Scaling Behavior and Structure of Denatured Proteins

Conformational Dynamics of the Nucleosomal Histone H2B Tails Revealed by Molecular Dynamics Simulations

Epigenetic modifications of histone N-terminal tails play a critical role in regulating the chromatin structure and biological processes such as transcription and DNA repair. One of the key post-translational modifications (PTMs) is the acetylation of lysine residues on histone tails. Epigenetic modifications are ubiquitous in the development of diseases, such as cancer and neurological disorders. Histone H2B tails are critical regulators of nucleosome dynamics, biological processes, and certain diseases. Here, we report all-atomistic molecular dynamics (MD) simulations of the nucleosome to demonstrate that acetylation of the histone tails changes their conformational space and interaction with DNA. We perform simulations of H2B tails, critical regulators of gene regulation, in both the lysine-acetylated (ACK) and unacetylated wild type (WT) states. To explore the effects of salt concentration, we use two different NaCl concentrations to perform simulations at microsecond time scales. Salt can modulate the effects of electrostatic interactions between the DNA phosphate backbone and histone tails. Upon acetylation, H2B tails shift their secondary structure helical propensity. The number of contacts between the DNA and the H2B tail decreases. We characterize the conformational dynamics of the H2B tails by principal component analysis (PCA). The ACK tails become more compact at increased salt concentrations, but conformations from the WT tails display the most contacts with DNA at both salt concentrations. Mainly, H2B acetylation may increase the DNA accessibility for regulatory proteins to bind, which can aid in gene regulation and NCP stability.

Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

Microcalorimetry reveals multi-state thermal denaturation of G. stearothermophilus tryptophanyl-tRNA synthetase

Mechanistic studies of Geobacillus stearothermophilus tryptophanyl-tRNA synthetase (TrpRS) afford an unusually detailed description-the escapement mechanism-for the distinct steps coupling catalysis to domain motion, efficiently converting the free energy of ATP hydrolysis into biologically useful alternative forms of information and work. Further elucidation of the escapement mechanism requires understanding thermodynamic linkages between domain configuration and conformational stability. To that end, we compare experimental thermal melting of fully liganded and apo TrpRS with a computational simulation of the melting of its fully liganded form. The simulation also provides important structural cameos at successively higher temperatures, enabling more confident interpretation. Experimental and simulated melting both proceed through a succession of three transitions at successively higher temperature. The low-temperature transition occurs at approximately the growth temperature of the organism and so may be functionally relevant but remains too subtle to characterize structurally. Structural metrics from the simulation imply that the two higher-temperature transitions entail forming a molten globular state followed by unfolding of secondary structures. Ligands that stabilize the enzyme in a pre-transition (PreTS) state compress the temperature range over which these transitions occur and sharpen the transitions to the molten globule and fully denatured states, while broadening the low-temperature transition. The experimental enthalpy changes provide a key parameter necessary to convert changes in melting temperature of combinatorial mutants into mutationally induced conformational free energy changes. The TrpRS urzyme, an excerpted model representing an early ancestral form, containing virtually the entire catalytic apparatus, remains largely intact at the highest simulated temperatures.

Pulse-field gradient nuclear magnetic resonance of protein translational diffusion from native to non-native states

Hydrodynamic radii (R_h -values) calculated from diffusion coefficients measured by pulse-field-gradient nuclear magnetic resonance are compared for folded and unfolded proteins. For native globular proteins, the R_h -values increase as a power of 0.35 with molecular size, close to the scaling factor of 0.33 predicted from polymer theory. Unfolded proteins were studied under four sets of conditions: in the absence of denaturants, in the presence of 6 M urea, in 95% dimethyl sulfoxide (DMSO), and in 40% hexafluoroisopropanol (HFIP). Scaling factors under all four unfolding conditions are similar (0.49-0.53) approaching the theoretical value of 0.60 for a fully unfolded random coil. Persistence lengths are also similar, except smaller in 95% DMSO, suggesting that the polypeptides are more disordered on a local scale with this solvent. Three of the proteins in our unfolded set have an asymmetric sequence-distribution of charged residues. While these proteins behave normally in water and 6 M urea, they give atypically low R_h -values in 40% HFIP and 95% DMSO suggesting they are forming electrostatic hairpins, favored by their asymmetric sequence charge distribution and the low dielectric constants of DMSO and HFIP. While diffusion-ordered NMR spectroscopy can separate small molecules, we show a number of factors combine to make protein-sized molecules much more difficult to resolve in mixtures. Finally, we look at the temperature dependence of apparent diffusion coefficients. Small molecules show a linear temperature response, while large proteins show abnormally large apparent diffusion coefficients at high temperatures due to convection, suggesting diffusion reference standards are only useful near 25°C.

