Measuring the rate of intramolecular contact formation in polypeptides

Structural and Functional Relevance of Charge Based Transient Interactions inside Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) perform a wide range of biological functions without adopting stable, well-defined, three-dimensional structures. Instead, IDPs exist as dynamic ensembles of flexible conformations, traditionally thought to be governed by weak, nonspecific interactions, which are well described by homopolymer theory. However, recent research highlights the presence of transient, specific interactions in several IDPs, suggesting that factors beyond overall size influence their conformational behavior. In this study, we investigate how the spatial arrangement of charged amino acids within IDP sequences shapes the prevalence of transient, specific interactions. Through a series of model peptides, we establish a quantitative empirical relationship between the fraction of transient interactions and a novel sequence metric, termed effective charged patch length, which characterizes the ability of charged patches to drive these interactions. By examining IDP ensembles with varying levels of transient interactions, we further explore their heteropolymeric structural behavior in phase-separated condensates, where we observe the formation of a condensate-spanning network structure. Additionally, we perform a proteome-wide scan for charge-based transient interactions within disordered regions of the human proteome, revealing that approximately 10% of these regions exhibit such charge-driven transient interactions, leading to heteropolymeric behaviors in their conformational ensembles. Finally, we examine how these charge-based transient interactions correlate with molecular functions, identifying specific biological roles in which these interactions are enriched.

Transient Non-local Interactions Dominate the Dynamics of Measles Virus NTAIL

The RNA genome of measles virus is encapsidated by the nucleoprotein within a helical nucleocapsid that serves as template for both transcription and replication. The intrinsically disordered domain of the nucleoprotein (NTAIL), partly protruding outward from the nucleocapsid, is essential for binding the polymerase complex responsible for viral transcription and replication. As for many IDPs, binding of NTAIL occurs through a short molecular recognition element (MoRE) that folds upon binding, with the majority of NTAIL remaining disordered. Though NTAIL regions far from the MoRE influence the binding affinity, interactions between them and the MoRE have not been investigated in depth. Using an integrated approach, relying on photo-induced electron transfer (PET) experiments between tryptophan and cysteine pairs placed at different positions in the protein under varying salt and pH conditions, combined with simulations and analytical models, we identified transient interactions between two disordered regions distant in sequence, which dominate NTAIL dynamics, and regulate the conformational preferences of both the MoRE and the entire NTAIL domain. Co-evolutionary analysis corroborates our findings, and suggests an important functional role for the same intramolecular interactions. We propose mechanisms by which these non-local interactions may regulate binding to the phosphoprotein, polymerase recruitment, and ultimately viral transcription and replication. Our findings may be extended to other IDPs, where non-local intra-protein interactions affect the conformational preferences of intermolecular binding sites.

Nanosecond chain dynamics of single-stranded nucleic acids

The conformational dynamics of single-stranded nucleic acids are fundamental for nucleic acid folding and function. However, their elementary chain dynamics have been difficult to resolve experimentally. Here we employ a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, and nanophotonic enhancement to determine the conformational ensembles and rapid chain dynamics of short single-stranded nucleic acids in solution. To interpret the experimental results in terms of end-to-end distance dynamics, we utilize the hierarchical chain growth approach, simple polymer models, and refinement with Bayesian inference to generate structural ensembles that closely align with the experimental data. The resulting chain reconfiguration times are exceedingly rapid, in the 10-ns range. Solvent viscosity-dependent measurements indicate that these dynamics of single-stranded nucleic acids exhibit negligible internal friction and are thus dominated by solvent friction. Our results provide a detailed view of the conformational distributions and rapid dynamics of single-stranded nucleic acids.

The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter

Challenging the basis of our chemical intuition, recent experimental evidence reveals the presence of a new type of intrinsic fluorescence in biomolecules that exists even in the absence of aromatic or electronically conjugated chemical compounds. The origin of this phenomenon has remained elusive so far. In the present study, we identify a mechanism underlying this new type of fluorescence in different biological aggregates. By employing non-adiabatic ab initio molecular dynamics simulations combined with a data-driven approach, we characterize the typical ultrafast non-radiative relaxation pathways active in non-fluorescent peptides. We show that the key vibrational mode for the non-radiative decay towards the ground state is the carbonyl elongation. Non-aromatic fluorescence appears to emerge from blocking this mode with strong local interactions such as hydrogen bonds. While we cannot rule out the existence of alternative non-aromatic fluorescence mechanisms in other systems, we demonstrate that this carbonyl-lock mechanism for trapping the excited state leads to the fluorescence yield increase observed experimentally, and set the stage for design principles to realize novel non-invasive biocompatible probes with applications in bioimaging, sensing, and biophotonics.

Ahrné L, Cardoso DR. UV-C light promotes the reductive cleavage of disulfide bonds in β-Lactoglobulin and improves in vitro gastric digestion

β-Lactoglobulin (β-Lg) is the main protein in whey and is known for its allergenicity and resistance to the digestion of pepsin and trypsin. The UV-C photoinduced cleavage of disulfide bonds in β-Lactoglobulin, as promoted by excitation of tryptophan residues (Trp), is shown to induce changes in the protein's secondary structure, significantly reducing the protein's resistance to pepsin digestion. The UV-C light-induced changes in the protein secondary structure are marked by an increase in the contribution of β-sheet and α-helix structures with a concomitantly smaller contribution of the β-turn structural motif. The photoinduced cleavage of disulfide bonds in β-Lg has an apparent quantum yield of ф = 0.0015 ± 0.0003 and was shown by transient absorption laser flash photolysis to arise by two different pathways: a) the reduction of the disulfide bond Cys₆₆Cys₁₆₀ occurs by direct electron transfer from the triplet-excited ³Trp to the disulfide bond due to the existence of a CysCys/Trp triad (Cys₆₆Cys₁₆₀/Trp₆₁) and b) the reduction of the buried Cys₁₀₆Cys₁₁₉ disulfide bond involves a reaction with a solvated electron originated by the photoejection of electrons from the triplet-excited ³Trp decay. The in vitro gastric digestion index for UV-C-treated β-Lg is revealed to have increased significantly by 36 ± 4 % and 9 ± 2 % under simulated elderly and young adult digestive conditions, respectively. When compared to the native protein, the peptide mass fingerprint profile of digested UV-C-treated β-Lg shows a higher content and variety of peptides, including the production of some exclusive bioactive peptides such as PMHIRL and EKFDKALKALPMH.

