Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.     

Hsc70-interacting HPD loop of the J domain of polyomavirus T antigens fluctuates in ps to ns and micros to ms

The backbone dynamics of the J domain from polyomavirus T antigens have been investigated using 15N NMR relaxation and molecular dynamics simulation. Model-free relaxation analysis revealed picosecond to nanosecond motions in the N terminus, the I-II loop, the C-terminal end of helix II through the HPD loop to the beginning of helix III, and the C-terminal end of helix III to the C terminus. The backbone dynamics of the HPD loop and termini are dominated by motions with moderately large amplitudes and correlation times of the order of a nanosecond or longer. Conformational exchange on the microsecond to millisecond timescale was identified in the HPD loop, the N and C termini, and the I-II loop. A 9.7ns MD trajectory manifested concerted swings of the HPD loop. Transitions between major and minor conformations of the HPD loop featured distinct patterns of change in backbone dihedral angles and hydrogen bonds. Fraying of the C-terminal end of helix II and the N-terminal end of helix III correlated with displacements of the HPD loop. Correlation of crankshaft motions of Gly46 and Gly47 with the collective motions of the HPD loop suggested an important role of the two glycine residues in the mobility of the loop. Fluctuations of the HPD loop correlated with relative reorientation of side-chains of Lys35 and Asp44 that interact with Hsc70.     

SymmRef: a flexible refinement method for symmetric multimers

Symmetric protein complexes are abundant in the living cell. Predicting their atomic structure can shed light on the mechanism of many important biological processes. Symmetric docking methods aim to predict the structure of these complexes given the unbound structure of a single monomer, or its model. Symmetry constraints reduce the search-space of these methods and make the prediction easier compared to asymmetric protein-protein docking. However, the challenge of modeling the conformational changes that the monomer might undergo is a major obstacle. In this article, we present SymmRef, a novel method for refinement and reranking of symmetric docking solutions. The method models backbone and side-chain movements and optimizes the rigid-body orientations of the monomers. The backbone movements are modeled by normal modes minimization and the conformations of the side-chains are modeled by selecting optimal rotamers. Since solved structures of symmetric multimers show asymmetric side-chain conformations, we do not use symmetry constraints in the side-chain optimization procedure. The refined models are re-ranked according to an energy score. We tested the method on a benchmark of unbound docking challenges. The results show that the method significantly improves the accuracy and the ranking of symmetric rigid docking solutions. SymmRef is available for download at http:// bioinfo3d.cs.tau.ac.il/SymmRef/download.html.     

A comparison of the dynamic behavior of monomeric and dimeric insulin shows structural rearrangements in the active monomer

Molecular dynamics (MD) simulations (5-10ns in length) and normal mode analyses were performed for the monomer and dimer of native porcine insulin in aqueous solution; both starting structures were obtained from an insulin hexamer. Several simulations were done to confirm that the results obtained are meaningful. The insulin dimer is very stable during the simulation and remains very close to the starting X-ray structure; the RMS fluctuations calculated from the MD simulation agree with the experimental B-factors. Correlated motions were found within each of the two monomers; they can be explained by persistent non-bonded interactions and disulfide bridges. The correlated motions between residues B24 and B26 of the two monomers are due to non-bonded interactions between the side-chains and backbone atoms. For the isolated monomer in solution, the A chain and the helix of the B chain are found to be stable during 5ns and 10ns MD simulations. However, the N-terminal and the C-terminal parts of the B chain are very flexible. The C-terminal part of the B chain moves away from the X-ray conformation after 0.5-2.5ns and exposes the N-terminal residues of the A chain that are thought to be important for the binding of insulin to its receptor. Our results thus support the hypothesis that, when monomeric insulin is released from the hexamer (or the dimer in our study), the C-terminal end of the monomer (residues B25-B30) is rearranged to allow binding to the insulin receptor. The greater flexibility of the C-terminal part of the beta chain in the B24 (Phe-->Gly) mutant is in accord with the NMR results. The details of the backbone and side-chain motions are presented. The transition between the starting conformation and the more dynamic structure of the monomers is characterized by displacements of the backbone of Phe B25 and Tyr B26; of these, Phe B25 has been implicated in insulin activation.     

