Large-scale comparison of protein essential dynamics from molecular dynamics simulations and coarse-grained normal mode analyses

Effective Molecular Dynamics from Neural Network-Based Structure Prediction Models

Recent breakthroughs in neural network-based structure prediction methods, such as AlphaFold2 and RoseTTAFold, have dramatically improved the quality of computational protein structure prediction. These models also provide statistical confidence scores that can estimate uncertainties in the predicted structures, but it remains unclear to what extent these scores are related to the intrinsic conformational dynamics of proteins. Here, we compare AlphaFold2 prediction scores with explicit large-scale molecular dynamics simulations of 28 one- and two-domain proteins with varying degrees of flexibility. We demonstrate a strong correlation between the statistical prediction scores and the explicit motion derived from extensive atomistic molecular dynamics simulations and further derive an elastic network model based on the statistical scores of AlphFold2 (AF-ENM), which we benchmark in combination with coarse-grained molecular dynamics simulations. We show that our AF-ENM method reproduces the global protein dynamics with improved accuracy, providing a powerful way to derive effective molecular dynamics using neural network-based structure prediction models.

Predicting allosteric sites using fast conformational sampling as guided by coarse-grained normal modes

To computationally identify cryptic binding sites for allosteric modulators, we have developed a fast and simple conformational sampling scheme guided by coarse-grained normal modes solved from the elastic network models followed by atomistic backbone and sidechain reconstruction. Despite the complexity of conformational changes associated with ligand binding, we previously showed that simply sampling along each of the lowest 30 modes can adequately restructure cryptic sites so they are detectable by pocket finding programs like Concavity. Here, we applied this method to study four classical examples of allosteric regulation (GluR2 receptor, GroEL chaperonin, GPCR, and myosin). Our method along with alternative methods has been utilized to locate known allosteric sites and predict new promising allosteric sites. Compared with other sampling methods based on extensive molecular dynamics simulation, our method is both faster (1-2 h for an average-size protein of ∼400 residues) and more flexible (it can be easily integrated with any structure-based pocket finding methods), so it is suitable for high-throughput screening of large datasets of protein structures at the genome scale.

The functional motions and related key residues behind the uncoating of coxsackievirus A16

The coxsackievirus A16 (CVA16) is a highly contagious virus that causes the hand, foot, and mouth disease, which seriously threatens the health of children. At present, there are still no available antiviral drugs or effective treatments against the infection of CVA16, and thus it is of great significance to develop anti-CVA16 vaccines. However, the intrinsic uncoating property of the capsid may destroy the neutralizing epitopes and influence its immunogenicity, which hinders the vaccine developments. In the present work, the functional-quantity-based elastic network model analysis method developed by our group was extended to combine with group theory to investigate the uncoating motions of the CVA16 capsid, and then the functionally key residues controlling the uncoating motions were identified by our functional-quantity-based perturbation method. Several motion modes encoded in the topological structure of the capsid were revealed to be responsible for the uncoating of CVA16 particle. These modes predominantly contribute to the fluctuation of the gyration radius of the capsid. Then, by using the perturbation method, four clusters of key sites involved in the uncoating motions were identified, whose perturbations induce significant changes in the fluctuation of the gyration radius. These key residues are mainly located at the 2-fold channels, the quasi 3-fold channels, the bottom of the canyons, and the inter-subunit interfaces around the 3-fold axes. Our studies are helpful for better understanding the uncoating mechanism of the CVA16 capsid and provide potential target sites to prevent the uncoating motions, which is valuable for the vaccine design against CVA16.

Predicting cryptic ligand binding sites based on normal modes guided conformational sampling

To greatly expand the druggable genome, fast and accurate predictions of cryptic sites for small molecules binding in target proteins are in high demand. In this study, we have developed a fast and simple conformational sampling scheme guided by normal modes solved from the coarse-grained elastic models followed by atomistic backbone refinement and side-chain repacking. Despite the observations of complex and diverse conformational changes associated with ligand binding, we found that simply sampling along each of the lowest 30 modes is near optimal for adequately restructuring cryptic sites so they can be detected by existing pocket finding programs like fpocket and concavity. We further trained machine-learning protocols to optimize the combination of the sampling-enhanced pocket scores with other dynamic and conservation scores, which only slightly improved the performance. As assessed based on a training set of 84 known cryptic sites and a test set of 14 proteins, our method achieved high accuracy of prediction (with area under the receiver operating characteristic curve >0.8) comparable to the CryptoSite server. Compared with CryptoSite and other methods based on extensive molecular dynamics simulation, our method is much faster (1-2 hours for an average-size protein) and simpler (using only pocket scores), so it is suitable for high-throughput processing of large datasets of protein structures at the genome scale.

