Analysis of domain motions in large proteins

Comment on elastic network models and proteins

Elastic network models have been used to study the properties of coarse grained models of proteins and larger biomolecular complexes. In this comment, we point out that it is important to build rotational symmetry, as well as translational symmetry, into these models that are designed to describe the rigidity, and the associated low-frequency deformations. This leads to strong restrictions on what form of interactions can be used. In particular, the only allowed two-center harmonic interactions are those corresponding to Hooke springs. Additional complexity can be introduced if required by using three-center harmonic interactions.

vGNM: a better model for understanding the dynamics of proteins in crystals

The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new GNM, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified and others to become less important. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.

Hierarchical and multi-resolution representation of protein flexibility

MOTIVATION

Conformational rearrangements during molecular interactions are observed in a wide range of biological systems. However, computational methods that aim at simulating and predicting molecular interactions are still largely ignoring the flexible nature of biological macromolecules as the number of degrees of freedom is computationally intractable when using brute force representations.

RESULTS

In this article, we present a computational data structure called the Flexibility Tree (FT) that enables a multi-resolution and hierarchical encoding of molecular flexibility. This tree-like data structure allows the encoding of relatively small, yet complex sub-spaces of a protein's conformational space. These conformational sub-spaces are parameterized by a small number of variables and can be searched efficiently using standard global search techniques. The FT structure makes it straightforward to combine and nest a wide variety of motion types such as hinge, shear, twist, screw, rotameric side chains, normal modes and essential dynamics. Moreover, the ability to assign shapes to the nodes in a FT allows the interactive manipulation of flexible protein shapes and the interactive visualization of the impact of conformational changes on the protein's overall shape. We describe the design of the FT and illustrate the construction of such trees to hierarchically combine motion information obtained from a variety of sources ranging from experiment to user intuition, and describing conformational changes at different biological scales. We show that the combination of various types of motion helps refine the encoded conformational sub-spaces to include experimentally determined structures, and we demonstrate searching these sub-spaces for specific conformations.

Luminescent metal-ligand complexes as probes of macromolecular interactions and biopolymer dynamics

The knowledge of microsecond dynamics is important for an understanding of the mechanism and function of biological systems. Fluorescent techniques are well established in biophysical studies, but their applicability to probe microsecond timescale processes is limited. Luminescent metal-ligand complexes (MLCs) have created interest mainly due to their unique luminescent properties, such as the exceptionally long decay times and large fundamental anisotropy values, allowing examination of microsecond dynamics by fluorescence methods. MLC properties also greatly simplify instrumentation requirements and enable the use of light emitting diode excitation for time-resolved measurements. Recent literature illustrates how MLC labels take full advantage of well developed fluorescence techniques and how those methods can be extended to timescales not easily accessible with nanosecond probes. MLCs are now commercially available as reactive labels which give researchers access to methods that previously required more complex approaches. The present paper gives an overview of the applications of MLC probes to studies of molecular dynamics and interactions of proteins, membranes and nucleic acids.

The change of protein intradomain mobility on ligand binding: is it a commonly observed phenomenon?

Analysis of changes in the dynamics of protein domains on ligand binding is important in several aspects: for the understanding of the hierarchical nature of protein folding and dynamics at equilibrium; for analysis of signal transduction mechanisms triggered by ligand binding, including allostery; for drug design; and for construction of biosensors reporting on the presence of target ligand in studied media. In this work we use the recently developed HCCP computational technique for the analysis of stabilities of dynamic domains in proteins, their intrinsic motions and of their changes on ligand binding. The work is based on comparative studies of 157 ligand binding proteins, for which several crystal structures (in ligand-free and ligand-bound forms) are available. We demonstrate that the domains of the proteins presented in the Protein DataBank are far more robust than it was thought before: in the majority of the studied proteins (152 out of 157), the ligand binding does not lead to significant change of domain stability. The exceptions from this rule are only four bacterial periplasmic transport proteins and calmodulin. Thus, as a rule, the pattern of correlated motions in dynamic domains, which determines their stability, is insensitive to ligand binding. This rule may be the general feature for a vast majority of proteins.

Wiggle-predicting functionally flexible regions from primary sequence

The Wiggle series are support vector machine-based predictors that identify regions of functional flexibility using only protein sequence information. Functionally flexible regions are defined as regions that can adopt different conformational states and are assumed to be necessary for bioactivity. Many advances have been made in understanding the relationship between protein sequence and structure. This work contributes to those efforts by making strides to understand the relationship between protein sequence and flexibility. A coarse-grained protein dynamic modeling approach was used to generate the dataset required for support vector machine training. We define our regions of interest based on the participation of residues in correlated large-scale fluctuations. Even with this structure-based approach to computationally define regions of functional flexibility, predictors successfully extract sequence-flexibility relationships that have been experimentally confirmed to be functionally important. Thus, a sequence-based tool to identify flexible regions important for protein function has been created. The ability to identify functional flexibility using a sequence based approach complements structure-based definitions and will be especially useful for the large majority of proteins with unknown structures. The methodology offers promise to identify structural genomics targets amenable to crystallization and the possibility to engineer more flexible or rigid regions within proteins to modify their bioactivity.

