. To overcome such modeling problems, a statistical reliability score was assigned for each prediction. This score is correlated to the quality of the prediction, in terms of rmsd, and thus improves the selection accuracy of the model. The algorithm efficiency was compared to CASP3 target loop predictions. Moreover, when tested on a test loop bank, this algorithm was shown to be robust when the loops are not precisely delimited, therefore proving to be a useful tool in practice for protein modeling.

Protein loops on structurally similar scaffolds: database and conformational analysis

A general problem in comparative modeling and protein design is the conformational evaluation of loops with a certain sequence in specific environmental protein frameworks. Loops of different sequences and structures on similar scaffolds are common in the Protein Data Bank (PDB). In order to explore both structural and sequential diversity of them, a data base of loops connecting similar secondary structure fragments is constructed by searching the data base of families of structurally similar proteins and PDB. A total of 84 loop families having 2-13 residues are found among the well-determined structures of resolution better than 2.5 A. Eight alpha-alpha, 20 alpha-beta, 19 beta-alpha, and 37 beta-beta families are identified. Every family contains more than 5 loop motifs. In each family, no loops share same sequence and all the frameworks are well superimposed. Forty-three new loop classes are distinguished in the data base. The structural variability of loops in homologous proteins are examined and shown in 44 families. Motif families are characterized with geometric parameters and sequence patterns. The conformations of loops in each family are clustered into subfamilies using average linkage cluster analysis method. Information such as geometric properties, sequence profile, sequential and structural variability in loop, structural alignment parameters, sequence similarities, and clustering results are provided. Correlations between the conformation of loops and loop sequence, motif sequence, and global sequence of PDB chain are examined in order to find how loop structures depend on their sequences and how they are affected by the local and global environment. Strong correlations (R > 0.75) are only found in 24 families. The best R value is 0.98. The data base is available through the Internet.

Molecular modeling of an active loop structure in lysozyme. Sequence effects or crystal packing?

The Val99-Gly 104 variable region in egg white lysozyme is part of the active site cleft and of the epitope recognized by some monoclonal antibodies. In general, this loop is found in a conformation inflected towards the active site (proximal conformational) such as in free hen lysozyme (HEL). But in a lysozyme such as Japanese quail's (JEL), the loop turns away from the active site cleft (distal conformation). In order to differentiate sequence effects from crystal packing, we generated and refined loop conformations for the 99-104 variable region in lysozyme, then estimated their relative conformational free energies. Some of the results indicate that (i) the flexibility of the 99-104 segment is much greater for HEL than for JEL sequences when unconstrained by the crystal lattice, (ii) for JEL, only distal structures are favored, while for HEL the states span the zone between proximal and distal regions, and (iii) epitopes elucidated from crystal structures may not always be conserved in solution. For the JEL loop, model building shows that an energy-costly distal to proximal transition appears necessary. Finally, analysis of available structural data indicates that changes of humidity, temperature and pressure on loop conformation are negligible.

Conformational sampling of CDR-H3 in antibodies by multicanonical molecular dynamics simulation

The diversity in the lengths and the amino acid sequences of the third complementarity determining region of the antibody heavy chain (CDR-H3) has made it difficult to establish a relationship between the sequences and the tertiary structures, in contrast to the other CDRs, which are classified by their canonical structures. Enhanced conformational sampling of two different CDR-H3s was performed by multicanonical molecular dynamics (multicanonical MD) simulation while restricting the base structures, with and without the other surrounding CDR segments. The results showed that the multicanonical MD sampled a much larger conformational space than the conventional MD, independent of the initial conformations of the simulations. When the other CDRs surrounding the CDR-H3 segments were included in the calculations, the predominant conformations at 300 K corresponded to the X-ray crystal structures. When only the single CDR-H3 loops were considered with the restricted base structures, a greater number of different conformations were sampled as putative loops, but only a small number of stable conformations appeared at 300 K. Analyses of the resultant conformations revealed a structural role for the glycine, when it is located at position three residues before the last residue of CDR-H3 (Gly-X-X-last residue), coincident with the statistical tendencies of many antibody crystal structures. This reflects the general consistency between the energetically stable conformations and the empirically observed conformations. The current method is expected to be applicable to the structural modeling and the design of antibodies, especially for the inherently flexible loops.

