Fluctuations within folded proteins: implications for thermodynamic and allosteric regulation

A Humanized Yeast Model for Studying TRAPP Complex Mutations; Proof-of-Concept Using Variants from an Individual with a TRAPPC1-Associated Neurodevelopmental Syndrome

Variants in membrane trafficking proteins are known to cause rare disorders with severe symptoms. The highly conserved transport protein particle (TRAPP) complexes are key membrane trafficking regulators that are also involved in autophagy. Pathogenic genetic variants in specific TRAPP subunits are linked to neurological disorders, muscular dystrophies, and skeletal dysplasias. Characterizing these variants and their phenotypes is important for understanding the general and specialized roles of TRAPP subunits as well as for patient diagnosis. Patient-derived cells are not always available, which poses a limitation for the study of these diseases. Therefore, other systems, like the yeast Saccharomyces cerevisiae, can be used to dissect the mechanisms at the intracellular level underlying these disorders. The development of CRISPR/Cas9 technology in yeast has enabled a scar-less editing method that creates an efficient humanized yeast model. In this study, core yeast subunits were humanized by replacing them with their human orthologs, and TRAPPC1, TRAPPC2, TRAPPC2L, TRAPPC6A, and TRAPPC6B were found to successfully replace their yeast counterparts. This system was used for studying the first reported individual with an autosomal recessive disorder caused by biallelic TRAPPC1 variants, a girl with a severe neurodevelopmental disorder and myopathy. We show that the maternal variant (TRAPPC1 p.(Val121Alafs*3)) is non-functional while the paternal variant (TRAPPC1 p.(His22_Lys24del)) is conditional-lethal and affects secretion and non-selective autophagy in yeast. This parallels defects seen in fibroblasts derived from this individual which also showed membrane trafficking defects and altered Golgi morphology, all of which were rescued in the human system by wild-type TRAPPC1. This study suggests that humanized yeast can be an efficient means to study TRAPP subunit variants in the absence of human cells and can assign significance to variants of unknown significance (VUS). This study lays the foundation for characterizing further TRAPP variants through this system, rapidly contributing to disease diagnosis.

Data-Efficient Generation of Protein Conformational Ensembles with Backbone-to-Side-Chain Transformers

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are currently no data sources with sufficient breadth to parametrize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here we introduce a modular strategy to generate conformations based on "backmapping" from a fixed protein backbone that (1) maintains conformational diversity of the side chains and (2) couples the side-chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side-chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquisition and hence a crucial ingredient for scalable physical simulation with generative neural networks.

Structural effect of the H992D/H418D mutation of angiotensin-converting enzyme in the Indian population: implications for health and disease

The Non synonymous SNPs (nsSNPs) of the renin-angiotensin-system (RAS) pathway, unique to the Indian population were investigated in view of its importance as an endocrine system. nsSNPs of the RAS pathway genes were mined from the IndiGenome database. Damaging nsSNPs were predicted using SIFT, PredictSNP, SNP and GO, Snap2 and Protein Variation Effect Analyzer. Loss of function was predicted based on protein stability change using I mutant, PremPS and CONSURF. The structural impact of the nsSNPs was predicted using HOPE and Missense3d followed by modeling, refinement, and energy minimization. Molecular Dynamics studies were carried out using Gromacsv2021.1. 23 Indian nsSNPs of the RAS pathway genes were selected for structural analysis and 8 were predicted to be damaging. Further sequence analysis showed that HEMGH zinc binding motif changes to HEMGD in somatic ACE-C domain (sACE-C) H992D and Testis ACE (tACE) H418D resulted in loss of zinc coordination, which is essential for enzymatic activity in this metalloprotease. There was a loss of internal interactions around the zinc coordination residues in the protein structural network. This was also confirmed by Principal Component Analysis, Free Energy Landscape and residue contact maps. Both mutations lead to broadening of the AngI binding cavity. The H992D mutation in sACE-C is likely to be favorable for cardiovascular health, but may lead to renal abnormalities with secondary impact on the heart. H418D in tACE is potentially associated with male infertility.Communicated by Ramaswamy H. Sarma.