An enhanced elastic network model to represent the motions of domain-swapped proteins

Domain swapping is a process where two (or more) protein molecules form a dimer (or higher oligomer) by exchanging an identical domain. In this article, based on the observation that domains are rigid and hinge loops are highly flexible, we propose a new Elastic Network Model, domain-ENM, for domain-swapped proteins. In this model, the rigidity of domains is taken into account by using a larger spring constant for intradomain contacts. The large-scale transition of domain swapping is then novelly decomposed into the relative motion between the rigid domains (only 6 degrees of freedom) plus the internal fluctuations of each domain. Consequently, this approach has the potential to produce much more meaningful transition pathways than other simulation approaches that try to find pathways in a search space of large numbers of dimensions. In this article, we also propose a new way to define the overlap measure. Past approaches used an inappropriate comparison of the large-scale conformation displacement against the computed infinitesimal motions of modes. Here, we propose an infinitesimal version of the large-scale conformation change and then compare it with the modes of motions. As a result, we obtain much better overlap values. Using this new overlap definition, we are also able for the first time to give a clear, intuitive explanation why "open" forms tend to produce better overlap values than "closed" forms with traditional ENMs. Finally, as an application, we present a simple approach to show how domain-ENM can be used to generated transition pathways for domain-swapped proteins.

Dynamic protein domains: identification, interdependence, and stability

Existing methods of domain identification in proteins usually provide no information about the degree of domain independence and stability. However, this information is vital for many areas of protein research. The recently developed hierarchical clustering of correlation patterns (HCCP) technique provides machine-based domain identification in a computationally simple and physically consistent way. Here we present the modification of this technique, which not only allows determination of the most plausible number of dynamic domains but also makes it possible to estimate the degree of their independence (the extent of correlated motion) and stability (the range of environmental conditions, where domains remain intact). With this technique we provided domain assignments and calculated intra- and interdomain correlations and interdomain energies for >2500 test proteins. It is shown that mean intradomain correlation of motions can serve as a quantitative criterion of domain independence, and the HCCP stability gap is a measure of their stability. Our data show that the motions of domains with high stability are usually independent. In contrast, the domains with moderate stability usually exhibit a substantial degree of correlated motions. It is shown that in multidomain proteins the domains are most stable if they are of similar size, and this correlates with the observed abundance of such proteins.

Automatic domain decomposition of proteins by a Gaussian Network Model

Proteins are often comprised of domains of apparently independent folding units. These domains can be defined in various ways, but one useful definition divides the protein into substructures that seem to move more or less independently. The same methods that allow fairly accurate calculation of motion can be used to help classify these substructures. We show how the Gaussian Network Model (GNM), commonly used for determining motion, can also be adapted to automatically classify domains in proteins. Parallels between this physical network model and graph theory implementation are apparent. The method is applied to a nonredundant set of 55 proteins, and the results are compared to the visual assignments by crystallographers. Apart from decomposing proteins into structural domains, the algorithm can generally be applied to any large macromolecular system to decompose it into motionally decoupled sub-systems.

Membrane association, mechanism of action, and structure of Arabidopsis embryonic factor 1 (FAC1)

Embryonic factor 1 (FAC1) is one of the earliest expressed plant genes and encodes an AMP deaminase (AMPD), which is also an identified herbicide target. This report identifies an N-terminal transmembrane domain in Arabidopsis FAC1, explores subcellular fractionation, and presents a 3.3-A globular catalytic domain x-ray crystal structure with a bound herbicide-based transition state inhibitor that provides the first glimpse of a complete AMPD active site. FAC1 contains an (alpha/beta)(8)-barrel characterized by loops in place of strands 5 and 6 that places it in a small subset of the amidohydrolase superfamily with imperfect folds. Unlike tetrameric animal orthologs, FAC1 is a dimer and each subunit contains an exposed Walker A motif that may be involved in the dramatic combined K(m) (25-80-fold lower) and V(max) (5-6-fold higher) activation by ATP. Normal mode analysis predicts a hinge motion that flattens basic surfaces on each monomer that flank the dimer interface, which suggests a reversible association between the FAC1 globular catalytic domain and intracellular membranes, with N-terminal transmembrane and disordered linker regions serving as the anchor and attachment to the globular catalytic domain, respectively.

Investigating the local flexibility of functional residues in hemoproteins

It is now widely accepted that protein function depends not only on structure, but also on flexibility. However, the way mechanical properties contribute to catalytic mechanisms remains unclear. Here, we propose a method for investigating local flexibility within protein structures that combines a reduced protein representation with Brownian dynamics simulations. An analysis of residue fluctuations during the dynamics simulation yields a rigidity profile for the protein made up of force constants describing the ease of displacing each residue with respect to the rest of the structure. This approach has been applied to the analysis of a set of hemoproteins, one of the functionally most diverse protein families. Six proteins containing one or two heme groups have been studied, paying particular attention to the mechanical properties of the active-site residues. The calculated rigidity profiles show that active site residues are generally associated with high force constants and thus rigidly held in place. This observation also holds for diheme proteins if their mechanical properties are analyzed domain by domain. We note, however, that residues other than those in the active site can also have high force constants, as in the case of residues belonging to the folding nucleus of c-type hemoproteins.

Normal mode analysis of the horseradish peroxidase collective motions: Correlation with spectroscopically observed heme distortions

Horseradish peroxidase C is a class III peroxidase whose structure is stabilized by the presence of two endogenous calcium atoms. Calcium removal has been shown to decrease the enzymatic activity of the enzyme and significantly affect the spectroscopically detectable properties of the heme, such as the spin state of the iron, heme normal modes, and distortions from planarity. In this work, we report on normal mode analysis (NMA) performed on models subjected to 2 ns of molecular dynamics simulations to describe the effect of calcium removal on protein collective motions and to investigate the correlation between active site (heme) and protein matrix fluctuations. We show that in the native peroxidase model, heme fluctuations are correlated to matrix fluctuations while they are not in the calcium-depleted model.

