Diffusion-limited association of disordered protein by non-native electrostatic interactions

Commonly asked questions about transcriptional activation domains

Eukaryotic transcription factors activate gene expression with their DNA-binding domains and activation domains. DNA-binding domains bind the genome by recognizing structurally related DNA sequences; they are structured, conserved, and predictable from protein sequences. Activation domains recruit chromatin modifiers, coactivator complexes, or basal transcriptional machinery via structurally diverse protein-protein interactions. Activation domains and DNA-binding domains have been called independent, modular units, but there are many departures from modularity, including interactions between these regions and overlap in function. Compared to DNA-binding domains, activation domains are poorly understood because they are poorly conserved, intrinsically disordered, and difficult to predict from protein sequences. This review, organized around commonly asked questions, describes recent progress that the field has made in understanding the sequence features that control activation domains and predicting them from sequence.

Recognition and coacervation of G-quadruplexes by a multifunctional disordered region in RECQ4 helicase

Biomolecular polyelectrolyte complexes can be formed between oppositely charged intrinsically disordered regions (IDRs) of proteins or between IDRs and nucleic acids. Highly charged IDRs are abundant in the nucleus, yet few have been functionally characterized. Here, we show that a positively charged IDR within the human ATP-dependent DNA helicase Q4 (RECQ4) forms coacervates with G-quadruplexes (G4s). We describe a three-step model of charge-driven coacervation by integrating equilibrium and kinetic binding data in a global numerical model. The oppositely charged IDR and G4 molecules form a complex in the solution that follows a rapid nucleation-growth mechanism leading to a dynamic equilibrium between dilute and condensed phases. We also discover a physical interaction with Replication Protein A (RPA) and demonstrate that the IDR can switch between the two extremes of the structural continuum of complexes. The structural, kinetic, and thermodynamic profile of its interactions revealed a dynamic disordered complex with nucleic acids and a static ordered complex with RPA protein. The two mutually exclusive binding modes suggest a regulatory role for the IDR in RECQ4 function by enabling molecular handoffs. Our study extends the functional repertoire of IDRs and demonstrates a role of polyelectrolyte complexes involved in G4 binding.

Clusters of acidic and hydrophobic residues can predict acidic transcriptional activation domains from protein sequence

Transcription factors activate gene expression in development, homeostasis, and stress with DNA binding domains and activation domains. Although there exist excellent computational models for predicting DNA binding domains from protein sequence, models for predicting activation domains from protein sequence have lagged, particularly in metazoans. We recently developed a simple and accurate predictor of acidic activation domains on human transcription factors. Here, we show how the accuracy of this human predictor arises from the clustering of aromatic, leucine, and acidic residues, which together are necessary for acidic activation domain function. When we combine our predictor with the predictions of convolutional neural network (CNN) models trained in yeast, the intersection is more accurate than individual models, emphasizing that each approach carries orthogonal information. We synthesize these findings into a new set of activation domain predictions on human transcription factors.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

Multilayered allosteric modulation of coupled folding and binding by phosphorylation, peptidyl-prolyl cis/trans isomerization, and diversity of interaction partners

Intrinsically disordered proteins (IDPs) play key roles in cellular regulation, including signal transduction, transcription, and cell-cycle control. Accordingly, IDPs can commonly interact with numerous different target proteins, and their interaction networks are expected to be highly regulated. However, many of the underlying regulatory mechanisms have remained unclear. Here, we examine the representative case of the nuclear coactivator binding domain (NCBD) of the large multidomain protein CBP, a hub in transcriptional regulation, and the interaction with several of its binding partners. Single-molecule Förster resonance energy transfer measurements show that phosphorylation of NCBD reduces its binding affinity, with effects that vary depending on the binding partner and the site and number of modifications. The complexity of the interaction is further increased by the dependence of the affinities on peptidyl-prolyl cis/trans isomerization in NCBD. Overall, our results reveal the potential for allosteric regulation on at least three levels: the different affinities of NCBD for its different binding partners, the differential modulation of these affinities by phosphorylation, and the effect of peptidyl-prolyl cis/trans isomerization on binding.