Equilibrium Dynamics of a Biomolecular Complex Analyzed at Single-amino Acid Resolution by Cryo-electron Microscopy

The biological function of macromolecular complexes depends not only on large-scale transitions between conformations, but also on small-scale conformational fluctuations at equilibrium. Information on the equilibrium dynamics of biomolecular complexes could, in principle, be obtained from local resolution (LR) data in cryo-electron microscopy (cryo-EM) maps. However, this possibility had not been validated by comparing, for a same biomolecular complex, LR data with quantitative information on equilibrium dynamics obtained by an established solution technique. In this study we determined the cryo-EM structure of the minute virus of mice (MVM) capsid as a model biomolecular complex. The LR values obtained correlated with crystallographic B factors and with hydrogen/deuterium exchange (HDX) rates obtained by mass spectrometry (HDX-MS), a gold standard for determining equilibrium dynamics in solution. This result validated a LR-based cryo-EM approach to investigate, with high spatial resolution, the equilibrium dynamics of biomolecular complexes. As an application of this approach, we determined the cryo-EM structure of two mutant MVM capsids and compared their equilibrium dynamics with that of the wild-type MVM capsid. The results supported a previously suggested linkage between mechanical stiffening and impaired equilibrium dynamics of a virus particle. Cryo-EM is emerging as a powerful approach for simultaneously acquiring information on the atomic structure and local equilibrium dynamics of biomolecular complexes.

Explicit models of motions to analyze NMR relaxation data in proteins

Nuclear Magnetic Resonance (NMR) is a tool of choice to characterize molecular motions. In biological macromolecules, pico- to nano-second motions, in particular, can be probed by nuclear spin relaxation rates which depend on the time fluctuations of the orientations of spin interaction frames. For the past 40 years, relaxation rates have been successfully analyzed using the Model Free (MF) approach which makes no assumption on the nature of motions and reports on the effective amplitude and time-scale of the motions. However, obtaining a mechanistic picture of motions from this type of analysis is difficult at best, unless complemented with molecular dynamics (MD) simulations. In spite of their limited accuracy, such simulations can be used to obtain the information necessary to build explicit models of motions designed to analyze NMR relaxation data. Here, we present how to build such models, suited in particular to describe motions of methyl-bearing protein side-chains and compare them with the MF approach. We show on synthetic data that explicit models of motions are more robust in the presence of rotamer jumps which dominate the relaxation in methyl groups of protein side-chains. We expect this work to motivate the use of explicit models of motion to analyze MD and NMR data.

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.

Autoencoder-based detection of the residues involved in G protein-coupled receptor signaling

Regulator binding and mutations alter protein dynamics. The transmission of the signal of these alterations to distant sites through protein motion results in changes in protein expression and cell function. The detection of residues involved in signal transmission contributes to an elucidation of the mechanisms underlying processes as vast as cellular function and disease pathogenesis. We developed an autoencoder (AE) based method that detects residues essential for signaling by comparing the fluctuation data, particularly the time fluctuation of the side-chain distances between residues, during molecular dynamics simulations between the ligand-bound and -unbound forms or wild-type and mutant forms of proteins. Here, the AE-based method was applied to the G protein-coupled receptor (GPCR) system, particularly a class A-type GPCR, CXCR4, to detect the essential residues involved in signaling. Among the residues involved in the signaling of the homolog CXCR2, which were extracted from the literature based on the complex structures of the ligand and G protein, our method could detect more than half of the essential residues involved in G protein signaling, including those spanning the fifth and sixth transmembrane helices in the intracellular region, despite the lack of information regarding the interaction with G protein in our CXCR4 models.

First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

Using a model β-hairpin protein as a representative example of simple two-state folders whose kinetics are uncomplicated by the presence of on- and off-pathway intermediates, it is studied how the search for the protein's native state among native-like states affects the folding kinetics. It is revealed that the first-passage time (FPT) distributions are essentially single-exponential not only for the times to overcome the free energy barrier between the unfolded and native-like states but also for the times to find the native state among the native-like ones. The FPT distributions of this type are observed through all studied two-state-like regimes of protein folding, varying from a regime close to two-state folding to a regime close to downhill folding. If the protein explores native-like states for a time much longer than the time to overcome the free energy barrier, which is characteristic of high temperatures, the resulting FPT distribution to reach the native state remains close to exponential but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like states. In particular, the mean time to overcome the free energy barrier is in reasonable agreement with the Kramers rate formula and generally far shorter than the overall MFPT to reach the native state. The observed increase of the overall MFPT, as a result of longer exploration of native-like states, may lead to an overestimate of the height of the free energy barrier between the unfolded and folded states when it is calculated from the overall MFPT.

