Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Disentangling Folding from Energetic Traps in Simulations of Disordered Proteins

Protein conformational heterogeneity plays an essential role in a myriad of different biological processes. Extensive conformational heterogeneity is especially characteristic of intrinsically disordered proteins and protein regions (collectively IDRs), which lack a well-defined three-dimensional structure and instead rapidly exchange between a diverse ensemble of configurations. An emerging paradigm recognizes that the conformational biases encoded in IDR ensembles can play a central role in their biological function, necessitating understanding these sequence-ensemble relations. All-atom simulations have provided critical insight into our modern understanding of the solution behavior of IDRs. However, effectively exploring the accessible conformational space associated with large, heterogeneous ensembles is challenging. In particular, identifying poorly sampled or energetically trapped regions of disordered proteins in simulations often relies on qualitative assessment based on visual inspection of simulations and/or analysis data. These approaches, while convenient, run the risk of masking poorly sampled simulations. In this work, we present an algorithm for quantifying per-residue local conformational heterogeneity in protein simulations. Our work builds on prior work and compares the similarity between backbone dihedral angle distributions generated from molecular simulations in a limiting polymer model and across independent all-atom simulations. In this regime, the polymer model serves as a statistical reference model for extensive conformational heterogeneity in a real chain. Quantitative comparisons of probability vectors generated from these simulations reveal the extent of conformational sampling in a simulation, enabling us to distinguish between situations in which protein regions are well-sampled, poorly sampled, or folded. To demonstrate the effectiveness of this approach, we apply our algorithm to several toy, synthetic, and biological systems. Accurately assessing local conformational sampling in simulations of IDRs will help better quantify new enhanced sampling methods, ensure force field comparisons are equivalent, and provide confidence that conclusions drawn from simulations are robust.

Intrinsic stiffness and Θ-solvent regime in intrinsically disordered proteins: Implications for liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) exhibited by intrinsically disordered proteins (IDPs) depends on the solvation state around the Θ-regime, which separates good from poor solvent. Experimentally, the Θ-solvent regime of the finite length (N) IDPs, as probed by small angle X-ray scattering (SAXS) and single molecular fluorescence resonance energy transfer (smFRET), is in disagreement. Using computer simulations of a coarse-grained IDP model, we address the effect of chain length on the Θ-regime of IDPs with polar side chains (polyglutamine) and hydrophobic side chains (polyleucine) subject to varying concentrations of cosolvents [ C ] , urea (denaturant) or trimethylamine N-oxide (protective osmolyte) in water. Due to their intrinsic stiffness, these IDPs are always expanded on short-length scales, independent of the solvent quality. As a result, for short IDP sequences ( ≈ 10 to 25 residues), their propensity to exhibit LLPS cannot be inferred from single-chain properties. Further, for finite-size IDPs, the cosolvent concentration to attain the Θ-regime ( [ C Θ ] ) extracted from the structure factor emulating SAXS and pair distances mimicking smFRET differs. They converge to the same cosolvent concentration only at large N, indicating that finite size corrections vary for different IDP properties. We show that the radius of gyration ( R g ) of the IDPs in the Θ-solvent regime satisfies the scaling relation R g 2 = N f ( c N ) , which can be exploited to accurately extract [ C Θ ] ( c = ( [ C ] / [ C Θ ] - 1 ) ). We demonstrate the importance of finite size aspects originating from the chain stiffness and thermal blob size in analyzing IDP properties to identify the Θ-solvent regime.

Unraveling the Molecular Complexity of N-Terminus Huntingtin Oligomers: Insights into Polymorphic Structures

Huntington's disease (HD) is a fatal neurodegenerative disorder resulting from an abnormal expansion of polyglutamine (polyQ) repeats in the N-terminus of the huntingtin protein. When the polyQ tract surpasses 35 repeats, the mutated protein undergoes misfolding, culminating in the formation of intracellular aggregates. Research in mouse models suggests that HD pathogenesis involves the aggregation of N-terminal fragments of the huntingtin protein (htt). These early oligomeric assemblies of htt, exhibiting diverse characteristics during aggregation, are implicated as potential toxic entities in HD. However, a consensus on their specific structures remains elusive. Understanding the heterogeneous nature of htt oligomers provides crucial insights into disease mechanisms, emphasizing the need to identify various oligomeric conformations as potential therapeutic targets. Employing coarse-grained molecular dynamics, our study aims to elucidate the mechanisms governing the aggregation process and resultant aggregate architectures of htt. The polyQ tract within htt is flanked by two regions: an N-terminal domain (N17) and a short C-terminal proline-rich segment. We conducted self-assembly simulations involving five distinct N17 + polyQ systems with polyQ lengths ranging from 7 to 45, utilizing the ProMPT force field. Prolongation of the polyQ domain correlates with an increase in β-sheet-rich structures. Longer polyQ lengths favor intramolecular β-sheets over intermolecular interactions due to the folding of the elongated polyQ domain into hairpin-rich conformations. Importantly, variations in polyQ length significantly influence resulting oligomeric structures. Shorter polyQ domains lead to N17 domain aggregation, forming a hydrophobic core, while longer polyQ lengths introduce a competition between N17 hydrophobic interactions and polyQ polar interactions, resulting in densely packed polyQ cores with outwardly distributed N17 domains. Additionally, at extended polyQ lengths, we observe distinct oligomeric conformations with varying degrees of N17 bundling. These findings can help explain the toxic gain-of-function that htt with expanded polyQ acquires.

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

Amyloid modifier SERF1a interacts with polyQ-expanded huntingtin-exon 1 via helical interactions and exacerbates polyQ-induced toxicity

Abnormal polyglutamine (polyQ) expansion and fibrillization occur in Huntington's disease (HD). Amyloid modifier SERF enhances amyloid formation, but the underlying mechanism is not revealed. Here, the fibrillization and toxicity effect of SERF1a on Htt-exon1 are examined. SERF1a enhances the fibrillization of and interacts with mutant thioredoxin (Trx)-fused Httex1. NMR studies with Htt peptides show that TrxHttex1-39Q interacts with the helical regions in SERF1a and SERF1a preferentially interacts with the N-terminal 17 residues of Htt. Time-course analysis shows that SERF1a induces mutant TrxHttex1 to a single conformation enriched of β-sheet. Co-expression of SERF1a and Httex1-polyQ in neuroblastoma and lentiviral infection of SERF1a in HD-induced polypotent stem cell (iPSC)-derived neurons demonstrates the detrimental effect of SERF1a in HD. Higher level of SERF1a transcript or protein is detected in HD iPSC, transgenic mice, and HD plasma. Overall, this study provides molecular mechanism for SERF1a and mutant Httex1 to facilitate therapeutic development for HD.