Hierarchical clustering of the correlation patterns: New method of domain identification in proteins

New method of identification of dynamical domains in proteins - Hierarchical Clustering of the Correlation Patterns (HCCP) is proposed. HCCP allows to identify the domains using single three-dimensional structure of the studied proteins and does not require any adjustable parameters that can influence the results. The method is based on hierarchical clustering performed on the matrices of correlation patterns, which are obtained by the transformation of ordinary pairwise correlation matrices. This approach allows to extract additional information from the correlation matrices, which increases reliability of domain identification. It is shown that HCCP is insensitive to small variations of the pairwise correlation matrices. Particularly it produces identical results if the data obtained for the same protein crystallized with different spatial positions of domains are used for analysis. HCCP can utilize correlation matrices obtained by any method such as normal mode or essential dynamics analysis, Gaussian network or anisotropic network models, etc. These features make HCCP an attractive method for domain identification in proteins.

Characterization of protein matrix motions in the Rb. sphaeroides photosynthetic reaction center

We use Normal Mode Analysis to investigate motions in the photosynthetic reaction center (RC) protein. We identify the regions involved in concerted fluctuations of the protein matrix and analyze the normalized amplitudes and the directionality of the first few dominant modes. We also seek to quantify the coupling of normal modes to long-range electron transfer (ET). We find that a quasi-continuous spectrum of protein motions rather than one individual mode contributes to light-driven electron transfer. This is consistent with existing theoretical models (e.g. the spin-boson/dispersed polaron model) for the coupling of the protein and solvent "bath" to charge separation events. [Figure: see text].

Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP(5)A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of (15)N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg(+2)*ATP + AMP --> Mg(+2)*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time tau( perpendicular) and low order parameters, and fast (picoseconds) motions with correlation time tau( parallel) and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP(5)A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, tau( parallel) and tau( perpendicular) are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time tau( perpendicular), is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.

Comparison of tRNA motions in the free and ribosomal bound structures

A general method is presented that allows the separation of the rigid body motions from the nonrigid body motions of structural subunits when bound in a complex. The application presented considers the motions of the tRNAs: free, bound to the ribosome and to a synthase. We observe that both the rigid body and nonrigid body motions of the structural subunits are highly controlled by the large ribosomal assembly and are important for the functional motions of the assembly. For the intact ribosome, its major parts, the 30S and the 50S subunits, are found to have counterrotational motions in the first few slowest modes, which are consistent with the experimentally observed ratchet motion. The tRNAs are found to have on average approximately 72-75% rigid body motions and principally translational motions within the first 100 slow modes of the complex. Although the three tRNAs exhibit different apparent total motions, after the rigid body motions are removed, the remaining internal motions of all three tRNAs are essentially the same. The direction of the translational motions of the tRNAs are in the same direction as the requisite translocation step, especially in the first slowest mode. Surprisingly the small intrinsically flexible mRNA has all of its internal motions completely inhibited and shows mainly a rigid-body translation in the slow modes of the ribosome complex. On the other hand, the required nonrigid body motions of the tRNA during translocation reveal that the anticodon-stem-loop, as well as the acceptor arm, of the tRNA enjoy a large mobility but act as rigid structural units. In summary, the ribosome exerts its control by enforcing rigidity in the functional parts of the tRNAs as well as in the mRNA.

Protein promiscuity: drug resistance and native functions--HIV-1 case

The association of a drug with its target protein has the effect of blocking the protein activity and is termed a promiscuous function to distinguish from the protein's native function (Tawfik and associates, Nat. Genet. 37, 73-6, 2005). Obviously, a protein has not evolved naturally for drug association or drug resistance. Promiscuous protein functions exhibit unique traits of evolutionary adaptability, or evolvability, which is dependent on the induction of novel phenotypic traits by a small number of mutations. These mutations might have small effects on native functions, but large effects on promiscuous function; for example, an evolving protein could become increasingly drug resistant while maintaining its original function. Ariel Fernandez, in his opinion piece, notes that drug-binding "promiscuity" can hardly be dissociated from native functions; a dominant approach to drug discovery is the protein-native-substrate transition-state mimetic strategy. Thus, man-made ligands (e.g. drugs) have been successfully crafted to restrain enzymatic activity by focusing on the very same structural features that determine the native function. Using the successful inhibition of HIV-1 protease as an example, Fernandez illustrates how drug designers have employed naturally evolved features of the protein to suppress its activity. Based on these arguments, he dismisses the notion that drug binding is quintessentially promiscuous, even though in principle, proteins did not evolve to associate with man made ligands. In short, Fernandez argues that there may not be separate protein domains that one could term promiscuous domains. While acknowledging that drugs may bind promiscuously or in a native-like manner a la Fernandez, Tawfik maintains the role of evolutionary adaptation, even when a drug binds native-like. In the case of HIV-1 protease, drugs bind natively, and the initial onset of mutations results in drug resistance in addition to a dramatic decline in enzymatic activity and fitness of the virus. A chain of compensatory mutations follows this, and then the virus becomes fully fit and drug resistant. Ben Berkhout and Rogier Sanders subscribe to the evolution of new protein functions through gene duplication. With two identical protein domains, one domain can be released from a constraint imposed by the original function and it is thus free to move in sequence space toward a new function without loss of the original function. They emphasize that the forced evolution of drug-resistance differs significantly from the spontaneous evolution of an additional protein function. For instance, the latter process could proceed gradually on an evolutionary time scale, whereas the acquisition of drug-resistance is an all or nothing process for a virus, leading to the failure or success of therapy. They find no evidence to the thesis that resistance-mutations appear more rapidly in promiscuous domains than native domains. Berkhout and Sanders illustrate the genetic plasticity of HIV-1 by citing examples in which well-conserved amino acid residues of catalytic domains are forced to mutate under drug-pressure. HIV drug resistance biology is very complex. Instead of a viral protein, a drug can be targeted at a cellular protein. For example, Berkhout and Sanders claim, a drug targeted at the cellular protein CCR5 inhibits the binding of the viral envelope glycoprotein (Env) to CCR5. However, Env mutates so that it binds to the CCR5-drug complex and develops drug resistance. Interestingly, CCR5 has not evolved to bind to Env, but to a series of chemokines. Andrzej Kloczkowski, Taner Sen, and Bob Jernigan point out the importance of protein motions for binding. They believe it is likely that different ligands can bind to the diverse protein conformations sampled in the course of normal protein conformational fluctuations. They have been applying simple elastic network models to extract the motions as normal modes, which yield relatively small numbers of conformations that are useful for developing protein mechanisms; while these are typically small motions, for some proteins they can be quite large in scale. One of the major advantages of the approach is that only relatively small numbers of modes are important contributors to the overall motion -- so the approach provides a way to systematically map out a protein's motions. These models successfully represent the conformational fluctuations manifested in the crystallographic B-factors, and often suggest motions related to protein functional behaviors, such as those observed for reverse transcriptase, where two dominant hinges clearly relate to the processing steps -- one showing anti-correlation between the polymerase and ribonuclease H sites related to the translation and positioning of the nucleic acid chain, and another for opening and closing the polymerase site. Disordered proteins represent a more extreme case where the set of accessible conformations is much larger; thus they could offer up a broader range of possible binding forms. Whether evolution controls the functional motions for proteins remains little studied. Intriguingly, buried in the existing databases of protein-protein interactions may be information that can shed light on the extent of promiscuous binding among proteins themselves. Within these data there are cases where large numbers of diverse proteins have been shown to interact with a single protein; some of these could represent promiscuous protein-protein binding. Uncovering these promiscuous behaviors could be important for comprehending the details of how proteins can bind promiscuously to one another, and can exhibit even greater promiscuity in their binding to small molecules. The evolutionary routes, the dynamics of the target protein, and the many other aspects that need to be addressed while designing a drug that may dodge drug resistance, indicate the complexity and multi-disciplinary nature of the issue of drug resistance.

