Ligand-induced protein responses and mechanical signal propagation described by linear response theories

Dynamics-based protein network features accurately discriminate neutral and rheostat positions

In some proteins, a unique class of nonconserved positions is characterized by their ability to generate diverse functional outcomes through single amino acid substitutions. Due to their ability to tune protein function, accurately identifying such "rheostat" positions is crucial for protein design, for understanding the impact of mutations observed in humans, and for predicting the evolution of pathogen drug resistance. However, identifying rheostat positions has been challenging, due-in part-to the absence of a clear structural relationship with binding sites. In this study, experimental data from our previous study of the Escherichia coli lactose repressor protein (LacI) was used to identify rheostat positions for which mutations tune in vivo EC50 for the allosteric ligand "IPTG." We next used the rheostat assignments to test the hypothesis that rheostat positions have unique dynamic features that will enable their identification. To that end, we integrated all-atom molecular dynamics simulations with perturbation residue response analysis. Results first revealed distinct dynamic behavior in IPTG-bound LacI compared with apo LacI, which was consistent with IPTG's role as an allosteric inducer. Next, we used a variety of dynamic features to build a classification model that discriminates experimentally characterized rheostat positions in LacI from positions with other types of substitution outcomes. In parallel, we built a second classifier model based on the 3D structural "static" network features of LacI. In comparative studies, the dynamic model better identified rheostat positions that were >8 Å from the binding site. In summary, our study provides insights into the dynamic characteristics of rheostat positions and suggests that models built on dynamic features may be useful for predicting the locations of rheostat positions in a wide range of proteins.

Probing local changes to α-helical structures with 2D IR spectroscopy and isotope labeling

α-Helical secondary structures impart specific mechanical and physiochemical properties to peptides and proteins, enabling them to perform a vast array of molecular tasks ranging from membrane insertion to molecular allostery. Loss of α-helical content in specific regions can inhibit native protein function or induce new, potentially toxic, biological activities. Thus, identifying specific residues that exhibit loss or gain of helicity is critical for understanding the molecular basis of function. Two-dimensional infrared (2D IR) spectroscopy coupled with isotope labeling is capable of capturing detailed structural changes in polypeptides. Yet, questions remain regarding the inherent sensitivity of isotope-labeled modes to local changes in α-helicity, such as terminal fraying; the origin of spectral shifts (hydrogen-bonding versus vibrational coupling); and the ability to definitively detect coupled isotopic signals in the presence of overlapping side chains. Here, we address each of these points individually by characterizing a short, model α-helix (DPAEAAKAAAGR-NH2) with 2D IR and isotope labeling. These results demonstrate that pairs of 13C18O probes placed three residues apart can detect subtle structural changes and variations along the length of the model peptide as the α-helicity is systematically tuned. Comparison of singly and doubly labeled peptides affirm that frequency shifts arise primarily from hydrogen-bonding, while vibrational coupling between paired isotopes leads to increased peak areas that can be clearly differentiated from underlying side-chain modes or uncoupled isotope labels not participating in helical structures. These results demonstrate that 2D IR in tandem with i,i+3 isotope-labeling schemes can capture residue-specific molecular interactions within a single turn of an α-helix.

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

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.

Helical structure motifs made searchable for functional peptide design

The systematic design of functional peptides has technological and therapeutic applications. However, there is a need for pattern-based search engines that help locate desired functional motifs in primary sequences regardless of their evolutionary conservation. Existing databases such as The Protein Secondary Structure database (PSS) no longer serves the community, while the Dictionary of Protein Secondary Structure (DSSP) annotates the secondary structures when tertiary structures of proteins are provided. Here, we extract 1.7 million helices from the PDB and compile them into a database (Therapeutic Peptide Design database; TP-DB) that allows queries of compounded patterns to facilitate the identification of sequence motifs of helical structures. We show how TP-DB helps us identify a known purification-tag-specific antibody that can be repurposed into a diagnostic kit for Helicobacter pylori. We also show how the database can be used to design a new antimicrobial peptide that shows better Candida albicans clearance and lower hemolysis than its template homologs. Finally, we demonstrate how TP-DB can suggest point mutations in helical peptide blockers to prevent a targeted tumorigenic protein-protein interaction. TP-DB is made available at http://dyn.life.nthu.edu.tw/design/ .