FIREBALL: A tool to fit protein phase diagrams based on mean-field theories for polymer solutions

Biomolecular condensates form via phase transitions of condensate-specific biomacromolecules. Intrinsically disordered regions featuring the appropriate sequence grammars can contribute via homotypic and heterotypic interactions to the driving forces for phase separation of multivalent proteins. Experiments and computations have matured to the point where the concentrations of coexisting dense and dilute phases can be measured or computed for individual intrinsically disordered regions in complex milieus. For a macromolecule such as a disordered protein in a solvent, the locus of points that connects concentrations of the two coexisting phases defines a phase boundary, or binodal. Often, only a few points along the binodal are accessible via measurements. In such cases, and for quantitative and comparative analysis of parameters that describe the driving forces for phase separation, it is useful to fit measured or computed binodals to mean-field free energies for polymer solutions. The nonlinearity of the underlying free energy functions makes it challenging to put mean-field theories into practice. Here, we present FIREBALL, a suite of computational tools designed to enable efficient construction, analysis, and fitting to experimental or computed data of binodals. We show that depending on the theory being used, one can also extract information regarding coil-to-globule transitions of individual macromolecules.

Possible Co-Evolution of Polyglutamine and Polyproline in Huntingtin Protein: Proline-Rich Domain as Transient Folding Chaperone

Huntington's disease is an inherited neurodegenerative disorder caused by the overduplication of CAG repeats in the Huntingtin gene. Recent findings revealed that among the orthologs, the expansion of CAG repeats (polyQ) in the Huntingtin gene occurs in tandem with the duplication of CCG repeats (polyP). However, the molecular mechanism of this possible co-evolution remains unknown. We examined the structures of Huntingtin exon 1 (HttEx1) from six species along with five designed mutants. We found that the polyP segments "chaperone" the rest of the HttEx1 by forming ad hoc polyP binding grooves. Such a process elongates the otherwise poorly solvated polyQ domain, while modulating its secondary structure propensity from β-strands to α-helices. This chaperoning effect is achieved mostly through transient hydrogen bond interactions between polyP and the rest of HttEx1, resulting in a striking golden ratio of ∼2:1 between the chain lengths of polyQ and polyP.

Moving beyond disease to function: Physiological roles for polyglutamine-rich sequences in cell decisions

Glutamine-rich tracts, also known as polyQ domains, have received a great deal of attention for their role in multiple neurodegenerative diseases, including Huntington's disease (HD), spinocerebellar ataxia (SCA), and others [22], [27]. Expansions in the normal polyQ tracts are thus commonly linked to disease, but polyQ domains themselves play multiple important functional roles in cells that are being increasingly appreciated. The biochemical nature of these domains allows them to adopt a number of different structures and form large assemblies that enable environmental responsiveness, localized signaling, and cellular memory. In many cases, these involve the formation of condensates that have varied material states. In this review, we highlight known and emerging functional roles for polyQ tracts in normal cell physiology.

Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs, also known as stickers, is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter, such as temperature, that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single-chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low-complexity domains. We also leverage theories to compute sequence-specific percolation lines and thereby provide a thermodynamic framework for hardening transitions that have been observed for many biomolecular condensates.

Single-Protein Collapse Determines Phase Equilibria of a Biological Condensate

Recent advances in microscopy of living cells have established membraneless organelles as critical elements of diverse biological processes. The body of experimental work suggests that formation of such organelles is driven by liquid-liquid phase separation, a physical process that has been studied extensively for both simple liquids and mixtures of polymers. Here, we combine molecular dynamics simulations with polymer theory to show that the thermodynamic behavior of one particular biomolecular condensate-fused in sarcoma (FUS)-can be quantitatively accounted for at the level of the chain collapse theory. First, we show that a particle-based molecular dynamics model can reproduce known phase separation properties of a FUS condensate, including its critical concentration and susceptibility to mutations. Next, we obtain a polymer physics representation of a FUS condensate by examining the behavior of a single FUS protein as a function of temperature. We use the chain collapse theory to determine the thermodynamic properties of the condensate and to characterize changes in the single-chain conformation at the onset of phase separation. Altogether, our findings suggest that the phase behavior of FUS condensates can be explained by the properties of individual FUS proteins and that the change in the FUS conformation is the main force driving for the phase separation.

Polyglutamine Solution-State Structural Propensity Is Repeat Length Dependent

Expanded polyglutamine (polyQ) tracts in proteins, which are known to induce their aggregation, are associated with numerous neurodegenerative diseases. Longer polyQ tracts correlate with faster protein aggregation kinetics and a decreased age of onset for polyQ disease symptoms. Here, we use UV resonance Raman spectroscopy, circular dichroism spectroscopy, and metadynamics simulations to investigate the solution-state structures of the D₂Q₁₅K₂ (Q15) and D₂Q₂₀K₂ (Q20) peptides. Using metadynamics, we explore the conformational energy landscapes of Q15 and Q20 and investigate the relative energies and activation barriers between these low-energy structures. We compare the solution-state structures of D₂Q₁₀K₂ (Q10), Q15, and Q20 to determine the dependence of polyQ structure on the Q tract length. We show that these peptides can adopt two distinct monomeric conformations: an aggregation-resistant PPII-like conformation and an aggregation-prone β-strand-like conformation. We find that longer polyQ peptides have an increased preference for the aggregation-prone β-strand-like conformation. This preference may play an important role in the increased aggregation rate of longer polyQ peptides that is thought to lead to decreased neurodegenerative disease age of onset for polyQ disease patients.

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.