Interpreting Transient Interactions of Intrinsically Disordered Proteins

The flexible nature of intrinsically disordered proteins (IDPs) gives rise to a conformational ensemble with a diverse set of conformations. The simplest way to describe this ensemble is through a homopolymer model without any specific interactions. However, there has been growing evidence that the conformational properties of IDPs and their relevant functions can be affected by transient interactions between specific and even nonlocal pairs of amino acids. Interpreting these interactions from experimental methods, each of which is most sensitive to a different distance regime referred to as probing length, remains a challenging and unsolved problem. Here, we first show that transient interactions can be realized between short fragments of charged amino acids by generating conformational ensembles using model disordered peptides and coarse-grained simulations. Using these ensembles, we investigate how sensitive different types of experimental measurements are to the presence of transient interactions. We find methods with shorter probing lengths to be more appropriate for detecting these transient interactions, but one experimental method is not sufficient due to the existence of other weak interactions typically seen in IDPs. Finally, we develop an adjusted polymer model with an additional short-distance peak which can robustly reproduce the distance distribution function from two experimental measurements with complementary short and long probing lengths. This new model can suggest whether a homopolymer model is insufficient for describing a specific IDP and meets the challenge of quantitatively identifying specific, transient interactions from a background of nonspecific, weak interactions.

Biophysical and Integrative Characterization of Protein Intrinsic Disorder as a Prime Target for Drug Discovery

Protein intrinsic disorder is increasingly recognized for its biological and disease-driven functions. However, it represents significant challenges for biophysical studies due to its high conformational flexibility. In addressing these challenges, we highlight the complementary and distinct capabilities of a range of experimental and computational methods and further describe integrative strategies available for combining these techniques. Integrative biophysics methods provide valuable insights into the sequence–structure–function relationship of disordered proteins, setting the stage for protein intrinsic disorder to become a promising target for drug discovery. Finally, we briefly summarize recent advances in the development of new small molecule inhibitors targeting the disordered N-terminal domains of three vital transcription factors.

Explicit analytical form for memory kernel in the generalized Langevin equation for end-to-end vector of Rouse chains

The generalized Langevin equation (GLE) provides an attractive theoretical framework for investigating the dynamics of conformational fluctuations of polymeric systems. While the memory kernel is a central function in the GLE, explicit analytical forms for this function have been challenging to obtain, even for the simple models of polymer dynamics. Here, we achieve an explicit analytical expression for the memory kernel in the GLE for the end-to-end vector of Rouse chains in the overdamped limit. Our derivation takes advantage of the finding that the dynamics of the end-to-end vector of Rouse chains with both free ends are equivalent to those of Rouse chains with one free end and the other fixed. For the latter model, we first show that the equations of motion of the Rouse modes as well as their statistical properties can be obtained under the boundary conditions where the free end is held fixed temporarily. We then analytically solve the terms associated with intrachain interactions in the GLE. By formally comparing these terms with the GLE based on the Rouse modes, we obtain an explicit expression for the memory kernel, along with analytical forms for the potential field and the random colored noise force. Our analytical memory kernel is confirmed by numerical calculations in the Laplace space and is shown to yield asymptotic behaviors that are consistent with previous studies. Finally, we utilize our analytical result to simulate the cyclization dynamics of Rouse chains and discuss the scaling of the cyclization time with chain length.

Characterizing Transient Protein-Protein Interactions by Trp-Cys Quenching and Computer Simulations

Transient protein-protein interactions occur frequently under the crowded conditions encountered in biological environments. Tryptophan-cysteine quenching is introduced as an experimental approach with minimal labeling for characterizing such interactions between proteins due to its sensitivity to nano- to microsecond dynamics on subnanometer length scales. The experiments are paired with computational modeling at different resolutions including fully atomistic molecular dynamics simulations for interpretation of the experimental observables and to gain molecular-level insights. This approach is applied to model systems, villin variants and the drkN SH3 domain, in the presence of protein G crowders. It is demonstrated that Trp-Cys quenching experiments can differentiate between overall attractive and repulsive interactions between different proteins, and they can discern variations in interaction preferences at different protein surface locations. The close integration between experiment and simulations also provides an opportunity to evaluate different molecular force fields for the simulation of concentrated protein solutions.

Impact of the Cellular Environment on Adenosine Triphosphate Conformations

The cytoplasm is an environment crowded by macromolecules and filled with metabolites and ions. Recent experimental and computational studies have addressed how this environment affects protein stability, folding kinetics, and protein-protein and protein-nucleic acid interactions, though its impact on metabolites remains largely unknown. Here we show how a simulated cytoplasm affects the conformation of adenosine triphosphate (ATP), a key energy source and regulatory metabolite present at high concentrations in cells. Analysis of our all-atom model of a small volume of the Escherichia coli cytoplasm when contrasted with ATP modeled in vitro or resolved with protein structures deposited in the Protein Data Bank reveals that ATP molecules bound to proteins in cell form specific pitched conformations that are not observed at significant concentrations in the other environments. We hypothesize that these interactions evolved to fulfill functional roles when ATP interacts with protein surfaces.

Non-Aromatic Fluorescence in Biological Matter: The Exception or the Rule?

While in the vast majority of cases fluorescence in biological matter has been attributed to aromatic or conjugated groups, peptides associated with neurodegenerative diseases, such as Alzheimer's, Parkinson's, or Huntington's, have been recently shown to display an intrinsic visible fluorescence even in the absence of aromatic residues. This has called the attention of researchers from many different fields, trying to understand the origin of this peculiar behavior and, at the same time, motivating the search for novel strategies to control the optical properties of new biophotonic materials. Today, after nearly 15 years of its discovery, there is a growing consensus about the mechanism underlying this phenomenon, namely, that electronic interactions between non-optically active molecules can result in supramolecular assemblies that are fluorescent. Despite this progress, many aspects of this phenomenon remain uncharted territory. In this Perspective, we lay down the state-of-the-art in the field highlighting the open questions from both experimental and theoretical fronts in this fascinating emerging area of non-aromatic fluorescence.

