Coarse-grained Elastic Network Models Research Articles

The ribosome structure controls and directs mRNA entry, translocation and exit dynamics

The protein-synthesizing ribosome undergoes large motions to effect the translocation of tRNAs and mRNA; here, the domain motions of this system are explored with a coarse-grained elastic network model using normal mode analysis. Crystal structures are used to construct various model systems of the 70S complex with/without tRNA, elongation factor Tu and the ribosomal proteins. Computed motions reveal the well-known ratchet-like rotational motion of the large subunits, as well as the head rotation of the small subunit and the high flexibility of the L1 and L7/L12 stalks, even in the absence of ribosomal proteins. This result indicates that these experimentally observed motions during translocation are inherently controlled by the ribosomal shape and only partially dependent upon GTP hydrolysis. Normal mode analysis further reveals the mobility of A- and P-tRNAs to increase in the absence of the E-tRNA. In addition, the dynamics of the E-tRNA is affected by the absence of the ribosomal protein L1. The mRNA in the entrance tunnel interacts directly with helicase proteins S3 and S4, which constrain the mRNA in a clamp-like fashion, as well as with protein S5, which likely orients the mRNA to ensure correct translation. The ribosomal proteins S7, S11 and S18 may also be involved in assuring translation fidelity by constraining the mRNA at the exit site of the channel. The mRNA also interacts with the 16S 3′ end forming the Shine–Dalgarno complex at the initiation step; the 3′ end may act as a ‘hook’ to reel in the mRNA to facilitate its exit.

Correspondences between low‐energy modes in enzymes: Dynamics‐based alignment of enzymatic functional families

Proteins that show similarity in their equilibrium dynamics can be aligned by identifying regions that undergo similar concerted movements. These movements are computed from protein native structures using coarse-grained elastic network models. We show the existence of common large-scale movements in enzymes selected from the main functional and structural classes. Alignment via dynamics does not require prior detection of sequence or structural correspondence. Indeed, a third of the statistically significant dynamics-based alignments involve enzymes that lack substantial global or local structural similarities. The analysis of specific residue-residue correspondences of these structurally dissimilar enzymes in some cases suggests a functional relationship of the detected common dynamic features. Including dynamics-based criteria in protein alignment thus provides a promising avenue for relating and grouping enzymes in terms of dynamic aspects that often, though not always, assist or accompany biological function.

Toward a Molecular Understanding of the Anisotropic Response of Proteins to External Forces: Insights from Elastic Network Models

With recent advances in single-molecule manipulation techniques, it is now possible to measure the mechanical resistance of proteins to external pulling forces applied at specific positions. Remarkably, such recent studies demonstrated that the pulling/stretching forces required to initiate unfolding vary considerably depending on the location of the application of the forces, unraveling residue/position-specific response of proteins to uniaxial tension. Here we show that coarse-grained elastic network models based on the topology of interresidue contacts in the native state can satisfactory explain the relative sizes of such stretching forces exerted on different residue pairs. Despite their simplicity, such models presumably capture a fundamental property that dominates the observed behavior: deformations that can be accommodated by the relatively lower frequency modes of motions intrinsically favored by the structure require weaker forces and vice versa. The mechanical response of proteins to external stress is therefore shown to correlate with the anisotropic fluctuation dynamics intrinsically accessible in the folded state. The dependence on the overall fold implies that evolutionarily related proteins sharing common structural features tend to possess similar mechanical properties. However, the theory cannot explain the differences observed in a number of structurally similar but sequentially distant domains, such as the fibronectin domains.