Structural Communication between the E. coli Chaperones DnaK and Hsp90

The 70 kDa and 90 kDa heat shock proteins Hsp70 and Hsp90 are two abundant and highly conserved ATP-dependent molecular chaperones that participate in the maintenance of cellular homeostasis. In Escherichia coli, Hsp90 (Hsp90Ec) and Hsp70 (DnaK) directly interact and collaborate in protein remodeling. Previous work has produced a model of the direct interaction of both chaperones. The locations of the residues involved have been confirmed and the model has been validated. In this study, we investigate the allosteric communication between Hsp90Ec and DnaK and how the chaperones couple their conformational cycles. Using elastic network models (ENM), normal mode analysis (NMA), and a structural perturbation method (SPM) of asymmetric and symmetric DnaK-Hsp90Ec, we extract biologically relevant vibrations and identify residues involved in allosteric signaling. When one DnaK is bound, the dominant normal modes favor biological motions that orient a substrate protein bound to DnaK within the substrate/client binding site of Hsp90Ec and release the substrate from the DnaK substrate binding domain. The presence of one DnaK molecule stabilizes the entire Hsp90Ec protomer to which it is bound. Conversely, the symmetric model of DnaK binding results in steric clashes of DnaK molecules and suggests that the Hsp90Ec and DnaK chaperone cycles operate independently. Together, this data supports an asymmetric binding of DnaK to Hsp90Ec.

Theoretical study of the adiponectin receptors: binding site characterization and molecular dynamics of possible ligands for drug design

The two adiponectin receptors (AdipoR1 and AdipoR2) have been implicated in glucose and lipid regulation involved in several metabolic pathologies including type II diabetes. Their exact biochemical functions and mechanisms remain poorly understood. Moreover, these receptors do not yet have data on possible co-crystallized active ligands. In this study, we applied different computational methodologies to address three main unanswered questions: first, the localization and validation of possible binding sites; second, the generation of novel ligands with amenable characteristics to target the receptors; and third, the determination of important chemical interactions between the ligands and the receptors. Computational analysis of the binding site reveals that the residues triad R267, F271, and Y310 could be responsible for changes in the spatial arrangement and geometry of the binding pocket in AdipoR1. Molecular docking results in high docking scores of − 13.6 and − 16.5 kcal/mol for the top best ligands in AdipoR1 and AdipoR2 respectively. Finally, molecular dynamics suggests that hydrolytic activity may be possible with these compounds and that this reaction could be mediated by aspartic acid residues. The two adiponectin receptors have an endogenous protein ligand, adiponectin. However the synthesis is expensive and technically challenging. Although some debatable agonists have been proposed investigations of suitable synthetic ligands are indeed, very much needed for targeting these receptors and their associate pathologies and metabolic pathways. Furthermore, these findings provide a framework for further biochemical investigations of amenable compounds for drug discovery in order to target these receptors and their associated pathologies.

Inhibition of α-amylase Activity by Zn2+: Insights from Spectroscopy and Molecular Dynamics Simulations

Background:

Inhibition of α-amylase activity is an important strategy in the treatment of diabetes mellitus. An important treatment for diabetes mellitus is to reduce the digestion of carbohydrates and blood glucose concentrations. Inhibiting the activity of carbohydrate-degrading enzymes such as α-amylase and glucosidase significantly decreases the blood glucose level. Most inhibitors of α-amylase have serious adverse effects, and the α-amylase inactivation mechanisms for the design of safer inhibitors are yet to be revealed.