Active and thermal fluctuations in multi-scale polymer structure and dynamics

The presence of athermal noise or biological fluctuations control and maintain crucial life-processes. In this work, we present an exact analytical treatment of the dynamic behavior of a flexible polymer chain that is subjected to both thermal and active forces. Our model for active forces incorporates temporal correlation associated with the characteristic time scale and processivity of enzymatic function (driven by ATP hydrolysis), leading to an active-force time scale that competes with relaxation processes within the polymer chain. We analyze the structure and dynamics of an active-Brownian polymer using our exact results for the dynamic structure factor and the looping time for the chain ends. The spectrum of relaxation times within a polymer chain implies two different behaviors at small and large length scales. Small length-scale relaxation is faster than the active-force time scale, and the dynamic and structural behavior at these scales are oblivious to active forces and, are thus governed by the true thermal temperature. Large length-scale behavior is governed by relaxation times that are much longer than the active-force time scale, resulting in an effective active-Brownian temperature that dramatically alters structural and dynamic behavior. These complex multi-scale effects imply a time-dependent temperature that governs living and non-equilibrium systems, serving as a unifying concept for interpreting and predicting their physical behavior.

Hydroxycinnamic Acid Derivatives from Coffee Extracts Prevent Amyloid Transformation of Alpha-Synuclein

Earlier we showed that derivatives of hydroxycinnamic acids prevent amyloid transformation of alpha-synuclein and prion protein. The aim of this work was to determine the content of 3-hydroxycinnamic acid derivatives in coffee extracts and to evaluate their activity in relation to alpha-synuclein amyloid aggregation. Hydroxycinnamic acid derivatives were identified in aqueous and ethanol extracts of coffee beans by quantitative mass spectrometric analysis. Only 3,4-dimethoxycinnamic acid (13–53 μg/mL) was detected in significant amounts in the coffee extracts, while ferulic acid was present in trace amounts. In addition, 3-methoxy-4-acetamidoxycinnamic acid (0.4–0.8 μg/mL) was detected in the roasted coffee extracts. The half-maximum inhibitory concentrations of alpha-synuclein fibrillization reaction in the presence of coffee extracts, as well as inhibitory constants, were determined using thioflavin T assay. The inhibitory effect of black and green coffee extracts on alpha-synuclein fibrillization is dose-dependent, and in a pairwise comparison, the constants of half-maximal inhibition of fibrillization for green coffee extracts are comparable to or greater than those for black coffee. Thus, coffee extracts prevent pathological transformation of alpha-synuclein in vitro, probably due to the presence of 3,4-dimethoxycinnamic acid in them. Consequently, coffee drinks and coffee extracts can be used for the prevention of synucleinopathies including Parkinson’s disease.

Multisite phosphorylation and binding alter conformational dynamics of the 4E-BP2 protein

Intrinsically disordered proteins (IDPs) play critical roles in regulatory protein interactions, but detailed structural/dynamic characterization of their ensembles remain challenging, both in isolation and when they form dynamic "fuzzy" complexes. Such is the case for mRNA cap-dependent translation initiation, which is regulated by the interaction of the predominantly folded eukaryotic initiation factor 4E (eIF4E) with the intrinsically disordered eIF4E binding proteins (4E-BPs) in a phosphorylation-dependent manner. Single-molecule Förster resonance energy transfer showed that the conformational changes of 4E-BP2 induced by binding to eIF4E are non-uniform along the sequence; while a central region containing both motifs that bind to eIF4E expands and becomes stiffer, the C-terminal region is less affected. Fluorescence anisotropy decay revealed a non-uniform segmental flexibility around six different labeling sites along the chain. Dynamic quenching of these fluorescent probes by intrinsic aromatic residues measured via fluorescence correlation spectroscopy report on transient intra- and inter-molecular contacts on nanosecond-to-microsecond timescales. Upon hyperphosphorylation, which induces folding of ∼40 residues in 4E-BP2, the quenching rates decreased at most labeling sites. The chain dynamics around sites in the C-terminal region far away from the two binding motifs significantly increased upon binding to eIF4E, suggesting that this region is also involved in the highly dynamic 4E-BP2:eIF4E complex. Our time-resolved fluorescence data paint a sequence-level rigidity map of three states of 4E-BP2 differing in phosphorylation or binding status and distinguish regions that form contacts with eIF4E. This study adds complementary structural and dynamics information to recent studies of 4E-BP2, and it constitutes an important step toward a mechanistic understanding of this important IDP via integrative modeling.

Direct Observation of Single-Protein Transition State Passage by Nanopore Ionic Current Jumps

Conformational transitions of proteins are governed by chemical kinetics, often toggled by passage through an activated state separating two conformational ensembles. The passage time of a protein through the activated state can be too fast to be detected by single-molecule experiments without the aid of viscogenic agents. Here, we use high-bandwidth nanopore measurements to resolve microsecond-duration transitions that occur between conformational states of individual protein molecules partly blocking pore current. We measure the transition state passage time between folded and unfolded states of a two-state λ_6-85 mutant and between metastable intermediates and the unfolded state of the multistate folder cytochrome c. Consistent with the principle of microscopic reversibility, the transition state passage time is the same for the forward and backward reactions. A passage time distribution whose tail is broader than a single exponential observed in cytochrome c suggests a multidimensional energy landscape for this protein.

Measuring (biological) materials mechanics with atomic force microscopy. 3. Mechanical unfolding of biopolymers

Biopolymers, such as polynucleotides, polypeptides and polysaccharides, are macromolecules that direct most of the functions in living beings. Studying the mechanical unfolding of biopolymers provides important information about their molecular elasticity and mechanical stability, as well as their energy landscape, which is especially important in proteins, since their three‐dimensional structure is essential for their correct activity. In this primer, we present how to study the mechanical properties of proteins with atomic force microscopy and how to obtain information about their stability and energetic landscape. In particular, we discuss the preparation of polyprotein constructs suitable for AFM single molecule force spectroscopy (SMFS), describe the parameters used in our force‐extension SMFS experiments and the models and equations employed in the analysis of the data. As a practical example, we show the effect of the temperature on the unfolding force, the distance to the transition state, the unfolding rate at zero force, the height of the transition state barrier, and the spring constant of the protein for a construct containing nine repeats of the I27 domain from the muscle protein titin.