The biophysics of disordered proteins from the point of view of single-molecule fluorescence spectroscopy

Intrinsically disordered proteins (IDPs) and regions (IDRs) have emerged as key players across many biological functions and diseases. Differently from structured proteins, disordered proteins lack stable structure and are particularly sensitive to changes in the surrounding environment. Investigation of disordered ensembles requires new approaches and concepts for quantifying conformations, dynamics, and interactions. Here, we provide a short description of the fundamental biophysical properties of disordered proteins as understood through the lens of single-molecule fluorescence observations. Single-molecule Förster resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) provides an extensive and versatile toolbox for quantifying the characteristics of conformational distributions and the dynamics of disordered proteins across many different solution conditions, both in vitro and in living cells.

A modular approach to map out the conformational landscapes of unbound intrinsically disordered proteins

SignificanceIntrinsically disordered proteins have the unique ability to morph in response to multiple partners and thereby process sophisticated inputs and outputs. It is, however, a mystery whether their response is passive, that is, entirely determined by the partner, or controlled via an internal, yet unknown, folding mechanism. Here we introduce an approach to examine this key question and demonstrate its potential by dissecting the conformational properties of the partially disordered protein NCBD and obtaining important clues about how it performs its biological function.

Interplay of Affinity and Surface Tethering in Protein Recognition

Surface-tethered ligand-receptor complexes are key components in biological signaling and adhesion. They also find increasing utility in single-molecule assays and biotechnological applications. Here, we study the real-time binding kinetics between various surface-immobilized peptide ligands and their unrestrained receptors. A long peptide tether increases the association of ligand-receptor complexes, experimentally proving the fly casting mechanism where the disorder accelerates protein recognition. On the other hand, a short peptide tether enhances the complex dissociation. Notably, the rate constants measured for the same receptor, but under different spatial constraints, are strongly correlated to one another. Furthermore, this correlation can be used to predict how surface tethering on a ligand-receptor complex alters its binding kinetics. Our results have immediate implications in the broad areas of biomolecular recognition, intrinsically disordered proteins, and biosensor technology.

Directed mutational scanning reveals a balance between acidic and hydrophobic residues in strong human activation domains

Acidic activation domains are intrinsically disordered regions of the transcription factors that bind coactivators. The intrinsic disorder and low evolutionary conservation of activation domains have made it difficult to identify the sequence features that control activity. To address this problem, we designed thousands of variants in seven acidic activation domains and measured their activities with a high-throughput assay in human cell culture. We found that strong activation domain activity requires a balance between the number of acidic residues and aromatic and leucine residues. These findings motivated a predictor of acidic activation domains that scans the human proteome for clusters of aromatic and leucine residues embedded in regions of high acidity. This predictor identifies known activation domains and accurately predicts previously unidentified ones. Our results support a flexible acidic exposure model of activation domains in which the acidic residues solubilize hydrophobic motifs so that they can interact with coactivators. A record of this paper’s transparent peer review process is included in the supplemental information.

Transcriptional activation domains are poorly conserved, intrinsically disordered regions of the transcription factors that remain difficult to predict from protein sequences. A high-throughput method reveals how strong activation domains require a balance between acidic and hydrophobic residues. This balance powers an accurate predictor of activation domains on human transcription factors.

Transient exposure of a buried phosphorylation site in an autoinhibited protein

Autoinhibition is a mechanism used to regulate protein function, often by making functional sites inaccessible through the interaction with a cis-acting inhibitory domain. Such autoinhibitory domains often display a substantial degree of structural disorder when unbound, and only become structured in the inhibited state. These conformational dynamics make it difficult to study the structural origin of regulation, including effects of regulatory post-translational modifications. Here, we study the autoinhibition of the Dbl Homology domain in the protein Vav1 by the so-called acidic inhibitory domain. We use molecular simulations to study the process by which a mostly unstructured inhibitory domain folds upon binding and how transient exposure of a key buried tyrosine residue makes it accessible for phosphorylation. We show that the inhibitory domain, which forms a helix in the bound and inhibited stated, samples helical structures already before binding and that binding occurs via a molten-globule-like intermediate state. Together, our results shed light on key interactions that enable the inhibitory domain to sample a finely tuned equilibrium between an inhibited and a kinase-accessible state.

