Universal Nature of Collapsibility in the Context of Protein Folding and Evolution

Unearthing phytochemicals as natural inhibitors for pantothenate synthetase in Mycobacterium tuberculosis: A computational approach

Pantothenate synthetase protein plays a pivotal role in the biosynthesis of coenzyme A (CoA), which is a crucial molecule involved in a number of cellular processes including the metabolism of fatty acid, energy production, and the synthesis of various biomolecules, which is necessary for the survival of Mycobacterium tuberculosis (Mtb). Therefore, inhibiting this protein could disrupt CoA synthesis, leading to the impairment of vital metabolic processes within the bacterium, ultimately inhibiting its growth and survival. This study employed molecular docking, structure-based virtual screening, and molecular dynamics (MD) simulation to identify promising phytochemical compounds targeting pantothenate synthetase for tuberculosis (TB) treatment. Among 239 compounds, the top three (rutin, sesamin, and catechin gallate) were selected, with binding energy values ranging from -11 to -10.3 kcal/mol, and the selected complexes showed RMSD (<3 Å) for 100 ns MD simulation time. Furthermore, molecular mechanics generalized Born surface area (MM/GBSA) binding free energy calculations affirmed the stability of these three selected phytochemicals with binding energy ranges from -82.24 ± 9.35 to -66.83 ± 4.5 kcal/mol. Hence, these identified natural plant-derived compounds as potential inhibitors of pantothenate synthetase could be used to inhibit TB infection in humans.

Exact Enumeration Approach to Estimate the Theta Temperature of Interacting Self-Avoiding Walks on the Simple Cubic Lattice

We compute the exact root-mean-square end-to-end distance of the interacting self-avoiding walk (ISAW) up to 27 steps on the simple cubic lattice. These data are used to construct a fixed point equation to estimate the theta temperature of the collapse transition of the ISAW. With the Bulirsch-Stoer extrapolation method, we obtain accurate results that can be compared with large-scale long-chain simulations. The free parameter ω in extrapolation is precisely determined using a parity property of the ISAW. The systematic improvement of this approach is feasible by adopting the combination of exact enumeration and multicanonical simulations.

Cooperativity and Folding Kinetics in a Multidomain Protein with Interwoven Chain Topology

Although a large percentage of eukaryotic proteomes consist of proteins with multiple domains, not much is known about their assembly mechanism, especially those with intricate native state architectures. Some have a complex topology in which the structural elements along the sequence are interwoven in such a manner that the domains cannot be separated by cutting at any location along the sequence. Such proteins are multiply connected multidomain proteins (MMPs) with the three-domain (NMP, LID, and CORE) phosphotransferase enzyme adenylate kinase (ADK) being an example. We devised a coarse-grained model to simulate ADK folding initiated by changing either the temperature or guanidinium chloride (GdmCl) concentration. The simulations reproduce the experimentally measured melting temperatures (associated with two equilibrium transitions), FRET efficiency as a function of GdmCl concentration, and the folding times quantitatively. Although the NMP domain orders independently, cooperative interactions between the LID and the CORE domains are required for complete assembly of the enzyme. Kinetic simulations show that, on the collapse time scale, multiple interconnected metastable states are populated, attesting to the folding heterogeneity. The network of kinetically connected states reveals that the CORE domain folds only after the NMP and LID domains, reflecting the interwoven nature of the chain topology.

Quantification of Entropic Excluded Volume Effects Driving Crowding-Induced Collapse and Folding of a Disordered Protein

We investigate the conformational properties of the intrinsically disordered DNA-binding domain of CytR in the presence of the polymeric crowder polyethylene glycol (PEG). Integrating circular dichroism, nuclear magnetic resonance, and single-molecule Förster resonance energy transfer measurements, we demonstrate that disordered CytR populates a well-folded minor conformation in its native ensemble, while the unfolded ensemble collapses and folds with an increase in crowder density independent of the crowder size. Employing a statistical-mechanical model, the effective reduction in the accessible conformational space of a residue in the unfolded state is estimated to be 10% at 300 mg/mL PEG8000, relative to dilute conditions. The experimentally consistent PEG-temperature phase diagram thus constructed reveals that entropic effects can stabilize disordered CytR by 10 kJ mol^-1, driving the equilibrium toward folded conformations under physiological conditions. Our work highlights the malleable conformational landscape of CytR, the presence of a folded conformation in the disordered ensemble, and proposes a scaling relation for quantifying excluded volume effects on protein stability.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Protein chain collapse modulation and folding stimulation by GroEL-ES