Polymer looping kinetics in active heterogeneous environments

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Denatured State Conformational Biases in Three-Helix Bundles Containing Divergent Sequences Localize near Turns and Helix Capping Residues

Rhodopseudomonas palustris cytochrome c', a four-helix bundle, and the second ubiquitin-associated domain, UBA(2), a three-helix bundle from the human homologue of yeast Rad23, HHR23A, deviate from random coil behavior under denaturing conditions in a fold-specific manner. The random coil deviations in each of these folds occur near interhelical turns and loops in their tertiary structures. Here, we examine an additional three-helix bundle with an identical fold to UBA(2), but a highly divergent sequence, the first ubiquitin-associated domain, UBA(1), of HHR23A. We use histidine-heme loop formation methods, employing eight single histidine variants, to probe for denatured state conformational bias of a UBA(1) domain fused to the N-terminus of iso-1-cytochrome c (iso-1-Cytc). Guanidine hydrochloride (GuHCl) denaturation shows that the iso-1-Cytc domain unfolds first, followed by the UBA(1) domain. Denatured state (4 and 6 M GuHCl) histidine-heme loop formation studies show that as the size of the histidine-heme loop increases, loop stability decreases, as expected for the Jacobson-Stockmayer relationship. However, loops formed with His35, His31, and His15, of UBA(1), are 0.6-1.1 kcal/mol more stable than expected from the Jacobson-Stockmayer relationship, confirming the importance of deviations of the denatured state from random coil behavior near interhelical turns of helical domains for facilitating folding to the correct topology. For UBA(1) and UBA(2), hydrophobic clusters on either side of the turns partially explain deviations from random coil behavior; however, helix capping also appears to be important.

Nucleation limits the lengths of actin filaments assembled by formin

Formins stimulate actin polymerization by promoting both filament nucleation and elongation. Because nucleation and elongation draw upon a common pool of actin monomers, the rate at which each reaction proceeds influences the other. This interdependent mechanism determines the number of filaments assembled over the course of a polymerization reaction, as well as their equilibrium lengths. In this study, we used kinetic modeling and in vitro polymerization reactions to dissect the contributions of filament nucleation and elongation to the process of formin-mediated actin assembly. We found that the rates of nucleation and elongation evolve over the course of a polymerization reaction. The period over which each process occurs is a key determinant of the total number of filaments that are assembled, as well as their average lengths at equilibrium. Inclusion of formin in polymerization reactions speeds filament nucleation, thus increasing the number and shortening the lengths of filaments that are assembled over the course of the reaction. Modulation of the elongation rate produces modest changes in the equilibrium lengths of formin-bound filaments. However, the dependence of filament length on the elongation rate is limited by the number of filament ends generated via formin's nucleation activity. Sustained elongation of small numbers of formin-bound filaments, therefore, requires inhibition of nucleation via monomer sequestration and a low concentration of activated formin. Our results underscore the mechanistic advantage for keeping formin's nucleation efficiency relatively low in cells, where unregulated actin assembly would produce deleterious effects on cytoskeletal dynamics. Under these conditions, differences in the elongation rates mediated by formin isoforms are most likely to impact the kinetics of actin assembly.

Comparative study of polymer looping kinetics in passive and active environments

Intra-chain looping in complex environments is significant in advancing our understanding of biological processes in life. We adopt Langevin dynamics simulations to perform a comparative study of polymer looping kinetics in passive and active environments. From the analysis of looping quantities, including looping-unlooping times and looping probabilities, we unraveled the intriguing effects of active crowder size, activity and crowding. Firstly, we figured out the phase diagram involving a novel facilitation-inhibition transition in the parameter space of active crowder size and active force, and the two-fold roles of activity are clarified. In particular, we find that active particles of a size comparable to the polymer monomer are most favorable for facilitated looping, while those with a similar size to the polymer gyration radius impede the looping most seriously. Secondly, the underlying looping mechanisms in different active crowder size regimes are rationalized by the interplay among diffusion, polymer conformational change and the free-energy barrier. For small active crowders, activity significantly promotes end-to-end distance diffusion, which dominantly facilitates both looping and unlooping processes. In the case of moderate active crowders, the polymer chain suffers from prominent swelling, and thus inevitable inhibited looping will occur. For large active crowders, activity induces a counterintuitive non-cage effect on the looping kinetics, through yielding a higher effective temperature and larger unlooping free-energy barrier. This is in sharp contrast to the caging phenomena observed in passive media. Lastly, the volume-fraction dependence of the looping quantities in an active bath demonstrates dramatic discrepancies from that in a passive bath, which highlights the contrasting effects of activity and crowding.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of KBFF20

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

Modern Kinetics and Mechanism of Protein Folding: A Retrospective

Modern experimental kinetics of protein folding began in the early 1990s with the introduction of nanosecond laser pulses to trigger the folding reaction, providing an almost 10⁶-fold improvement in time resolution over the stopped-flow method being employed at the time. These experiments marked the beginning of the "fast-folding" subfield that enabled investigation of the kinetics of formation of secondary structural elements and disordered loops for the first time, as well as the fastest folding proteins. When I started to work on this subject, a fast folding protein was one that folded in milliseconds. There were, moreover, no analytical theoretical models and no atomistic or coarse-grained molecular dynamics simulations to describe the mechanism. Two of the most important discoveries from my lab since then are a protein that folds in hundreds of nanoseconds, as determined from nanosecond laser temperature experiments, and the discovery that the theoretically predicted barrier crossing time is about the same for proteins that differ in folding rates by 10⁴-fold, as determined from single molecule fluorescence measurements. We also developed what has been called the "Hückel model" of protein folding, which quantitatively explains a wide range of equilibrium and kinetic measurements. This retrospective traces the history of contributions to the "fast folding" subfield from my lab until about 3 years ago, when I left protein folding to spend the rest of my research career trying to discover an inexpensive drug for treating sickle cell disease.

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.

Roles, Characteristics, and Analysis of Intrinsically Disordered Proteins: A Minireview

In recent years, there has been a growing understanding that a significant fraction of the eukaryotic proteome is intrinsically disordered, and that these conformationally dynamic proteins play a myriad of vital biological roles in both normal and pathological states. In this review, selected examples of intrinsically disordered proteins are highlighted, with particular attention for a few which are relevant in neurological disorders and in viral infection. Next, the underlying causes for the intrinsic disorder are discussed, along with computational methods used to predict whether a given amino acid sequence is likely to adopt a folded or unfolded state in the solution. Finally, biophysical methods for the analysis of intrinsically disordered proteins will be discussed, as well as the unique challenges they pose in this context due to their highly dynamic nature.

