Ligand-induced conformational change of a protein reproduced by a linear combination of displacement vectors obtained from normal mode analysis

The conformational change of a protein upon ligand binding was examined by normal mode analysis (NMA) based on an elastic-network model (ENM) for a full-atom system using dihedral angles as independent variables. Specifically, we investigated the extent to which conformational change vectors of atoms from an apo form to a holo form of a protein can be represented by a linear combination of the displacement vectors of atoms in the apo form calculated for the lowest-frequency m normal modes (m=1, 2,…, 20). In this analysis, the latter vectors were best fitted to the former ones by the least-squares method. Twenty-two paired proteins in the holo and apo forms, including three dimer pairs, were examined. The results showed that, in most cases, the conformational change vectors were reproduced well by a linear combination of the displacement vectors of a small number of low-frequency normal modes. The conformational change around an active site was reproduced as well as the entire conformational change, except for some proteins that only undergo significant conformational changes around active sites. The weighting factors for 20 normal modes optimized by the least-squares fitting characterize the conformational changes upon ligand binding for these proteins. The conformational changes sampled around the apo form of a protein by the linear combination of the displacement vectors obtained by ENM-based NMA may help solve the flexible-docking problem of a protein with another molecule because the results presented herein suggest that they have a relatively high probability of being involved in an actual conformational change.     

Hinge-bending motion in citrate synthase arising from normal mode calculations

A normal mode analysis of the closed form of dimeric citrate synthase has been performed. The largest-amplitude collective motion predicted by this method compares well with the crystallographically observed hinge-bending motion. Such a result supports those obtained previously in the case of hinge-bending motions of smaller systems, such as lysozyme or hexokinase. Taken together, all these results suggest that low-frequency normal modes may become useful for determining a first approximation of the conformational path between the closed and open forms of these proteins. © 1995 Wiley-Liss, Inc.     

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse‐grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass‐weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well‐known proteins of which both closed and open conformations are available as well as three α‐helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.     

Domain motions and the open-to-closed conformational transition of an enzyme: a normal mode analysis of S-adenosyl-L-homocysteine hydrolase

The structure and fluctuations of the enzyme S-adenosyl-L-homocysteine hydrolase (SAHH) are analyzed in an effort to explain its biological function. Besides the previously identified open structure, characteristic of the substrate-free enzyme, we find two distinct structures in enzyme-inhibitor complexes, the closed and closed-twisted conformers. Both closed conformers differ from the open form by a hinge bending motion of two large domains within each subunit, which isolate the inhibitor bound in the active site from the bulk solvent. The closed-twisted form further differs from the closed form by a rigid body twist of the two-subunit dimers. The local structural fluctuations of SAHH are analyzed by performing block normal mode analysis of the tetrameric enzyme in its three forms. For the open form, we find that the four lowest-frequency normal modes, corresponding to the collective motions of the protein with the largest amplitudes, are essentially combinations of the hinge bending deformations of the individual subunits. Thus, the mechanical properties of the open structure of SAHH lead to the presence of structural fluctuations in the direction of the open-to-closed conformational transition. A candidate for such a motion has been observed in previous fluorescence depolarization studies of the enzyme. Both structural and normal mode analyses indicate that residues 180-190 and 350-356 form hinge regions, connecting large domains which tend to move as rigid bodies in response to interactions with substrate, intermediates, and the product of the enzymatic reactions. We propose that these hinge regions play a crucial role in the enzymatic mechanism of SAHH. In contrast to the open form, normal mode calculations for the closed conformations show strong coupling of the hinge bending motions of the individual subunits to each other and to other low-frequency vibrations. Thus, information about structural changes related to reaction progress in one active site may be mechanically transmitted to other subunits of the protein, explaining the cooperativity found in the enzyme kinetics.     