Objective:

In this study, we focused on the inhibitory effect of Zn2+ on the structure and dynamic characteristics of α-amylase from Anoxybacillus sp. GXS-BL (AGXA), which shares the same catalytic residues and similar structures as human pancreatic and salivary α-amylase (HPA and HSA, respectively).

Methods:

Circular dichroism (CD) spectra of the protein (AGXA) in the absence and presence of Zn2+ were recorded on a Chirascan instrument. The content of different secondary structures of AGXA in the absence and presence of Zn2+ was analyzed using the online SELCON3 program. An AGXA amino acid sequence similarity search was performed on the BLAST online server to find the most similar protein sequence to use as a template for homology modeling. The pocket volume measurer (POVME) program 3.0 was applied to calculate the active site pocket shape and volume, and molecular dynamics simulations were performed with the Amber14 software package.

Results:

According to circular dichroism experiments, upon Zn2+ binding, the protein secondary structure changed obviously, with the α-helix content decreasing and β-sheet, β-turn and randomcoil content increasing. The structural model of AGXA showed that His217 was near the active site pocket and that Phe178 was at the outer rim of the pocket. Based on the molecular dynamics trajectories, in the free AGXA model, the dihedral angle of C-CA-CB-CG displayed both acute and planar orientations, which corresponded to the open and closed states of the active site pocket, respectively. In the AGXA-Zn model, the dihedral angle of C-CA-CB-CG only showed the planar orientation. As Zn2+ was introduced, the metal center formed a coordination interaction with H217, a cation-π interaction with W244, a coordination interaction with E242 and a cation-π interaction with F178, which prevented F178 from easily rotating to the open state and inhibited the activity of the enzyme.

Conclusion:

This research may have uncovered a subtle mechanism for inhibiting the activity of α-amylase with transition metal ions, and this finding will help to design more potent and specific inhibitors of α-amylases.

Allostery and cooperativity in multimeric proteins: bond-to-bond propensities in ATCase

Aspartate carbamoyltransferase (ATCase) is a large dodecameric enzyme with six active sites that exhibits allostery: its catalytic rate is modulated by the binding of various substrates at distal points from the active sites. A recently developed method, bond-to-bond propensity analysis, has proven capable of predicting allosteric sites in a wide range of proteins using an energy-weighted atomistic graph obtained from the protein structure and given knowledge only of the location of the active site. Bond-to-bond propensity establishes if energy fluctuations at given bonds have significant effects on any other bond in the protein, by considering their propagation through the protein graph. In this work, we use bond-to-bond propensity analysis to study different aspects of ATCase activity using three different protein structures and sources of fluctuations. First, we predict key residues and bonds involved in the transition between inactive (T) and active (R) states of ATCase by analysing allosteric substrate binding as a source of energy perturbations in the protein graph. Our computational results also indicate that the effect of multiple allosteric binding is non linear: a switching effect is observed after a particular number and arrangement of substrates is bound suggesting a form of long range communication between the distantly arranged allosteric sites. Second, cooperativity is explored by considering a bisubstrate analogue as the source of energy fluctuations at the active site, also leading to the identification of highly significant residues to the T ↔ R transition that enhance cooperativity across active sites. Finally, the inactive (T) structure is shown to exhibit a strong, non linear communication between the allosteric sites and the interface between catalytic subunits, rather than the active site. Bond-to-bond propensity thus offers an alternative route to explain allosteric and cooperative effects in terms of detailed atomistic changes to individual bonds within the protein, rather than through phenomenological, global thermodynamic arguments.

Elastic network model of learned maintained contacts to predict protein motion

We present a novel elastic network model, lmcENM, to determine protein motion even for localized functional motions that involve substantial changes in the protein's contact topology. Existing elastic network models assume that the contact topology remains unchanged throughout the motion and are thus most appropriate to simulate highly collective function-related movements. lmcENM uses machine learning to differentiate breaking from maintained contacts. We show that lmcENM accurately captures functional transitions unexplained by the classical ENM and three reference ENM variants, while preserving the simplicity of classical ENM. We demonstrate the effectiveness of our approach on a large set of proteins covering different motion types. Our results suggest that accurately predicting a "deformation-invariant" contact topology offers a promising route to increase the general applicability of ENMs. We also find that to correctly predict this contact topology a combination of several features seems to be relevant which may vary slightly depending on the protein. Additionally, we present case studies of two biologically interesting systems, Ferric Citrate membrane transporter FecA and Arachidonate 15-Lipoxygenase.