Molecular dynamics simulations and linear response theories jointly describe biphasic responses of myoglobin relaxation and reveal evolutionarily conserved frequent communicators

In this study, we provide a time-dependent mechanical model, taking advantage of molecular dynamics simulations, quasiharmonic analysis of molecular dynamics trajectories, and time-dependent linear response theories to describe vibrational energy redistribution within the protein matrix. The theoretical description explained the observed biphasic responses of specific residues in myoglobin to CO-photolysis and photoexcitation on heme. The fast responses were found to be triggered by impulsive forces and propagated mainly by principal modes <40 cm⁻¹. The predicted fast responses for individual atoms were then used to study signal propagation within the protein matrix and signals were found to propagate ~8 times faster across helices (4076 m/s) than within the helices, suggesting the importance of tertiary packing in the sensitivity of proteins to external perturbations. We further developed a method to integrate multiple intramolecular signal pathways and discover frequent “communicators”. These communicators were found to be evolutionarily conserved including those distant from the heme.

Resolution-exchanged structural modeling and simulations jointly unravel that subunit rolling underlies the mechanism of programmed ribosomal frameshifting

MOTIVATION

Programmed ribosomal frameshifting (PRF) is widely used by viruses and bacteria to produce different proteins from a single mRNA template. How steric hindrance of a PRF-stimulatory mRNA structure transiently modifies the conformational dynamics of the ribosome, and thereby allows tRNA slippage, remains elusive.

RESULTS

Here, we leverage linear response theories and resolution-exchanged simulations to construct a structural/dynamics model that connects and rationalizes existing structural, single-molecule and mutagenesis data by resolution-exchanged structural modelling and simulations. Our combined theoretical techniques provide a temporal and spatial description of PRF with unprecedented mechanistic details. We discover that ribosomal unfolding of the PRF-stimulating pseudoknot exerts resistant forces on the mRNA entrance of the ribosome, and thereby drives 30S subunit rolling. Such motion distorts tRNAs, leads to tRNA slippage, and in turn serves as a delicate control of cis-element's unwinding forces over PRF.

AVAILABILITY AND IMPLEMENTATION

All the simulation scripts and computational implementations of our methods/analyses (including linear response theory) are included in the bioStructureM suite, provided through GitHub at https://github.com/Yuan-Yu/bioStructureM.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An Efficient Timer and Sizer of Biomacromolecular Motions

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods," t, for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods" are mapped to the eigenvalues (λ_ENM) of the corresponding ENM modes. Thus, the power laws t(ns) = 56.1λ_ENM^-1.6 and σ²(Ų) = 32.7λ_ENM^-3.0 can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.

DynOmics: dynamics of structural proteome and beyond

DynOmics (dynomics.pitt.edu) is a portal developed to leverage rapidly growing structural proteomics data by efficiently and accurately evaluating the dynamics of structurally resolved systems, from individual molecules to large complexes and assemblies, in the context of their physiological environment. At the core of the portal is a newly developed server, ENM 1.0, which permits users to efficiently generate information on the collective dynamics of any structure in PDB format, user-uploaded or database-retrieved. ENM 1.0 integrates two widely used elastic network models (ENMs)—the Gaussian Network Model (GNM) and the Anisotropic Network Model (ANM), extended to take account of molecular environment. It enables users to assess potentially functional sites, signal transduction or allosteric communication mechanisms, and protein–protein and protein–DNA interaction poses, in addition to delivering ensembles of accessible conformers reconstructed at atomic details based on the global modes of motions predicted by the ANM. The ‘environment’ is defined in a flexible manner, from lipid bilayer and crystal contacts, to substrate or ligands bound to a protein, or surrounding subunits in a multimeric structure or assembly. User-friendly interactive features permit users to easily visualize how the environment alter the intrinsic dynamics of the query systems. ENM 1.0 can be accessed at http://enm.pitt.edu/ or http://dyn.life.nthu.edu.tw/oENM/.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

A computational model for controlling conformational cooperativity and function in proteins

We present a computational model that allows for rapid prediction of correlations among a set of residue pairs when the fluctuations of another set of residues are perturbed. The simple theory presented here is based on the knowledge of the fluctuation covariance matrix only. In this sense, the theory is model independent and therefore universal. Perturbation of any set of fluctuations and the resulting response of the remaining set are calculated using conditional probabilities of a multivariate normal distribution. The model is expected to rapidly and accurately map the consequences of mutations in proteins, as well as allosteric activity and ligand binding. Knowledge of triple correlations of fluctuations of residues i, j, and k, 〈 Δ R i Δ R j Δ R k 〉 emerges as the necessary source of information for controlling residue pairs by perturbing a distant residue. Triple correlations have not received wide attention in literature. Perturbation-response-function relations for ubiquitin (UBQ) are discussed as an example. Covariance matrix for UBQ obtained from the Gaussian Network Model combined with the present computational algorithm is able to reflect the millisecond molecular dynamics correlations and observed NMR results. © 2018 Wiley Periodicals, Inc.