Allostery without conformational change

A general model is presented whereby lignand-induced changes in protein dynamics could produce allosteric communication between distinct binding sites, even in the absence of a macromolecular conformational change. Theoretical analysis, based on the statistical thermodynamics of ligand binding, shows that cooperative interaction free energies amounting to several kJ · mol^-1 may be generated by this means. The effect arises out of the possible changes in frequencies and amplitudes of macromolecular thermal fluctuations in response to ligand attachment, and can involve all forms of dynamic behaviour, ranging from highly correlated, low-frequency normal mode vibrations to random local anharmonic motions of individual atoms or groups. Dynamic allostery of this form is primarily an entropy effect, and we derive approximate expressions which might allow the magnitude of the interaction in real systems to be calculated directly from experimental observations such as changes in normal mode frequencies and mean-square atomic displacements. Long-range influence of kinetic processes at different sites might also be mediated by a similar mechanism. We suggest that proteins and other biological macromolecules may have evolved to take functional advantage not only of mean conformational states but also of the inevitable thermal fluctuations about the mean.     

Building-block approach for determining low-frequency normal modes of macromolecules

Normal mode analysis of proteins of various sizes, ranging from 46 (crambin) up to 858 residues (dimeric citrate synthase) were performed, by using standard approaches, as well as a recently proposed method that rests on the hypothesis that low-frequency normal modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino-acid residues. Such a hypothesis is strongly supported by our results, because we show that the latter method, named RTB, yields very accurate approximations for the low-frequency normal modes of all proteins considered. Moreover, the quality of the normal modes thus obtained depends very little on the way the polypeptidic chain is split into blocks. Noteworthy, with six amino-acids per block, the normal modes are almost as accurate as with a single amino-acid per block. In this case, for a protein of n residues and N atoms, the RTB method requires the diagonalization of an n x n matrix, whereas standard procedures require the diagonalization of a 3N x 3N matrix. Being a fast method, our approach can be useful for normal mode analyses of large systems, paving the way for further developments and applications in contexts for which the normal modes are needed frequently, as for example during molecular dynamics calculations.     

Normal-modes-based prediction of protein conformational changes guided by distance constraints

Based on the elastic network model, we develop a novel method that predicts the conformational change of a protein complex given its initial-state crystal structure together with a small set of pairwise distance constraints for the end state. The predicted conformational change, which is a linear combination of multiple low-frequency normal modes that are solved from the elastic network model, is computed as a response displacement induced by a perturbation to the system Hamiltonian that incorporates the given distance constraints. For a list of test cases, we find that the computed response displacement overlaps significantly with the measured conformational changes, when only a handful of pairwise constraints are used (相似文献   

Modeling protein conformational transitions by a combination of coarse-grained normal mode analysis and robotics-inspired methods

Background

Obtaining atomic-scale information about large-amplitude conformational transitions in proteins is a challenging problem for both experimental and computational methods. Such information is, however, important for understanding the mechanisms of interaction of many proteins.

Methods

This paper presents a computationally efficient approach, combining methods originating from robotics and computational biophysics, to model protein conformational transitions. The ability of normal mode analysis to predict directions of collective, large-amplitude motions is applied to bias the conformational exploration performed by a motion planning algorithm. To reduce the dimension of the problem, normal modes are computed for a coarse-grained elastic network model built on short fragments of three residues. Nevertheless, the validity of intermediate conformations is checked using the all-atom model, which is accurately reconstructed from the coarse-grained one using closed-form inverse kinematics.

Results

Tests on a set of ten proteins demonstrate the ability of the method to model conformational transitions of proteins within a few hours of computing time on a single processor. These results also show that the computing time scales linearly with the protein size, independently of the protein topology. Further experiments on adenylate kinase show that main features of the transition between the open and closed conformations of this protein are well captured in the computed path.

Conclusions

The proposed method enables the simulation of large-amplitude conformational transitions in proteins using very few computational resources. The resulting paths are a first approximation that can directly provide important information on the molecular mechanisms involved in the conformational transition. This approximation can be subsequently refined and analyzed using state-of-the-art energy models and molecular modeling methods.

     

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.     