Spontaneous Switching among Conformational Ensembles in Intrinsically Disordered Proteins

The common conception of intrinsically disordered proteins (IDPs) is that they stochastically sample all possible configurations driven by thermal fluctuations. This is certainly true for many IDPs, which behave as swollen random coils that can be described using polymer models developed for homopolymers. However, the variability in interaction energy between different amino acid sequences provides the possibility that some configurations may be strongly preferred while others are forbidden. In compact globular IDPs, core hydration and packing density can vary between segments of the polypeptide chain leading to complex conformational dynamics. Here, we describe a growing number of proteins that appear intrinsically disordered by biochemical and bioinformatic characterization but switch between restricted regions of conformational space. In some cases, spontaneous switching between conformational ensembles was directly observed, but few methods can identify when an IDP is acting as a restricted chain. Such switching between disparate corners of conformational space could bias ligand binding and regulate the volume of IDPs acting as structural or entropic elements. Thus, mapping the accessible energy landscape and capturing dynamics across a wide range of timescales are essential to recognize when an IDP is acting as such a switch.

UV Resonance Raman Structural Characterization of an (In)soluble Polyglutamine Peptide

Fibrillization of polyglutamine (polyQ) tracts in proteins is implicated in at least 10 neurodegenerative diseases. This generates great interest in the structure and the aggregation mechanism(s) of polyQ peptides. The fibrillization of polyQ is thought to result from the peptide's insolubility in aqueous solutions; longer polyQ tracts show decreased aqueous solution solubility, which is thought to lead to faster fibrillization kinetics. However, few studies have characterized the structure(s) of polyQ peptides with low solubility. In the work here, we use UV resonance Raman spectroscopy to examine the secondary structures, backbone hydrogen bonding, and side chain hydrogen bonding for a variety of solution-state, solid, and fibril forms of D₂Q₂₀K₂ (Q20). Q20 is insoluble in water and has a β-strand-like conformation with extensive inter- and intrapeptide hydrogen bonding in both dry and aqueous environments. We find that Q20 has weaker backbone-backbone and backbone-side chain hydrogen bonding and is less ordered compared to that of polyQ fibrils. Interestingly, we find that the insoluble Q20 will form fibrils when incubated in water at room temperature for ∼5 h. Also, Q20 can be prepared using a well-known disaggregation procedure to produce a water-soluble PPII-like conformation with negligible inter- and intrapeptide hydrogen bonding and a resistance to aggregation.

Conformational preferences and phase behavior of intrinsically disordered low complexity sequences: insights from multiscale simulations

While many proteins and protein regions utilize a complex repertoire of amino acids to achieve their biological function, a subset of protein sequences are enriched in a reduced set of amino acids. These so-called low complexity (LC) sequences, specifically intrinsically disordered variants of LC sequences, have been the focus of recent investigations owing to their roles in a range of biological functions, specifically phase separation. Computational studies of LC sequences have provided rich insights into their behavior both as individual proteins in dilute solutions and as the drivers and modulators of higher-order assemblies. Here, we review how simulations performed across distinct resolutions have provided different types of insights into the biological role of LC sequences.

The Conformational Ensemble of Polyglutamine-14 Chains: Specific Influences of Solubility Tail and Chromophores

We address polyglutamine-14 in aqueous solution with specific chromophores and a solubility chain by means of a multiscale simulation approach, combining atomistic molecular dynamics simulations and coarse-grained Monte-Carlo conformational sampling. Despite the intrinsically disordered nature of the amyloidogenic polyglutamine, we observe transient characteristic structural motifs which exhibit a specific hydrogen bonding pattern. We illustrate the relationship between structure pattern and the distance distribution of a pair of chromophores attached to the peptide termini, in light of specific influence of a short solubility tail and the chromophores themselves on the conformational ensemble.

Structural insights into pro-aggregation effects of C. elegans CRAM-1 and its human ortholog SERF2

Toxic protein aggregates are key features of progressive neurodegenerative diseases. In addition to “seed” proteins diagnostic for each neuropathy (e.g., Aβ_1–42 and tau in Alzheimer’s disease), aggregates contain numerous other proteins, many of which are common to aggregates from diverse diseases. We reported that CRAM-1, discovered in insoluble aggregates of C. elegans expressing Q40::YFP, blocks proteasomal degradation of ubiquitinated proteins and thus promotes aggregation. We now show that CRAM-1 contains three α-helical segments forming a UBA-like domain, structurally similar to those of mammalian adaptor proteins (e.g. RAD23, SQSTM1/p62) that shuttle ubiquitinated cargos to proteasomes or autophagosomes for degradation. Molecular modeling indicates that CRAM-1, through this UBA-like domain, can form tight complexes with mono- and di-ubiquitin and may thus prevent tagged proteins from interacting with adaptor/shuttle proteins required for degradation. A human ortholog of CRAM-1, SERF2 (also largely disordered), promotes aggregation in SH-SY5Y-APP_Sw human neuroblastoma cells, since SERF2 knockdown protects these cells from amyloid formation. Atomistic molecular-dynamic simulations predict spontaneous unfolding of SERF2, and computational large-scale protein-protein interactions predict its stable binding to ubiquitins. SERF2 is also predicted to bind to most proteins screened at random, although with lower average stability than to ubiquitins, suggesting roles in aggregation initiation and/or progression.

Temperature-induced collapse of a disordered peptide observed by three sampling methods in molecular dynamics simulations

The conformational ensembles of a disordered peptide, polyglutamine Q15, over a wide temperature range were sampled using multiple replicates of conventional molecular dynamics (cMD) simulations as well as two enhanced sampling methods, temperature replica exchange (TREMD) and replica exchange with solute tempering (REST). The radius of gyration, asphericity, secondary structure, and hydrogen bonding patterns were used for the comparison of the sampling methods. Overall, the three sampling methods generated similar conformational ensembles, with progressive collapse at higher temperatures. Although accumulating the longest simulation time (90 μs), cMD at room temperature missed a small subspace that was sampled by both TREMD and REST. This subspace was high in α-helical content and separated from the main conformational space by an energy barrier. REST used less simulation time than TREMD (36 μs versus 42 μs), and this gap is expected to widen significantly for larger disordered proteins. We conclude that REST is the method of choice for conformational sampling of intrinsically disordered proteins.

Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Proteins can collapse into compact globules or form expanded, solvent-accessible, coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

Interaction Enthalpy of Side Chain and Backbone Amides in Polyglutamine Solution Monomers and Fibrils

We determined an empirical correlation that relates the amide I vibrational band frequencies of the glutamine (Q) side chain to the strength of hydrogen bonding, van der Waals, and Lewis acid-base interactions of its primary amide carbonyl. We used this correlation to determine the Q side chain carbonyl interaction enthalpy (Δ H_int) in monomeric and amyloid-like fibril conformations of D₂Q₁₀K₂ (Q10). We independently verified these Δ H_int values through molecular dynamics simulations that showed excellent agreement with experiments. We found that side chain-side chain and side chain-peptide backbone interactions in fibrils and monomers are more enthalpically favorable than are Q side chain-water interactions. Q10 fibrils also showed a more favorable Δ H_int for side chain-side chain interactions compared to backbone-backbone interactions. This work experimentally demonstrates that interamide side chain interactions are important in the formation and stabilization of polyQ fibrils.

Tadpole-like Conformations of Huntingtin Exon 1 Are Characterized by Conformational Heterogeneity that Persists regardless of Polyglutamine Length

Soluble huntingtin exon 1 (Httex1) with expanded polyglutamine (polyQ) engenders neurotoxicity in Huntington's disease. To uncover the physical basis of this toxicity, we performed structural studies of soluble Httex1 for wild-type and mutant polyQ lengths. Nuclear magnetic resonance experiments show evidence for conformational rigidity across the polyQ region. In contrast, hydrogen-deuterium exchange shows absence of backbone amide protection, suggesting negligible persistence of hydrogen bonds. The seemingly conflicting results are explained by all-atom simulations, which show that Httex1 adopts tadpole-like structures with a globular head encompassing the N-terminal amphipathic and polyQ regions and the tail encompassing the C-terminal proline-rich region. The surface area of the globular domain increases monotonically with polyQ length. This stimulates sharp increases in gain-of-function interactions in cells for expanded polyQ, and one of these interactions is with the stress-granule protein Fus. Our results highlight plausible connections between Httex1 structure and routes to neurotoxicity.

Relationship of Sequence and Phase Separation in Protein Low-Complexity Regions

Liquid-liquid phase separation seems to play critical roles in the compartmentalization of cells through the formation of biomolecular condensates. Many proteins with low-complexity regions are found in these condensates, and they can undergo phase separation in vitro in response to changes in temperature, pH, and ion concentration. Low-complexity regions are thus likely important players in mediating compartmentalization in response to stress. However, how the phase behavior is encoded in their amino acid composition and patterning is only poorly understood. We discuss here that polymer physics provides a powerful framework for our understanding of the thermodynamics of mixing and demixing and for how the phase behavior is encoded in the primary sequence. We propose to classify low-complexity regions further into subcategories based on their sequence properties and phase behavior. Ongoing research promises to improve our ability to link the primary sequence of low-complexity regions to their phase behavior as well as the emerging miscibility and material properties of the resulting biomolecular condensates, providing mechanistic insight into this fundamental biological process across length scales.

Force field development and simulations of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in many physiological processes such as signal transduction and transcriptional regulation. Computer simulations that are based on empirical force fields have been increasingly used to understand the biophysics of disordered proteins. In this review, we focus on recent improvement of protein force fields, including polarizable force fields, concerning their accuracy in modeling intrinsically disordered proteins. Some recent benchmarks and applications of these force fields are also overviewed.

Proteins Containing Expanded Polyglutamine Tracts and Neurodegenerative Disease

Several hereditary neurological and neuromuscular diseases are caused by an abnormal expansion of trinucleotide repeats. To date, there have been 10 of these trinucleotide repeat disorders associated with an expansion of the codon CAG encoding glutamine (Q). For these polyglutamine (polyQ) diseases, there is a critical threshold length of the CAG repeat required for disease, and further expansion beyond this threshold is correlated with age of onset and symptom severity. PolyQ expansion in the translated proteins promotes their self-assembly into a variety of oligomeric and fibrillar aggregate species that accumulate into the hallmark proteinaceous inclusion bodies associated with each disease. Here, we review aggregation mechanisms of proteins with expanded polyQ-tracts, structural consequences of expanded polyQ ranging from monomers to fibrillar aggregates, the impact of protein context and post-translational modifications on aggregation, and a potential role for lipid membranes in aggregation. As the pathogenic mechanisms that underlie these disorders are often classified as either a gain of toxic function or loss of normal protein function, some toxic mechanisms associated with mutant polyQ tracts will also be discussed.

Comparative analysis of anti-polyglutamine Fab crystals grown on Earth and in microgravity

Huntington's disease is one of nine neurodegenerative diseases caused by a polyglutamine (polyQ)-repeat expansion. An anti-polyQ antigen-binding fragment, MW1 Fab, was crystallized both on Earth and on the International Space Station, a microgravity environment where convection is limited. Once the crystals returned to Earth, the number, size and morphology of all crystals were recorded, and X-ray data were collected from representative crystals. The results generally agreed with previous microgravity crystallization studies. On average, microgravity-grown crystals were 20% larger than control crystals grown on Earth, and microgravity-grown crystals had a slightly improved mosaicity (decreased by 0.03°) and diffraction resolution (decreased by 0.2 Å) compared with control crystals grown on Earth. However, the highest resolution and lowest mosaicity crystals were formed on Earth, and the highest-quality crystal overall was formed on Earth after return from microgravity.

Folding Landscape of Mutant Huntingtin Exon1: Diffusible Multimers, Oligomers and Fibrils, and No Detectable Monomer