Observing the base-by-base search for native structure along transition paths during the folding of single nucleic acid hairpins

Biomolecular folding involves searching among myriad possibilities for the native conformation, but the elementary steps expected from theory for this search have never been detected directly. We probed the dynamics of folding at high resolution using optical tweezers, measuring individual trajectories as nucleic acid hairpins passed through the high-energy transition states that dominate kinetics and define folding mechanisms. We observed brief but ubiquitous pauses in the transition states, with a dwell time distribution that matched microscopic theories of folding quantitatively. The sequence dependence suggested that pauses were dominated by microbarriers from nonnative conformations during the search by each nucleotide residue for the native base-pairing conformation. Furthermore, the pauses were position dependent, revealing subtle local variations in energy-landscape roughness and allowing the diffusion coefficient describing the microscopic dynamics within the barrier to be found without reconstructing the shape of the energy landscape. These results show how high-resolution measurements can elucidate key microscopic events during folding to test fundamental theories of folding.

Diffusion of a disordered protein on its folded ligand

Flexibility in complexes between intrinsically disordered proteins and folded ligands is widespread in nature. However, timescales and spatial amplitudes of such dynamics remained unexplored for most systems. Our results show that the disordered cytoplasmic tail of the cell adhesion protein E-cadherin diffuses across the entire surface of its folded binding partner β-catenin at fast submillisecond timescales. The nanometer amplitude of these motions could allow kinases to access their recognition motifs without requiring a dissociation of the complex. We expect that the rugged energy landscape found in the E-cadherin/β-catenin complex is a defining feature of dynamic and partially disordered protein complexes.

Intrinsically disordered proteins often form dynamic complexes with their ligands. Yet, the speed and amplitude of these motions are hidden in classical binding kinetics. Here, we directly measure the dynamics in an exceptionally mobile, high-affinity complex. We show that the disordered tail of the cell adhesion protein E-cadherin dynamically samples a large surface area of the protooncogene β-catenin. Single-molecule experiments and molecular simulations resolve these motions with high resolution in space and time. Contacts break and form within hundreds of microseconds without a dissociation of the complex. The energy landscape of this complex is rugged with many small barriers (3 to 4 k_BT) and reconciles specificity, high affinity, and extreme disorder. A few persistent contacts provide specificity, whereas unspecific interactions boost affinity.

FRET-based dynamic structural biology: Challenges, perspectives and an appeal for open-science practices

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. Several labs that employ smFRET approaches have joined forces to inform the smFRET community about streamlining how to perform experiments and analyze results for obtaining quantitative information on biomolecular structure and dynamics. The recent efforts include blind tests to assess the accuracy and the precision of smFRET experiments among different labs using various procedures. These multi-lab studies have led to the development of smFRET procedures and documentation, which are important when submitting entries into the archiving system for integrative structure models, PDB-Dev. This position paper describes the current 'state of the art' from different perspectives, points to unresolved methodological issues for quantitative structural studies, provides a set of 'soft recommendations' about which an emerging consensus exists, and lists openly available resources for newcomers and seasoned practitioners. To make further progress, we strongly encourage 'open science' practices.

Barrier Crossing Dynamics from Single-Molecule Measurements

Chemists visualize chemical reactions as motion along one-dimensional "reaction coordinates" over free energy barriers. Various rate theories, such as transition state theory and the Kramers theory of diffusive barrier crossing, differ in their assumptions regarding the mathematical specifics of this motion. Direct experimental observation of the motion along reaction coordinates requires single-molecule experiments performed with unprecedented time resolution. Toward this goal, recent single-molecule studies achieved time resolution sufficient to catch biomolecules in the act of crossing free energy barriers as they fold, bind to their targets, or undergo other large structural changes, offering a window into the elusive reaction "mechanisms". This Perspective describes what we can learn (and what we have already learned) about barrier crossing dynamics through synergy of single-molecule experiments, theory, and molecular simulations. In particular, I will discuss how emerging experimental data can be used to answer several questions of principle. For example, is motion along the reaction coordinate diffusive, is there conformational memory, and is reduction to just one degree of freedom to represent the reaction mechanism justified? It turns out that these questions can be formulated as experimentally testable mathematical inequalities, and their application to experimental and simulated data has already led to a number of insights. I will also discuss open issues and current challenges in this fast evolving field of research.