On the potential alternate binding change mechanism in a dimeric structure of Pyruvate Phosphate Dikinase

The pyruvate phosphate dikinase (PPDK) reaction mechanism is characterized by a distinct spatial separation of reaction centers and large conformational changes involving an opening-closing motion of the nucleotide-binding domain (NBD) and a swiveling motion of the central domain (CD). However, why PPDK is active only in a dimeric form and to what extent an alternate binding change mechanism could underlie this fact has remained elusive. We performed unbiased molecular dynamics simulations, configurational free energy computations, and rigidity analysis to address this question. Our results support the hypothesis that PPDK dimerization influences the opening-closing motion of the NBDs, and that this influence is mediated via the CDs of both chains. Such an influence would be a prerequisite for an alternate binding change mechanism to occur. To the best of our knowledge, this is the first time that a possible explanation has been suggested as to why only dimeric PPDK is active.

Structural intermediates and directionality of the swiveling motion of Pyruvate Phosphate Dikinase

Pyruvate phosphate dikinase (PPDK) is a vital enzyme in cellular energy metabolism catalyzing the ATP- and Pi-dependent formation of phosphoenolpyruvate from pyruvate in C4 -plants, but the reverse reaction forming ATP in bacteria and protozoa. The multi-domain enzyme is considered an efficient molecular machine that performs one of the largest single domain movements in proteins. However, a comprehensive understanding of the proposed swiveling domain motion has been limited by not knowing structural intermediates or molecular dynamics of the catalytic process. Here, we present crystal structures of PPDKs from Flaveria, a model genus for studying the evolution of C4 -enzymes from phylogenetic ancestors. These structures resolve yet unknown conformational intermediates and provide the first detailed view on the large conformational transitions of the protein in the catalytic cycle. Independently performed unrestrained MD simulations and configurational free energy calculations also identified these intermediates. In all, our experimental and computational data reveal strict coupling of the CD swiveling motion to the conformational state of the NBD. Moreover, structural asymmetries and nucleotide binding states in the PPDK dimer support an alternate binding change mechanism for this intriguing bioenergetic enzyme.

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.

Selection on protein structure, interaction, and sequence

Characterizing the probabilities of observing amino acid substitutions at specific sites in a protein over evolutionary time is a major goal in the field of molecular evolution. While purely statistical approaches at different levels of complexity exist, approaches rooted in underlying biological processes are necessary to characterize both the context-dependence of sequence changes (epistasis) and to extrapolate to sequences not observed in biological databases. To develop such approaches, an understanding of the different selective forces that act on amino acid substitution is necessary. Here, an overview of selection on and corresponding modeling of folding stability, folding specificity, binding affinity and specificity for ligands, the evolution of new binding sites on protein surfaces, protein dynamics, intrinsic disorder, and protein aggregation as well as the interplay with protein expression level (concentration) and biased mutational processes are presented.

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

Specific non-local interactions are not necessary for recovering native protein dynamics

The elastic network model (ENM) is a widely used method to study native protein dynamics by normal mode analysis (NMA). In ENM we need information about all pairwise distances, and the distance between contacting atoms is restrained to the native value. Therefore ENM requires O(N²) information to realize its dynamics for a protein consisting of N amino acid residues. To see if (or to what extent) such a large amount of specific structural information is required to realize native protein dynamics, here we introduce a novel model based on only O(N) restraints. This model, named the ‘contact number diffusion’ model (CND), includes specific distance restraints for only local (along the amino acid sequence) atom pairs, and semi-specific non-local restraints imposed on each atom, rather than atom pairs. The semi-specific non-local restraints are defined in terms of the non-local contact numbers of atoms. The CND model exhibits the dynamic characteristics comparable to ENM and more correlated with the explicit-solvent molecular dynamics simulation than ENM. Moreover, unrealistic surface fluctuations often observed in ENM were suppressed in CND. On the other hand, in some ligand-bound structures CND showed larger fluctuations of buried protein atoms interacting with the ligand compared to ENM. In addition, fluctuations from CND and ENM show comparable correlations with the experimental B-factor. Although there are some indications of the importance of some specific non-local interactions, the semi-specific non-local interactions are mostly sufficient for reproducing the native protein dynamics.