Interaction of Cucurbit[7]uril With Protease Substrates: Application to Nanosecond Time-Resolved Fluorescence Assays

We report the use of the macrocyclic host cucurbit[7]uril (CB7) as a supramolecular additive in nanosecond time-resolved fluorescence (Nano-TRF) assays for proteases to enhance the discrimination of substrates and products and, thereby, the sensitivity. A peptide substrate was labeled with 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) as a long-lived (>300 ns) fluorescent probe and 3-nitrotyrosine was established as a non-fluorescent fluorescence resonance energy transfer (FRET) acceptor that acts as a “dark quencher.” The substrate was cleaved by the model proteases trypsin and chymotrypsin and the effects of the addition of CB7 to the enzyme assay mixture were investigated in detail using UV/VIS absorption as well as steady-state and time-resolved fluorescence spectroscopy. This also allowed us to identify the DBO and nitrotyrosine residues as preferential binding sites for CB7 and suggested a hairpin conformation of the peptide, in which the guanidinium side chain of an arginine residue is additionally bound to a vacant ureido rim of one of the CB7 hosts.

Proper adsorptive confinement for efficient production of cyclic polymers: a dissipative particle dynamics study

Efficient production of cyclic polymers has been a hot topic in the past few decades. In this work, we found that an adsorptive porous template with an appropriate size has the capability to accelerate the ring closure of a linear polymer chain in a dilute solution with a higher yield. The restricted pore provides a confined space and the effect of its characteristics, such as pore size, shape and adsorption strength on cyclization time, is systematically studied by using dissipative particle dynamics simulations. As a prerequisite of cyclization in confinement, the entry process of linear precursors has been studied as well. Total production time is governed by a tradeoff between the size effect caused by decreasing the size of the pore and the adsorption of the pore. The strong size effect suppresses polymer entry but accelerates cyclization. The stronger adsorption promotes polymer entry but decelerates cyclization. According to our defined total production time, a small spherical confinement with strong adsorption results in a shorter total production time of cyclic polymers compared to that in free solution. If chain cyclization is permitted during its entering the confinement, the interplay between steric hindrance caused by pore size and adsorption provides an additional 'virtual' confinement at the boundary between confinement and free solution. In this case, an optimal cyclization time is observed with an appropriate adsorption strength under small confinement. Our results provide useful guidance for designing suitable porous templates for producing cyclic polymers with high efficiency.

N-Terminal Decarboxylation as a Probe for Intramolecular Contact Formation in γ-Glu-(Pro)n-Met Peptides

The kinetics of intramolecular-contact formation between remote functional groups in peptides with restricted conformational flexibility were examined using designed peptides with variable-length proline bridges. As probes for this motion, free radicals were produced using the ^•OH-induced oxidation at the C-terminal methionine residue of γ-Glu-(Pro)_n-Met peptides (n = 0-3). The progress of the radicals' motion along the proline bridges was monitored as the radicals underwent reactions along the peptides' backbones. Of particular interest was the reaction between the sulfur atom located in the side chain of the oxidized Met residue and the unprotonated amino group of the glutamic acid moiety. Interactions between them were probed by the radiation-chemical yields (expressed as G values) of the formation of C-centered, α-aminoalkyl radicals (αN) on the Glu residue. These radicals were monitored directly or via their reaction with p-nitroacetophenone (PNAP) to generate the optically detected PNAP^•- radical anions. The yields of these αN radicals were found to be linearly dependent on the number of Pro residues. A constant decrease by 0.09 μM J^-1 per spacing Pro residue of the radiation-chemical yields of G(αN) was observed. Previous reports support the conclusion that the αN radicals in these cases would have to result from (S∴N)⁺-bonded cyclic radical cations that arose as a result from direct contact between the ends of the peptides. Furthermore, by analogy with the rate constants for the formation of intramolecularly (S∴S)⁺-bonded radical cations in Met-(Pro)_n-Met peptides ( J. Phys. Chem. B 2016, 120, 9732), the rate constants for the formation of intramolecularly (S∴N)⁺-bonded radical cations are activated to the same extent for all of the γ-Glu-(Pro)_n-Met peptides. Thus, the continuous decrease of G(αN) with the number of Pro residues (from 0 to 3) suggests that the formation of a contact between the S-atom in the C-terminal Met residue and the N-atom of a deprotonated N-terminal amino group of Glu is controlled in peptides with 0 to 3 Pro residues by the relative diffusion of the S^•+ and unoxidized N-atom. The overall rate constants of cyclization to form the (S∴N)-bonded radical cations were estimated to be 3.8 × 10⁶, 1.8 × 10⁶, and 8.1 × 10⁵ s^-1 for peptides with n = 0, 1, and 2 Pro residues, respectively. If activation is the same for all of the peptides, then these rate constants are a direct indication for the end-to-end dynamics along the chain.

4-Cyanoindole-based fluorophores for biological spectroscopy and microscopy

Most biological molecules are intrinsically non- or weakly-fluorescent, hence requiring labeling with an external fluorophore(s) to be studied via fluorescence-based techniques. However, such labeling could perturb the native property of the system in question. One effective strategy to minimize such undesirable perturbation is to use fluorophores that are simple analogs of natural amino acids. In this chapter, we describe the synthesis and spectroscopic utility of two indole-based fluorophores, 4-cynaotryprophan (4CN-Trp) and 4-cyanoindole-2'-deoxyribonucleoside (4CNI-NS), with a focus on 4CN-Trp. This unnatural amino acid, which is only slightly larger than its natural counterpart, tryptophan (Trp), exhibits unique photophysical properties, making it a versatile fluorophore in biological spectroscopic and imaging applications. Through several specific examples, we highlight its broad utility in the study of various biological problems and processes.

Kinetics of Loop Closure in Disordered Proteins: Theory vs Simulations vs Experiments

We study intrachain dynamics of intrinsically disordered proteins, as manifested by the time scales of loop formation, using atomistic simulations, experiment-parametrized coarse-grained models, and one-dimensional theories assuming Markov or non-Markov dynamics along the reaction coordinate. Despite the generally non-Markov character of monomer dynamics in polymers, we find that the simplest model of one-dimensional diffusion along the reaction coordinate (equated to the distance between the loop-forming monomers) well captures the mean first passage times to loop closure measured in coarse-grained and atomistic simulations, which, in turn, agree with the experimental values. This justifies use of the one-dimensional diffusion model in interpretation of experimental data. At the same time, the transition path times for loop closure in longer polypeptide chains show significant non-Markov effects; at intermediate times, these effects are better captured by the generalized Langevin equation model. At long times, however, atomistic simulations predict long tails in the distributions of transition path times, which are at odds with both the one-dimensional diffusion model and the generalized Langevin equation model.