Langevin Network Model of Myosin

Langevin mode theory and the coarse-grained elastic network model (ENM) for proteins are combined to yield the Langevin network model (LNM). Hydrodynamic radii of 6 A were assigned to each alpha-carbon on the basis of matching experimental translational and rotational diffusion constants of lysozyme, myoglobin, and hemoglobin with those calculated using a rigid body bead model with hydrodynamic interactions described by the Rotne-Prager tensor. LNM analysis of myosin II indicates that all ENM-like modes are overdamped at water viscosities. The low-frequency LNM modes in the pre-power stroke structure (PDB code: 1VOM) are substantially less mixed than the corresponding modes of the post-power stroke structure (1Q5G). Results from a four-bead model of the myosin "lever arm" indicate that coupling between modes increases as the array departs from linearity and are consistent with the results for 1VOM and 1Q5G. The decay times for all overdamped Langevin modes are shorter than the calculated rotational tumbling times found for lysozyme and myosin.

Combining Elastic Network Analysis and Molecular Dynamics Simulations by Hamiltonian Replica Exchange.

Coarse-grained elastic network models (ENM) of proteins can be used efficiently to explore the global mobility of a protein around a reference structure. A new Hamiltonian-replica exchange molecular dynamics (H-RexMD) method has been designed that effectively combines information extracted from an ENM analysis with atomic-resolution MD simulations. The ENM analysis is used to construct a distance-dependent penalty (flooding or biasing) potential that can drive the structure away from its current conformation in directions compatible with the ENM model. Various levels of the penalty or biasing potential are added to the force field description of the MD simulation along the replica coordinate. One replica runs at the original force field. By focusing the penalty potential on the relevant soft degrees of freedom the method avoids the rapid increase of the replica number with increasing system size to cover a desired temperature range in conventional (temperature) RexMD simulations. The application to domain motions in lysozyme of bacteriophage T4 and to peptide folding indicates significantly improved conformational sampling compared to conventional MD simulations.

Coarse-grained models reveal functional dynamics--I. Elastic network models--theories, comparisons and perspectives.

In this review, we summarize the progress on coarse-grained elastic network models (CG-ENMs) in the past decade. Theories were formulated to allow study of conformational dynamics in time/space frames of biological interest. Several highlighted models and their underlined hypotheses are introduced in physical depth. Important ENM offshoots, motivated to reproduce experimental data as well as to address the slow-mode-encoded configurational transitions, are also introduced. With the theoretical developments, computational cost is significantly reduced due to simplified potentials and coarse-grained schemes. Accumulating wealth of data suggest that ENMs agree equally well with experiment in describing equilibrium dynamics despite their distinct potentials and levels of coarse-graining. They however do differ in the slowest motional components that are essential to address large conformational changes of functional significance. The difference stems from the dissimilar curvatures of the harmonic energy wells described for each model. We also provide our views on the predictability of 'open to close' (open-->close) transitions of biomolecules on the basis of conformational selection theory. Lastly, we address the limitations of the ENM formalism which are partially alleviated by the complementary CG-MD approach, to be introduced in the second paper of this two-part series.

How Well Can We Understand Large-Scale Protein Motions Using Normal Modes of Elastic Network Models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having “open” and “closed” structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.

The Extent of Cooperativity of Protein Motions Observed with Elastic Network Models Is Similar for Atomic and Coarser-Grained Models.

Coarse-grained elastic network models have been successful in determining functionally relevant collective motions. The level of coarse-graining, however, has usually focused on the level of one point per residue. In this work, we compare the applicability of elastic network models over a broader range of representational scales. We apply normal mode analysis for multiple scales on a high-resolution protein data set using various cutoff radii to define the residues considered to be interacting, or the extent of cooperativity of their motions. These scales include the residue-, atomic-, proton-, and explicit solvent-levels. Interestingly, atomic, proton, and explicit solvent level calculations all provide similar results at the same cutoff value, with the computed mean-square fluctuations showing only a slightly higher correlation (0.61) with the experimental temperature factors from crystallography than the results of the residue-level coarse-graining. The qualitative behavior of each level of coarse graining is similar at different cutoff values. The correlations between these fluctuations and the number of internal contacts improve with increased cutoff values. Our results demonstrate that atomic level elastic network models provide an improved representation for the collective motions of proteins compared to the coarse-grained models.