Mutual information analysis of the dynamic correlation between side chains in proteins

Protein dynamics play an essential role in function regulation. In recent years, many experimental and theoretical studies have shown that changes in protein fluctuations in the backbone and side chains fulfill a pivotal role associated with amino acid mutations, chemical modifications, and ligand binding. The dynamic correlations between protein side chains have not been sufficiently studied, and no reliable analysis method has been available so far. Therefore, we developed a method to evaluate the dynamic correlation between protein side chains using mutual information and molecular dynamics simulations. To eliminate the structural superposition errors dealing with conventional analysis methods, and to accurately extract the intrinsic fluctuation properties of the side chains, we employed distance principal component analysis (distPCA). The motion of the side chain was then projected onto the eigenvector space obtained by distPCA, and the mutual information between the projected motions was calculated. The proposed method was then applied to a small protein "eglin c" and the mutants. The results show that even a single mutation significantly changed the dynamic correlations and also suggest that the dynamic change is deeply related to the stability. Those results indicate that our developed method could be useful for analyzing the molecular mechanism of allosteric communication in proteins.

Characterizing the Interplay between Polymer Solvation and Conformation

Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and extended states can be quantified by the strength of the requisite potential. Our results also provide mechanistic insights into the collapse transition, highlighting that the bottleneck to polymer collapse is the formation of a sufficiently large cluster, and the collective dewetting of such a cluster. We also study the collapse of the hydrophobic polymer in octane, a nonpolar solvent, and interestingly, we find that the mechanistic details of the transition are qualitatively similar to that in water.

Influence of Disease-Causing Mutations on Protein Structural Networks

The interactions between residues in a protein tertiary structure can be studied effectively using the approach of protein structure network (PSN). A PSN is a node-edge representation of the structure with nodes representing residues and interactions between residues represented by edges. In this study, we have employed weighted PSNs to understand the influence of disease-causing mutations on proteins of known 3D structures. We have used manually curated information on disease mutations from UniProtKB/Swiss-Prot and their corresponding protein structures of wildtype and disease variant from the protein data bank. The PSNs of the wildtype and disease-causing mutant are compared to analyse variation of global and local dissimilarity in the overall network and at specific sites. We study how a mutation at a given site can affect the structural network at a distant site which may be involved in the function of the protein. We have discussed specific examples of the disease cases where the protein structure undergoes limited structural divergence in their backbone but have large dissimilarity in their all atom networks and vice versa, wherein large conformational alterations are observed while retaining overall network. We analyse the effect of variation of network parameters that characterize alteration of function or stability.

In silico investigation on alkaloids of Rauwolfia serpentina as potential inhibitors of 3-hydroxy-3-methyl-glutaryl-CoA reductase

Present work aimed to investigate the in silico activity of the alkaloids of roots of Rauwolfia serpentina as inhibitors of 3-hydroxy-3-methyl-glutaryl-CoA reductase (HMGCR). For this purpose, the three-dimensional (3D) structure of the protein HMGCR (PDB ID: 1HW9) was downloaded from Protein Data Bank (PDB) database, as a target enzyme. The structures of twelve alkaloids from the roots of R. serpentina were selected as ligands and docked with the selected HMGCR enzyme using Molegro Virtual Docker (MVD) software. The software ‘MVD’ computes the binding (atom) energies of selected protein (enzyme) and each ligand at minimum energetic conformation state by using the PLP (Piecewise Linear Potential) scoring mechanism. Docking results of twelve tested alkaloids showed that five alkaloids including compound 1 (ajmalicine), 2 (reserpine), 3 (indobinine), 4 (yohimbine), and 5 (indobine) have displayed the highest MolDock scores and best fit within the prominent active site residues (positioned between 684 and 692 of cis-loop) of HMGCR. According to the lowest MolDock energies obtained through non-covalent interactions of alkaloids with HMGCR, these are characterized to be the potential inhibitors of HMGCR. Therefore, the alkaloids from R. serpentina can effectively suppress the cholesterol biosynthesis pathway through inhibition of HMGCR and can serve as potential lead compounds for the development of new drugs for the treatment of hyperlipidaemia.