Competition for delivery of profilin-actin to barbed ends limits the rate of formin-mediated actin filament elongation

Formins direct the elongation of unbranched actin filaments by binding their barbed ends and processively stepping onto incoming actin monomers to incorporate them into the filament. Binding of profilin to actin monomers creates profilin-actin complexes, which then bind polyproline tracts located in formin homology 1 (FH1) domains. Diffusion of these natively disordered domains enables direct delivery of profilin-actin to the barbed end, speeding the rate of filament elongation. In this study, we investigated the mechanism of coordinated actin delivery from the multiple polyproline tracts in formin FH1 domains. We found that each polyproline tract can efficiently mediate polymerization, but that all tracts do not generate the same rate of elongation. In WT FH1 domains, the multiple polyproline tracts compete to deliver profilin-actin to the barbed end. This competition ultimately limits the rate of formin-mediated elongation. We propose that intrinsic properties of the filament-binding FH2 domain tune the efficiency of FH1-mediated elongation by directly regulating the rate of monomer incorporation at the barbed end. A strong correlation between competitive FH1-mediated profilin-actin delivery and FH2-regulated gating of the barbed end effectively limits the elongation rate, thereby obviating the need for evolutionary optimization of FH1 domain sequences.

Loop formation and translational diffusion of intrinsically disordered proteins

The conformational flexibility and dynamics of unfolded peptide chains is of major interest in the context of protein folding and protein functioning. The rate with which amino acids at different positions along the peptide chain meet sets an upper speed limit for protein folding. By using single-molecule photo-induced energy transfer spectroscopy, we have systematically measured end-to-end and end-to-internal site contact formation rates for several intrinsically disordered protein fragments (IDPs) (11 to 41 amino acids) and have also determined their hydrodynamic radius using dual-focus fluorescence correlation spectroscopy. For interpreting the measured values, we have developed a Brownian dynamics model (based on bead-rod chain dynamics in a thermal bath including hydrodynamic interactions) which quantitatively reproduces all measured data surprisingly well while requiring only two fit parameters. The model provides a complete picture of the peptides' dynamics and allows us to translate the experimental rates and radii into molecular properties of the peptides: We find a persistence length of l_{P}=5.2±1.9Å, a hydrodynamic radius of a=3.5±0.7Å per amino acid, and that excluded volume effects play an important role in the dynamics of IDPs.

The Influence of Molecular Reach and Diffusivity on the Efficacy of Membrane-Confined Reactions

Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered enzyme will contact the substrate in the volume proximal to the membrane when separated by different distances within the membrane plane. In this work, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy for slowly diffusing receptors, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the three-dimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.

Distinct Binding Interactions of α5β1-Integrin and Proteoglycans with Fibronectin

Dynamic single-molecule force spectroscopy was performed to monitor the unbinding of fibronectin with the proteoglycans syndecan-4 (SDC4) and decorin and to compare this with the unbinding characteristics of α₅β₁-integrin. A single energy barrier was sufficient to describe the unbinding of both SDC4 and decorin from fibronectin, whereas two barriers were observed for the dissociation of α₅β₁-integrin from fibronectin. The outer (high-affinity) barriers in the interactions of fibronectin with α₅β₁-integrin and SDC4 are characterized by larger barrier heights and widths and slower dissociation rates than those of the inner (low-affinity) barriers in the interactions of fibronectin with α₅β₁-integrin and decorin. These results indicate that SDC4 and (ultimately) α₅β₁-integrin have the ability to withstand deformation in their interactions with fibronectin, whereas the decorin-fibronectin interaction is considerably more brittle.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Microsecond sub-domain motions and the folding and misfolding of the mouse prion protein

Protein aggregation appears to originate from partially unfolded conformations that are sampled through stochastic fluctuations of the native protein. It has been a challenge to characterize these fluctuations, under native like conditions. Here, the conformational dynamics of the full-length (23-231) mouse prion protein were studied under native conditions, using photoinduced electron transfer coupled to fluorescence correlation spectroscopy (PET-FCS). The slowest fluctuations could be associated with the folding of the unfolded state to an intermediate state, by the use of microsecond mixing experiments. The two faster fluctuations observed by PET-FCS, could be attributed to fluctuations within the native state ensemble. The addition of salt, which is known to initiate the aggregation of the protein, resulted in an enhancement in the time scale of fluctuations in the core of the protein. The results indicate the importance of native state dynamics in initiating the aggregation of proteins.

Nature's Shortcut to Protein Folding

This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.

Cyclization and Relaxation Dynamics of Finite-Length Collapsed Self-Avoiding Polymers

We study the cyclization and relaxation dynamics of ideal as well as interacting polymers as a function of chain length N. For the cyclization time τ_{cyc} of ideal chains we recover the known scaling τ_{cyc}∼N^{2} for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling τ_{cyc}∼N^{5/3}. The cyclization and relaxation dynamics of a finite-length collapsed chain scale differently; this unexpected dynamic multiscale behavior is rationalized by the crossover between swollen and collapsed chain behavior.

Atmospheric protein chemistry influenced by anthropogenic air pollutants: nitration and oligomerization upon exposure to ozone and nitrogen dioxide

The allergenic potential of airborne proteins may be enhanced via post-translational modification induced by air pollutants like ozone (O₃) and nitrogen dioxide (NO₂). The molecular mechanisms and kinetics of the chemical modifications that enhance the allergenicity of proteins, however, are still not fully understood. Here, protein tyrosine nitration and oligomerization upon simultaneous exposure of O₃ and NO₂ were studied in coated-wall flow-tube and bulk solution experiments under varying atmospherically relevant conditions (5-200 ppb O₃, 5-200 ppb NO₂, 45-96% RH), using bovine serum albumin as a model protein. Generally, more tyrosine residues were found to react via the nitration pathway than via the oligomerization pathway. Depending on reaction conditions, oligomer mass fractions and nitration degrees were in the ranges of 2.5-25% and 0.5-7%, respectively. The experimental results were well reproduced by the kinetic multilayer model of aerosol surface and bulk chemistry (KM-SUB). The extent of nitration and oligomerization strongly depends on relative humidity (RH) due to moisture-induced phase transition of proteins, highlighting the importance of cloud processing conditions for accelerated protein chemistry. Dimeric and nitrated species were major products in the liquid phase, while protein oligomerization was observed to a greater extent for the solid and semi-solid phase states of proteins. Our results show that the rate of both processes was sensitive towards ambient ozone concentration, but rather insensitive towards different NO₂ levels. An increase of tropospheric ozone concentrations in the Anthropocene may thus promote pro-allergic protein modifications and contribute to the observed increase of allergies over the past decades.