Soluble State of Villin Headpiece Protein as a Tool in the Assessment of MD Force Fields

Protein self-assembly plays an important role in cellular processes. Whereas molecular dynamics (MD) represents a powerful tool in studying assembly mechanisms, its predictions depend on the accuracy of underlying force fields, which are known to overly promote protein assembly. We here examine villin headpiece domain, HP36, which remains soluble at concentrations amenable to MD studies. The experimental characterization of soluble HP36 at concentrations of 0.05 to 1 mM reveals concentration-independent 90% monomeric and 10% dimeric populations. Extensive all-atom MD simulations at two protein concentrations, 0.9 and 8.5 mM, probe the HP36 dimer population, stability, and kinetics of dimer formation within two MD force fields, Amber ff14SB and CHARMM36m. MD results demonstrate that whereas CHARMM36m captures experimental HP36 monomer populations at the lower concentration, both force fields overly promote HP36 association at the higher concentration. Moreover, contacts stabilizing HP36 dimers are force-field-dependent. CHARMM36m produces consistently higher HP36 monomer populations, lower association rates, and weaker dependence of these quantities on the protein concentration than Amber ff14SB. Nonetheless, the highest monomer populations and dissociation constants are observed when the TIP3P water model in Amber ff14SB is replaced by TIP4P/2005, showcasing the critical role of the water model in addressing the protein solubility problem in MD.

Nanoscale programming of cellular and physiological phenotypes: inorganic meets organic programming

The advent of protein design in recent years has brought us within reach of developing a "nanoscale programing language," in which molecules serve as operands with their conformational states functioning as logic gates. Combining these operands into a set of operations will result in a functional program, which is executed using nanoscale computing agents (NCAs). These agents would respond to any given input and return the desired output signal. The ability to utilize natural evolutionary processes would allow code to "evolve" in the course of computation, thus enabling radically new algorithmic developments. NCAs will revolutionize the studies of biological systems, enable a deeper understanding of human biology and disease, and facilitate the development of in situ precision therapeutics. Since NCAs can be extended to novel reactions and processes not seen in biological systems, the growth of this field will spark the growth of biotechnological applications with wide-ranging impacts, including fields not typically considered relevant to biology. Unlike traditional approaches in synthetic biology that are based on the rewiring of signaling pathways in cells, NCAs are autonomous vehicles based on single-chain proteins. In this perspective, I will introduce and discuss this new field of biological computing, as well as challenges and the future of the NCA. Addressing these challenges will provide a significant leap in technology for programming living cells.

Engineering an Allosteric Control of Protein Function

Allosteric regulation in proteins is fundamental to many important biological processes. Allostery has been employed to control protein functions by regulating protein activity. Engineered allosteric regulation allows controlling protein activity in subsecond time scale and has a broad range of applications, from dissecting spatiotemporal dynamics in biochemical cascades to applications in biotechnology and medicine. Here, we review the concept of allostery in proteins and various approaches to identify allosteric sites and pathways. We then provide an overview of strategies and tools used in allosteric protein regulation and their utility in biological applications. We highlight various classes of proteins, where regulation is achieved through allostery. Finally, we analyze the current problems, critical challenges, and future prospective in achieving allosteric regulation in proteins.

Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis

Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.

Glutenin and Gliadin, a Piece in the Puzzle of their Structural Properties in the Cell Described through Monte Carlo Simulations

Gluten protein crosslinking is a predetermined process where specific intra- and intermolecular disulfide bonds differ depending on the protein and cysteine motif. In this article, all-atom Monte Carlo simulations were used to understand the formation of disulfide bonds in gliadins and low molecular weight glutenin subunits (LMW-GS). The two intrinsically disordered proteins appeared to contain mostly turns and loops and showed "self-avoiding walk" behavior in water. Cysteine residues involved in intramolecular disulfide bonds were located next to hydrophobic peptide sections in the primary sequence. Hydrophobicity of neighboring peptide sections, synthesis chronology, and amino acid chain flexibility were identified as important factors in securing the specificity of intramolecular disulfide bonds formed directly after synthesis. The two LMW-GS cysteine residues that form intermolecular disulfide bonds were positioned next to peptide sections of lower hydrophobicity, and these cysteine residues are more exposed to the cytosolic conditions, which influence the crosslinking behavior. In addition, coarse-grained Monte Carlo simulations revealed that the protein folding is independent of ionic strength. The potential molecular behavior associated with disulfide bonds, as reported here, increases the biological understanding of seed storage protein function and provides opportunities to tailor their functional properties for different applications.

Protein disorder-to-order transition enhances the nucleosome-binding affinity of H1

Intrinsically disordered proteins are crucial elements of chromatin heterogenous organization. While disorder in the histone tails enables a large variation of inter-nucleosome arrangements, disorder within the chromatin-binding proteins facilitates promiscuous binding to a wide range of different molecular targets, consistent with structural heterogeneity. Among the partially disordered chromatin-binding proteins, the H1 linker histone influences a myriad of chromatin characteristics including compaction, nucleosome spacing, transcription regulation, and the recruitment of other chromatin regulating proteins. Although it is now established that the long C-terminal domain (CTD) of H1 remains disordered upon nucleosome binding and that such disorder favours chromatin fluidity, the structural behaviour and thereby the role/function of the N-terminal domain (NTD) within chromatin is yet unresolved. On the basis of microsecond-long parallel-tempering metadynamics and temperature-replica exchange atomistic molecular dynamics simulations of different H1 NTD subtypes, we demonstrate that the NTD is completely unstructured in solution but undergoes an important disorder-to-order transition upon nucleosome binding: it forms a helix that enhances its DNA binding ability. Further, we show that the helical propensity of the H1 NTD is subtype-dependent and correlates with the experimentally observed binding affinity of H1 subtypes, suggesting an important functional implication of this disorder-to-order transition.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