A connection rule for [formula omitted]-carbon coarse-grained elastic network models using chemical bond information

A sparser but more efficient connection rule (called a bond-cutoff method) for a simplified α -carbon coarse-grained elastic network model is presented. One of conventional connection rules for elastic network models is the distance-cutoff method, where virtual springs connect an α -carbon with all neighbor α -carbons within predefined distance-cutoff value. However, though the maximum interaction distance between α -carbons is reported as 7Å, this cutoff value can make the elastic network unstable in many cases of protein structures. Thus, a larger cutoff value (>11Å) is often used to establish a stable elastic network model in previous researches. To overcome this problem, a connection rule for backbone model is proposed, which satisfies the minimum condition to stabilize an elastic network. Based on the backbone connections, each type of chemical interactions is considered and added to the elastic network model: disulfide bonds, hydrogen bonds, and salt-bridges. In addition, the van der Waals forces between α -carbons are modeled by using the distance-cutoff method. With the proposed connection rule, one can make an elastic network model with less than 7Å distance cutoff, which can reveal protein flexibility more sharply. Moreover, the normal modes from the new elastic network model can reflect conformational changes of a given protein better than ones by the distance-cutoff method. This method can save the computational cost when calculating normal modes of a given protein structure, because it can reduce the total number of connections. As a validation, six example proteins are tested. Computational times and the overlap values between the conformational change and infinitesimal motion calculated by normal mode analysis are presented. Those animations are also available at UMass Morph Server ( http://biomechanics.ecs.umass.edu/umms.html).

Collective Dynamics of Large Proteins from Mixed Coarse-Grained Elastic Network Model

Elastic network model- a coarse-grained normal mode analysis- is widely used to investigate the functionally important collective motions of proteins and their complexes. Mixed coarse-graining approach has been recently introduced to the elastic network model, so that the protein's native conformation can be modeled with regions of low and high resolution. In the mixed resolution model, each node of the elastic network may represent either a single atom (high-resolution) or a residue (low-resolution), and close-neighboring nodes are connected by harmonic springs. Here, the high-resolution parts constitute the interesting parts of the protein, such as the active site, while the rest of the structure is retained at lower resolution. By performing normal mode analysis of the resulting network, the collective dynamics (low-frequency modes) and consequent conformational changes can be analyzed even for supramolecular assemblages with reasonable computational efficiency, which may serve as a means of incorporating protein flexibility into docking algorithms and drug design. In this study, the mixed coarse-graining methodology is applied to analyze the functional motions of an important enzyme, triosephosphate isomerase.

How Does Protein Architecture Facilitate the Transduction of ATP Chemical-Bond Energy into Mechanical Work? The Cases of Nitrogenase and ATP Binding-Cassette Proteins

Transduction of adenosine triphosphate (ATP) chemical-bond energy into work to drive large-scale conformational changes is common in proteins. Two specific examples of ATP-utilizing proteins are the nitrogenase iron protein and the ATP binding-cassette transporter protein, BtuCD. Nitrogenase catalyzes biological nitrogen fixation whereas BtuCD transports vitamin B 12 across membranes. Both proteins drive their reactions with ATP. To interpret how the mechanical force generated by ATP binding and hydrolysis is propagated in these proteins, a coarse-grained elastic network model is employed. The analysis shows that subunits of the proteins move against each other in a concerted manner. The lowest-frequency modes of the nitrogenase iron protein and of the ATP binding-cassette transporter BtuCD protein are found to link the functionally critical domains, and these modes are suggested to be responsible for (at least the initial stages) large-scale ATP-coupled conformational changes.

Myosin flexibility: structural domains and collective vibrations.