Expansion of the polyglutamine (polyQ) track of the Huntingtin (HTT) protein above 36 is associated with a sharply enhanced risk of Huntington’s disease (HD). Although there is general agreement that HTT toxicity resides primarily in N-terminal fragments such as the HTT exon1 protein, there is no consensus on the nature of the physical states of HTT exon1 that are induced by polyQ expansion, nor on which of these states might be responsible for toxicity. One hypothesis is that polyQ expansion induces an alternative, toxic conformation in the HTT exon1 monomer. Alternative hypotheses posit that the toxic species is one of several possible aggregated states. Defining the nature of the toxic species is particularly challenging because of facile interconversion between physical states as well as challenges to identifying these states, especially in vivo. Here we describe the use of fluorescence correlation spectroscopy (FCS) to characterize the detailed time and repeat length dependent self-association of HTT exon1-like fragments both with chemically synthesized peptides in vitro and with cell-produced proteins in extracts and in living cells. We find that, in vitro, mutant HTT exon1 peptides engage in polyQ repeat length dependent dimer and tetramer formation, followed by time dependent formation of diffusible spherical and fibrillar oligomers and finally by larger, sedimentable amyloid fibrils. For expanded polyQ HTT exon1 expressed in PC12 cells, monomers are absent, with tetramers being the smallest molecular form detected, followed in the incubation time course by small, diffusible aggregates at 6–9 hours and larger, sedimentable aggregates that begin to build up at 12 hrs. In these cell cultures, significant nuclear DNA damage appears by 6 hours, followed at later times by caspase 3 induction, mitochondrial dysfunction, and cell death. Our data thus defines limits on the sizes and concentrations of different physical states of HTT exon1 along the reaction profile in the context of emerging cellular distress. The data provide some new candidates for the toxic species and some new reservations about more well-established candidates. Compared to other known markers of HTT toxicity, nuclear DNA damage appears to be a relatively early pathological event.

Effects of the enlargement of polyglutamine segments on the structure and folding of ataxin-2 and ataxin-3 proteins

Spinocerebellar ataxia type 2 (SCA2) and type 3 (SCA3) are two common autosomal-dominant inherited ataxia syndromes, both of which are related to the unstable expansion of trinucleotide CAG repeats in the coding region of the related ATXN2 and ATXN3 genes, respectively. The poly-glutamine (poly-Q) tract encoded by the CAG repeats has long been recognized as an important factor in disease pathogenesis and progress. In this study, using the I-TASSER method for 3D structure prediction, we investigated the effect of poly-Q tract enlargement on the structure and folding of ataxin-2 and ataxin-3 proteins. Our results show good agreement with the known experimental structures of the Josephin and UIM domains providing credence to the simulation results presented here, which show that the enlargement of the poly-Q region not only affects the local structure of these regions but also affects the structures of functional domains as well as the whole protein. The changes observed in the predicted models of the UIM domains in ataxin-3 when the poly-Q track is enlarged provide new insights on possible pathogenic mechanisms.

The emerging role of the first 17 amino acids of huntingtin in Huntington's disease

Huntington's disease (HD) is caused by a polyglutamine (polyQ) domain that is expanded beyond a critical threshold near the N-terminus of the huntingtin (htt) protein, directly leading to htt aggregation. While full-length htt is a large (on the order of ∼350 kDa) protein, it is proteolyzed into a variety of N-terminal fragments that accumulate in oligomers, fibrils, and larger aggregates. It is clear that polyQ length is a key determinant of htt aggregation and toxicity. However, the flanking sequences around the polyQ domain, such as the first 17 amino acids on the N terminus (Nt17), influence aggregation, aggregate stability, influence other important biochemical properties of the protein and ultimately its role in pathogenesis. Here, we review the impact of Nt17 on htt aggregation mechanisms and kinetics, structural properties of Nt17 in both monomeric and aggregate forms, the potential role of posttranslational modifications (PTMs) that occur in Nt17 in HD, and the function of Nt17 as a membrane targeting domain.

A coarse-grained model for polyglutamine aggregation modulated by amphipathic flanking sequences

The aggregation of proteins with expanded polyglutamine (polyQ) tracts is directly relevant to the formation of neuronal intranuclear inclusions in Huntington's disease. In vitro studies have uncovered the effects of flanking sequences as modulators of the driving forces and mechanisms of polyQ aggregation in sequence segments associated with HD. Specifically, a seventeen-residue amphipathic stretch (N17) that is directly N-terminal to the polyQ tract in huntingtin decreases the overall solubility, destabilizes nonfibrillar aggregates, and accelerates fibril formation. Published results from atomistic simulations showed that the N17 module reduces the frequency of intermolecular association. Our reanalysis of these simulation results demonstrates that the N17 module also reduces interchain entanglements between polyQ domains. These two effects, which are observed on the smallest lengthscales, are incorporated into phenomenological pair potentials and used in coarse-grained Brownian dynamics simulations to investigate their impact on large-scale aggregation. We analyze the results from Brownian dynamics simulations using the framework of diffusion-limited cluster aggregation. When entanglements prevail, which is true in the absence of N17, small spherical clusters and large linear aggregates form on distinct timescales, in accord with in vitro experiments. Conversely, when entanglements are quenched and a barrier to intermolecular associations is introduced, both of which are attributable to N17, the timescales for forming small species and large linear aggregates become similar. Therefore, the combination of a reduction of interchain entanglements through homopolymeric polyQ and barriers to intermolecular associations appears to be sufficient for providing a minimalist phenomenological rationalization of in vitro observations regarding the effects of N17 on polyQ aggregation.

An Analysis of Biomolecular Force Fields for Simulations of Polyglutamine in Solution

Polyglutamine (polyQ) peptides are a useful model system for biophysical studies of protein folding and aggregation, both for their intriguing aggregation properties and their own relevance to human disease. The genetic expansion of a polyQ tract triggers the formation of amyloid aggregates associated with nine neurodegenerative diseases. Several clearly identifiable and separable factors, notably the length of the polyQ tract, influence the mechanism of aggregation, its associated kinetics, and the ensemble of structures formed. Atomistic simulations are well positioned to answer open questions regarding the thermodynamics and kinetics of polyQ folding and aggregation. The additional, explicit representation of water permits deeper investigation of the role of solvent dynamics, and it permits a direct comparison of simulation results with infrared spectroscopy experiments. The generation of meaningful simulation results hinges on satisfying two essential criteria: achieving sufficient conformational sampling to draw statistically valid conclusions, and accurately reproducing the intermolecular forces that govern system structure and dynamics. In this work, we examine the ability of 12 biomolecular force fields to reproduce the properties of a simple, 30-residue polyQ peptide (Q30) in explicit water. In addition to secondary and tertiary structure, we consider generic structural properties of polymers that provide additional dimensions for analysis of the highly degenerate disordered states of the molecule. We find that the 12 force fields produce a wide range of predictions. We identify AMBER ff99SB, AMBER ff99SB*, and OPLS-AA/L to be most suitable for studies of polyQ folding and aggregation.