Improving the Sensitivity of Fluorescence-Based Immunoassays by Photobleaching the Autofluorescence of Magnetic Beads

In fluorescence-based assays, usually a target molecule is captured using a probe conjugated to a capture surface, and then detected using a second fluorescently labeled probe. One of the most common capture surfaces is a magnetic bead. However, magnetic beads exhibit strong autofluorescence, which often overlaps with the emission of the reporter fluorescent dyes and limits the analytical performance of the assay. Here, several widely used magnetic beads are photobleached and their autofluorescence is reduced to 1% of the initial value. Their autofluorescence properties, including their photobleaching decay rates and autofluorescence spectra pre- and post-photobleaching, and the stability of the photobleaching over a period of two months are analyzed. The photobleached beads are stable over time and their surface functionality is retained. In a high-sensitivity LX-200 system using photobleached magnetic beads, human interleukin-8 is detected with a threefold improvement in detection limit and signal-to-noise ratio over results achievable with nonbleached beads. Since many contemporary immunoassays rely on magnetic beads as capture surfaces, prebleaching the beads may significantly improve the analytical performance of these assays. Moreover, nonmagnetic beads with low autofluorescence are also successfully photobleached, suggesting that photobleaching can be applied to various capture surfaces used in fluorescence-based assays.

The role of solvent quality and chain stiffness on the end-to-end contact kinetics of semiflexible polymers

Motivated by loop closure during protein folding and DNA packing, we systemically studied the effects of the solvent quality and chain stiffness on the thermodynamics and kinetics of the end-to-end contact formation for semiflexible polymer chains with reactive ends by Langevin dynamics simulations. In thermodynamics, a rich variety of products of the end-to-end contact have been discovered, such as loop, hairpin, toroid, and rodlike bundle, the populations of which are dependent on the solvent quality and chain stiffness. In kinetics, the overall pathways to form the end-to-end contact have been identified. The change of solvent quality and chain stiffness can tune the roughness of energy landscape and modulate the kinetic partitioning of the end-to-end contact formation pathways, leading to differing kinetic behaviors. In good or poor solvents, the first end-to-end contact rate k _c decreases with increasing the strength of bending stiffness k _θ monotonically. In very poor solvents, however, the dependence of the logarithm of the first end-to-end contact rate ln k _c on k _θ exhibits erratic behavior, which stems from more rugged energy landscape due to the polymer chain getting trapped into the intermediate state composed of the rodlike bundles with two ends in separation. For semiflexible chains, with increasing chain length N, the rate k _c increases initially and then decreases: in good solvents, the rate k _c exhibits a power-law relationship to chain length N with an exponent of ∼-1.50 in the region of long chains, which is in good agreement with the value derived from the experiment in the asymptotic limit of large N; and in poor solvents, the rate k _c exhibits a significantly stronger chain length dependence than those observed in good solvents in the region of long chains due to frustration to form the end-to-end contact along a specific path, especially the scaling exponent between the rate k _c and chain length N is ∼-3.62 for the case of polymer chains with k _θ = 4 at the solvent quality ε _ij = 1, in accord with the value obtained from the experiments.

Complex Folding Landscape of Apomyoglobin at Acidic pH Revealed by Ultrafast Kinetic Analysis of Core Mutants

Under mildly acidic conditions (pH 4-4.5) apomyoglobin (apoMb) adopts a partially structured equilibrium state ( M-state) that structurally resembles a kinetic intermediate encountered at a late stage of folding to the native structure at neutral pH. We have previously reported that the M-state is formed rapidly (<1 ms) via a multistate process and thus offers a unique opportunity for exploring early stages of folding by both experimental and computational techniques. In order to gain structural insight into intermediates and barriers at the residue level, we studied the folding/unfolding kinetics of 12 apoMb mutants at pH 4.2 using fluorescence-detected ultrafast mixing techniques. Global analysis of the submillisecond folding/unfolding kinetics vs urea concentration for each variant, based on a sequential four-state mechanism ( U ⇔ I ⇔ L ⇔ M), allowed us to determine elementary rate constants and their dependence on urea concentration for most transitions. Comparison of the free energy diagrams constructed from the kinetic data of the mutants with that of wild-type apoMb yielded quantitative information on the effects of mutations on the free energy (ΔΔ G) of both intermediates and the first two kinetic barriers encountered during folding. Truncation of conserved aliphatic side chains on helices A, G, and H gives rise to a stepwise increase in ΔΔ G as the protein advances from U toward M, consistent with progressive stabilization of native-like contacts within the primary core of apoMb. Helix-helix contacts in the primary core contribute little to the first folding barrier ( U ⇔ I) and thus are not required for folding initiation but are critical for the stability of the late intermediate, L, and the M-state. Alanine substitution of hydrophobic residues at more peripheral helix-helix contact sites of the native structure, which are still absent or unstable in the M-state, shows both positive (destabilizing) and negative (stabilizing) ΔΔ G, indicating that non-native contacts are formed initially and weakened or lost as a result of subsequent structural rearrangement steps.

The Sensitivity of Computational Protein Folding to Contact Map Perturbations: The Case of Ubiquitin Folding and Function

Ubiquitin is a small model protein, commonly used in protein folding experiments and simulations. We simulated ubiquitin using a well-tested structure-based model coarse-grained to a C_α level (C_α-SBM) and found that the simulated folding route did not agree with the experimentally observed one. Simulating the C_α-SBM with a cutoff contact map, instead of a screened contact map, switched the folding route with the new route matching the experimental route. Thus, the simulated folding of ubiquitin is sensitive to contact map definition. The screened contact map, which is used in folding simulations because it captures protein folding cooperativity, removes contacts in which the atoms in contact are occluded by a third atom and is less sensitive to the value of the cutoff distance in well-packed regions of the protein. In sparsely packed regions, the larger cutoff distance creates bridging contacts between atoms which are separated by voids. Such contacts do not seem to affect the folding of most proteins, including those of the ubiquitin fold. However, the surface of ubiquitin has several protruding functional side chains which naturally create bridging contacts. Together, our results show that subtle structural features of a protein that may not be apparent by mere observation can be identified by comparing folding simulations of SBMs in which these features are differently encoded. When such structural features are preserved for functional reasons, differences in computational folding can be leveraged to identify functional features. Notably, such features are accessible to a gradation of SBMs even in commonly studied proteins such as ubiquitin.