Insight into the Structure of the "Unstructured" Tau Protein

Combining structural proteomics experimental data with computational methods is a powerful tool for protein structure prediction. Here, we apply a recently developed approach for de novo protein structure determination based on the incorporation of short-distance crosslinking data as constraints in discrete molecular dynamics simulations (CL-DMD), for the determination of the conformational ensemble of tau protein in solution. The predicted structures were in agreement with surface modification and long-distance crosslinking data. Tau in solution was found as an ensemble of rather compact globular conformations with distinct topology, inter-residue contacts, and a number of transient secondary-structure elements. Regions important for pathological aggregation consistently were found to contain β strands. The determined structures are compatible with the tau protein in solution being a molten globule at near-ground state with persistent residual structural features which we were able to capture by CL-DMD. The predicted structure may facilitate an understanding of the misfolding and oligomerization pathways of the tau protein.

Tau local structure shields an amyloid-forming motif and controls aggregation propensity

Tauopathies are neurodegenerative diseases characterized by intracellular amyloid deposits of tau protein. Missense mutations in the tau gene (MAPT) correlate with aggregation propensity and cause dominantly inherited tauopathies, but their biophysical mechanism driving amyloid formation is poorly understood. Many disease-associated mutations localize within tau's repeat domain at inter-repeat interfaces proximal to amyloidogenic sequences, such as 306VQIVYK311. We use cross-linking mass spectrometry, recombinant protein and synthetic peptide systems, in silico modeling, and cell models to conclude that the aggregation-prone 306VQIVYK311 motif forms metastable compact structures with its upstream sequence that modulates aggregation propensity. We report that disease-associated mutations, isomerization of a critical proline, or alternative splicing are all sufficient to destabilize this local structure and trigger spontaneous aggregation. These findings provide a biophysical framework to explain the basis of early conformational changes that may underlie genetic and sporadic tau pathogenesis.

Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension. Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

General Purpose Water Model Can Improve Atomistic Simulations of Intrinsically Disordered Proteins

Unconstrained atomistic simulations of intrinsically disordered proteins and peptides (IDP) remain a challenge: widely used, "general purpose" water models tend to favor overly compact structures relative to experiment. Here we have performed a total of 93 μs of unrestrained MD simulations to explore, in the context of IDPs, a recently developed "general-purpose" 4-point rigid water model OPC, which describes liquid state of water close to experiment. We demonstrate that OPC, together with a popular AMBER force field ff99SB, offers a noticeable improvement over TIP3P in producing more realistic structural ensembles of three common IDPs benchmarks: 55-residue apo N-terminal zinc-binding domain of HIV-1 integrase ("protein IN"), amyloid β-peptide (Aβ₄₂) (residues 1-42), and 26-reside H4 histone tail. As a negative control, computed folding profile of a regular globular miniprotein (CLN025) in OPC water is in appreciably better agreement with experiment than that obtained in TIP3P, which tends to overstabilize the compact native state relative to the extended conformations. We employed Aβ₄₂ peptide to investigate the possible influence of the solvent box size on simulation outcomes. We advocate a cautious approach for simulations of IDPs: we suggest that the solvent box size should be at least four times the radius of gyration of the random coil corresponding to the IDP. The computed free energy landscape of protein IN in OPC resembles a shallow "tub" - conformations with substantially different degrees of compactness that are within 2 k_B T of each other. Conformations with very different secondary structure content coexist within 1 k_B T of the global free energy minimum. States with higher free energy tend to have less secondary structure. Computed low helical content of the protein has virtually no correlation with its degree of compactness, which calls into question the possibility of using the helicity as a metric for assessing performance of water models for IDPs, when the helicity is low. Predicted radius of gyration ( R _g) of H4 histone tail in OPC water falls in-between that of a typical globular protein and a fully denatured protein of the same size; the predicted R _g is consistent with two independent predictions. In contrast, H4 tail in TIP3P water is as compact as the corresponding globular protein. The computed free energy landscape of H4 tail in OPC is relatively flat over a significant range of compactness, which, we argue, is consistent with its biological function as facilitator of internucleosome interactions.

An Efficient Method for Estimating the Hydrodynamic Radius of Disordered Protein Conformations

Intrinsically disordered proteins play important roles throughout biology, yet our understanding of the relationship between their sequences, structural properties, and functions remains incomplete. The dynamic nature of these proteins, however, makes them difficult to characterize structurally. Many disordered proteins can attain both compact and expanded conformations, and the level of expansion may be regulated and important for function. Experimentally, the level of compaction and shape is often determined either by small-angle x-ray scattering experiments or pulsed-field-gradient NMR diffusion measurements, which provide ensemble-averaged estimates of the radius of gyration and hydrodynamic radius, respectively. Often, these experiments are interpreted using molecular simulations or are used to validate them. We here provide, to our knowledge, a new and efficient method to calculate the hydrodynamic radius of a disordered protein chain from a model of its structural ensemble. In particular, starting from basic concepts in polymer physics, we derive a relationship between the radius of gyration of a structure and its hydrodynamic ratio, which in turn can be used, for example, to compare a simulated ensemble of conformations to NMR diffusion measurements. The relationship may also be valuable when using NMR diffusion measurements to restrain molecular simulations.