The In Situ Tryptophan Analogue Probes the Conformational Dynamics in Asparaginase Isozymes

Dynamic water solvation is crucial to protein conformational reorganization and hence to protein structure and functionality. We report here the characterization of water dynamics on the L-asparaginase structural homology isozymes L-asparaginases I (AnsA) and II (AnsB), which are shown via fluorescence spectroscopy and dynamics in combination with molecular dynamics simulation to have distinct catalytic activity. By use of the tryptophan (Trp) analog probe 2,7-diaza-tryptophan ((2,7-aza)Trp), which exhibits unique water-catalyzed proton-transfer properties, AnsA and AnsB are shown to have drastically different local water environments surrounding the single Trp. In AnsA, (2,7-aza)Trp exhibits prominent green N(7)-H emission resulting from water-catalyzed excited-state proton transfer. In stark contrast, the N(7)-H emission is virtually absent in AnsB, which supports a water-accessible and a water-scant environment in the proximity of Trp for AnsA and AnsB, respectively. In addition, careful analysis of the emission spectra and corresponding relaxation dynamics, together with the results of molecular dynamics simulations, led us to propose two structural states associated with the rearrangement of the hydrogen-bond network in the vicinity of Trp for the two Ans. The water molecules revealed in the proximity of the Trp residue have semiquantitative correlation with the observed emission spectral variations of (2,7-aza)Trp between AnsA and AnsB. Titration of aspartate, a competitive inhibitor of Ans, revealed an increase in N(7)-H emission intensity in AnsA but no obvious spectral changes in AnsB. The changes in the emission profiles reflect the modulation of structural states by locally confined environment and trapped-water collective motions.

Adaptive BP-Dock: An Induced Fit Docking Approach for Full Receptor Flexibility

We present an induced fit docking approach called Adaptive BP-Dock that integrates perturbation response scanning (PRS) with the flexible docking protocol of RosettaLigand in an adaptive manner. We first perturb the binding pocket residues of a receptor and obtain a new conformation based on the residue response fluctuation profile using PRS. Next, we dock a ligand to this new conformation by RosettaLigand, where we repeat these steps for several iterations. We test this approach on several protein test sets including difficult unbound docking cases such as HIV-1 reverse transcriptase and HIV-1 protease. Adaptive BP-Dock results show better correlation with experimental binding affinities compared to other docking protocols. Overall, the results imply that Adaptive BP-Dock can easily capture binding induced conformational changes by simultaneous sampling of protein and ligand conformations. This can provide faster and efficient docking of novel targets for rational drug design.

Long-Range Conformational Response of a PDZ Domain to Ligand Binding and Release: A Molecular Dynamics Study

The binding of a ligand to a protein may induce long-range structural or dynamical changes in the biomacromolecule even at sites physically well separated from the binding pocket. A system for which such behavior has been widely discussed is the PDZ2 domain of human tyrosine phosphatase 1E. Here, we present results from equilibrium trajectories of the PDZ2 domain in the free and ligand-bound state, as well as nonequilibrium simulations of the relaxation of PDZ2 after removal of its peptide ligand. The study reveals changes in inter-residue contacts, backbone dihedral angles, and C(α) positions upon ligand release. Our findings show a long-range conformational response of the PDZ2 domain to ligand release in the form of a collective shift of the secondary structure elements α2, β2, β3, α1-β4, and the C terminal loop relative to the rest of the protein away from the N-terminus, and a shift of the loops β2-β3 and β1-β2 in the opposite direction. The shifts lead to conformational changes in the backbone, especially in the β2-β3 loop but also in the β5-α2 and the α2-β6 loop, and are accompanied by changes of inter-residue contacts mainly within the β2-β3 loop as well as between the α2 helix and other segments. The residues showing substantial changes of inter-residue contacts, backbone conformations, or C(α) positions are considered "key residues" for the long-range conformational response of PDZ2. By comparing these residues with various sets of residues highlighted by previous studies of PDZ2, we investigate the statistical correlation of the various approaches. Interestingly, we find a considerable correlation of our findings with several works considering structural changes but no significant correlations with approaches considering energy flow or networks based on inter-residue energies.