Understanding chain looping kinetics in polymer solutions: crowding effects of microviscosity and collapse

A theoretical framework based on a generalized Langevin equation with fractional Gaussian noise is presented to describe the looping kinetics of chains in polymer solutions. Particular attention is paid to quantitatively revealing crowding effects on the loop formation rate in terms of microviscosity and collapse. By the aid of empirical relations for these two crowding associated physical quantities, we explicitly investigate the relationship between the looping rate and polymer concentration, the degree of polymerization, and system parameters. According to our analysis, the dependence of the looping rate on the crowder volume fraction exhibits three typical regimes: monotonic decreasing, a non-monotonic trend and monotonic increasing. We reveal that these non-trivial behaviors can be attributed to the competition between the two opposing factors of viscosity-associated inhibition and collapse-induced facilitation of loop formation. We apply our theory to analyze the kinetics of single-stranded DNA hairpin base pairing in polyethylene glycol solutions. The theoretical results can reproduce the experimental data on the closing rate of hairpins quantitatively to a certain degree with reasonable fitting parameters. The unexpected increase of the closing rate upon the addition of increasing amounts of polymer is well rationalised. Such good agreements clearly demonstrate the validity of our theory, appropriately addressing the very role of crowding effects in the relevant kinetics.

Dynamics of Structural Elements of GB1 β-Hairpin Revealed by Tryptophan-Cysteine Contact Formation Experiments

Quenching of the triplet state of tryptophan by close contact with cysteine provides a tool for measuring the rate of intramolecular contact formation, one of the most elementary events in the folding process, in peptides and proteins using only natural probes. Here we present a study performed on a stabilized mutant of the second β-hairpin of the GB1 domain, where we combine steady-state fluorescence, laser-induced temperature-jump, and contact formation measurements to unveil the role of elementary structural components on hairpin dynamics and overall stability. In particular, our methodology provides access to the conformational dynamics of both the folded and unfolded state of the hairpin under native conditions, revealing the presence of extremely slow dynamics on the microsecond time scale in the unfolded state and coexistence of structures with partial pairing of the tails in the folded state. Comparing model peptides that mimic the turn sequence, we found that both ion pairing and hydrogen bonding due to the threonine side chain contribute to the propensity of turn formation but not to the much slower dynamics of the hydrophobic core formation. Interestingly, the dynamics of the turn region in isolation are significantly faster than the dynamics measured for the unfolded state of the complete hairpin, suggesting that non-native hydrophobic contacts slow down the reconfiguration dynamics of the unfolded state. Overall, the information extracted from these experiments provides kinetic limits on interconversions among conformational populations, hence enabling a simplified multistate free-energy landscape for the GB1 hairpin to be drawn.

Intramolecular Diffusion in α-Synuclein: It Depends on How You Measure It

Intramolecular protein diffusion, the motion of one part of the polypeptide chain relative to another part, is a fundamental aspect of protein folding and may modulate amyloidogenesis of disease-associated intrinsically disordered proteins. Much work has determined such diffusion coefficients using a variety of probes, but there has been an apparent discrepancy between measurements using long-range probes, such as fluorescence resonance energy transfer, and short-range probes, such as Trp-Cys quenching. In this work, we make both such measurements on the same protein, α-synuclein, and confirm that such discrepancy exists. Molecular dynamics simulations suggest that such differences result from a diffusion coefficient that depends on the spatial distance between probes. Diffusional estimates in good quantitative agreement with experiment are obtained by accounting for the distinct distance ranges probed by fluorescence resonance energy transfer and Trp-Cys quenching.

Dynamics of Disordered Proteins under Confinement: Memory Effects and Internal Friction

Many proteins are disordered under physiological conditions. How efficiently they can search for their cellular targets and how fast they can fold upon target binding is determined by their intrinsic dynamics, which have thus attracted much recent attention. Experiments and molecular simulations show that the inherent reconfiguration timescale for unfolded proteins has a solvent friction component and an internal friction component, and the microscopic origin of the latter, along with its proper mathematical description, has been a topic of considerable debate. Internal friction varies across different proteins of comparable length and increases with decreasing denaturant concentration, showing that it depends on how compact the protein is. Here we report on a systematic atomistic simulation study of how confinement, which induces a more compact unfolded state, affects dynamics and friction in disordered peptides. We find that the average reconfiguration timescales increase exponentially as the peptide's spatial dimensions are reduced; at the same time, confinement broadens the spectrum of relaxation timescales exhibited by the peptide. There are two important implications of this broadening: First, it limits applicability of the common Rouse and Zimm models with internal friction, as those models attempt to capture internal friction effects by introducing a single internal friction timescale. Second, the long-tailed distribution of relaxation times leads to anomalous diffusion effects in the dynamics of intramolecular distances. Analysis and interpretation of experimental signals from various measurements that probe intramolecular protein dynamics (such as single-molecule fluorescence correlation spectroscopy and single-molecule force spectroscopy) rely on the assumption of diffusive dynamics along the distances being probed; hence, our results suggest the need for more general models allowing for anomalous diffusion effects.

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.

Perspective: Chain dynamics of unfolded and intrinsically disordered proteins from nanosecond fluorescence correlation spectroscopy combined with single-molecule FRET

The dynamics of unfolded proteins are important both for the process of protein folding and for the behavior of intrinsically disordered proteins. However, methods for investigating the global chain dynamics of these structurally diverse systems have been limited. A versatile experimental approach is single-molecule spectroscopy in combination with Förster resonance energy transfer and nanosecond fluorescence correlation spectroscopy. The concepts of polymer physics offer a powerful framework both for interpreting the results and for understanding and classifying the properties of unfolded and intrinsically disordered proteins. This information on long-range chain dynamics can be complemented with spectroscopic techniques that probe different length scales and time scales, and integration of these results greatly benefits from recent advances in molecular simulations. This increasing convergence between the experiment, theory, and simulation is thus starting to enable an increasingly detailed view of the dynamics of disordered proteins.