Revealing chemical processes and kinetics of drug action within single living cells via plasmonic Raman probes

Better understanding the drug action within cells may extend our knowledge on drug action mechanisms and promote new drugs discovery. Herein, we studied the processes of drug induced chemical changes on proteins and nucleic acids in human breast adenocarcinoma (MCF-7) cells via time-resolved plasmonic-enhanced Raman spectroscopy (PERS) in combination with principal component analysis (PCA). Using three popular chemotherapy drugs (fluorouracil, cisplatin and camptothecin) as models, chemical changes during drug action process were clearly discriminated. Reaction kinetics related to protein denaturation, conformational modification, DNA damage and their associated biomolecular events were calculated. Through rate constants and reaction delay times, the different action modes of these drugs could be distinguished. These results may provide vital insights into understanding the chemical reactions associated with drug-cell interactions.

Insights into Unfolded Proteins from the Intrinsic ϕ/ψ Propensities of the AAXAA Host-Guest Series

Various host-guest peptide series are used by experimentalists as reference conformational states. One such use is as a baseline for random-coil NMR chemical shifts. Comparison to this random-coil baseline, through secondary chemical shifts, is used to infer protein secondary structure. The use of these random-coil data sets rests on the perception that the reference chemical shifts arise from states where there is little or no conformational bias. However, there is growing evidence that the conformational composition of natively and nonnatively unfolded proteins fail to approach anything that can be construed as random coil. Here, we use molecular dynamics simulations of an alanine-based host-guest peptide series (AAXAA) as a model of unfolded and denatured states to examine the intrinsic propensities of the amino acids. We produced ensembles that are in good agreement with the experimental NMR chemical shifts and confirm that the sampling of the 20 natural amino acids in this peptide series is be far from random. Preferences toward certain regions of conformational space were both present and dependent upon the environment when compared under conditions typically used to denature proteins, i.e., thermal and chemical denaturation. Moreover, the simulations allowed us to examine the conformational makeup of the underlying ensembles giving rise to the ensemble-averaged chemical shifts. We present these data as an intrinsic backbone propensity library that forms part of our Structural Library of Intrinsic Residue Propensities to inform model building, to aid in interpretation of experiment, and for structure prediction of natively and nonnatively unfolded states.

Dynamic Protein Interaction Networks and New Structural Paradigms in Signaling

Understanding signaling and other complex biological processes requires elucidating the critical roles of intrinsically disordered proteins (IDPs) and regions (IDRs), which represent ∼30% of the proteome and enable unique regulatory mechanisms. In this review, we describe the structural heterogeneity of disordered proteins that underpins these mechanisms and the latest progress in obtaining structural descriptions of conformational ensembles of disordered proteins that are needed for linking structure and dynamics to function. We describe the diverse interactions of IDPs that can have unusual characteristics such as "ultrasensitivity" and "regulated folding and unfolding". We also summarize the mounting data showing that large-scale assembly and protein phase separation occurs within a variety of signaling complexes and cellular structures. In addition, we discuss efforts to therapeutically target disordered proteins with small molecules. Overall, we interpret the remodeling of disordered state ensembles due to binding and post-translational modifications within an expanded framework for allostery that provides significant insights into how disordered proteins transmit biological information.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Hierarchical molecular dynamics of bovine serum albumin in concentrated aqueous solution below and above thermal denaturation

The dynamics of proteins in solution is a complex and hierarchical process, affected by the aqueous environment as well as temperature. We present a comprehensive study on nanosecond time and nanometer length scales below, at, and above the denaturation temperature Td. Our experimental data evidence dynamical processes in protein solutions on three distinct time scales. We suggest a consistent physical picture of hierarchical protein dynamics: (i) self-diffusion of the entire protein molecule is confirmed to agree with colloid theory for all temperatures where the protein is in its native conformational state. At higher temperatures T > Td, the self-diffusion is strongly obstructed by cross-linking or entanglement. (ii) The amplitude of backbone fluctuations grows with increasing T, and a transition in its dynamics is observed above Td. (iii) The number of mobile side-chains increases sharply at Td while their average dynamics exhibits only little variations. The combination of quasi-elastic neutron scattering and the presented analytical framework provides a detailed microscopic picture of the protein molecular dynamics in solution, thereby reflecting the changes of macroscopic properties such as cluster formation and gelation.

A practical guide to small angle X-ray scattering (SAXS) of flexible and intrinsically disordered proteins

Small-angle X-ray scattering (SAXS) is a biophysical method to study the overall shape and structural transitions of biological macromolecules in solution. SAXS provides low resolution information on the shape, conformation and assembly state of proteins, nucleic acids and various macromolecular complexes. The technique also offers powerful means for the quantitative analysis of flexible systems, including intrinsically disordered proteins (IDPs). Here, the basic principles of SAXS are presented, and profits and pitfalls of the characterization of multidomain flexible proteins and IDPs using SAXS are discussed from the practical point of view. Examples of the synergistic use of SAXS with high resolution methods like X-ray crystallography and nuclear magnetic resonance (NMR), as well as other experimental and in silico techniques to characterize completely, or partially unstructured proteins, are presented.