Novel insights in linking solvent relaxation dynamics and protein conformations utilizing red edge excitation shift approach

Protein hydration dynamics plays an important role in many physiological processes since protein fluctuations, slow solvation, and the dynamics of hydrating water are all intrinsically related. Red edge excitation shift (REES) is a unique and powerful wavelength-selective (i.e. excitation-energy dependent) fluorescence approach that can be used to directly monitor the environment-induced restriction and dynamics around a polar fluorophore in a complex biological system. This review is mainly focused on recent applications of REES and a novel analysis of REES data to monitor the structural dynamics, functionally relevant conformational transitions and to unmask the structural ensembles in proteins. In addition, the novel utility of REES in imaging protein aggregates in a cellular context is discussed. We believe that the enormous potential of REES approach showcased in this review will engage more researchers, particularly from life sciences.

Protein conformational entropy is not slaved to water

Conformational entropy can be an important element of the thermodynamics of protein functions such as the binding of ligands. The observed role for conformational entropy in modulating molecular recognition by proteins is in opposition to an often-invoked theory for the interaction of protein molecules with solvent water. The "solvent slaving" model predicts that protein motion is strongly coupled to various aspects of water such as bulk solvent viscosity and local hydration shell dynamics. Changes in conformational entropy are manifested in alterations of fast internal side chain motion that is detectable by NMR relaxation. We show here that the fast-internal side chain dynamics of several proteins are unaffected by changes to the hydration layer and bulk water. These observations indicate that the participation of conformational entropy in protein function is not dictated by the interaction of protein molecules and solvent water under the range of conditions normally encountered.

A beginner's guide to molecular dynamics simulations and the identification of cross-correlation networks for enzyme engineering

The functional properties of proteins are decided not only by their relatively rigid overall structures, but even more importantly, by their dynamic properties. In a protein, some regions of structure exhibit highly correlated or anti-correlated motions with others, some are highly dynamic but uncorrelated, while other regions are relatively static. The residues with correlated or anti-correlated motions can form a so-called dynamic cross-correlation network, through which information can be transmitted. Such networks have been shown to be critical to allosteric transitions, and ligand binding, and have also been shown to be able to mediate epistatic interactions between mutations. As a result, they are likely to play a significant role in the development of new enzyme engineering strategies. In this chapter, protocols are provided for the assessment of dynamic cross-correlation networks, and for their application in protein engineering. Transketolase from E. coli is used as a model and the software GROMACS is applied for carrying out MD simulations to generate trajectories containing structural ensembles. The trajectory is then used for a dynamic cross correlation analysis using the R package, Bio3D. A matrix of all atom-wise cross-correlation coefficients is finally obtained, which can be displayed in a graphical representation termed a dynamical cross-correlation matrix.

Entropy Hotspots for the Binding of Intrinsically Disordered Ligands to a Receptor Domain

Proline-rich motifs (PRMs) are widely used for mediating protein-protein interactions with weak binding affinities. Because they are intrinsically disordered when unbound, conformational entropy plays a significant role for the binding. However, residue-level differences of the entropic contribution in the binding of different ligands remain not well understood. We use all-atom molecular dynamics simulation and the maximal information spanning tree formalism to analyze conformational entropy associated with the binding of two PRMs, one from the Abl kinase and the other from the nonstructural protein 1 of the 1918 Spanish influenza A virus, to the N-terminal SH3 (nSH3) domain of the CrkII protein. Side chains of the stably folded nSH3 experience more entropy change upon ligand binding than the backbone, whereas PRMs involve comparable but heterogeneous entropy changes among the backbone and side chains. In nSH3, two conserved nonpolar residues forming contacts with the PRM experience the largest side-chain entropy loss. In contrast, the C-terminal charged residues of PRMs that form polar contacts with nSH3 experience the greatest side-chain entropy loss, although their "fuzzy" nature is attributable to the backbone that remains relatively flexible. Thus, residues that form high-occupancy contacts between nSH3 and PRM do not reciprocally contribute to entropy loss. Furthermore, certain surface residues of nSH3 distal to the interface with PRMs gain entropy, indicating a nonlocal effect of ligand binding. Comparing between the PRMs from cAbl and nonstructural protein 1, the latter involves a larger side-chain entropy loss and forms more contacts with nSH3. Consistent with experiments, this indicates stronger binding of the viral ligand at the expense of losing the flexibility of side chains, whereas the backbone experiences less entropy loss. The entropy "hotspots" as identified in this study will be important for tuning the binding affinity of various ligands to a receptor.