Functional dynamics of PDZ binding domains: a normal-mode analysis

Postsynaptic density-95/disks large/zonula occludens-1 (PDZ) domains are relatively small (80-120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible for communication between distant regions of the protein, in agreement with recent NMR experiments. Thus, PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbinding events.

Normal mode analysis suggests a quaternary twist model for the nicotinic receptor gating mechanism

We present a three-dimensional model of the homopentameric alpha7 nicotinic acetylcholine receptor (nAChR), that includes the extracellular and membrane domains, developed by comparative modeling on the basis of: 1), the x-ray crystal structure of the snail acetylcholine binding protein, an homolog of the extracellular domain of nAChRs; and 2), cryo-electron microscopy data of the membrane domain collected on Torpedo marmorata nAChRs. We performed normal mode analysis on the complete three-dimensional model to explore protein flexibility. Among the first 10 lowest frequency modes, only the first mode produces a structural reorganization compatible with channel gating: a wide opening of the channel pore caused by a concerted symmetrical quaternary twist motion of the protein with opposing rotations of the upper (extracellular) and lower (transmembrane) domains. Still, significant reorganizations are observed within each subunit, that involve their bending at the domain interface, an increase of angle between the two beta-sheets composing the extracellular domain, the internal beta-sheet being significantly correlated to the movement of the M2 alpha-helical segment. This global symmetrical twist motion of the pentameric protein complex, which resembles the opening transition of other multimeric ion channels, reasonably accounts for the available experimental data and thus likely describes the nAChR gating process.

Collective motions of RNA polymerases. Analysis of core enzyme, elongation complex and holoenzyme

The anisotropic network model (ANM), a coarse-grained normal mode analysis, is used to study the vibrational dynamics of RNA polymerases (RNAP) around the native states. The theoretical temperature factors obtained from ANM are in conformity with the experimental values for yeast and bacterial RNAP structures in free and complex forms. In the low-frequency collective modes that are related to biological function, both bacterial and yeast RNAPs with a crab claw shape display an opening/closing of the cleft due to the rigid-body motion of the clamp (bottom pincer), which has been also predicted by experiments, together with the motion of the top pincer. Even though slightly lower fluctuations are observed in the elongation complex of yeast RNAP, similar clamp motion still exists in collective modes, which should be concerted with the flexible switches and the bridge helix in driving the transcription process, pointing at the possibility of a ratchet-like mechanism. Two different bacterial holoenzyme (HE) structures are studied, which may have functional significance at different stages of transcription initiation. In a specific closed conformation of the HE, the clamp and top pincer are highly immobilized due to interactions with the sigma subunit. In contrast, the deformation of the top pincer is not inhibited in a relatively open conformation of another HE, which may help load the DNA into the cleft during transcription initiation, even though the clamp motion is still inhibited.

Exploring the common dynamics of homologous proteins. Application to the globin family

We present a procedure to explore the global dynamics shared between members of the same protein family. The method allows the comparison of patterns of vibrational motion obtained by Gaussian network model analysis. After the identification of collective coordinates that were conserved during evolution, we quantify the common dynamics within a family. Representative vectors that describe these dynamics are defined using a singular value decomposition approach. As a test case, the globin heme-binding family is considered. The two lowest normal modes are shown to be conserved within this family. Our results encourage the development of models for protein evolution that take into account the conservation of dynamical features.

Probing protein mechanics: residue-level properties and their use in defining domains

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.

Maturation Dynamics of Bacteriophage HK97 Capsid

Maturation of the bacteriophage HK97 capsid requires a large conformational change of the virus capsid. Experimental studies have identified several intermediates along this maturation pathway. To gain insights into the molecular mechanisms of capsid maturation, we examined the fluctuation dynamics of the procapsid and mature capsid using a residue-level computational approach. The most cooperative motions of the procapsid are found to be consistent with the observed change in configuration that takes place during maturation. A few dominant modes of motion are sufficient to describe the anisotropic expansion that accompanies maturation. Based upon these modes, maturation is proposed to occur via an overall expansion and reconfiguration of the capsid initiated by puckering of the pentamers, followed by flattening and crosslinking of the hexameric subunits, and finally crosslinking of the pentameric subunits. The highly mobile E loops are stabilized by anchoring to highly stable residues belonging to neighboring subunits.