Elastic Network Models of Nucleic Acids Flexibility

Elastic network models (ENMs) are a useful tool for describing large scale motions in protein systems. While they are well validated in the context of proteins, relatively little is known about their applicability to nucleic acids, whose different architecture does not necessarily warrant comparable performance. In this study we thoroughly evaluate and optimize the efficiency of popular ENMs for capturing RNA and DNA flexibility. We also introduce two alternative models in which the strength of elastic connections at a coarse-grained level is governed by distance distribution at atomic resolution. For each of the considered ENMs we report the optimal length of spring connections as well as the scaling of elastic force constants that provides the best agreement of vibrational frequencies with normal modes based on atomic force field. In order to determine the absolute values of force constants we introduce a novel method based on the overlap of pseudoinverse of Hessian matrices.

Allostery without conformation change: modelling protein dynamics at multiple scales

The original ideas of Cooper and Dryden, that allosteric signalling can be induced between distant binding sites on proteins without any change in mean structural conformation, has proved to be a remarkably prescient insight into the rich structure of protein dynamics. It represents an alternative to the celebrated Monod-Wyman-Changeux mechanism and proposes that modulation of the amplitude of thermal fluctuations around a mean structure, rather than shifts in the structure itself, give rise to allostery in ligand binding. In a complementary approach to experiments on real proteins, here we take a theoretical route to identify the necessary structural components of this mechanism. By reviewing and extending an approach that moves from very coarse-grained to more detailed models, we show that, a fundamental requirement for a body supporting fluctuation-induced allostery is a strongly inhomogeneous elastic modulus. This requirement is reflected in many real proteins, where a good approximation of the elastic structure maps strongly coherent domains onto rigid blocks connected by more flexible interface regions.

Buried and accessible surface area control intrinsic protein flexibility

Proteins experience a wide variety of conformational dynamics that can be crucial for facilitating their diverse functions. How is the intrinsic flexibility required for these motions encoded in their three-dimensional structures? Here, the overall flexibility of a protein is demonstrated to be tightly coupled to the total amount of surface area buried within its fold. A simple proxy for this, the relative solvent-accessible surface area (Arel), therefore shows excellent agreement with independent measures of global protein flexibility derived from various experimental and computational methods. Application of Arel on a large scale demonstrates its utility by revealing unique sequence and structural properties associated with intrinsic flexibility. In particular, flexibility as measured by Arel shows little correspondence with intrinsic disorder, but instead tends to be associated with multiple domains and increased α-helical structure. Furthermore, the apparent flexibility of monomeric proteins is found to be useful for identifying quaternary-structure errors in published crystal structures. There is also a strong tendency for the crystal structures of more flexible proteins to be solved to lower resolutions. Finally, local solvent accessibility is shown to be a primary determinant of local residue flexibility. Overall, this work provides both fundamental mechanistic insight into the origin of protein flexibility and a simple, practical method for predicting flexibility from protein structures.

Counterbalance of ligand- and self-coupled motions characterizes multispecificity of ubiquitin

Date hub proteins are a type of proteins that show multispecificity in a time-dependent manner. To understand dynamic aspects of such multispecificity we studied Ubiquitin as a typical example of a date hub protein. Here we analyzed 9 biologically relevant Ubiquitin-protein (ligand) heterodimer structures by using normal mode analysis based on an elastic network model. Our result showed that the self-coupled motion of Ubiquitin in the complex, rather than its ligand-coupled motion, is similar to the motion of Ubiquitin in the unbound condition. The ligand-coupled motions are correlated to the conformational change between the unbound and bound conditions of Ubiquitin. Moreover, ligand-coupled motions favor the formation of the bound states, due to its in-phase movements of the contacting atoms at the interface. The self-coupled motions at the interface indicated loss of conformational entropy due to binding. Therefore, such motions disfavor the formation of the bound state. We observed that the ligand-coupled motions are embedded in the motions of unbound Ubiquitin. In conclusion, multispecificity of Ubiquitin can be characterized by an intricate balance of the ligand- and self-coupled motions, both of which are embedded in the motions of the unbound form.