Theoretical and computational framework for the analysis of the relaxation properties of arbitrary spin systems. Application to high-resolution relaxometry

A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in the course of the experiment, such as dissolution dynamic nuclear polarization or high-resolution relaxometry. Understanding the relaxation properties of nuclear spin systems over orders of magnitude of magnetic fields is essential to rationalize the results of these experiments. For example, during a high-resolution relaxometry experiment, the absence of control of nuclear spin relaxation pathways during the sample transfers and relaxation delays leads to systematic deviations of polarization decays from an ideal mono-exponential decay with the pure longitudinal relaxation rate. These deviations have to be taken into account to describe quantitatively the dynamics of the system. Here, we present computational tools to (1) calculate analytical expressions of relaxation rates for a broad variety of spin systems and (2) use these analytical expressions to correct the deviations arising in high-resolution relaxometry experiments. These tools lead to a better understanding of nuclear spin relaxation, which is required to improve the sensitivity of many pulse sequences, and to better characterize motions in macromolecules.

Clustering of atomic displacement parameters in bovine trypsin reveals a distributed lattice of atoms with shared chemical properties

Low-frequency vibrations are crucial for protein structure and function, but only a few experimental techniques can shine light on them. The main challenge when addressing protein dynamics in the terahertz domain is the ubiquitous water that exhibit strong absorption. In this paper, we observe the protein atoms directly using X-ray crystallography in bovine trypsin at 100 K while irradiating the crystals with 0.5 THz radiation alternating on and off states. We observed that the anisotropy of atomic displacements increased upon terahertz irradiation. Atomic displacement similarities developed between chemically related atoms and between atoms of the catalytic machinery. This pattern likely arises from delocalized polar vibrational modes rather than delocalized elastic deformations or rigid-body displacements. The displacement correlation between these atoms were detected by a hierarchical clustering method, which can assist the analysis of other ultra-high resolution crystal structures. These experimental and analytical tools provide a detailed description of protein dynamics to complement the structural information from static diffraction experiments.

Can Conformational Changes of Proteins Be Represented in Torsion Angle Space? A Study with Rescaled Ridge Regression

Torsion angles are the natural degrees of freedom of protein structures. The ability to determine torsional variations corresponding to observed changes in Cartesian coordinates is highly valuable, notably to investigate the mechanisms of functional conformational changes or to develop computational models of protein dynamics. This issue is far from trivial in practice since the impact of modifying one torsion angle strongly depends on all other angles, and the compounding effects of small variations in bond lengths and valence angles can completely disrupt a protein fold. We demonstrate that naive strategies, such as directly comparing torsion angles between structures without correcting for variations in bond lengths and valence angles or fitting torsional variations without a proper regularization scheme, fail at producing an adequate representation of conformational changes in internal coordinates. In contrast, rescaled ridge regression, a method recently introduced to regularize multidimensional regressions with correlated explanatory variables, is shown to consistently identify a minimal set of torsion angles variations that closely reproduce changes in Cartesian coordinates. This torsional representation of conformational changes is shown to be robust to the choice of experimental structures. It also provides a better agreement with theoretical models of protein dynamics than the Cartesian representation, regarding notably the predominance of low-frequency normal modes in functional motions and the presence, in predicted equilibrium dynamics, of hints of natural selection for specific functional motions. The software is available at https://github.com/ugobas/tnm .

Autoencoder-Based Detection of Dynamic Allostery Triggered by Ligand Binding Based on Molecular Dynamics

Dynamic allostery on proteins, triggered by regulator binding or chemical modifications, transmits information from the binding site to distant regions, dramatically altering protein function. It is accompanied by subtle changes in side-chain conformations of the protein, indicating that the changes in dynamics, and not rigid or large conformational changes, are essential to understand regulation of protein function. Although a lot of experimental and theoretical studies have been dedicated to investigate this issue, the regulation mechanism of protein function is still being debated. Here, we propose an autoencoder-based method that can detect dynamic allostery. The method is based on the comparison of time fluctuations of protein structures, in the form of distance matrices, obtained from molecular dynamics simulations in ligand-bound and -unbound forms. Our method detected that the changes in dynamics by ligand binding in the PDZ2 domain led to the reorganization of correlative fluctuation motions among residue pairs, which revealed a different view of the correlated motions from the PCA and DCCM. In addition, other correlative motions were also found as a result of the dynamic perturbation from the ligand binding, which may lead to dynamic allostery. This autoencoder-based method would be usefully applied to the signal transduction and mutagenesis systems involved in protein functions and severe diseases.