Molecular mechanism of domain swapping in proteins: an analysis of slower motions

Domain swapping is a structural phenomenon that plays an important role in the mechanism of oligomerization of some proteins. The monomer units in the oligomeric structure become entangled with each other. Here we investigate the mechanism of domain swapping in diphtheria toxin and the structural criteria required for it to occur by analyzing the slower modes of motion with elastic network models, Gaussian network model and anisotropic network model. We take diphtheria toxin as a representative of this class of domain-swapped proteins and show that the domain, which is being swapped in the dimeric state, rotates and twists, in going from the "open" to the "closed" state, about a hinge axis that passes through the middle of the loop extending between two domains. A combination of the intra- and intermolecular contacts of the dimer is almost equivalent to that of the monomer, which shows that the relative orientations of the residues in both forms are almost identical. This is also reflected in the calculated B-factors when compared with the experimentally determined B-factors in x-ray crystal structures. The slowest modes of both the monomer and dimer show a common hinge centered on residue 387. The differences in distances between the monomer and the dimer also shows the hinge at nearly the same location (residue 381). Finally, the first three dominant modes of anisotropic network model together shows a twisting motion about the hinge centered on residue 387. We further identify the location of hinges for a set of another 12 domain swapped proteins and give the quantitative measures of the motions of the swapped domains toward their "closed" state, i.e., the overlap and correlation between vectors.

Comparative estimation of vibrational entropy changes in proteins through normal modes analysis

We compare the vibrational entropy changes of proteins calculated using a full and a number of approximate normal modes analysis methods. The vibrational entropy differences for three conformational changes and three protein binding interactions were computed. In general, the approximate methods yield good estimates of the vibrational entropy change in a fraction of the time required by full normal modes analysis. The absolute entropies are either overestimated or greatly underestimated, but the difference is sufficiently accurate for some methods. This indicates that some of the approximate methods can give reasonable estimates of the associated vibrational entropy changes, making them suitable for inclusion in free energy calculations.

Global ribosome motions revealed with elastic network model

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at.

Transconformations of the SERCA1 Ca-ATPase: a normal mode study

The transport of Ca(2+) by Ca-ATPase across the sarcoplasmic reticulum membrane is accompanied by several transconformations of the protein. Relying on the already established functional importance of low-frequency modes in dynamics of proteins, we report here a normal mode analysis of the Ca(2+)-ATPase based on the crystallographic structures of the E1Ca(2) and E2TG forms. The lowest-frequency modes reveal that the N and A(+Nter) domains undergo the largest amplitude movements. The dynamical domain analysis performed with the DomainFinder program suggests that they behave as rigid bodies, unlike the highly flexible P domain. We highlight two types of movements of the transmembrane helices: i), a concerted movement around an axis perpendicular to the membrane which "twists open" the lumenal side of the protein and ii), an individual translational and rotational mobility which is of lower amplitude for the helices hosting the calcium binding sites. Among all modes calculated for E1Ca, only three are enough to describe the transition to E2TG; the associated movements involve almost exclusively the A and N domains, reflecting the closure of the cytoplasmic headpiece and high displacement of the L7-8 lumenal loop. Subsequently, we discuss the potential contribution of the remaining low-frequency normal modes to the transconformations occurring within the overall calcium transport cycle.

A comparative study of motor-protein motions by using a simple elastic-network model

In this work, we report on a study of the structure-function relationships for three families of motor proteins, including kinesins, myosins, and F1-ATPases, by using a version of the simple elastic-network model of large-scale protein motions originally proposed by Tirion [Tirion, M. (1996) Phys. Rev. Lett. 77, 1905-1908]. We find a surprising dichotomy between kinesins and the other motor proteins (myosins and F1-ATPase). For the latter, there exist one or two dominant lowest-frequency modes (one for myosin, two for F1-ATPase) obtained from normal-mode analysis of the elastic-network model, which overlap remarkably well with the measured conformational changes derived from pairs of solved crystal structures in different states. Furthermore, we find that the computed global conformational changes induced by the measured deformation of the nucleotide-binding pocket also overlap well with the measured conformational changes, which is consistent with the "nucleotide-binding-induced power-stroke" scenario. In contrast, for kinesins, this simplicity breaks down. Multiple modes are needed to generate the measured conformational changes, and the computed displacements induced by deforming the nucleotide-binding pocket also overlap poorly with the measured conformational changes, and are insufficient to explain the large-scale motion of the relay helix and the linker region. This finding may suggest the presence of two different mechanisms for myosins and kinesins, despite their strong evolutionary ties and structural similarities.

Comparative modeling of GABA(A) receptors: limits, insights, future developments

GABA(A) receptors are chloride ion channels that mediate fast synaptic transmission and belong to a superfamily of pentameric ligand-gated ion channels. The recently published crystal structure of the acetylcholine binding protein can be used as a template for comparative modeling of the extracellular domain of GABA(A) receptors. In this commentary, difficulties with comparative modeling at low sequence identity are discussed, the degree of structural conservation to be expected within the superfamily is analyzed and numerical estimates of model uncertainties in functional regions are provided. Topography of the binding sites at subunit-interfaces is examined and possible targets for rational mutagenesis studies are suggested. Allosteric motions are considered and a mechanism for mediation of positive cooperativity at the benzodiazepine site is proposed.