Anti-PolyQ Antibodies Recognize a Short PolyQ Stretch in Both Normal and Mutant Huntingtin Exon 1

Huntington's disease is caused by expansion of a polyglutamine (polyQ) repeat in the huntingtin protein. A structural basis for the apparent transition between normal and disease-causing expanded polyQ repeats of huntingtin is unknown. The "linear lattice" model proposed random-coil structures for both normal and expanded polyQ in the preaggregation state. Consistent with this model, the affinity and stoichiometry of the anti-polyQ antibody MW1 increased with the number of glutamines. An opposing "structural toxic threshold" model proposed a conformational change above the pathogenic polyQ threshold resulting in a specific toxic conformation for expanded polyQ. Support for this model was provided by the anti-polyQ antibody 3B5H10, which was reported to specifically recognize a distinct pathologic conformation of soluble expanded polyQ. To distinguish between these models, we directly compared binding of MW1 and 3B5H10 to normal and expanded polyQ repeats within huntingtin exon 1 fusion proteins. We found similar binding characteristics for both antibodies. First, both antibodies bound to normal, as well as expanded, polyQ in huntingtin exon 1 fusion proteins. Second, an expanded polyQ tract contained multiple epitopes for fragments antigen-binding (Fabs) of both antibodies, demonstrating that 3B5H10 does not recognize a single epitope specific to expanded polyQ. Finally, small-angle X-ray scattering and dynamic light scattering revealed similar binding modes for MW1 and 3B5H10 Fab-huntingtin exon 1 complexes. Together, these results support the linear lattice model for polyQ binding proteins, suggesting that the hypothesized pathologic conformation of soluble expanded polyQ is not a valid target for drug design.

Proteins in aggregates functionally impact multiple neurodegenerative disease models by forming proteasome-blocking complexes

Age-dependent neurodegenerative diseases progressively form aggregates containing both shared components (e.g., TDP-43, phosphorylated tau) and proteins specific to each disease. We investigated whether diverse neuropathies might have additional aggregation-prone proteins in common, discoverable by proteomics. Caenorhabditis elegans expressing unc-54p/Q40::YFP, a model of polyglutamine array diseases such as Huntington's, accrues aggregates in muscle 2–6 days posthatch. These foci, isolated on antibody-coupled magnetic beads, were characterized by high-resolution mass spectrometry. Three Q40::YFP-associated proteins were inferred to promote aggregation and cytotoxicity, traits reduced or delayed by their RNA interference knockdown. These RNAi treatments also retarded aggregation/cytotoxicity in Alzheimer's disease models, nematodes with muscle or pan-neuronal Aβ_1–42 expression and behavioral phenotypes. The most abundant aggregated proteins are glutamine/asparagine-rich, favoring hydrophobic interactions with other random-coil domains. A particularly potent modulator of aggregation, CRAM-1/HYPK, contributed < 1% of protein aggregate peptides, yet its knockdown reduced Q40::YFP aggregates 72–86% (P < 10⁻⁶). In worms expressing Aβ_1–42, knockdown of cram-1 reduced β-amyloid 60% (P < 0.002) and slowed age-dependent paralysis > 30% (P < 10⁻⁶). In wild-type worms, cram-1 knockdown reduced aggregation and extended lifespan, but impaired early reproduction. Protection against seeded aggregates requires proteasome function, implying that normal CRAM-1 levels promote aggregation by interfering with proteasomal degradation of misfolded proteins. Molecular dynamic modeling predicts spontaneous and stable interactions of CRAM-1 (or human orthologs) with ubiquitin, and we verified that CRAM-1 reduces degradation of a tagged-ubiquitin reporter. We propose that CRAM-1 exemplifies a class of primitive chaperones that are initially protective and highly beneficial for early reproduction, but ultimately impair aggregate clearance and limit longevity.

Overexpression of Q-rich prion-like proteins suppresses polyQ cytotoxicity and alters the polyQ interactome

Expansion of a poly-glutamine (polyQ) repeat in a group of functionally unrelated proteins is the cause of several inherited neurodegenerative disorders, including Huntington's disease. The polyQ length-dependent aggregation and toxicity of these disease proteins can be reproduced in Saccharomyces cerevisiae. This system allowed us to screen for genes that when overexpressed reduce the toxic effects of an N-terminal fragment of mutant huntingtin with 103 Q. Surprisingly, among the identified suppressors were three proteins with Q-rich, prion-like domains (PrDs): glycine threonine serine repeat protein (Gts1p), nuclear polyadenylated RNA-binding protein 3, and minichromosome maintenance protein 1. Overexpression of the PrD of Gts1p, containing an imperfect 28 residue glutamine-alanine repeat, was sufficient for suppression of toxicity. Association with this discontinuous polyQ domain did not prevent 103Q aggregation, but altered the physical properties of the aggregates, most likely early in the assembly pathway, as reflected in their increased SDS solubility. Molecular simulations suggested that Gts1p arrests the aggregation of polyQ molecules at the level of nonfibrillar species, acting as a cap that destabilizes intermediates on path to form large fibrils. Quantitative proteomic analysis of polyQ interactors showed that expression of Gts1p reduced the interaction between polyQ and other prion-like proteins, and enhanced the association of molecular chaperones with the aggregates. These findings demonstrate that short, Q-rich peptides are able to shield the interactive surfaces of toxic forms of polyQ proteins and direct them into nontoxic aggregates.

The intrinsically disordered regions of the Drosophila melanogaster Hox protein ultrabithorax select interacting proteins based on partner topology

Interactions between structured proteins require a complementary topology and surface chemistry to form sufficient contacts for stable binding. However, approximately one third of protein interactions are estimated to involve intrinsically disordered regions of proteins. The dynamic nature of disordered regions before and, in some cases, after binding calls into question the role of partner topology in forming protein interactions. To understand how intrinsically disordered proteins identify the correct interacting partner proteins, we evaluated interactions formed by the Drosophila melanogaster Hox transcription factor Ultrabithorax (Ubx), which contains both structured and disordered regions. Ubx binding proteins are enriched in specific folds: 23 of its 39 partners include one of 7 folds, out of the 1195 folds recognized by SCOP. For the proteins harboring the two most populated folds, DNA-RNA binding 3-helical bundles and α-α superhelices, the regions of the partner proteins that exhibit these preferred folds are sufficient for Ubx binding. Three disorder-containing regions in Ubx are required to bind these partners. These regions are either alternatively spliced or multiply phosphorylated, providing a mechanism for cellular processes to regulate Ubx-partner interactions. Indeed, partner topology correlates with the ability of individual partner proteins to bind Ubx spliceoforms. Partners bind different disordered regions within Ubx to varying extents, creating the potential for competition between partners and cooperative binding by partners. The ability of partners to bind regions of Ubx that activate transcription and regulate DNA binding provides a mechanism for partners to modulate transcription regulation by Ubx, and suggests that one role of disorder in Ubx is to coordinate multiple molecular functions in response to tissue-specific cues.