Global and local indices for characterizing biomolecular flexibility and rigidity

Understanding flexibility and rigidity characteristics of biomolecules is a prerequisite for understanding biomolecular structural stability and function. Computational methods have been implemented that directly characterize biomolecular flexibility and rigidity by constraint network analysis. For deriving maximal advantage from these analyses, their results need to be linked to biologically relevant characteristics of a structure. Such links are provided by global and local measures ("indices") of biomolecular flexibility and rigidity. To date, more than 14 indices are available with sometimes overlapping or only vague definitions. We present concise definitions of these indices, analyze the relation between, and the scope and limitations of them, and compare their informative value. For this, we probe the structural stability of the calcium binding protein α-lactalbumin as a showcase, both in the "ground state" and after perturbing the system by changing the network topology. In addition, we introduce three indices for the first time that extend the application domain of flexibility and rigidity analyses. The results allow us to provide guidelines for future studies suggesting which of these indices could best be used for analyzing, understanding, and quantifying structural features that are important for biomolecular stability and function. Finally, we make suggestions for proper index notations in future studies to prevent the misinterpretation and to facilitate the comparison of results obtained from flexibility and rigidity analyses.

Measuring and comparing structural fluctuation patterns in large protein datasets

MOTIVATION

The function of a protein depends not only on its structure but also on its dynamics. This is at the basis of a large body of experimental and theoretical work on protein dynamics. Further insight into the dynamics-function relationship can be gained by studying the evolutionary divergence of protein motions. To investigate this, we need appropriate comparative dynamics methods. The most used dynamical similarity score is the correlation between the root mean square fluctuations (RMSF) of aligned residues. Despite its usefulness, RMSF is in general less evolutionarily conserved than the native structure. A fundamental issue is whether RMSF is not as conserved as structure because dynamics is less conserved or because RMSF is not the best property to use to study its conservation.

RESULTS

We performed a systematic assessment of several scores that quantify the (dis)similarity between protein fluctuation patterns. We show that the best scores perform as well as or better than structural dissimilarity, as assessed by their consistency with the SCOP classification. We conclude that to uncover the full extent of the evolutionary conservation of protein fluctuation patterns, it is important to measure the directions of fluctuations and their correlations between sites.

CONTACT

Nathalie.Reuter@mbi.uib.no

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Online.

Why are the low-energy protein normal modes evolutionarily conserved?

Proteins fluctuate, and such fluctuations are functionally important. As with any functionally relevant trait, it is interesting to study how fluctuations change during evolution. In contrast with sequence and structure, the study of the evolution of protein motions is much more recent. Yet, it has been shown that the overall fluctuation pattern is evolutionarily conserved. Moreover, the lowest-energy normal modes have been found to be the most conserved. The reasons behind such a differential conservation have not been explicitly studied. There are two limiting explanations. A “biological” explanation is that because such modes are functional, there is natural selection pressure against their variation. An alternative “physical” explanation is that the lowest-energy normal modes may be more conserved because they are just more robust with respect to random mutations. To investigate this issue, I studied a set of globin-like proteins using a perturbed elastic network model (ENM) of the effect of random mutations on normal modes. I show that the conservation predicted by the model is in excellent agreement with observations. These results support the physical explanation: the lowest normal modes are more conserved because they are more robust.