Correlation between normal modes in the 20-200 cm-1 frequency range and localized torsion motions related to certain collective motions in proteins

In certain biologically relevant collective motions, such as protein domain motions and sub-domain motions, large amplitude movements are localized in one or a few flexible regions consisting of a small number of residues. This paper explores the possible use of normal mode analysis in probing localized vibrational torsion motions in these flexible regions that may be related to certain collective motions. The normal modes of 10 structures of five proteins in different conformation (TRP repressor, calmodulin, calbindin D(9k), HIV-1 protease and troponin C), known to have shear or hinge domain or sub-domain motion, respectively, are analyzed. Our study identifies, for each structure, unique normal modes in the 20-200 cm-1 frequency range, whose corresponding motions are primarily concentrated in the region where large amplitude torsion movements of a known domain or sub-domain motion occur. This suggests possible correlation between normal modes at 20-200 cm-1 frequency range and initial fluctuational motions leading to localized collective motions in proteins, and thus the potential application of normal mode analysis in facilitating the study of biologically important localized motions in biomolecules.

Comparison of full-atomic and coarse-grained models to examine the molecular fluctuations of c-AMP dependent protein kinase

Molecular fluctuations of the native conformation of c-AMP dependent protein kinase (cAPK) have been investigated with three different approaches. The first approach is the full atomic normal mode analysis (NMA) with empirical force fields. The second and third approaches are based on a coarse-grained model with a single single-parameter- harmonic potential between close residues in the crystal structure of the molecule without any residue specificity. The second method calculates only the magnitude of fluctuations whereas the third method is developed to find the directionality of the fluctuations which are essential to understand the functional importance of biological molecules. The aim, in this study, is to determine whether using such coarse-grained models are appropriate for elucidating the global dynamic characteristics of large proteins which reduces the size of the system at least by a factor of ten. The mean-square fluctuations of C(alpha) atoms and the residue cross-correlations are obtained by three approaches. These results are then compared to test the results of coarse grained models on the overall collective motions. All three of the approaches show that highly flexible regions correspond to the activation and solvent exposed loops, whereas the conserved residues (especially in substrate binding regions) exhibit almost no flexibility, adding stability to the structure. The anti-correlated motions of the two lobes of the catalytic core provide flexibility to the molecule. High similarities among the results of these methods indicate that the slowest modes governing the most global motions are preserved in the coarse grained models for proteins. This finding may suggest that the general shapes of the structures are representative of their dynamic characteristics and the dominant motions of protein structures are robust at coarse-grained levels.

Molecular motions and conformational changes of HPPK

6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) belongs to a class of catalytic enzymes involved in phosphoryl transfer and is a new target for the development of novel antimicrobial agents. In the present study, the fundamental consideration is to view the overall structure of HPPK as a network of interacting residues and to extract the most cooperative collective motions that define its global dynamics. A coarse-grained model, harmonically constrained according to HPPK's crystal structure is used. Four crystal structures of HPPK (one apo and three holo forms with different nucleotide and pterin analogs) are studied with the goal of providing insights about the function-dynamic correlation and ligand induced conformational changes. The dynamic differences are examined between HPPK's apo- and holo-forms, because they are involved in the catalytic reaction steps. Our results indicate that the palm-like structure of HPPK is nearly rigid, whereas the two flexible loops: L2 (residues 43-53) and L3 (residues 82-92) exhibit the most concerted motions for ligand recognition and presumably, catalysis. These two flexible loops are involved in the recognition of HPPKs nucleotide and pterin ligands, whereas the rigid palm region is associated with binding of these cognate ligands. Six domains of collective motions are identified, comprised of structurally close but not necessarily sequential residues. Two of these domains correspond to the flexible loops (L2 and L3), whereas the remaining domains correspond to the rigid part of the molecule.

Inhibitor binding alters the directions of domain motions in HIV-1 reverse transcriptase

Understanding the molecular mechanisms of HIV-1 reverse transcriptase (RT) action and drug inhibition is essential for designing effective antiretroviral therapies. Although comparisons of the different crystal forms of RT give insights into the flexibility of different domains, a direct computational assessment of the effect of inhibitor binding on the collective dynamics of RT is lacking. A structure-based approach is used here for exploring the dynamics of RT in unliganded and inhibitor-bound forms. Non-nucleoside RT inhibitors (NNRTI) are shown to interfere directly with the global hinge-bending mechanism that controls the cooperative motions of the p66 fingers and thumb subdomains. The net effect of nevirapine binding is to change the direction of domain movements rather than suppress their mobilities. The second generation NNRTI, efavirenz, on the other hand, shows the stronger effect of simultaneously reorienting domain motions and obstructing the p66 thumb fluctuations. A second hinge site controlling the global rotational reorientations of the RNase H domain is identified, which could serve as a target for potential inhibitors of RNase H activity.

Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic

We investigated protein motions using normal modes within a database framework, determining on a large sample the degree to which normal modes anticipate the direction of the observed motion and were useful for motions classification. As a starting point for our analysis, we identified a large number of examples of protein flexibility from a comprehensive set of structural alignments of the proteins in the PDB. Each example consisted of a pair of proteins that were considerably different in structure given their sequence similarity. On each pair, we performed geometric comparisons and adiabatic-mapping interpolations in a high-throughput pipeline, arriving at a final list of 3,814 putative motions and standardized statistics for each. We then computed the normal modes of each motion in this list, determining the linear combination of modes that best approximated the direction of the observed motion. We integrated our new motions and normal mode calculations in the Macromolecular Motions Database, through a new ranking interface at http://molmovdb.org. Based on the normal mode calculations and the interpolations, we identified a new statistic, mode concentration, related to the mathematical concept of information content, which describes the degree to which the direction of the observed motion can be summarized by a few modes. Using this statistic, we were able to determine the fraction of the 3,814 motions where one could anticipate the direction of the actual motion from only a few modes. We also investigated mode concentration in comparison to related statistics on combinations of normal modes and correlated it with quantities characterizing protein flexibility (e.g., maximum backbone displacement or number of mobile atoms). Finally, we evaluated the ability of mode concentration to automatically classify motions into a variety of simple categories (e.g., whether or not they are "fragment-like"), in comparison to motion statistics. This involved the application of decision trees and feature selection (particular machine-learning techniques) to training and testing sets derived from merging the "list" of motions with manually classified ones.