Effect of disorder on the contact probability of elongated conformations of biopolymers

Biopolymers are characterized by heterogeneous interactions, and usually perform their biological tasks forming contacts within domains of limited size. Combining polymer theory with a replica approach, we study the scaling properties of the probability of contact formation in random heteropolymers as a function of their linear distance. It is found that, close to or above the θ point, it is possible to define a contact probability which is typical (i.e., "self-averaging") for different realizations of the heterogeneous interactions, and which displays an exponential cutoff, dependent on temperature and on the interaction range. In many cases this cutoff is comparable with the typical sizes of domains in biopolymers. While it is well known that disorder causes interesting effects at low temperature, the behavior elucidated in the present study is an example of a nontrivial effect at high temperature.

Denatured state ensembles with the same radii of gyration can form significantly different long-range contacts

Defining the structural, dynamic, and energetic properties of the unfolded state of proteins is critical for an in-depth understanding of protein folding, protein thermodynamics, and protein aggregation. Here we analyze long-range contacts and compactness in two apparently fully unfolded ensembles of the same protein: the acid unfolded state of the C-terminal domain of ribosomal protein L9 in the absence of high concentrations of urea as well as the urea unfolded state at low pH. Small angle X-ray scattering reveals that the two states are expanded with values of Rg differing by <7%. Paramagnetic relaxation enhancement (PRE) nuclear magnetic resonance studies, however, reveal that the acid unfolded state samples conformations that facilitate contacts between residues that are distant in sequence while the urea unfolded state ensemble does not. The experimental PRE profiles for the acid unfolded state differ significantly from these predicted using an excluded volume limit ensemble, but these long-range contacts are largely eliminated by the addition of 8 M urea. The work shows that expanded unfolded states can sample very different distributions of long-range contacts yet still have similar radii of gyration. The implications for protein folding and for the characterization of unfolded states are discussed.

Experiments and simulations show how long-range contacts can form in expanded unfolded proteins with negligible secondary structure

The sizes of unfolded proteins under highly denaturing conditions scale as N(0.59) with chain length. This suggests that denaturing conditions mimic good solvents, whereby the preference for favorable chain-solvent interactions causes intrachain interactions to be repulsive, on average. Beyond this generic inference, the broader implications of N(0.59) scaling for quantitative descriptions of denatured state ensembles (DSEs) remain unresolved. Of particular interest is the degree to which N(0.59) scaling can simultaneously accommodate intrachain attractions and detectable long-range contacts. Here we present data showing that the DSE of the N-terminal domain of the L9 (NTL9) ribosomal protein in 8.3 M urea lacks detectable secondary structure and forms expanded conformations in accord with the expected N(0.59) scaling behavior. Paramagnetic relaxation enhancements, however, indicate the presence of detectable long-range contacts in the denatured-state ensemble of NTL9. To explain these observations we used atomistic thermal unfolding simulations to identify ensembles whose properties are consistent with all of the experimental observations, thus serving as useful proxies for the DSE of NTL9 in 8.3 M urea. Analysis of these ensembles shows that residual attractions are present under mimics of good solvent conditions, and for NTL9 they result from low-likelihood, medium/long-range contacts between hydrophobic residues. Our analysis provides a quantitative framework for the simultaneous observation of N(0.59) scaling and low-likelihood long-range contacts for the DSE of NTL9. We propose that such low-likelihood intramolecular hydrophobic clusters might be a generic feature of DSEs that play a gatekeeping role to protect against aggregation during protein folding.

Describing sequence-ensemble relationships for intrinsically disordered proteins

Intrinsically disordered proteins participate in important protein-protein and protein-nucleic acid interactions and control cellular phenotypes through their prominence as dynamic organizers of transcriptional, post-transcriptional and signalling networks. These proteins challenge the tenets of the structure-function paradigm and their functional mechanisms remain a mystery given that they fail to fold autonomously into specific structures. Solving this mystery requires a first principles understanding of the quantitative relationships between information encoded in the sequences of disordered proteins and the ensemble of conformations they sample. Advances in quantifying sequence-ensemble relationships have been facilitated through a four-way synergy between bioinformatics, biophysical experiments, computer simulations and polymer physics theories. In the present review we evaluate these advances and the resultant insights that allow us to develop a concise quantitative framework for describing the sequence-ensemble relationships of intrinsically disordered proteins.

Structural analysis of intrinsically disordered proteins by small-angle X-ray scattering

Small-angle scattering of X-rays (SAXS) is an established method to study the overall structure and structural transitions of biological macromolecules in solution. For folded proteins, the technique provides three-dimensional low resolution structures ab initio or it can be used to drive rigid-body modeling. SAXS is also a powerful tool for the quantitative analysis of flexible systems, including intrinsically disordered proteins (IDPs), and is highly complementary to the high resolution methods of X-ray crystallography and NMR. Here we present the basic principles of SAXS and review the main approaches to the characterization of IDPs and flexible multidomain proteins using SAXS. Together with the standard approaches based on the analysis of overall parameters, a recently developed Ensemble Optimization Method (EOM) is now available. The latter method allows for the co-existence of multiple protein conformations in solution compatible with the scattering data. Analysis of the selected ensembles provides quantitative information about flexibility and also offers insights into structural features. Examples of the use of SAXS and combined approaches with NMR, X-ray crystallography, and computational methods to characterize completely or partially disordered proteins are presented.

Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics

Histone tails are highly flexible N- or C-terminal protrusions of histone proteins which facilitate the compaction of DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolytes with high degree of conformational disorder which allows them to function as biomolecular "switches", regulating various genetic processes. Unfortunately, their intrinsically disordered nature creates obstacles for comprehensive experimental investigation of both the structural and dynamical aspects of histone tails, because of which their conformational behaviors are still not well understood. In this work we have carried out ∼3 microsecond long all atom replica exchange molecular dynamics (REMD) simulations for each of four histone tails, H4, H3, H2B, and H2A, and probed their intrinsic conformational preferences. Our subsequent free energy landscape analysis demonstrated that most tails are not fully disordered, but show distinct conformational organization, containing specific flickering secondary structural elements. In particular, H4 forms β-hairpins, H3 and H2B adopt α-helical elements, while H2A is fully disordered. We rationalized observed patterns of conformational dynamics of various histone tails using ideas from physics of polyelectrolytes and disordered systems. We also discovered an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by subtle interplay between ionic screening and chain entropy.

Geometrical Analysis of Cytochrome c Unfolding

We have developed a geometrical model to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n= 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. Our calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, we performed lattice Monte Carlo simulations to study systematically the possible importance of asynchronicity. Our calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.

Insights into protein aggregation by NMR characterization of insoluble SH3 mutants solubilized in salt-free water

Protein aggregation in vivo has been extensively associated with a large spectrum of human diseases. On the other hand, mechanistic insights into protein aggregation in vitro were incomplete due to the inability in solubilizing insoluble proteins for high-resolution biophysical investigations. However, a new avenue may be opened up by our recent discovery that previously-thought insoluble proteins can in fact be solubilized in salt-free water. Here we use this approach to study the NMR structural and dynamic properties of an insoluble SH3 mutant with a naturally-occurring insertion of Val22 at the tip of the diverging turn. The obtained results reveal: 1) regardless of whether the residue is Val, Ala, Asp or Arg, the insertion will render the first hNck2 SH3 domain to be insoluble in buffers. Nevertheless, all four mutants could be solubilized in salt-free water and appear to be largely unfolded as evident from their CD and NMR HSQC spectra. 2) Comparison of the chemical shift deviations reveals that while in V22-SH3 the second helical region is similarly populated as in the wild-type SH3 at pH 2.0, the first helical region is largely unformed. 3) In V22-SH3, many non-native medium-range NOEs manifest to define non-native helical conformations. In the meanwhile a small group of native-like long-range NOEs still persists, indicating the existence of a rudimentary native-like tertiary topology. 4) Although overall, V22-SH3 has significantly increased backbone motions on the ps-ns time scale, some regions still own restricted backbone motions as revealed by analyzing ¹⁵N relaxation data. Our study not only leads to the establishment of the first high-resolution structural and dynamic picture for an insoluble protein, but also shed more light on the molecular events for the nonhierarchical folding mechanism. Furthermore, a general mechanism is also proposed for in vivo protein aggregation triggered by the genetic mutation and posttranslational modification.

A self-consistent description of the conformational behavior of chemically denatured proteins from NMR and small angle scattering

Characterization of the conformational properties of unfolded proteins is essential for understanding the mechanisms of protein folding and misfolding. This information is also fundamental to determining the relationship between flexibility and function in the highly diverse families of intrinsically disordered proteins. Here we present a self-consistent model of conformational sampling of chemically denatured proteins in agreement with experimental data reporting on long-range distance distributions in unfolded proteins using small-angle x-ray scattering and nuclear magnetic resonance pulse-field gradient-based measurements. We find that standard statistical coil models, selected from folded protein databases with secondary structural elements removed, need to be refined to correct backbone dihedral angle sampling of denatured proteins, although they appear to be appropriate for intrinsically disordered proteins. For denatured proteins, pervasive increases in the sampling of more-extended regions of Ramachandran space {50 degrees Collapse

Key Words Collapse

MESH Headings

• Computer Simulation
• Databases, Protein
• Models, Chemical
• Nuclear Magnetic Resonance, Biomolecular
• Protein Conformation
• Protein Denaturation
• Protein Folding
• Protein Structure, Secondary
• Scattering, Small Angle

Collapse

Grants Collapse

Affiliation(s)

Pau Bernadó Institute for Research in Biomedicine, c/ Baldiri Reixac, Barcelona, Spain
Martin Blackledge Protein Dynamics and Flexibility, Institut de Biologie Structurale, UMR 5075, Commissariat à l'Énergie Atomique-Centre National de la Recherche Scientifique-Université Joseph Fourier, Grenoble, France

Collapse

Bayesian single-exponential kinetics in single-molecule experiments and simulations

In this work, we develop a fully Bayesian method for the calculation of probability distributions of single-exponential rates for any single-molecule process. These distributions can even be derived when no transitions from one state to another have been observed, since in that case the data can be used to estimate a lower bound on the rate. Using a Bayesian hypothesis test, one can easily test whether a transition occurs at the same rate or at different rates in two data sets. We illustrate these methods with molecular dynamics simulations of the folding of a beta-sheet protein. However, the theory presented here can be used on any data from simulation or experiment for which a two-state description is appropriate.