Protein plasticity driven by disorder and collapse governs the heterogeneous binding of CytR to DNA

The amplitude of thermodynamic fluctuations in biological macromolecules determines their conformational behavior, dimensions, nature of phase transitions and effectively their specificity and affinity, thus contributing to fine-tuned molecular recognition. Unique among large-scale conformational changes in proteins are temperature-induced collapse transitions in intrinsically disordered proteins (IDPs). Here, we show that CytR DNA-binding domain, an IDP that folds on binding DNA, undergoes a coil-to-globule transition with temperature in the absence of DNA while exhibiting energetically decoupled local and global structural rearrangements, and maximal thermodynamic fluctuations at the optimal bacterial growth temperature. The collapse is shown to be a continuous transition through a combination of statistical-mechanical modeling and all-atom implicit solvent simulations. Surprisingly, CytR binds single-site cognate DNA with negative cooperativity, described by Hill coefficients less than one, resulting in a graded binding response. We show that heterogeneity arising from varying binding-competent CytR conformations or orientations at the single-molecular level contributes to negative binding cooperativity at the level of bulk measurements due to the conflicting requirements of collapse transition, large fluctuations and folding-upon-binding. Our work reports strong evidence for functionally driven thermodynamic fluctuations in determining the extent of collapse and disorder with implications in protein search efficiency of target DNA sites and regulation.

Slow Motion Protein Dance Visualized Using Red-Edge Excitation Shift of a Buried Fluorophore

It has been extremely challenging to detect protein structures with a dynamic core, such as dry molten globules, that remain in equilibrium with the tightly packed native (N) state and that are important for a myriad of entropy-driven protein functions. Here, we detect the higher entropy conformations of a human serum protein, using red-edge excitation shift experiments. We covalently introduced a fluorophore inside the protein core and observed that in a subset of native population, the side chains of the polar and buried residues have different spatial arrangements than the mean population and that they solvate the fluorophore on a timescale much slower than the nanosecond timescale of fluorescence. Our results provide direct evidence for the dense fluidity of protein core and show that alternate side-chain packing arrangements exist in the core that might be important for multiple binding functions of this protein.

Modulation of allosteric coupling by mutations: from protein dynamics and packing to altered native ensembles and function

A large body of work has gone into understanding the effect of mutations on protein structure and function. Conventional treatments have involved quantifying the change in stability, activity and relaxation rates of the mutants with respect to the wild-type protein. However, it is now becoming increasingly apparent that mutational perturbations consistently modulate the packing and dynamics of a significant fraction of protein residues, even those that are located >10–15 Å from the mutated site. Such long-range modulation of protein features can distinctly tune protein stability and the native conformational ensemble contributing to allosteric modulation of function. In this review, I summarize a series of experimental and computational observations that highlight the incredibly pliable nature of proteins and their response to mutational perturbations manifested via the intra-protein interaction network. I highlight how an intimate understanding of mutational effects could pave the way for integrating stability, folding, cooperativity and even allostery within a single physical framework.

Cryptic binding sites on proteins: definition, detection, and druggability

Many proteins in their unbound structures lack surface pockets appropriately sized for drug binding. Hence, a variety of experimental and computational tools have been developed for the identification of cryptic sites that are not evident in the unbound protein but form upon ligand binding, and can provide tractable drug target sites. The goal of this review is to discuss the definition, detection, and druggability of such sites, and their potential value for drug discovery. Novel methods based on molecular dynamics simulations are particularly promising and yield a large number of transient pockets, but it has been shown that only a minority of such sites are generally capable of binding ligands with substantial affinity. Based on recent studies, current methodology can be improved by combining molecular dynamics with fragment docking and machine learning approaches.

Measuring Entropy in Molecular Recognition by Proteins

Molecular recognition by proteins is fundamental to the molecular basis of biology. Dissection of the thermodynamic landscape governing protein-ligand interactions has proven difficult because determination of various entropic contributions is quite challenging. Nuclear magnetic resonance relaxation measurements, theory, and simulations suggest that conformational entropy can be accessed through a dynamical proxy. Here, we review the relationship between measures of fast side-chain motion and the underlying conformational entropy. The dynamical proxy reveals that the contribution of conformational entropy can range from highly favorable to highly unfavorable and demonstrates the potential of this key thermodynamic variable to modulate protein-ligand interactions. The dynamical so-called entropy meter also refines the role of solvent entropy and directly determines the loss in rotational-translational entropy that occurs upon formation of high-affinity complexes. The ability to quantify the roles of entropy through an entropy meter based on measurable dynamical properties promises to highlight its role in protein function.