Relating molecular flexibility to function: a case study of tubulin

Microtubules (MT), along with a variety of associated motor proteins, are involved in a range of cellular functions including vesicle movement, chromosome segregation, and cell motility. MTs are assemblies of heterodimeric proteins, alpha beta-tubulins, the structure of which has been determined by electron crystallography of zinc-induced, pacilitaxel-stabilized tubulin sheets. These data provide a basis for examining relationships between structural features and protein function. Here, we study the fluctuation dynamics of the tubulin dimer with the aim of elucidating its functional motions relevant to substrate binding, polymerization/depolymerization and MT assembly. A coarse-grained model, harmonically constrained according to the crystal structure, is used to explore the global dynamics of the dimer. Our results identify six regions of collective motion, comprised of structurally close but discontinuous sequence fragments, observed only in the dimeric form, dimerization being a prerequisite for domain identification. Boundaries between regions of collective motions appear to act as linkages, found primarily within secondary-structure elements that lack sequence conservation, but are located at minima in the fluctuation curve, at positions of hydrophobic residues. Residue fluctuations within these domains identify the most mobile regions as loops involved in recognition of the adjacent regions. The least mobile regions are associated with nucleotide binding sites where lethal mutations occur. The functional coupling of motions between and within regions identifies three global motions: torsional and wobbling movements, en bloc, between the alpha- and beta-tubulin monomers, and stretching longitudinally. Further analysis finds the antitumor drug pacilitaxel (TaxotereR) to reduce flexibility in the M loop of the beta-tubulin monomer; an effect that may contribute to tightening lateral interactions between protofilaments assembled into MTs. Our analysis provides insights into relationships between intramolecular tubulin movements of MT organization and function.

Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model

The Elastic Network Model is used to investigate the open/closed transition in all DNA-dependent polymerases whose structure is known in both forms. For each structure the model accounts well for experimental crystallographic B-factors. It is found in all cases that the transition can be well described with just a handful of the normal modes. Usually, only the lowest and/or the second lowest frequency normal modes deduced from the open form give rise to calculated displacement vectors that have a correlation coefficient larger than 0.50 with the observed difference vectors between the two forms. This is true for every structural class of DNA-dependent polymerases where a direct comparison with experimental structural data is available. In cases where only one form has been observed by X-ray crystallography, it is possible to make predictions concerning the possible existence of another form in solution by carefully examining the vector displacements predicted for the lowest frequency normal modes. This simple model, which has the advantage to be computationally inexpensive, could be used to design novel kind of drugs directed against polymerases, namely drugs preventing the open/closed transition from occurring in bacterial or viral DNA-dependent polymerases.

Functional motions of influenza virus hemagglutinin: a structure-based analytical approach

Influenza virus hemagglutinin (HA), a homotrimeric integral membrane glycoprotein essential for viral infection, is engaged in two biological functions: recognition of target cells' receptor proteins and fusion of viral and endosomal membranes, both requiring substantial conformational flexibility from the part of the glycoprotein. The different modes of collective motions underlying the functional mobility/adaptability of the protein are determined in the present study using an extension of the Gaussian network model (GNM) to treat concerted anisotropic motions. We determine the molecular mechanisms that may underlie HA function, along with the structural regions or residues whose mutations are expected to impede function. Good agreement between theoretically predicted fluctuations of individual residues and corresponding x-ray crystallographic temperature factors is found, which lends support to the GNM elucidation of the conformational dynamics of HA by focusing upon a subset of dominant modes. The lowest frequency mode indicates a global torsion of the HA trimer about its longitudinal axis, accompanied by a substantial mobility at the viral membrane connection. This mode is proposed to constitute the dominant molecular mechanism for the translocation and aggregation of HAs, and for the opening and dilation of the fusion pore. The second and third collective modes indicate a global bending, allowing for a large lateral surface exposure, which is likely to facilitate the close association of the viral and endosomal membranes before pore opening. The analysis of kinetically hot residues, in contrast, reveals a localization of energy centered around the HA2 residue Asp112, which apparently triggers the solvent exposure of the fusion peptide.

Dynamics of large proteins through hierarchical levels of coarse-grained structures

Elastic network models have been successful in elucidating the largest scale collective motions of proteins. These models are based on a set of highly coupled springs, where only the close neighboring amino acids interact, without any residue specificity. Our objective here is to determine whether the equivalent cooperative motions can be obtained upon further coarse-graining of the protein structure along the backbone. The influenza virus hemagglutinin A (HA), composed of N = 1509 residues, is utilized for this analysis. Elastic network model calculations are performed for coarse-grained HA structures containing only N/2, N/10, N/20, and N/40 residues along the backbone. High correlations (>0.95) between residue fluctuations are obtained for the first dominant (slowest) mode of motion between the original model and the coarse-grained models. In the case of coarse-graining by a factor of 1/40, the slowest mode shape for HA is reconstructed for all residues by successively selecting different subsets of residues, shifting one residue at a time. The correlation for this reconstructed first mode shape with the original all-residue case is 0.73, while the computational time is reduced by about three orders of magnitude. The reduction in computational time will be much more significant for larger targeted structures. Thus, the dominant motions of protein structures are robust enough to be captured at extremely high levels of coarse-graining. And more importantly, the dynamics of extremely large complexes are now accessible with this new methodology.