Revisiting the Rate-Limiting Step of the ANS-Protein Binding at the Protein Surface and Inside the Hydrophobic Cavity

8-Anilino-1-naphthalenesulfonic acid (ANS) is used as a hydrophobic fluorescence probe due to its high intensity in hydrophobic environments, and also as a microenvironment probe because of its unique ability to exhibit peak shift and intensity change depending on the surrounding solvent environment. The difference in fluorescence can not only be caused by the microenvironment but can also be affected by the binding affinity, which is represented by the binding constant (K). However, the overall binding process considering the binding constant is not fully understood, which requires the ANS fluorescence binding mechanism to be examined. In this study, to reveal the rate-limiting step of the ANS-protein binding process, protein concentration-dependent measurements of the ANS fluorescence of lysozyme and bovine serum albumin were performed, and the binding constants were analyzed. The results suggest that the main factor of the binding process is the microenvironment at the binding site, which restricts the attached ANS molecule, rather than the attractive diffusion-limited association. The molecular mechanism of ANS-protein binding will help us to interpret the molecular motions of ANS molecules at the binding site in detail, especially with respect to an equilibrium perspective.

Broad distributions of transition-path times are fingerprints of multidimensionality of the underlying free energy landscapes

Recent single-molecule experiments have observed transition paths, i.e., brief events where molecules (particularly biomolecules) are caught in the act of surmounting activation barriers. Such measurements offer unprecedented mechanistic insights into the dynamics of biomolecular folding and binding, molecular machines, and biological membrane channels. A key challenge to these studies is to infer the complex details of the multidimensional energy landscape traversed by the transition paths from inherently low-dimensional experimental signals. A common minimalist model attempting to do so is that of one-dimensional diffusion along a reaction coordinate, yet its validity has been called into question. Here, we show that the distribution of the transition path time, which is a common experimental observable, can be used to differentiate between the dynamics described by models of one-dimensional diffusion from the dynamics in which multidimensionality is essential. Specifically, we prove that the coefficient of variation obtained from this distribution cannot possibly exceed 1 for any one-dimensional diffusive model, no matter how rugged its underlying free energy landscape is: In other words, this distribution cannot be broader than the single-exponential one. Thus, a coefficient of variation exceeding 1 is a fingerprint of multidimensional dynamics. Analysis of transition paths in atomistic simulations of proteins shows that this coefficient often exceeds 1, signifying essential multidimensionality of those systems.

Fast three-color single-molecule FRET using statistical inference

We describe theory, experiments, and analyses of three-color Förster resonance energy transfer (FRET) spectroscopy for probing sub-millisecond conformational dynamics of protein folding and binding of disordered proteins. We devise a scheme that uses single continuous-wave laser excitation of the donor instead of alternating excitation of the donor and one of the acceptors. This scheme alleviates photophysical problems of acceptors such as rapid photobleaching, which is crucial for high time resolution experiments with elevated illumination intensity. Our method exploits the molecular species with one of the acceptors absent or photobleached, from which two-color FRET data is collected in the same experiment. We show that three FRET efficiencies and kinetic parameters can be determined without alternating excitation from a global maximum likelihood analysis of two-color and three-color photon trajectories. We implement co-parallelization of CPU-GPU processing, which leads to a significant reduction of the likelihood calculation time for efficient parameter determination.