Collective motions in proteins investigated by X-ray diffuse scattering

We have developed theoretical models for analysis of X-ray diffuse scattering from protein crystals. A series of models are proposed to be used for experimental data with different degrees of precision. First, we propose the normal mode model, where conformational dynamics of a protein is assumed to occur mostly in a limited conformational subspace spanned by a small number of low-frequency normal modes in the protein. When high precision data are available, variances and covariances of the normal mode variables can be determined from experimental data using this model. For experimental data with lower degrees of precision, we introduce a series of simpler models. These models express the covariance matrix using relatively simple empirical correlation functions by assuming the correlation between a pair of atoms to be isotropic. As an application of these simpler models, we calculate diffuse-scattering patterns from a human lysozyme crystal to examine how each adjustable parameter in the models affects general features of the resulting patterns. The results of the calculation are summarized as follows. (1) The higher order scattering makes a significant contribution at high resolutions. (2) The resulting simulated patterns are sensitive to changes in correlation lengths of about 1 Å, as well as to changes of the functional form of the correlation function. (3) But only the “average” value of the intra- and intermolecular correlation lengths seems to determine the gross features of the pattern. (4) The effect of the atom-dependent amplitude of fluctuations is difficult to observe. © 1994 John Wiley & Sons, Inc.     

Kinetic mechanism of ligand binding in human ileal bile acid binding protein as determined by stopped-flow fluorescence analysis

Cooperative ligand binding to human ileal bile acid binding protein (I-BABP) was studied using the stopped-flow fluorescence technique. The kinetic data obtained for wild-type protein are in agreement with a four-step mechanism where after a fast conformational change on the millisecond time scale, the ligands bind in a sequential manner, followed by another, slow conformational change on the time scale of seconds. This last step is more pronounced in the case of glycocholate (GCA), the bile salt that binds with high positive cooperativity and is absent in mutant I-BABP proteins that lack positive cooperativity in their bile salt binding. These results suggest that positive cooperativity in human I-BABP is related to a slow conformational change of the protein, which occurs after the second binding step. Analogous to that in the intestinal fatty acid binding protein (I-FABP), we hypothesize that ligand binding in I-BABP is linked to a disorder-order transition between an open and a closed form of the protein.     

Domain-Based Protein Docking with Extremely Large Conformational Changes

Proteins are key components in many processes in living cells, and physical interactions with other proteins and nucleic acids often form key parts of their functions. In many cases, large flexibility of proteins as they interact is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D structures of such protein complexes. When such structures are not yet experimentally determined, protein docking has long been present to computationally generate useful structure models. However, protein docking has long had the limitation that the consideration of flexibility is usually limited to very small movements or very small structures. Methods have been developed which handle minor flexibility via normal mode or other structure sampling, but new methods are required to model ordered proteins which undergo large-scale conformational changes to elucidate their function at the molecular level. Here, we present Flex-LZerD, a framework for docking such complexes. Via partial assembly multidomain docking and an iterative normal mode analysis admitting curvilinear motions, we demonstrate the ability to model the assembly of a variety of protein–protein and protein-nucleic acid complexes.     

Thorough validation of protein normal mode analysis: a comparative study with essential dynamics

The deformation patterns of a large set of representative proteins determined by essential dynamics extracted from atomistic simulations and coarse-grained normal mode analysis are compared. Our analysis shows that the deformational space obtained with both approaches is quite similar when taking into account a representative number of modes. The results provide not only a comprehensive validation of the use of a low-frequency modal spectrum to describe protein flexibility, but also a complete picture of normal mode limitations.     

Conformational Changes of Three Periplasmic Receptors for Bacterial Chemotaxis and Transport: The Maltose-, Glucose/Galactose- and Ribose-binding Proteins.

Small-angle X-ray scattering experiments were carried out for the maltose-, glucose/galactose- and ribose-binding proteins of Gram negative bacteria. All were shown to be monomers that decrease in radius of gyration on ligand binding.The results obtained for the maltose-binding protein agree well with crystal structures of the closed, ligand-bound, and open, ligand-free protein, suggesting that these are indeed the primary forms in solution. The closed form is stabilized by protein – sugar interactions, while the open conformation is stabilized by close contacts between the two domains. Since it is the proper spacial relationship of the domains in the closed form that is most important for interaction with chemotaxis and transport partners, the stabilization of the open form would help keep ligand-free molecules from interfering in function.The scattering results also provide evidence that a large conformational change takes place in association with ligand binding to the glucose/galactose- and ribose-binding proteins, and that the two changes are similar. Modeling suggests that the open forms resemble those found in the related leucine and leucine/isoleucine/valine-binding proteins, but are different from those observed for the maltose-binding protein and the related purine repressor.     