Dopamine-induced α-synuclein oligomers show self- and cross-propagation properties

Amyloid aggregates of α-synuclein (αS) protein are the predominant species present within the intracellular inclusions called Lewy bodies in Parkinson's disease (PD) patients. Among various aggregates, the low-molecular weight ones broadly ranging between 2 and 30 mers are known to be the primary neurotoxic agents responsible for the impairment of neuronal function. Recent research has indicated that the neurotransmitter dopamine (DA) is one of the key physiological agents promoting and augmenting αS aggregation, which is thought to be a significant event in PD pathologenesis. Specifically, DA is known to induce the formation of soluble oligomers of αS, which in turn are responsible for inducing several important cellular changes leading to cellular toxicity. In this report, we present the generation, isolation, and biophysical characterization of five different dopamine-derived αS oligomers (DSOs) ranging between 3 and 15 mers, corroborating previously published reports. More importantly, we establish that these DSOs are also capable of replication by self-propagation, which leads to the replication of DSOs upon interaction with αS monomers, a process similar to that observed in mammilian prions. In addition, DSOs are also able to cross-propagate amyloid-β (Aβ) aggregates involved in Alzheimer's disease (AD). Interestingly, while self-propagation of DSOs occur with no net gain in protein structure, cross-propagation proceeds with an overall gain in β-sheet conformation. These results implicate the involvement of DSOs in the progression of PD, and, in part, provide a molecular basis for the observed co-existence of AD-like pathology among PD patients.

Synthesis and disaggregation of asparagine repeat-containing peptides

Of all amino acid repeats in eukaryotes, polyglutamine (polyQ) is the most frequent, followed by polyasparagine (polyN). Glutamine repeats are expanded in proteins associated with several neurodegenerative disorders. The expanded polyQ domain is known to induce aggregation, and it is hypothesized that aggregation is directly causative of pathology. Despite the widespread presence of asparagine repeats in invertebrate eukaryotes, polyN is curiously quite rare in vertebrates. Several investigators have characterized the conformational and aggregation properties of polyQ-containing peptides and proteins, and to a lesser extent, peptides containing mixed glutamine and asparagine, but to our knowledge, there is no detailed characterization of polyN-containing peptides. Such a comparison could elucidate reasons for the paucity of asparagine repeats in humans. In this study, we synthesized a peptide containing a 24-asparagine repeat (N24). For aggregation studies, it is critical to start with monomeric unaggregated peptide. A protocol involving dissolution in mixed trifluoroacetic acid and hexafluoroisopropanol (TFA + HFIP) solvents is widely used for disaggregation of polyQ peptides. We used the same protocol for N24 but discovered that there was both oxidative damage and insufficient disaggregation. Oxidation of tryptophan, used as a flanking residue, was common. Moreover, we found evidence of Förster resonance energy transfer between Trp and its oxidation product N-formylkynurenine, even in chemical denaturants. This suggested that N24 was insufficiently disaggregated, a conclusion that was further supported by gel electrophoresis analysis. Oxidation was reduced, but not eliminated, by addition of methionine to the buffer. Formic acid proved to be a better disaggregator and caused no oxidative damage. The glutamine repeat peptide Q24 also underwent some oxidation after extended incubation in TFA + HFIP, but there was no evidence of Förster resonance energy transfer, and samples appeared monomeric by gel electrophoresis. This result indicates that polyN-containing peptides self-associate more strongly than polyQ-containing peptides. Circular dichroism spectra reveal a greater propensity for β-turn formation in polyN than polyQ, providing an explanation for the increased stability of polyN aggregates relative to polyQ.

A quantitative measure for protein conformational heterogeneity

Conformational heterogeneity is a defining characteristic of proteins. Intrinsically disordered proteins (IDPs) and denatured state ensembles are extreme manifestations of this heterogeneity. Inferences regarding globule versus coil formation can be drawn from analysis of polymeric properties such as average size, shape, and density fluctuations. Here we introduce a new parameter to quantify the degree of conformational heterogeneity within an ensemble to complement polymeric descriptors. The design of this parameter is guided by the need to distinguish between systems that couple their unfolding-folding transitions with coil-to-globule transitions and those systems that undergo coil-to-globule transitions with no evidence of acquiring a homogeneous ensemble of conformations upon collapse. The approach is as follows: Each conformation in an ensemble is converted into a conformational vector where the elements are inter-residue distances. Similarity between pairs of conformations is quantified using the projection between the corresponding conformational vectors. An ensemble of conformations yields a distribution of pairwise projections, which is converted into a distribution of pairwise conformational dissimilarities. The first moment of this dissimilarity distribution is normalized against the first moment of the distribution obtained by comparing conformations from the ensemble of interest to conformations drawn from a Flory random coil model. The latter sets an upper bound on conformational heterogeneity thus ensuring that the proposed measure for intra-ensemble heterogeneity is properly calibrated and can be used to compare ensembles for different sequences and across different temperatures. The new measure of conformational heterogeneity will be useful in quantitative studies of coupled folding and binding of IDPs and in de novo sequence design efforts that are geared toward controlling the degree of heterogeneity in unbound forms of IDPs.

