Features of large hinge-bending conformational transitions. Prediction of closed structure from open state

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small ligands is of fundamental importance for understanding molecular principles of chemotherapy and for designing new and more effective drugs. Due to the still high costs and to the several limitations of experimental techniques, it is most often desirable to predict these ligand-protein complexes in silico, particularly when screening for new putative drugs from databases of millions of compounds. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology aimed at generating bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites. Validation was performed on the enzyme adenylate kinase (ADK), a paradigmatic example of proteins that undergo very large conformational changes upon ligand binding. By only exploiting the unbound structure and the putative binding sites of the protein, we generated a significant fraction of bound-like structures, which employed in ensemble-docking calculations allowed to find native-like poses of substrates, inhibitors, and catalytically incompetent binders. Our protocol provides a general framework for the generation of bound-like conformations of flexible proteins that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening for difficult targets, prediction of the impact of amino acid mutations on structure and dynamics, and protein engineering.

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

Protein conformational transitions explored by a morphing approach based on normal mode analysis in internal coordinates

Large-scale conformational changes are essential for proteins to function properly. Given that these transition events rarely occur, however, it is challenging to comprehend their underlying mechanisms through experimental and theoretical approaches. In this study, we propose a new computational methodology called internal coordinate normal mode-guided elastic network interpolation (ICONGENI) to predict conformational transition pathways in proteins. Its basic approach is to sample intermediate conformations by interpolating the interatomic distance between two end-point conformations with the degrees of freedom constrained by the low-frequency dynamics afforded by normal mode analysis in internal coordinates. For validation of ICONGENI, it is applied to proteins that undergo open-closed transitions, and the simulation results (i.e., simulated transition pathways) are compared with those of another technique, to demonstrate that ICONGENI can explore highly reliable pathways in terms of thermal and chemical stability. Furthermore, we generate an ensemble of transition pathways through ICONGENI and investigate the possibility of using this method to reveal the transition mechanisms even when there are unknown metastable states on rough energy landscapes.

Exploring Conformational Space with Thermal Fluctuations Obtained by Normal-Mode Analysis

Proteins in their native states can be represented as ensembles of conformers in dynamical equilibrium. Thermal fluctuations are responsible for transitions between these conformers. Normal-modes analysis (NMA) using elastic network models (ENMs) provides an efficient procedure to explore global dynamics of proteins commonly associated with conformational transitions. In the present work, we present an iterative approach to explore protein conformational spaces by introducing structural distortions according to their equilibrium dynamics at room temperature. The approach can be used either to perform unbiased explorations of conformational space or to explore guided pathways connecting two different conformations, e.g., apo and holo forms. In order to test its performance, four proteins with different magnitudes of structural distortions upon ligand binding have been tested. In all cases, the conformational selection model has been confirmed and the conformational space between apo and holo forms has been encompassed. Different strategies have been tested that impact on the efficiency either to achieve a desired conformational change or to achieve a balanced exploration of the protein conformational multiplicity.

Essential site scanning analysis: A new approach for detecting sites that modulate the dispersion of protein global motions

Despite the wealth of methods developed for exploring the molecular basis of allostery in biomolecular systems, there is still a need for structure-based predictive tools that can efficiently detect susceptible sites for triggering allosteric responses. Toward this goal, we introduce here an elastic network model (ENM)-based method, Essential Site Scanning Analysis (ESSA). Essential sites are here defined as residues that would significantly alter the protein's global dynamics if bound to a ligand. To mimic the crowding induced upon substrate binding, the heavy atoms of each residue are incorporated as additional network nodes into the α-carbon-based ENM, and the resulting shifts in soft mode frequencies are used as a metric for evaluating the essentiality of each residue. Results on a dataset of monomeric proteins indicate the enrichment of allosteric and orthosteric binding sites, as well as global hinge regions among essential residues, highlighting the significant role of these sites in controlling the overall structural dynamics. Further integration of ESSA with information on predicted pockets and their local hydrophobicity density enables successful predictions of allosteric pockets for both ligand-bound and -unbound structures. ESSA can be efficiently applied to large multimeric systems. Three case studies, namely (i) G-protein binding to a GPCR, (ii) heterotrimeric assembly of the Ser/Thr protein phosphatase PP2A, and (iii) allo-targeting of AMPA receptor, demonstrate the utility of ESSA for identifying essential sites and narrowing down target allosteric sites identified by druggability simulations.

Protein-Ligand Complexes as Constrained Dynamical Systems

This study focuses on how the low-frequency end of the vibrational spectrum related to the functional motions changes as a protein binds to a small ligand(s). Our recently proposed residue-specific (RESPEC) elastic network model provides a natural laboratory for this aim due to its systematic mixed coarse-graining approach and parametrization. Current analysis on a large data set of protein-ligand complexes reveals a universal curve enclosing the frequency distributions, which bears the features of previous computational and experimental studies. We mostly observe positive frequency shifts in the collective modes of the protein upon ligand binding. This observation, conforming to the Rayleigh-Courant-Fisher theorem, points to a constraining effect imposed by ligands on protein dynamics, which may be accompanied by a negative vibrational entropy difference. Positive frequency shifts in the global modes can thus be linked to the harmonic well getting steeper, because of interactions with the ligand(s).