Elastic Network Models are Robust to Variations in Formalism

Understanding the functions of biomolecules requires insight not only from structures, but from dynamics as well. Often, the most interesting processes occur on time scales too slow for exploration by conventional molecular dynamics (MD) simulations. For this reason, alternative computational methods such as elastic network models (ENMs) have become increasingly popular. These simple, coarse-grained models represent molecules as beads connected by harmonic springs; the system's motions are solved analytically by normal mode analysis. In the past few years, many different formalisms for performing ENM calculations have emerged, and several have been optimized using all-atom MD simulations. In contrast to other studies, we have compared the various formalisms in a systematic, quantitative way. In this study, we optimize many ENM functional forms using a uniform dataset containing only long (> 1 μs) all-atom MD simulations. Our results show that all models once optimized produce spring constants for immediate neighboring residues that are orders of magnitude stiffer than more distal contacts. In addition, the statistical significance of ENM performance varied with model resolution. We also show that fitting long trajectories does not improve ENM performance due to a problem inherent in all network models tested: they underestimate the relative importance of the most concerted motions. Finally, we characterize ENMs' resilience by tessellating the parameter space to show that broad ranges of parameters produce similar quality predictions. Taken together our data reveals that choice of spring function and parameters are not vital to performance of a network model and that simple parameters can by derived "by hand" when no data is available for fitting, thus illustrating the robustness of these models.

The interface of protein structure, protein biophysics, and molecular evolution

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.

On the applicability of elastic network normal modes in small-molecule docking

Incorporating backbone flexibility into protein-ligand docking is still a challenging problem. In protein-protein docking, normal mode analysis (NMA) has become increasingly popular as it can be used to describe the collective motions of a biological system, but the question of whether NMA can also be useful in predicting the conformational changes observed upon small-molecule binding has only been addressed in a few case studies. Here, we describe a large-scale study on the applicability of NMA for protein-ligand docking using 433 apo/holo pairs of the Astex data sets. On the basis of sets of the first normal modes from the apo structure, we first generated for each paired holo structure a set of conformations that optimally reproduce its C(α) trace with respect to the underlying normal mode subspace. Using AutoDock, GOLD, and FlexX we then docked the original ligands into these conformations to assess how the docking performance depends on the number of modes used to reproduce the holo structure. The results of our study indicate that, even for such a best-case scenario, the use of normal mode analysis in small-molecule docking is restricted and that a general rule on how many modes to use does not seem to exist or at least is not easy to find.

Normal mode-based approaches in receptor ensemble docking

Explicitly accounting for target flexibility in docking still constitutes a difficult challenge due to the high dimensionality of the conformational space to be sampled. This especially applies to the high-throughput scenario, where the screening of hundreds of thousands compounds takes place. The use of multiple receptor conformations (MRCs) to perform ensemble docking in a sequential fashion is a simple but powerful approach that allows to incorporate binding site structural diversity in the docking process. Whenever enough experimental structures to build a diverse ensemble are not available, normal mode analysis provides an appealing and efficient approach to in silico generate MRCs by distortion along few low-frequency modes that represent collective mid- and large-scale displacements. In this way, the dimension of the conformational space to be sampled is heavily reduced. This methodology is especially suited to incorporate target flexibility at the backbone level. In this chapter, the main components of normal mode-based approaches in the context of ensemble docking are presented and explained, including the theoretical and practical considerations needed for the successful development and implementation of this methodology.

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Characterizing protein motions from structure

To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

ATP binding enables broad antibiotic selectivity of aminoglycoside phosphotransferase(3')-IIIa: an elastic network analysis

The bacterial enzyme aminoglycoside phosphotransferase(3')-IIIa (APH) confers resistance against a wide range of aminoglycoside antibiotics. In this study, we use the Gaussian network model to investigate how the binding of nucleotides and antibiotics influences the dynamics and thereby the ligand binding properties of APH. Interestingly, in NMR experiments, the dynamics differ significantly in various APH complexes, although crystallographic studies indicate that no larger conformational changes occur upon ligand binding. Isothermal titration calorimetry also shows different thermodynamic contributions to ligand binding. Formation of aminoglycoside-APH complexes is enthalpically driven, while the enthalpic change upon aminoglycoside binding to the nucleotide-APH complex is much smaller. The differential effects of nucleotide binding and antibiotic binding to APH can be explained theoretically by single-residue fluctuations and correlated motions of the enzyme. The surprising destabilization of β-sheet residues upon nucleotide binding, as seen in hydrogen/deuterium exchange experiments, shows that the number of closest neighbors does not fully explain residue flexibility. Additionally, we must consider correlated motions of dynamic protein domains, which show that not only connectivity but also the overall protein architecture is important for protein dynamics.