Atomistic mechanisms of huntingtin N-terminal fragment insertion on a phospholipid bilayer revealed by molecular dynamics simulations

The huntingtin protein is characterized by a segment of consecutive glutamines (Q(N)) that is responsible for its fibrillation. As with other amyloid proteins, misfolding of huntingtin is related to Huntington's disease through pathways that can involve interactions with phospholipid membranes. Experimental results suggest that the N-terminal 17-amino-acid sequence (htt(NT)) positioned just before the Q(N) region is important for the binding of huntingtin to membranes. Through all-atom explicit solvent molecular dynamics simulations, we unveil the structure and dynamics of the htt(NT)Q(N) fragment on a phospholipid membrane at the atomic level. We observe that the insertion dynamics of this peptide can be described by four main steps-approach, reorganization, anchoring, and insertion-that are very diverse at the atomic level. On the membrane, the htt(NT) peptide forms a stable α-helix essentially parallel to the membrane with its nonpolar side-chains-mainly Leu-4, Leu-7, Phe-11 and Leu-14-positioned in the hydrophobic core of the membrane. Salt-bridges involving Glu-5, Glu-12, Lys-6, and Lys-15, as well as hydrogen bonds involving Thr-3 and Ser-13 with the phospholipids also stabilize the structure and orientation of the htt(NT) peptide. These observations do not significantly change upon adding the Q(N) region whose role is rather to provide, through its hydrogen bonds with the phospholipids' head group, a stable scaffold facilitating the partitioning of the htt(NT) region in the membrane. Moreover, by staying accessible to the solvent, the amyloidogenic Q(N) region could also play a key role for the oligomerization of htt(NT)Q(N) on phospholipid membranes.

Using a reduced dimensionality model to compute the thermodynamic properties of finite polypeptide aggregates

By implementing a simple reduced dimensionality model to describe the interactions in finite systems composed of two seven-amino-acid peptides, the thermodynamic properties of ordered and disordered aggregates were computed. Within this model, the hydrophobicity of each amino acid was varied, and the stability of the systems computed. Accurate averages in the canonical ensemble were obtained using various replica exchange Monte Carlo algorithms. Low and high temperature regions were encountered where the ordered and disordered aggregates were stabilized. It was observed that as the degree of hydrophobicity increased, the stability of the aggregates increased, with a significant energetic stabilization obtained for the ordered aggregates. Upon decreasing the concentration of the solution, the stability of the amorphous aggregates increased when compared to the ordered systems.

A decade and a half of protein intrinsic disorder: biology still waits for physics

The abundant existence of proteins and regions that possess specific functions without being uniquely folded into unique 3D structures has become accepted by a significant number of protein scientists. Sequences of these intrinsically disordered proteins (IDPs) and IDP regions (IDPRs) are characterized by a number of specific features, such as low overall hydrophobicity and high net charge which makes these proteins predictable. IDPs/IDPRs possess large hydrodynamic volumes, low contents of ordered secondary structure, and are characterized by high structural heterogeneity. They are very flexible, but some may undergo disorder to order transitions in the presence of natural ligands. The degree of these structural rearrangements varies over a very wide range. IDPs/IDPRs are tightly controlled under the normal conditions and have numerous specific functions that complement functions of ordered proteins and domains. When lacking proper control, they have multiple roles in pathogenesis of various human diseases. Gaining structural and functional information about these proteins is a challenge, since they do not typically "freeze" while their "pictures are taken." However, despite or perhaps because of the experimental challenges, these fuzzy objects with fuzzy structures and fuzzy functions are among the most interesting targets for modern protein research. This review briefly summarizes some of the recent advances in this exciting field and considers some of the basic lessons learned from the analysis of physics, chemistry, and biology of IDPs.

Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier

A reformulation and generalization of the Zwanzig model (ZW model) for ideal homopolymer chains poly-X, where X represents any of the twenty naturally occurring proteinogenic amino acid residues is presented. This reformulation and generalization provides a direct connection between coarse-grained parameters originally proposed in the ZW model with variables from the Lifson-Roig (LR) theory, such as the helical propensity per residue ω, and new variables introduced here, such as the energy gap Δ between unfolded and folded structures, as well as the ratio f of the energy scales involved. This enables us to discover the relevance of the energy spectrum E to the onset of configurational phase transitions. From the configurational partition function Q, thermodynamic properties such as the configurational entropy S, specific heat v and average energy <E> are calculated in terms of the number of residues K, temperature T, helical propensity ω and energy barrier ΔH for different poly-X chains in vacuo. Results obtained here provide substantial evidence that configurational phase transitions for ideal poly-X chains correspond to first-order phase transitions. An anomalous behavior of the thermodynamic functions <E>, Cv, S with respect to the number K of residues is also highlighted. On-going methods of solution are outlined.

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.

Conformational properties of polyglutamine sequences in guanidine hydrochloride solutions

Two sets of iso-1-cytochrome c variants have been prepared with N-terminal insertions of pure polyglutamine, i.e., PolyQ variants, or polyglutamine interrupted with lysine every sixth residue, i.e., Gln-rich variants. The polymer properties of these pure polyGln or Gln-rich sequences have been evaluated using equilibrium and kinetic His-heme loop formation methods for loop sizes ranging from 22 to 46 in 1.5, 3.0, and 6.0 M guanidine hydrochloride (GdnHCl). In 6.0 M GdnHCl, the scaling exponent, ν(3), for the pure polyGln sequences, is ~1.7--significantly less than ν(3) ≈ 2.15 for the Gln-rich sequences. The stability of the His-heme loops becomes progressively greater for the pure polyGln sequences relative to the Gln-rich sequences as GdnHCl concentration decreases from 6.0 to 1.5 M. Thus, the context of the sequence effects the polymer properties of Gln repeats even in denaturing concentrations of GdnHCl. Comparison of data for the Gln-rich variants with previous results for Gly-rich and Ala-rich variants shows that ν(3) ~ 2.2 for the Gln-rich, Gly-rich, and Ala-rich sequences in 6.0 M GdnHCl, whereas ν(3) remains unchanged at 3.0 M GdnHCl concentration for the Gln-rich and Ala-rich sequences but decreases to ~1.7 for the Gly-rich sequences. Thus, the polymer properties of Gln-rich and Ala-rich sequences are less sensitive to solvent quality in denaturing solutions of GdnHCl than Gly-rich sequences. Evaluation of Flory's characteristic ratio, C(n), for the Gln-rich and Ala-rich sequences relative to the Gly-rich sequences shows that Gln-rich sequences are stiffer than Ala-rich sequences at both 3.0 and 6.0 M GdnHCl.