Temperature evolution of Trp-cage folding pathways: An analysis by dividing the probability flux field into stream tubes

Owing to its small size and very fast folding rate, the Trp-cage miniprotein has become a benchmark system to study protein folding. Two folding pathways were found to be characteristic of this protein: pathway I, in which the hydrophobic collapse precedes the formation of α-helix, and pathway II, in which the events occur in the reverse order. At the same time, the relative contribution of these pathways at different temperatures as well as the nature of transition from one pathway to the other remain unclear. To gain insight into this issue, we employ a recently proposed hydrodynamic description of protein folding, in which the process of folding is considered as a motion of a "folding fluid" (Chekmarev et al., Phys. Rev. Lett. 100(1), 018107 2008). Using molecular dynamics simulations, we determine the field of probability fluxes of transitions in a space of collective variables and divide it into stream tubes. Each tube contains a definite fraction of the total folding flow and can be associated with a certain pathway. Specifically, three temperatures were considered, T = 285K, T = 315K, and T = 325K. We have found that as the temperature increases, the contribution of pathway I, which is approximately 90% of the total folding flow at T = 285K, decreases to approximately 10% at T = 325K, i.e., pathway II becomes dominant. At T = 315K, both pathways contribute approximately equally. All these temperatures are found below the calculated melting point, which suggests that the Trp-cage folding mechanism is determined by kinetic factors rather than thermodynamics.

A Universal Pattern in the Percolation and Dissipation of Protein Structural Perturbations

Understanding the extent to which information is transmitted through the intramolecular interaction network of proteins upon a perturbation, that is, an allosteric effect, has long remained an unsolved problem. Through an analysis of high-resolution NMR data from the literature on 28 different proteins and 49 structural perturbations, we show that the extent of induced structural changes through mutations and molecular events including protein-protein, protein-peptide, protein-ligand binding, and post-translational modifications exhibit a near-universal exponential functional form. The extent of percolation into the protein structures can be up to 20-25 Å despite no apparent change in the 3D structures. These observations are also consistent with theoretical expectations, elementary graph theoretic analysis of protein structures, detailed molecular dynamics simulations, and experimental double-mutant cycles. Our analysis highlights that most molecular events would contribute to allosteric effects independent of protein structure, topology, or identity and provides a simple avenue to test and potentially model their effects.

Exploring the Denatured State Ensemble by Single-Molecule Chemo-Mechanical Unfolding: The Effect of Force, Temperature, and Urea

While it is widely appreciated that the denatured state of a protein is a heterogeneous conformational ensemble, there is still debate over how this ensemble changes with environmental conditions. Here, we use single-molecule chemo-mechanical unfolding, which combines force and urea using the optical tweezers, together with traditional protein unfolding studies to explore how perturbants commonly used to unfold proteins (urea, force, and temperature) affect the denatured-state ensemble. We compare the urea m-values, which report on the change in solvent accessible surface area for unfolding, to probe the denatured state as a function of force, temperature, and urea. We find that while the urea- and force-induced denatured states expose similar amounts of surface area, the denatured state at high temperature and low urea concentration is more compact. To disentangle these two effects, we use destabilizing mutations that shift the T_m and C_m. We find that the compaction of the denatured state is related to changing temperature as the different variants of acyl-coenzyme A binding protein have similar m-values when they are at the same temperature but different urea concentration. These results have important implications for protein folding and stability under different environmental conditions.

A self-consistent structural perturbation approach for determining the magnitude and extent of allosteric coupling in proteins

Elucidating the extent of energetic coupling between residues in single-domain proteins, which is a fundamental determinant of allostery, information transfer and folding cooperativity, has remained a grand challenge. While several sequence- and structure-based approaches have been proposed, a self-consistent description that is simultaneously compatible with unfolding thermodynamics is lacking. We recently developed a simple structural perturbation protocol that captures the changes in thermodynamic stabilities induced by point mutations within the protein interior. Here, we show that a fundamental residue-specific component of this perturbation approach, the coupling distance, is uniquely sensitive to the environment of a residue in the protein to a distance of ∼15 Å. With just the protein contact map as an input, we reproduce the extent of percolation of perturbations within the structure as observed in network analysis of intra-protein interactions, molecular dynamics simulations and NMR-observed changes in chemical shifts. Using this rapid protocol that relies on a single structure, we explain the results of statistical coupling analysis (SCA) that requires hundreds of sequences to identify functionally critical sectors, the propagation and dissipation of perturbations within proteins and the higher-order couplings deduced from detailed NMR experiments. Our results thus shed light on the possible mechanistic origins of signaling through the interaction network within proteins, the likely distance dependence of perturbations induced by ligands and post-translational modifications and the origins of folding cooperativity through many-body interactions.