Investigation of the mechanism of domain closure in citrate synthase by molecular dynamics simulation

Six, 2 ns molecular dynamics simulations have been performed on the homodimeric enzyme citrate synthase. In three, both monomers were started from the open, unliganded X-ray conformation. In the remaining three, both monomers started from a closed, liganded X-ray conformation, with the ligands removed. Projecting the motion from the simulations onto the experimental domain motion revealed that the free-energy profile is rather flat around the open conformation, with steep sides. The most closed conformations correspond to hinge-bending angles of 12-14 compared to the 20 degrees that occurs upon the binding of oxaloacetate. It is also found that the open, unliganded X-ray conformation is situated at the edge of the steep rise in free energy, although conformations that are about 5 degrees more open were sampled. A rigid-body essential dynamics analysis of the combined open trajectories has shown that domain motions in the direction of the closed X-ray conformation are compatible with the natural domain motion of the unliganded protein, which has just two main degrees of freedom. The simulations starting from the closed conformation suggest a free-energy profile with a small barrier in going from the closed to open conformation. A combined essential dynamics and hinge-bending analysis of a trajectory that spontaneously converts from the closed to open state shows an almost exact correspondence to the experimental transition that occurs upon ligand binding. The simulations support the conclusion from an earlier analysis of the experimental transition that the beta-hairpin acts as a mechanical hinge by attaching the small domain to the large domain through a conserved main-chain hydrogen bond and salt-bridges, and allowing rotation to occur via its two flexible termini. The results point to a mechanism of domain closure in citrate synthase that has analogy to the process of closing a door.

E. coli 5'-nucleotidase undergoes a hinge-bending domain rotation resembling a ball-and-socket motion

Structures of nine independent conformers of E. coli 5'-nucleotidase (5'-NT) have been analyzed using four different crystal forms. These data show that the two-domain protein undergoes an unusual 96 degrees hinge-bending domain rotation. Structures of the open and closed forms with substrates and inhibitors reveal that the substrate moves by approximately 25 A with the large domain rotation into the catalytic site. The domain motions derived from a comparison of the nine conformations agree well with motions obtained from a normal mode analysis in that all independent domain rotations are around axes that are roughly located in the plane which includes the domain centers and the hinge. Two residues, Lys355 and Gly356, form the core of the hinge region and undergo a large change of the main-chain torsion angles. The hinge-bending movement observed for 5'-nucleotidase differs markedly from a classical hinge-bending closure motion which involves an opening of the substrate or ligand-binding cleft between two domains. In contrast, the movement observed in 5'-nucleotidase resembles that of a ball-and-socket joint. The smaller C-terminal domain rotates approximately around its center such that the residues at the domain interface move in a sliding motion along the interface. Few direct interdomain contacts and a layer of water molecules between the two domains facilitate the sliding motion.

Elucidating the structural mechanisms for biological activity of the chemokine family

Chemokines are a family of proteins involved in inflammatory and immune response. They share a common fold, made up of a three-stranded beta-sheet, and an overlaying alpha-helix. Chemokines are mainly categorized into two subfamilies distinguished by the presence or absence of a residue between two conserved cysteines in the N-terminus. Although dimers and higher-order quaternary structures are common in chemokines, they are known to function as monomers. Yet, there is quite a bit of controversy on how the actual function takes place. The mechanisms of binding and activation in the chemokine family are investigated using the gaussian network model of proteins, a low-resolution model that monitors the collective motions in proteins. It is particularly suitable for elucidating the global dynamic characteristics of large proteins or the common properties of a group of related proteins such as the chemokine family presently investigated. A sample of 16 proteins that belong to the CC, CXC, or CX(3)C subfamilies are inspected. Local packing density and packing order of residues are used to determine the type and range of motions on a global scale, such as those occurring between various loop regions. The 30s-loop, although not directly involved in the binding interface like the N-terminus and the N-loop, is identified as having a prominent role in both binding/activation and dimerization. Two mechanisms are distinguished based on the communication among the three flexible regions. In these two-step mechanisms, the 30s-loop assists either the N-loop or the N-terminus during binding and activation. The findings are verified by molecular mechanics and molecular dynamics simulations carried out on the detailed structure of representative proteins from each mechanism type. A basis for the construction of hybrids of chemokines to bind and/or activate various chemokine receptors is presented. Proteins 2001;43:150-160.

Anisotropy of fluctuation dynamics of proteins with an elastic network model

Fluctuations about the native conformation of proteins have proven to be suitably reproduced with a simple elastic network model, which has shown excellent agreement with a number of different properties for a wide variety of proteins. This scalar model simply investigates the magnitudes of motion of individual residues in the structure. To use the elastic model approach further for developing the details of protein mechanisms, it becomes essential to expand this model to include the added details of the directions of individual residue fluctuations. In this paper a new tool is presented for this purpose and applied to the retinol-binding protein, which indicates enhanced flexibility in the region of entry to the ligand binding site and for the portion of the protein binding to its carrier protein.

Conformational change of proteins arising from normal mode calculations

A normal mode analysis of 20 proteins in 'open' or 'closed' forms was performed using simple potential and protein models. The quality of the results was found to depend upon the form of the protein studied, normal modes obtained with the open form of a given protein comparing better with the conformational change than those obtained with the closed form. Moreover, when the motion of the protein is a highly collective one, then, in all cases considered, there is a single low-frequency normal mode whose direction compares well with the conformational change. When it is not, in most cases there is still a single low-frequency normal mode giving a good description of the pattern of the atomic displacements, as they are observed experimentally during the conformational change. Hence a lot of information on the nature of the conformational change of a protein is often found in a single low-frequency normal mode of its open form. Since this information can be obtained through the normal mode analysis of a model as simple as that used in the present study, it is likely that the property captured by such an analysis is for the most part a property of the shape of the protein itself. One of the points that has to be clarified now is whether or not amino acid sequences have been selected in order to allow proteins to follow a single normal mode direction, as least at the very beginning of their conformational change.