Electrophoretic investigations of the acid conformational change of alpha-lactalbumin.

In order to clarify how the electrophoretic behavior reflects the conformational transition of globular proteins, moving boundary electrophoresis was applied to analysis of the acid conformational change of alpha-lactalbumin. The appearance of only a single electrophoretic boundary in the transition region of the protein suggests a very rapid transition with a half-time estimated to be smaller than 7 min on the basis of the theory of isomerizing systems in electrophoresis. The transition is clearly reflected in the dependence of the mobility on the protein net charge, which shows a sigmoidal curve closely similar to that obtained by a Linderstr?m-Lang pH-tritration plot for the carboxyl groups of alpha-lactalbumin. It was also concluded from the transition curves that the acidfication does not result in complete unfolding, but that a compact structure is maintained in the acidic region with an apparently expanded form as compared to the native state of the protein. All results obtained by electrophoresis were also supported by the results of pH-jump studies, analytical gel chromatography, and CD measurements.     

Binding leverage as a molecular basis for allosteric regulation

Allosteric regulation involves conformational transitions or fluctuations between a few closely related states, caused by the binding of effector molecules. We introduce a quantity called binding leverage that measures the ability of a binding site to couple to the intrinsic motions of a protein. We use Monte Carlo simulations to generate potential binding sites and either normal modes or pairs of crystal structures to describe relevant motions. We analyze single catalytic domains and multimeric allosteric enzymes with complex regulation. For the majority of the analyzed proteins, we find that both catalytic and allosteric sites have high binding leverage. Furthermore, our analysis of the catabolite activator protein, which is allosteric without conformational change, shows that its regulation involves other types of motion than those modulated at sites with high binding leverage. Our results point to the importance of incorporating dynamic information when predicting functional sites. Because it is possible to calculate binding leverage from a single crystal structure it can be used for characterizing proteins of unknown function and predicting latent allosteric sites in any protein, with implications for drug design.     

New insights of membrane environment effects on MscL channel mechanics from theoretical approaches

The prokaryotic mechanosensitive channel of large conductance (MscL) is a remarkable integral membrane protein. During hypo-osmotic shock, it responses to membrane tension through large conformational changes, that lead to an open state of the pore. The structure of the channel from Mycobacterium tuberculosis has been resolved in the closed state. Numerous experiments have attempted to trap the channel in its open state but they did not succeed in obtaining a structure. A gating mechanism has been proposed based on different experimental data but there is no experimental technique available to follow this process in atomic details. In addition, it has been shown that a decrease of the lipid bilayer thickness lowered MscL activation energy and stabilized a structurally distinct closed channel intermediate. Here, we use atomistic molecular dynamics simulations to investigate the effect of the lipid bilayer thinning on our model of the structure of the Escherichia coli. We thoroughly analyze simulations of the channel embedded in two pre-equilibrated membranes differing by their hydrophobic tail length (DMPE and POPE). The MscL structure remains stable in POPE, whereas a distinct structural state is obtained in DMPE in response to hydrophobic mismatch. This latter is obtained by tilts and kinks of the transmembrane helices, leading to a widening and a diminution of the channel height. Part of these motions is guided by a competition between solvent and lipids for the interaction with the periplasmic loops. We finally conduct a principal component analysis of the simulation and compare anharmonic motions with harmonic ones, previously obtained from a coarse-grained normal mode analysis performed on the same structural model. Significant similarities exist between low-frequency harmonic motions and those observed with essential dynamics in DMPE. In summary, change in membrane thickness permits to accelerate the conformational changes involved in the mechanics of the E. coli channel, providing a closed structural intermediate en route to the open state. These results give clues for better understanding why the channel activation energy is lowered in a thinner membrane.