The collapse of polypeptides is thought important to protein folding, aggregation, intrinsic disorder, and phase separation. However, whether polypeptide collapse is modulated in cells to control protein states is unclear. Here, using integrated protein manipulation and imaging, we show that the chaperonin GroEL-ES can accelerate the folding of proteins by strengthening their collapse. GroEL induces contractile forces in substrate chains, which draws them into the cavity and triggers a general compaction and discrete folding transitions, even for slow-folding proteins. This collapse enhancement is strongest in the nucleotide-bound states of GroEL and is aided by GroES binding to the cavity rim and by the amphiphilic C-terminal tails at the cavity bottom. Collapse modulation is distinct from other proposed GroEL-ES folding acceleration mechanisms, including steric confinement and misfold unfolding. Given the prevalence of collapse throughout the proteome, we conjecture that collapse modulation is more generally relevant within the protein quality control machinery.

Effects of ionic strength on the folding and stability of SAMP1, a ubiquitin-like halophilic protein

Our knowledge of the folding behavior of proteins from extremophiles is limited at this time. These proteins may more closely resemble the primordial proteins selected in early evolution under extreme conditions. The small archaeal modifier protein 1 (SAMP1) studied in this report is an 87-residue protein with a β-grasp fold found in the halophile Haloferax volcanii from the Dead Sea. To gain insight into the effects of salt on the stability and folding mechanism of SAMP1, we conducted equilibrium and kinetic folding experiments as a function of sodium chloride concentration. The results revealed that increasing ionic strength accelerates refolding and slows down unfolding of SAMP1, giving rise to a pronounced salt-induced stabilization. With increasing NaCl concentration, the rate of folding observed via a combination of continuous-flow (0.1-2 ms time range) and stopped-flow measurements (>2 ms) exhibited a >100-fold increase between 0.1 and 1.5 M NaCl and leveled off at higher concentrations. Using the Linderström-Lang smeared charge formalism to model electrostatic interactions in ground and transition states encountered during folding, we showed that the observed salt dependence is dominated by Debye-Hückel screening of electrostatic repulsion among numerous negatively charged residues. Comparisons are also drawn with three well-studied mesophilic members of the β-grasp superfamily: protein G, protein L, and ubiquitin. Interestingly, the folding rate of SAMP1 in 3 M sodium chloride is comparable to that of protein G, ubiquitin, and protein L at lower ionic strength. The results indicate the important role of electrostatic interactions in protein folding and imply that proteins have evolved to minimize unfavorable charge-charge interactions under their specific native conditions.

First events in the coil-to-globule transition of PVME in water: An ultrafast temperature jump - time-resolved elastic light scattering study

HYPOTHESIS

The coil-to-globule transition is an essential phenomenon in protein and polymer solutions. Late stages of such transitions, >1 µs, have been thoroughly studied. Yet, the initial ones are a matter of speculations. Here, we present the first observation of a sub-nanosecond stage of the coil-to-globule transition of poly (vinyl methyl ether), PVME, in water.

EXPERIMENTS

The detection of an early stage of the coil-to-globule transition has been possible thanks to a novel experimental approach - time-resolved elastic light scattering study, following an ultrafast temperature jump. We identified a molecular process active in the observed stage of the transition with use of broadband dielectric spectroscopy.

FINDINGS

In the experiment's time window, from a few ps to around 600 ps, we observed an increase in the light scattering intensity 300-400 ps after the temperature jump that heated the sample above its lower critical solution temperature (LCST). The observed time coincides with the time of segmental relaxation of PVME, determined by broadband dielectric spectroscopy in the temperature range of the LCST of the PVME/water mixture. This coincidence strongly suggests that the observed herein stage of coil-to-globule transition is the rapid formation of local nuclei along the polymer chain. Those nuclei may grow and aggregate in later stages of the process, which are out of our experimental time window.

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Integrating single-molecule spectroscopy and simulations for the study of intrinsically disordered proteins

Over the last two decades, intrinsically disordered proteins and protein regions (IDRs) have emerged from a niche corner of biophysics to be recognized as essential drivers of cellular function. Various techniques have provided fundamental insight into the function and dysfunction of IDRs. Among these techniques, single-molecule fluorescence spectroscopy and molecular simulations have played a major role in shaping our modern understanding of the sequence-encoded conformational behavior of disordered proteins. While both techniques are frequently used in isolation, when combined they offer synergistic and complementary information that can help uncover complex molecular details. Here we offer an overview of single-molecule fluorescence spectroscopy and molecular simulations in the context of studying disordered proteins. We discuss the various means in which simulations and single-molecule spectroscopy can be integrated, and consider a number of studies in which this integration has uncovered biological and biophysical mechanisms.