Thermal Fluctuations in Amphipol A8-35 Particles: A Neutron Scattering and Molecular Dynamics Study

Amphipols are a class of polymeric surfactants that can stabilize membrane proteins in aqueous solutions as compared to detergents. A8-35, the best-characterized amphipol to date, is composed of a polyacrylate backbone with ~35 % of the carboxylates free, ~25 % grafted with octyl side-chains, and ~40 % with isopropyl ones. In aqueous solutions, A8-35 self-organizes into globular particles with a molecular mass of ~40 kDa. The thermal dynamics of A8-35 particles was measured by neutron scattering in the 10-picosecond, 18-picosecond, and 1-nanosecond time-scales on natural abundance and deuterium-labeled molecules, which permitted to separate backbone and side-chain motions. A parallel analysis was performed on molecular dynamics trajectories (Perlmutter et al., Langmuir 27:10523–10537, 2011). Experimental results and simulations converge, from their respective time-scales, to show that A8-35 particles feature a more fluid hydrophobic core, predominantly containing the octyl chains, and a more rigid solvent-exposed surface, made up predominantly of the hydrophilic polymer backbone. The fluidity of the core is comparable to that of the lipid environment around proteins in the center of biological membranes, as also measured by neutron scattering. The biological activity of proteins depends sensitively on molecular dynamics, which itself is strongly dependent on the immediate macromolecular environment. In this context, the characterization of A8-35 particle dynamics constitutes a step toward understanding the effect of amphipols on membrane protein stability and function.     

Projection Methods for the Analysis of Complex Motions in Macromolecules

Abstract

In studies of macromolecular dynamics it is often desirable to analyze complex motions in terms of a small number of coordinates. Only for simple types of motion, e.g., rigid-body motions, these coordinates can be easily constructed from the Cartesian atomic coordinates. This article presents an approach that is applicable to infinitesimal or approximately infinitesimal motions, e.g., Cartesian velocities, normal modes, or atomic fluctuations. The basic idea is to characterize the subspace of interesting motions by a set of (possibly linearly dependent) vectors describing elementary displacements, and then project the dynamics onto this subspace. Often the elementary displacements can be found by physical intuition. The restriction to small displacements facilitates the study of complicated coupled motions and permits the construction of collective-motion subspaces that do not correspond to any set of generalized coordinates.

As an example for this technique, we analyze the low-frequency normal modes of proteins up to ≈ 20 THz (600 cm^?1) in order to see what kinds of motions occupy which frequency range. This kind of analysis is useful for the interpretation of spectroscopic measurements on proteins, e.g., inelastic neutron scattering experiments.     

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from ¹⁵N relaxation and side-chain dynamics from ¹³C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.     

The influence of solvent composition on global dynamics of human butyrylcholinesterase powders: a neutron-scattering study

A major result of incoherent elastic neutron-scattering experiments on protein powders is the strong dependence of the intramolecular dynamics on the sample environment. We performed a series of incoherent elastic neutron-scattering experiments on lyophilized human butyrylcholinesterase (HuBChE) powders under different conditions (solvent composition and hydration degree) in the temperature range from 20 to 285 K to elucidate the effect of the environment on the enzyme atomic mean-square displacements. Comparing D(2)O- with H(2)O-hydrated samples, we were able to investigate protein as well as hydration water molecular dynamics. HuBChE lyophilized from three distinct buffers showed completely different atomic mean-square displacements at temperatures above approximately 200 K: a salt-free sample and a sample containing Tris-HCl showed identical small-amplitude motions. A third sample, containing sodium phosphate, displayed highly reduced mean-square displacements at ambient temperature with respect to the other two samples. Below 200 K, all samples displayed similar mean-square displacements. We draw the conclusion that the reduction of intramolecular protein mean-square displacements on an Angstrom-nanosecond scale by the solvent depends not only on the presence of salt ions but also on their type.     