Non-covalent forces tune the electron transfer complex between ferredoxin and sulfite reductase to optimize enzymatic activity

Although electrostatic interactions between negatively charged ferredoxin (Fd) and positively charged sulfite reductase (SiR) have been predominantly highlighted to characterize complex formation, the detailed nature of intermolecular forces remains to be fully elucidated. We investigated interprotein forces for the formation of an electron transfer complex between Fd and SiR and their relationship to SiR activity using various approaches over NaCl concentrations between 0 and 400 mM. Fd-dependent SiR activity assays revealed a bell-shaped activity curve with a maximum ∼40-70 mM NaCl and a reverse bell-shaped dependence of interprotein affinity. Meanwhile, intrinsic SiR activity, as measured in a methyl viologen-dependent assay, exhibited saturation above 100 mM NaCl. Thus, two assays suggested that interprotein interaction is crucial in controlling Fd-dependent SiR activity. Calorimetric analyses showed the monotonic decrease in interprotein affinity on increasing NaCl concentrations, distinguished from a reverse bell-shaped interprotein affinity observed from Fd-dependent SiR activity assay. Furthermore, Fd:SiR complex formation and interprotein affinity were thermodynamically adjusted by both enthalpy and entropy through electrostatic and non-electrostatic interactions. A residue-based NMR investigation on the addition of SiR to ¹⁵N-labeled Fd at the various NaCl concentrations also demonstrated that a combination of electrostatic and non-electrostatic forces stabilized the complex with similar interfaces and modulated the binding affinity and mode. Our findings elucidate that non-electrostatic forces are also essential for the formation and modulation of the Fd:SiR complex. We suggest that a complex configuration optimized for maximum enzymatic activity near physiological salt conditions is achieved by structural rearrangement through controlled non-covalent interprotein interactions.

Flexibility and Disorder in Gene Regulation: LacI/GalR and Hox Proteins

To modulate transcription, a variety of input signals must be sensed by genetic regulatory proteins. In these proteins, flexibility and disorder are emerging as common themes. Prokaryotic regulators generally have short, flexible segments, whereas eukaryotic regulators have extended regions that lack predicted secondary structure (intrinsic disorder). Two examples illustrate the impact of flexibility and disorder on gene regulation: the prokaryotic LacI/GalR family, with detailed information from studies on LacI, and the eukaryotic family of Hox proteins, with specific insights from investigations of Ultrabithorax (Ubx). The widespread importance of structural disorder in gene regulatory proteins may derive from the need for flexibility in signal response and, particularly in eukaryotes, in protein partner selection.

Accurately modeling nanosecond protein dynamics requires at least microseconds of simulation

Advances in hardware and algorithms have greatly extended the timescales accessible to molecular simulation. This article assesses whether such long timescale simulations improve our ability to calculate order parameters that describe conformational heterogeneity on ps-ns timescales or if force fields are now a limiting factor. Order parameters from experiment are compared with order parameters calculated in three different ways from simulations ranging from 10 ns to 100 μs in length. Importantly, bootstrapping is employed to assess the variability in results for each simulation length. The results of 10-100 ns timescale simulations are highly variable, possibly explaining the variation in levels of agreement between simulation and experiment in published works examining different proteins. Fortunately, microsecond timescale simulations improve both the accuracy and precision of calculated order parameters, at least so long as the full exponential fit or truncated average approximation is used instead of the common long-time limit approximation. The improved precision of these long timescale simulations allows a statistically sound comparison of a number of modern force fields, such as Amber03, Amber99sb-ILDN, and Charmm27. While there is some variation between these force fields, they generally give very similar results for sufficiently long simulations. The fact that so much simulation is required to precisely capture ps-ns timescale processes suggests that extremely extensive simulations are required for slower processes. Advanced sampling techniques could aid greatly, however, such methods will need to maintain accurate kinetics if they are to be of value for calculating dynamical properties like order parameters. © 2015 Wiley Periodicals, Inc.