Deconstructing the native state: energy landscapes, function, and dynamics of globular proteins

Proteins are highly complex molecules with features exquisitely selected by nature to carry out essential biological functions. Physical chemistry and polymer physics provide us with the tools needed to make sense of this complexity. Upon translation, many proteins fold to a thermodynamically stable form known as the native state. The native state is not static, but consists of a hierarchy of conformations, that are continuously explored through dynamics. In this review we provide a brief introduction to some of the core concepts required in the discussion of the protein native dynamics using energy landscapes ideas. We first discuss recent works which have challenged the structure-function paradigm by demonstrating function in disordered proteins. Next we examine the hierarchical organization in the energy landscapes using atomistic molecular dynamics simulations and principal component analysis. In particular, the role of direct and water-mediated contacts in sculpting the landscape is elaborated. Another approach to studying the native state ensemble is based on choosing high-resolution order parameters for computing one- or two-dimensional free energy surfaces. We demonstrate that 2D free energy surfaces provide rich thermodynamic and kinetic information about the native state ensemble. Brownian dynamics simulations on such a surface indicate that protein conformational dynamics is weakly activated. Finally, we briefly discuss implicit and coarse-grained protein models and emphasize the solvent role in determining native state structure and dynamics.

Multiscale approaches for studying energy transduction in dynein

Cytoplasmic dynein is an important motor that drives all minus-end directed movement along microtubules. Dynein is a complex motor whose processive motion is driven by ATP-hydrolysis. Dynein's run length has been measured to be several millimetres with typical velocities in the order of a few nanometres per second. Therefore, the average time between steps is a fraction of a second. When this time scale is compared with typical time scales for protein side chain and backbone movements (approximately 10(-9) s and approximately 10(-5) s, respectively), it becomes clear that a multi-timescale modelling approach is required to understand energy transduction in this protein. Here, we review recent efforts to use computational and mathematical modelling to understand various aspects of dynein's chemomechanical cycle. First, we describe a structural model of dynein's motor unit showing a heptameric organization of the motor subunits. Second, we describe our molecular dynamics simulations of the motor unit that are used to investigate the dynamics of the various motor domains. Third, we present a kinetic model of the coordination between the two dynein heads. Lastly, we investigate the various potential geometries of the dimer during its hydrolytic and stepping cycle.

Characterization of the unfolded state of repeat proteins

The unfolded state ensemble of proteins has been described as a structurally featureless state. While this approach is supported by the fact that many unfolded proteins follow the scaling law behavior of a random coil, there is evidence that the unfolded states of various proteins are stabilized by native or non-native interactions. Recently, the existence of extensive non-native structure was reported for a repeat protein, which resulted in a scaling law exponent that is significantly smaller than that of a random polymer [Cortajarena et al., J. Mol. Biol. 382(1), 203-212 (2008)]. It was concluded that the high compactness of this protein stems from a significant fraction of interacting PP(II) helical segments in the unfolded state. In this study, we aim at providing possible molecular understanding of this anomalous compactness of the unfolded state and to investigate its origin. Using a hierarchy of computational models, we ask whether in general the unfolded state of a repeat protein is likely to be intrinsically more compact than the unfolded state of globular proteins, or whether this phenomenon depends mostly on the occurrence of a specific sequence that promotes PP(II) conformations. Our results suggest that the formation of the PP(II) conformation is indeed essential, yet the recurring sequence of repeat proteins promotes the interactions between these PP(II) segments and the formation of non-native interactions in the unfolded state.

Small-angle X-ray scattering of reduced ribonuclease A: effects of solution conditions and comparisons with a computational model of unfolded proteins

The disulfide-reduced form of bovine ribonuclease A, with the Cys thiols irreversibly blocked, was characterized by small-angle x-ray scattering. To help resolve the conflicting results and interpretations from previous studies of this model unfolded protein, we measured scattering profiles using a range of solution conditions and compared them with the profiles predicted by a computational model for a random-coil polypeptide. Analysis of the simulated and experimental profiles reveals that scattering intensities at intermediate angles, corresponding to interatomic distances in the range of 5-20 A, are particularly sensitive to changes in solvation and can be used to assess the internal scaling behavior of the polypeptide chain, expressed as a mass fractal dimension, D(m). This region of the scattering curve is also much less sensitive to experimental artifacts than is the very small angle regime (the Guinier region) that has been more typically used to characterize unfolded proteins. The experimental small-angle x-ray scattering profiles closely matched those predicted by the computational model assuming relatively small solvation energies. The scaling behavior of the polypeptide approaches that of a well-solvated polymer under conditions where it has a large net charge and at high urea concentrations. At lower urea concentrations and neutral pH, the behavior of the chain approaches that expected for theta-conditions, where the effects of slightly unfavorable interactions with solvent balance those of excluded volume, leading to scaling behavior comparable to that of an idealized random walk chain. Though detectable, the shift toward more compact conformations at lower urea concentrations does not correspond to a transition to a globule state and is associated with little or no reduction in conformational entropy. This type of collapse, therefore, is unlikely to greatly reduce the conformational search for the native state.