Side-chain dynamics of the SAP SH2 domain correlate with a binding hot spot and a region with conformational plasticity

X-linked lymphoproliferative disease is caused by mutations in the protein SAP, which consists almost entirely of a single SH2 domain. SAP interacts with the Tyr281 site of the T<-->B cell signaling protein SLAM via its SH2 domain. Interestingly, binding is not dependent on phosphorylation but does involve interactions with residues N-terminal to the Tyr. We have used 15N and 2H NMR relaxation experiments to investigate the motional properties of the SAP SH2 domain backbone amides and side-chain methyl groups in the free protein and complexes with phosphorylated and non-phosphorylated peptides derived from the Tyr281 site of SLAM. The most mobile methyl groups are in side-chains with large RMSD values between the three crystal structures of SAP, suggesting that fast time-scale dynamics in side-chains is associated with conformational plasticity. The backbone amides of two residues which interact with the C-terminal part of the peptides experience fast time-scale motions in the free SH2 domain that are quenched upon binding of either the phosphorylated or non-phosphorylated peptide. Of most importance, the mobility of methyl groups in and around the binding site for residues in the N-terminus of the peptide is significantly restricted in the complexes, underscoring the dominance of this interaction with SAP and demonstrating a correlation between changes in rapid side-chain motion upon binding with local binding energy.     

FireDock: fast interaction refinement in molecular docking

Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

A molecular dynamics simulation of bacteriophage T4 lysozyme.

An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. The simulation was carried out with all hydrogen atoms modeled explicitly, the inclusion of all 152 crystallographic waters and at a temperature of 300 K. Temporal analysis of the trajectory versus energy, hydrogen bond stability, r.m.s. deviation from the starting crystal structure and radius of gyration, demonstrates that the simulation was both stable and representative of the average experimental structure. Average structural properties were calculated from the enzyme trajectory and compared with the crystal structure. The mean value of the C alpha displacements of the average simulated structure from the X-ray structure was 1.1 +/- 0.1 A; differences of the backbone phi and psi angles between the average simulated structure and the crystal structure were also examined. Thermal-B factors were calculated from the simulation for heavy and backbone atoms and both were in good agreement with experimental values. Relationships between protein secondary structure elements and internal motions were studied by examining the positional fluctuations of individual helix, sheet and turn structures. The structural integrity in the secondary structure units was preserved throughout the simulation; however, the A helix did show some unusually high atomic fluctuations. The largest backbone atom r.m.s. fluctuations were found in non-secondary structure regions; similar results were observed for r.m.s. fluctuations of non-secondary structure phi and psi angles. In general, the calculated values of r.m.s. fluctuations were quite small for the secondary structure elements. In contrast, surface loops and turns exhibited much larger values, being able to sample larger regions of conformational space. The C alpha difference distance matrix and super-positioning analyses comparing the X-ray structure with the average dynamics structure suggest that a 'hinge-bending' motion occurs between the N- and C-terminal domains.     

Atomic mean-square displacements in proteins by molecular dynamics: a case for analysis of variance

Information on protein internal motions is usually obtained through the analysis of atomic mean-square displacements, which are a measure of variability of the atomic positions distribution functions. We report a statistical approach to analyze molecular dynamics data on these displacements that is based on probability distribution functions. Using a technique inspired by the analysis of variance, we compute unbiased, reliable mean-square displacements of the atoms and analyze them statistically. We applied this procedure to characterize protein thermostability by comparing the results for a thermophilic enzyme and a mesophilic homolog. In agreement with previous experimental observations, our analysis suggests that the proteins surface regions can play a role in the different thermal behavior.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Systematic Study of Anharmonic Features in a Principal Component Analysis of Gramicidin A

We use principal component analysis (PCA) to detect functionally interesting collective motions in molecular-dynamics simulations of membrane-bound gramicidin A. We examine the statistical and structural properties of all PCA eigenvectors and eigenvalues for the backbone and side-chain atoms. All eigenvalue spectra show two distinct power-law scaling regimes, quantitatively separating large from small covariance motions. Time trajectories of the largest PCs converge to Gaussian distributions at long timescales, but groups of small-covariance PCs, which are usually ignored as noise, have subdiffusive distributions. These non-Gaussian distributions imply anharmonic motions on the free-energy surface. We characterize the anharmonic components of motion by analyzing the mean-square displacement for all PCs. The subdiffusive components reveal picosecond-scale oscillations in the mean-square displacement at frequencies consistent with infrared measurements. In this regime, the slowest backbone mode exhibits tilting of the peptide planes, which allows carbonyl oxygen atoms to provide surrogate solvation for water and cation transport in the channel lumen. Higher-frequency modes are also apparent, and we describe their vibrational spectra. Our findings expand the utility of PCA for quantifying the essential features of motion on the anharmonic free-energy surface made accessible by atomistic molecular-dynamics simulations.     