The movement of the myosin motor along an actin filament involves a directed conformational change within the cross-bridge formed between the protein and the filament. Despite the structural data that has been obtained on this system, little is known of the mechanics of this conformational change. We have used existing crystallographic structures of three conformations of the myosin head, containing the motor domain and the lever arm, for structural comparisons and mechanical studies with a coarse-grained elastic network model. The results enable us to define structurally conserved domains within the protein and to better understand myosin flexibility. Notably they point to the role of the light chains in rigidifying the lever arm and to changes in flexibility as a consequence of nucleotide binding.

Efficiently explore the energy landscape of proteins in molecular dynamics simulations by amplifying collective motions

We describe a method for efficient sampling of the energy landscape of a protein in atomic molecular dynamics simulations. A simulation is divided into alternatively occurring relaxation phases and excitation phases. In the relaxation phase (conventional simulation), we use a frequently updated reference structure and deviations from this reference structure to mark whether the system has been trapped in a local minimum. In that case, the simulation enters the excitation phase, during which a few slow collective modes of the system are coupled to a higher temperature bath. After the system has escaped from the minimum (also judged by deviations from the reference structure) the simulation reenters the relaxation phase. The collective modes are obtained from a coarse-grained Gaussian elastic network model. The scheme, which we call ACM-AME (amplified collective motion-assisted minimum escaping), is compared with conventional simulations as well as an alternative scheme that elevates the temperature of all degrees of freedom during the excitation phase (amplified overall motion-assisted minimum escaping, or AOM-AME). Comparison is made using simulations on four peptides starting from non-native extended or all helical structures. In terms of sampling low energy conformations and continuously sampling new conformations throughout a simulation, the ACM-AME scheme demonstrates very good performance while the AOM-AME scheme shows little improvement upon conventional simulations. Limited success is achieved in producing structures close to the native structures of the peptides: for an S-peptide analog, the ACM-AME approach is able to reproduce its native helical structure, and starting from an all-helical structure of the villin headpiece subdomain (HP-36) in implicit solvent, two out of three 150 ns ACM-AME runs are able to sample structures with 3–4 Å backbone root-mean-square deviations from the nuclear magnetic resonance structure of the protein.

Efficient Generation of Feasible Pathways for Protein Conformational Transitions

We develop a computationally efficient method to simulate the transition of a protein between two conformations. Our method is based on a coarse-grained elastic network model in which distances between spatially proximal amino acids are interpolated between the values specified by the two end conformations. The computational speed of this method depends strongly on the choice of cutoff distance used to define interactions as measured by the density of entries of the constant linking/contact matrix. To circumvent this problem we introduce the concept of using a cutoff based on a maximum number of nearest neighbors. This generates linking matrices that are both sparse and uniform, hence allowing for efficient computations that are independent of the arbitrariness of cutoff distance choices. Simulation results demonstrate that the method developed here reliably generates feasible intermediate conformations, because our method observes steric constraints and produces monotonic changes in virtual bond and torsion angles. Applications are readily made to large proteins, and we demonstrate our method on lactate dehydrogenase, citrate synthase, and lactoferrin. We also illustrate how this framework can be used to complement experimental techniques that partially observe protein motions.

Elastic models of conformational transitions in macromolecules

We develop a computationally efficient and physically realistic method to simulate the transition of a macromolecule between two conformations. Our method is based on a coarse-grained elastic network model in which contact interactions between spatially proximal parts of the macromolecule are modelled with Gaussian/harmonic potentials. To delimit the interactions in such models, we introduce a cutoff to the permitted number of nearest neighbors. This generates stiffness (Hessian) matrices that are both sparse and quite uniform, hence, allowing for efficient computations. Several toy models are tested using our method to mimic simple classes of macromolecular motions such as stretching, hinge bending, shear, compression, ligand binding and nucleic acid structural transitions. Simulation results demonstrate that the method developed here reliably generates sequences of feasible intermediate conformations of macromolecules, since our method observes steric constraints and produces monotonic changes to virtual bond angles and torsion angles. A final application is made to the opening process of the protein lactoferrin.