Normal mode-guided transition pathway generation in proteins

The biological function of proteins is closely related to its structural motion. For instance, structurally misfolded proteins do not function properly. Although we are able to experimentally obtain structural information on proteins, it is still challenging to capture their dynamics, such as transition processes. Therefore, we need a simulation method to predict the transition pathways of a protein in order to understand and study large functional deformations. Here, we present a new simulation method called normal mode-guided elastic network interpolation (NGENI) that performs normal modes analysis iteratively to predict transition pathways of proteins. To be more specific, NGENI obtains displacement vectors that determine intermediate structures by interpolating the distance between two end-point conformations, similar to a morphing method called elastic network interpolation. However, the displacement vector is regarded as a linear combination of the normal mode vectors of each intermediate structure, in order to enhance the physical sense of the proposed pathways. As a result, we can generate more reasonable transition pathways geometrically and thermodynamically. By using not only all normal modes, but also in part using only the lowest normal modes, NGENI can still generate reasonable pathways for large deformations in proteins. This study shows that global protein transitions are dominated by collective motion, which means that a few lowest normal modes play an important role in this process. NGENI has considerable merit in terms of computational cost because it is possible to generate transition pathways by partial degrees of freedom, while conventional methods are not capable of this.

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.

ClustENM: ENM-Based Sampling of Essential Conformational Space at Full Atomic Resolution

Accurate sampling of conformational space and, in particular, the transitions between functional substates has been a challenge in molecular dynamic (MD) simulations of large biomolecular systems. We developed an Elastic Network Model (ENM)-based computational method, ClustENM, for sampling large conformational changes of biomolecules with various sizes and oligomerization states. ClustENM is an iterative method that combines ENM with energy minimization and clustering steps. It is an unbiased technique, which requires only an initial structure as input, and no information about the target conformation. To test the performance of ClustENM, we applied it to six biomolecular systems: adenylate kinase (AK), calmodulin, p38 MAP kinase, HIV-1 reverse transcriptase (RT), triosephosphate isomerase (TIM), and the 70S ribosomal complex. The generated ensembles of conformers determined at atomic resolution show good agreement with experimental data (979 structures resolved by X-ray and/or NMR) and encompass the subspaces covered in independent MD simulations for TIM, p38, and RT. ClustENM emerges as a computationally efficient tool for characterizing the conformational space of large systems at atomic detail, in addition to generating a representative ensemble of conformers that can be advantageously used in simulating substrate/ligand-binding events.

Ligand Docking to Intermediate and Close-To-Bound Conformers Generated by an Elastic Network Model Based Algorithm for Highly Flexible Proteins

Incorporating receptor flexibility in small ligand-protein docking still poses a challenge for proteins undergoing large conformational changes. In the absence of bound structures, sampling conformers that are accessible by apo state may facilitate docking and drug design studies. For this aim, we developed an unbiased conformational search algorithm, by integrating global modes from elastic network model, clustering and energy minimization with implicit solvation. Our dataset consists of five diverse proteins with apo to complex RMSDs 4.7-15 Å. Applying this iterative algorithm on apo structures, conformers close to the bound-state (RMSD 1.4-3.8 Å), as well as the intermediate states were generated. Dockings to a sequence of conformers consisting of a closed structure and its "parents" up to the apo were performed to compare binding poses on different states of the receptor. For two periplasmic binding proteins and biotin carboxylase that exhibit hinge-type closure of two dynamics domains, the best pose was obtained for the conformer closest to the bound structure (ligand RMSDs 1.5-2 Å). In contrast, the best pose for adenylate kinase corresponded to an intermediate state with partially closed LID domain and open NMP domain, in line with recent studies (ligand RMSD 2.9 Å). The docking of a helical peptide to calmodulin was the most challenging case due to the complexity of its 15 Å transition, for which a two-stage procedure was necessary. The technique was first applied on the extended calmodulin to generate intermediate conformers; then peptide docking and a second generation stage on the complex were performed, which in turn yielded a final peptide RMSD of 2.9 Å. Our algorithm is effective in producing conformational states based on the apo state. This study underlines the importance of such intermediate states for ligand docking to proteins undergoing large transitions.

A Model for the Molecular Mechanism of an Engineered Light-Driven Protein Machine

Controllable protein-based machines and materials are of considerable interest for diverse biotechnological applications. We previously re-engineered an ATP-driven protein machine, a group II chaperonin, to function as a light-gated nanocage. Here we develop and test a model for the molecular mechanism of the re-engineered chaperonin, which undergoes a large-scale closed to open conformational change triggered by reversible photo-isomerization of a site-specifically attached azobenzene crosslinker. In silico experiments using all-atom simulations suggest that rigid body motions of protein subdomains couple the length changes of the crosslinker to rearrangements of the nucleotide-binding pocket, leading to cage opening. We tested this model by designing a mutant for which the orientation of the two protein subdomains forming the nucleotide-binding pocket is directly controlled by the crosslinker, and confirmed successful reversible photoswitching in vitro. The model probes the conformational cycle of group II chaperonins and offers a design principle for engineering other light-driven protein-based molecular machines.

Use of network model to explore dynamic and allosteric properties of three GPCR homodimers

We used an elastic network model and protein structure network to study three class A GPCR homodimers.

Adaptability of protein structures to enable functional interactions and evolutionary implications

Several studies in recent years have drawn attention to the ability of proteins to adapt to intermolecular interactions by conformational changes along structure-encoded collective modes of motions. These so-called soft modes, primarily driven by entropic effects, facilitate, if not enable, functional interactions. They represent excursions on the conformational space along principal low-ascent directions/paths away from the original free energy minimum, and they are accessible to the protein even before protein-protein/ligand interactions. An emerging concept from these studies is the evolution of structures or modular domains to favor such modes of motion that will be recruited or integrated for enabling functional interactions. Structural dynamics, including the allosteric switches in conformation that are often stabilized upon formation of complexes and multimeric assemblies, emerge as key properties that are evolutionarily maintained to accomplish biological activities, consistent with the paradigm sequence→structure→dynamics→function where 'dynamics' bridges structure and function.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.