Structural dynamics of liganded myoglobin.

X-ray crystallography can reveal the magnitudes and principal directions of the mean-square displacements of every atom in a protein. This structural information is complementary to the temporal information obtainable by spectroscopic techniques such as nuclear magnetic resonance. Determination of the temperature dependence of the mean-square displacements makes it possible to separate large conformational motions from simple thermal vibrations. The contribution of crystal lattice disorder to the overall apparent displacement can be estimated by Mössbauer spectroscopy. This technique has been applied to high resolution x-ray diffraction data from sperm whale myoglobin in its Met iron and oxy cobalt forms. Both crystal structures display regions of large conformational motions, particularly at the chain termini and in the region of the proximal histidine. Overall, the mean-square displacement increases with increasing distance from the center of gravity of the molecule. Some regions of the heme pocket in oxy cobalt myoglobin are more rigid than the corresponding regions in Met myoglobin.     

Combination of Neutron Scattering and Molecular Dynamics to Determine Internal Motions in Biomolecules

Abstract

The forms and frequencies of atomic dynamics on the pico- and nanosecond timescales are accessible experimentally using incoherent neutron scattering. Molecular dynamics simulations cover the same space and time domains and neutron scattering intensities can be calculated from the simulations for direct comparison with experiment. To illustrate the complementarity of neutron scattering and molecular dynamics we examine measured and simulation-derived elastic incoherent scattering profiles from myoglobin and from the crystalline alanine dipeptide. Elastic incoherent scattering gives information on the geometry of the volume accessible to the atoms in the samples. The simulation-derived dipeptide elastic scattering profiles are in reasonable accord with experiment, deviations being due to the sampling limitations in the simulations and experimental detector normalisation procedures. The simulated dynamics is decomposed, revealing characteristic profiles due to rotational diffusional and translational vibrational motions of the methyl groups. In myoglobin, for which the timescale of the simulation matches more closely that accessible to the experiment, good agreement is seen for the elastic incoherent structure factor. This indicates that the space sampled by the hydrogen atoms in the protein on the timescale <100 ps is well represented by the simulation. Part of the helix atom fluctuations can be described in terms of rigid helix motions.     

Progress in protein-protein docking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of side-chain flexibility

RosettaDock uses real-space Monte Carlo minimization (MCM) on both rigid-body and side-chain degrees of freedom to identify the lowest free energy docked arrangement of 2 protein structures. An improved version of the method that uses gradient-based minimization for off-rotamer side-chain optimization and includes information from unbound structures was used to create predictions for Rounds 4 and 5 of CAPRI. First, large numbers of independent MCM trajectories were carried out and the lowest free energy docked configurations identified. Second, new trajectories were started from these lowest energy structures to thoroughly sample the surrounding conformation space, and the lowest energy configurations were submitted as predictions. For all cases in which there were no significant backbone conformational changes, a small number of very low-energy configurations were identified in the first, global search and subsequently found to be close to the center of the basin of attraction in the free energy landscape in the second, local search. Following the release of the experimental coordinates, it was found that the centers of these free energy minima were remarkably close to the native structures in not only the rigid-body orientation but also the detailed conformations of the side-chains. Out of 8 targets, the lowest energy models had interface root-mean-square deviations (RMSDs) less than 1.1 A from the correct structures for 6 targets, and interface RMSDs less than 0.4 A for 3 targets. The predictions were top submissions to CAPRI for Targets 11, 12, 14, 15, and 19. The close correspondence of the lowest free energy structures found in our searches to the experimental structures suggests that our free energy function is a reasonable representation of the physical chemistry, and that the real space search with full side-chain flexibility to some extent solves the protein-protein docking problem in the absence of significant backbone conformational changes. On the other hand, the approach fails when there are significant backbone conformational changes as the steric complementarity of the 2 proteins cannot be modeled without incorporating backbone flexibility, and this is the major goal of our current work.     