Denaturant-induced expansion and compaction of a multi-domain protein: IgG

It is generally believed that unfolded or denatured proteins show random-coil statistics and hence their radius of gyration simply scales with solvent quality (or concentration of denaturant). Indeed, nearly all proteins studied thus far have been shown to undergo a gradual and continuous expansion with increasing concentration of denaturant. Here, we use fluorescence correlation spectroscopy (FCS) to show that while protein A, a multi-domain and predominantly helical protein, expands gradually and continuously with increasing concentration of guanidine hydrochloride (GdnHCl), the F(ab')2 fragment of goat anti-rabbit antibody IgG, a multi-subunit all beta-sheet protein does not show such continuous expansion behavior. Instead, it first expands and then contracts with increasing concentration of GdnHCl. Even more striking is the fact that the hydrodynamic radius of the most expanded F(ab')2 ensemble, observed at 3-4 M GdnHCl, is approximately 3.6 times that of the native protein. Further FCS measurements involving urea and NaCl show that the unusually expanded F(ab')2 conformations might be due to electrostatic repulsions. Taken together, these results suggest that specific interactions need to be considered while assessing the conformational and statistical properties of unfolded proteins, particularly under conditions of low solvent quality.

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.

Folding versus aggregation: polypeptide conformations on competing pathways

Protein aggregation has now become recognised as an important and generic aspect of protein energy landscapes. Since the discovery that numerous human diseases are caused by protein aggregation, the biophysical characterisation of misfolded states and their aggregation mechanisms has received increased attention. Utilising experimental techniques and computational approaches established for the analysis of protein folding reactions has ensured rapid advances in the study of pathways leading to amyloid fibrils and amyloid-related aggregates. Here we describe recent experimental and theoretical advances in the elucidation of the conformational properties of dynamic, heterogeneous and/or insoluble protein ensembles populated on complex, multidimensional protein energy landscapes. We discuss current understanding of aggregation mechanisms in this context and describe how the synergy between biochemical, biophysical and cell-biological experiments are beginning to provide detailed insights into the partitioning of non-native species between protein folding and aggregation pathways.

Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories

Intrinsically disordered proteins (IDPs) are unfolded under physiological conditions. Here we ask if archetypal IDPs in aqueous milieus are best described as swollen disordered coils in a good solvent or collapsed disordered globules in a poor solvent. To answer this question, we analyzed data from molecular simulations for a 20-residue polyglutamine peptide and concluded, in accord with experimental results, that water is a poor solvent for this system. The relevance of monomeric polyglutamine is twofold: It is an archetypal IDP sequence and its aggregation is associated with nine neurodegenerative diseases. The main advance in this work lies in our ability to make accurate assessments of solvent quality from analysis of simulations for a single, rather than multiple chain lengths. We achieved this through the proper design of simulations and analysis of order parameters that are used to describe conformational equilibria in polymer physics theories. Despite the preference for collapsed structures, we find that polyglutamine is disordered because a heterogeneous ensemble of conformations of equivalent compactness is populated at equilibrium. It is surprising that water is a poor solvent for polar polyglutamine and the question is: why? Our preliminary analysis suggests that intrabackbone interactions provide at least part of the driving force for the collapse of polyglutamine in water. We also show that dynamics for conversion between distinct conformations resemble structural relaxation in disordered, glassy systems, i.e., the energy landscape for monomeric polyglutamine is rugged. We end by discussing generalizations of our methods to quantitative studies of conformational equilibria of other low-complexity IDP sequences.

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed "cold sites", which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.

Mapping protein collapse with single-molecule fluorescence and kinetic synchrotron radiation circular dichroism spectroscopy

We have used the combination of single-molecule Förster resonance energy transfer and kinetic synchrotron radiation circular dichroism experiments to probe the conformational ensemble of the collapsed unfolded state of the small cold shock protein CspTm under near-native conditions. This regime is physiologically most relevant but difficult to access experimentally, because the equilibrium signal in ensemble experiments is dominated by folded molecules. Here, we avoid this problem in two ways. One is the use of single-molecule Förster resonance energy transfer, which allows the separation of folded and unfolded subpopulations at equilibrium and provides information on long-range intramolecular distance distributions. From experiments with donor and acceptor chromophores placed at different positions within the chain, we find that the distance distributions in unfolded CspTm agree surprisingly well with a Gaussian chain not only at high concentrations of denaturant, where the polypeptide chain is expanded, but also at low denaturant concentrations, where the chain is collapsed. The second, complementary approach is synchrotron radiation circular dichroism spectroscopy of collapsed unfolded molecules transiently populated with a microfluidic device that enables rapid mixing. The results indicate a beta-structure content of the collapsed unfolded state of approximately 20% compared with the folded protein. This suggests that collapse can induce secondary structure in an unfolded state without interfering with long-range distance distributions characteristic of a random coil, which were previously found only for highly expanded unfolded proteins.

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.