Slow Escape from a Helical Misfolded State of the Pore-Forming Toxin Cytolysin A

The pore-forming toxin cytolysin A (ClyA) is expressed as a large α-helical monomer that, upon interaction with membranes, undergoes a major conformational rearrangement into the protomer conformation, which then assembles into a cytolytic pore. Here, we investigate the folding kinetics of the ClyA monomer with single-molecule Förster resonance energy transfer spectroscopy in combination with microfluidic mixing, stopped-flow circular dichroism experiments, and molecular simulations. The complex folding process occurs over a broad range of time scales, from hundreds of nanoseconds to minutes. The very slow formation of the native state occurs from a rapidly formed and highly collapsed intermediate with large helical content and nonnative topology. Molecular dynamics simulations suggest pronounced non-native interactions as the origin of the slow escape from this deep trap in the free-energy surface, and a variational enhanced path-sampling approach enables a glimpse of the folding process that is supported by the experimental data.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Resolving Site-Specific Heterogeneity of the Unfolded State under Folding Conditions

Understanding the properties of the unfolded state under folding conditions is of fundamental importance for gaining mechanistic insight into folding as well as misfolding reactions. Toward achieving this objective, the folding reaction of a small protein, monellin, has been resolved structurally and temporally, with the use of the multisite time-resolved FRET methodology. The present study establishes that the initial polypeptide chain collapse is not only heterogeneous but also structurally asymmetric and nonuniform. The population-averaged size for the segments spanning parts of the β-sheet decreases much more than that for the α-helix. Multisite measurements enabled specific and nonspecific components of the initial chain collapse to be discerned. The expanded and compact intermediate subensembles have the properties of a nonspecifically collapsed (hence, random-coil-like) and specifically collapsed (hence, globular) polymer, respectively. During subsequent folding, both the subensembles underwent contraction to varying extents at the four monitored segments, which was close to gradual in nature. The expanded intermediate subensemble exhibited an additional very slow contraction, suggestive of the presence of non-native interactions that result in a higher effective viscosity slowing down intrachain motions under folding conditions.

The Last Secret of Protein Folding: The Real Relationship Between Long-Range Interactions and Local Structures

The protein folding problem has been extensively studied for decades, and hundreds of thousands of protein structures have been solved. Yet, how proteins fold from a linear peptide chain to their unique 3D structures is not fully understood. With key clues having emerged unexpectedly from the field of nanoscience, a "Confined Lowest Energy Fragment" (CLEF) hypothesis was proposed. The CLEF hypothesis states that a protein chain can be divided into CLEFs, the semi-independent folding units, by a small number of key residues that form key long-range interactions. The native structure of a CLEF is the lowest energy state under the constraints of the key long-range interactions, but the native structure of the whole protein is not necessary the lowest energy state as Anfinsen's thermodynamic hypothesis suggested. The CLEF hypothesis proposes a unified CLEF mechanism for protein folding, basically a two-step process. In the first step, the favorable enthalpy of CLEFs for native structures quickly brings those residues for the key long-range interactions together, forming intermediates corresponding to the so-called hydrophobic collapse. In the second step, those collapsed key residues shuffle for the right combination to form the native key long-range interactions. The CLEF hypothesis provides a simple solution to all protein folding paradoxes, and proposes a "CLEF Age" or "Stone Age" for the prebiotic evolution of proteins.

Synthesis runs counter to directional folding of a nascent protein domain

Folding of individual domains in large proteins during translation helps to avoid otherwise prevalent inter-domain misfolding. How folding intermediates observed in vitro for the majority of proteins relate to co-translational folding remains unclear. Combining in vivo and single-molecule experiments, we followed the co-translational folding of the G-domain, encompassing the first 293 amino acids of elongation factor G. Surprisingly, the domain remains unfolded until it is fully synthesized, without collapsing into molten globule-like states or forming stable intermediates. Upon fully emerging from the ribosome, the G-domain transitions to its stable native structure via folding intermediates. Our results suggest a strictly sequential folding pathway initiating from the C-terminus. Folding and synthesis thus proceed in opposite directions. The folding mechanism is likely imposed by the final structure and might have evolved to ensure efficient, timely folding of a highly abundant and essential protein.

In vivo experiments and optical tweezers force-spectroscopy measurements assessing the co-translational folding of the G-domain from bacterial elongation factor G reveal a sequential folding pathway initiating from the C-terminus. These results suggest that protein folding and synthesis proceed in opposite directions.