PDB-based protein loop prediction: parameters for selection and methods for optimization

An approach to loop prediction that starts with a database search is presented and analyzed. To obtain meaningful statistics, 130 loops from 21 proteins were studied. The correlation between the internal conformation of the loop and the conformation of the neighboring stem residues was examined. Distances between C(alpha) and C(beta) of the immediate neighbor residues at each end select template loops as well as more complex (e.g. three residues on either side) matching criteria. To have a high probability that the best possible loop candidate in the database is included in the set, relatively large cutoffs for matching the interatomic distances of the stem residues have to be used in the template loop selection procedure; for loops of length 5, this results in an average of 1000 loops and for loops of length 9, the number is about 1500. The required number increases only slowly with loop length, in contrast to the exponential time increase involved in direct searches of the conformational space. The best loops among the large number of candidates can be determined by ranking them with the standard CHARMM non-bonded energy function (without electrostatics) applied to the backbone and C(beta) atoms. The same representation (backbone plus C(beta)) can be used to optimize the loop orientations relative to the rest of the protein by constrained energy minimization. Target loops that have many non-bonded contacts with the protein yield better results so that analysis of the non-bonded contacts of the selected template loops is useful in determining the expected accuracy of a prediction. The method for loop selection and optimization predicted eight (out of 18) loops of up to nine residues to an RMSD better than 1.07 A relative to the crystal structure; for 17 of the 18 loops, one of the three lowest energy template loops had an RMSD of less than 1.79 A. The prediction of antibody loops from a database search is more effective than that for non-antibody loops. Provided that they belong to one of the canonical classes, very similar antibody loops are certain to exist in the database. Superposition of the stem residues for antibody loops also results in a better orientation than with arbitrary target loops because the neighboring residues tend to have a more similar beta-strand structure. Two H3 loops (for which no canonical structures have been proposed) were predicted with reasonable accuracy (RMSD of 0.49 A and 1.07 A) even though no corresponding antibody loops were in the database.

Structural classification of CDR-H3 in antibodies

Large varieties in the lengths and the amino acid sequences of the third complementarity determining region of the antibody heavy chain (CDR-H3) have made it difficult to establish a relationship between the sequences and the tertiary structures, in contrast to the other CDRs, which are classified by their canonical structures. A total of 55 CDR-H3 segments from well determined crystal structures were analyzed, and we have derived several remarkable rules, which could partly govern the CDR-H3 conformation dependence on the sequence. Since the rules are physically reasonable, they are expected to be applicable to structural modeling and design of antibodies.

Constructing optimal backbone segments for joining fixed DNA base pairs

A method is presented to link a sequence of space-fixed base pairs by the sugar-phosphate segments of single nucleotides and to evaluate the effects in the backbone caused by this positioning of the bases. The entire computational unit comprises several nucleotides that are energy-minimized, subject to constraints imposed by the sugar-phosphate backbone segments being anchored to space-fixed base pairs. The minimization schemes are based on two stages, a conjugate gradient method followed by a Newton-Raphson algorithm. Because our purpose is to examine the response, or relaxation, of an artificially stressed backbone, it is essential to be able to obtain, as closely as possible, a lowest minimum energy conformation of the backbone segment in conformational space. For this purpose, an algorithm is developed that leads to the generation of an assembly of many local energy minima. From these sets of local minima, one conformation corresponding to the one with the lowest minimum is then selected and designated to represent the backbone segment at its minimum. The effective electrostatic potential of mean force is expressed in terms of adjustable parameters that incorporate solvent screening action in the Coulombic interactions between charged backbone atoms; these parameters are adjusted to obtain the best fit of the nearest-neighbor phosphorous atoms in an x-ray structure.

Computational screening of combinatorial libraries

We first review existing computational methods with an intrinsic combinatorial feature, then describe a new computational method for screening combinatorial libraries using a recently developed multicopy sampling technique. The new method differs from the existing ones in that it can be used to screen simultaneously an entire library of molecules, instead of the individual molecules in a library. As an example, we have applied the method to study site-directed amino acid substitutions in a protein. After two rounds of library screening, we identified the energetically most stable substitutions along with their optimal conformations from all natural amino acids. In principle, the method is generally applicable to study ligand-host systems.