High-resolution solution structure of reduced French bean plastocyanin and comparison with the crystal structure of poplar plastocyanin

The three-dimensional solution structure of reduced (CuI) plastocyanin from French bean leaves has been determined by distance geometry and restrained molecular dynamics methods using constraints obtained from 1H n.m.r. (nuclear magnetic resonance) spectroscopy. A total of 1244 experimental constraints were used, including 1120 distance constraints, 103 dihedral angle constraints and 21 hydrogen bond constraints. Stereospecific assignments were made for 26 methylene groups and the methyls of 11 valines. Additional constraints on copper co-ordination were included in the restrained dynamics calculations. The structures are well defined with average atomic root-mean-square deviations from the mean of 0.45 A for all backbone heavy atoms and 1.08 A for side-chain heavy atoms. French bean plastocyanin adopts a beta-sandwich structure in solution that is similar to the X-ray structure of reduced poplar plastocyanin; the average atomic root-mean-square difference between 16 n.m.r. structures and the X-ray structure is 0.76 A for all backbone heavy atoms. The conformations of the side-chains that constitute the hydrophobic core of French bean plastocyanin are very well defined. Of 47 conserved residues that populate a single chi 1 angle in solution, 43 have the same rotamer in the X-ray structure. Many surface side-chains adopt highly preferred conformations in solution, although the 3J alpha beta coupling constants often indicate some degree of conformational averaging. Some surface side-chains are disordered in both the solution and crystal structures of plastocyanin. There is a striking correlation between measures of side-chain disorder in solution and side-chain temperature factors in the X-ray structure. Side-chains that form a distinctive acidic surface region, believed to be important in binding other electron transfer proteins, appear to be disordered. Fifty backbone amide protons form hydrogen bonds to carbonyls in more than 60% of the n.m.r. structures; 45 of these amide protons exchange slowly with solvent deuterons. Ten hydrogen bonds are formed between side-chain and backbone atoms, eight of which are correlated with decreased proton exchange. Of the 60 hydrogen bonds formed in French bean plastocyanin, 56 occur in the X-ray structure of the poplar protein; two of the missing hydrogen bonds are absent as a result of mutations. It appears that molecular dynamics refinement of highly constrained n.m.r. structures allows accurate prediction of the pattern of hydrogen bonding.     

A molecular dynamics study of the C-terminal fragment of the L7/L12 ribosomal protein. Secondary structure motion in a 150 picosecond trajectory

A 150 picosecond molecular dynamics computer simulation of the C-terminal fragment of the L7/L12 ribosomal protein from Escherichia coli is reported. The molecular dynamics results are compared with the available high-resolution X-ray data in terms of atomic positions, distances and positional fluctuations. Good agreement is found between the molecular dynamics results and the X-ray data. The form and parameters of the interaction potential energy function and the procedures for deriving it are discussed. Some current misunderstandings concerning the ways of evaluating the efficiency of molecular dynamics algorithms and of application of bond-length constraints in protein simulations are cleared up. The 150 picosecond trajectory has been scanned in a search for correlated motions within and between secondary structure elements. The beta-strands have diffusional stretching modes, and uncorrelated transversal displacements. The dynamic analysis of alpha-helices shows a variety of features. The atomic fluctuations differ between the helix ends; this effect reflects long time-scale motions. Two alpha-helices, alpha A and alpha C, show diffusive longitudinal stretching modes. The third helix, alpha B, has a correlated asymmetric longitudinal stretching; the N-terminal part dominates this behaviour. Furthermore, alpha B presents a librational motion with respect to the other parts of the molecule with a frequency of approximately 5 cm-1. This motion is coupled to helix stretching. Interestingly, the regions of highly conserved residues contain the most mobile parts of the molecule.