Dramatic Shape Changes Occur as Cytochrome c Folds

Extensive experimental studies on the folding of cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the stochastic difference equation in length to calculate the time-dependent changes in the small-angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time-dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways, we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which are in unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, show that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accordance with ultrafast hydrogen/deuterium exchange studies. Based on these results, we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model

Intrinsically disordered proteins (IDPs) play an important role in an array of biological processes but present a number of fundamental challenges for computational modeling. Recently, simple polymer models have regained popularity for interpreting the experimental characterization of IDPs. Homopolymer theory provides a strong foundation for understanding generic features of phenomena ranging from single-chain conformational dynamics to the properties of entangled polymer melts, but is difficult to extend to the copolymer context. This challenge is magnified for proteins due to the variety of competing interactions and large deviations in side-chain properties. In this work, we apply a simple physics-based coarse-grained model for describing largely disordered conformational ensembles of peptides, based on the premise that sampling sterically forbidden conformations can compromise the faithful description of both static and dynamical properties. The Hamiltonian of the employed model can be easily adjusted to investigate the impact of distinct interactions and sequence specificity on the randomness of the resulting conformational ensemble. In particular, starting with a bead–spring-like model and then adding more detailed interactions one by one, we construct a hierarchical set of models and perform a detailed comparison of their properties. Our analysis clarifies the role of generic attractions, electrostatics, and side-chain sterics, while providing a foundation for developing efficient models for IDPs that retain an accurate description of the hierarchy of conformational dynamics, which is nontrivially influenced by interactions with surrounding proteins and solvent molecules.

Hydropathy Patterning Complements Charge Patterning to Describe Conformational Preferences of Disordered Proteins

Understanding the conformational ensemble of an intrinsically disordered protein (IDP) is of great interest due to its relevance to critical intracellular functions and diseases. It is now well established that the polymer scaling behavior can provide a great deal of information about the conformational properties as well as liquid-liquid phase separation of an IDP. It is, therefore, extremely desirable to be able to predict an IDP's scaling behavior from the protein sequence itself. The work in this direction so far has focused on highly charged proteins and how charge patterning can perturb their structural properties. As naturally occurring IDPs are composed of a significant fraction of uncharged amino acids, the rules based on charge content and patterning are only partially helpful in solving the problem. Here, we propose a new order parameter, sequence hydropathy decoration, which can provide a near-quantitative understanding of scaling and structural properties of IDPs devoid of charged residues. We combine this with a charge patterning parameter, sequence charge decoration, to obtain a general equation, parametrized from extensive coarse-grained simulation data, for predicting protein dimensions from the sequence. We finally test this equation against available experimental data and find a semiquantitative match in predicting the scaling behavior. We also provide guidance on how to extend this approach to experimental data, which should be feasible in the near future.

Water as a Good Solvent for Unfolded Proteins: Folding and Collapse are Fundamentally Different

The argument that the hydrophobic effect is the primary effect driving the folding of globular proteins is nearly universally accepted (including by the authors). But does this view also imply that water is a "poor" solvent for the unfolded states of these same proteins? Here we argue that the answer is "no," that is, folding to a well-packed, extensively hydrogen-bonded native structure differs fundamentally from the nonspecific chain collapse that defines a poor solvent. Thus, the observation that a protein folds in water does not necessitate that water is a poor solvent for its unfolded state. Indeed, chain-solvent interactions that are marginally more favorable than nonspecific intrachain interactions are beneficial to protein function because they destabilize deleterious misfolded conformations and inter-chain interactions.

Emerging consensus on the collapse of unfolded and intrinsically disordered proteins in water

Establishing the degree of collapse of unfolded or disordered proteins is a fundamental problem in biophysics, because of its relation to protein folding and to the function of intrinsically disordered proteins. However, until recently, different experiments gave qualitatively different results on collapse and there were large discrepancies between experiments and all-atom simulations. New methodology introduced in the past three years has helped to resolve the differences between experiments, and improvements in simulations have closed the gap between experiment and simulation. These advances have led to an emerging consensus on the collapse of disordered proteins in water.

Binding without folding - the biomolecular function of disordered polyelectrolyte complexes

Recent evidence shows that oppositely charged intrinsically disordered proteins (IDPs) can form high-affinity complexes that involve neither the formation of secondary or tertiary structure nor site-specific interactions between individual residues. Similar electrostatically dominated interactions have also been identified for positively charged IDPs binding to nucleic acids. These highly disordered polyelectrolyte complexes constitute an extreme case within the spectrum of biomolecular interactions involving disorder. Such interactions are likely to be widespread, since sequence analysis predicts proteins with highly charged disordered regions to be surprisingly numerous. Here, we summarize the insights that have emerged from the highly disordered polyelectrolyte complexes identified so far, and we highlight recent developments and future challenges in (i) establishing models for the underlying highly dynamic structural ensembles, (ii) understanding the novel binding mechanisms associated with them, and (iii) identifying the functional consequences.