Mean-field minimization methods for biological macromolecules

Simulations of macromolecular structures involve the minimization of a potential-energy function that presents many local minima. Mean-field theory provides a tool that enables us to escape these minima, by enhancing sampling in conformational space. The number of applications of this technique has increased significantly over the past year, enabling problems with protein-homology modelling and inverted protein structure prediction to be solved.

Modeling side-chain conformation

Over the past few years, a number of methods for the calculation of side-chain conformations in proteins have been described. More recent studies have considered the effect of combinatorial packing, derivations from idealized rotameric structures and, to a limited extent, backbone flexibility on the quality and efficiency of calculations of protein side-chain conformation. Although further work is needed to address the issue of backbone displacements, the recent progress solves the packing problem to a significant degree. This opens the way for fruitful incorporation of these methods into general procedures for homology modeling and studies of ligand-protein interactions.

Accuracy and reliability of the scaling-relaxation method for loop closure: an evaluation based on extensive and multiple copy conformational samplings

The accuracy and reliability of the recently proposed scaling-relaxation method for loop closure were examined by using extensive conformational sampling. For each of the eight heptapeptides chosen to represent a variety of protein conformations, 1,000-2,000 conformations were sampled. Each segment contained 14 rotatable backbone dihedral angles. The average root mean square deviations (RMSDs) between the predicted and the native conformations were 0.7 angstrom for the backbone and 1.2 angstroms for the side chain atoms. These predictions were substantially more accurate than the previous predictions (1.1 angstroms for the backbone and 2.2 angstroms for the side chain atoms) of the same eight protein segments based on limited conformational sampling (100 conformations for each segment). Large prediction errors mostly occurred at polar and surface side chains that are unlikely to have any meaningful conformation. Moreover, the reliability of seven of the eight predictions was demonstrated with their energy-RMSD and stability-RMSD correlations of the low-energy conformations, where the conformational stability was estimated by using the multiple copy simultaneous sampling method.

Modeling mutations and homologous proteins

A protein sequence with at lease 40% identity to a known structure can now be modelled automatically, with an accuracy approaching that o fa low-resolution X-ray structure or a medium-resolution nuclear magnetic resonance structure. In general, these models have goods stereochemistry and an overall structural accuracy that is as high as the similarity between the template and the actual structure being predicted. As a result, the number of sequences that can be modelled is an order of magnitude larger then the number of experimentally determined protein structures. In addition, evaluation techniques are available that can estimated errors in different regions of the model. Thus, the number of applications where homology modelling is proving useful is growing rapidly.

A self consistent mean field approach to simultaneous gap closure and side-chain positioning in homology modelling

A new computational procedure which simultaneously provides gap closure and side-chain positioning in homology modelling is described. It uses a database search scheme to generate fragments to model gaps, a rotamer library to define side-chain conformations, and iteratively refines a conformational matrix CM, such that its elements CM(i,j,o) and CM(i,j,k) give the probabilities that the backbone of residue i adopts the conformation described by fragment j and that its side-chain adopts the conformation of its possible rotamer k. Each residue experiences the average of all possible environments, weighted by their respective probabilities. The method converges, thereby deserving the name of 'self consistent mean field' approach.

Multiple copy sampling: rigid versus flexible protein

Effects of protein flexibility on multiple copy conformational sampling were systematically evaluated by studying the side-chain placement of Phe-14 in protein Zif268. The multiple copy sampling is shown to be significantly more efficient when a flexible but harmonically constrained protein is used instead of a rigid protein. A range of constraint force from 1 to 25 kcal/mol.A per atom is determined to be sufficient to prevent the protein from distortion while allowing the protein to fluctuate for enhanced sampling. The protein fluctuations are essential in smoothing the effective energy surface as shown by the opening-closing of a protein hydrophobic pocket during a multiple copy energy minimization, a phenomenon that has been previously observed only in molecular dynamics. These results provide a practical guidance for applying the multiple copy techniques to molecular modeling and computer-aided drug design.