Sequence-Dependent Correlated Segments in the Intrinsically Disordered Region of ChiZ

How sequences of intrinsically disordered proteins (IDPs) code for their conformational dynamics is poorly understood. Here, we combined NMR spectroscopy, small-angle X-ray scattering (SAXS), and molecular dynamics (MD) simulations to characterize the conformations and dynamics of ChiZ1-64. MD simulations, first validated by SAXS and secondary chemical shift data, found scant α-helices or β-strands but a considerable propensity for polyproline II (PPII) torsion angles. Importantly, several blocks of residues (e.g., 11–29) emerge as “correlated segments”, identified by their frequent formation of PPII stretches, salt bridges, cation-π interactions, and sidechain-backbone hydrogen bonds. NMR relaxation experiments showed non-uniform transverse relaxation rates (R₂s) and nuclear Overhauser enhancements (NOEs) along the sequence (e.g., high R₂s and NOEs for residues 11–14 and 23–28). MD simulations further revealed that the extent of segmental correlation is sequence-dependent; segments where internal interactions are more prevalent manifest elevated “collective” motions on the 5–10 ns timescale and suppressed local motions on the sub-ns timescale. Amide proton exchange rates provides corroboration, with residues in the most correlated segment exhibiting the highest protection factors. We propose the correlated segment as a defining feature for the conformations and dynamics of IDPs.

Disordered proteins follow diverse transition paths as they fold and bind to a partner

Transition paths of macromolecular conformational changes such as protein folding are predicted to be heterogeneous. However, experimental characterization of the diversity of transition paths is extremely challenging because it requires measuring more than one distance during individual transitions. In this work, we used fast three-color single-molecule Förster resonance energy transfer spectroscopy to obtain the distribution of binding transition paths of a disordered protein. About half of the transitions follow a path involving strong non-native electrostatic interactions, resulting in a transition time of 300 to 800 microseconds. The remaining half follow more diverse paths characterized by weaker electrostatic interactions and more than 10 times shorter transition path times. The chain flexibility and non-native interactions make diverse binding pathways possible, allowing disordered proteins to bind faster than folded proteins.

Tau protein- induced sequestration of the eukaryotic ribosome: Implications in neurodegenerative disease

The human tau is a microtubule-associated intrinsically unstructured protein that forms intraneuronal cytotoxic deposits in neurodegenerative diseases, like tauopathies. Recent studies indicate that in Alzheimer's disease, ribosomal dysfunction might be a crucial event in the disease pathology. Our earlier studies had demonstrated that amorphous protein aggregation in the presence of ribosome can lead to sequestration of the ribosomal components. The present study aims at determining the effect of incubation of the full-length tau protein (Ht40) and its microtubule binding 4-repeat domain (K18) on the eukaryotic ribosome. Our in vitro studies show that incubation of Ht40 and the K18 tau variants with isolated non-translating yeast ribosome can induce a loss of ribosome physical integrity resulting in formation of tau-rRNA-ribosomal protein aggregates. Incubation with the tau protein variants also led to a disappearance of the peak indicating the ribosome profile of the HeLa cell lysate and suppression of translation in the human in vitro translation system. The incubation of tau protein with the ribosomal RNA leads to the formation of tau-rRNA aggregates. The effect of K18 on the yeast ribosome can be mitigated in the presence of cellular polyanions like heparin and tRNA, thereby indicating the electrostatic nature of the aggregation process.

Multisite reversible association in membranes and solutions: From non-Markovian to Markovian kinetics

The role of diffusion on the kinetics of reversible association to a macromolecule with two inequivalent sites is studied. Previously, we found that, in the simplest possible description, it is not sufficient to just renormalize the rate constants of chemical kinetics, but one must introduce direct transitions between the bound states in the kinetic scheme. The physical reason for this is that a molecule that just dissociated from one site can directly rebind to the other rather than diffuse away into the bulk. Such a simple description is not valid in two dimensions because reactants can never diffuse away into the bulk. In this work, we consider a variety of more sophisticated implementations of our recent general theory that are valid in both two and three dimensions. We compare the predicted time dependence of the concentrations for a wide range of parameters and establish the range of validity of various levels of the general theory.

Structural dynamics of P-type ATPase ion pumps

P-type ATPases transport ions across biological membranes against concentration gradients and are essential for all cells. They use the energy from ATP hydrolysis to propel large intramolecular movements, which drive vectorial transport of ions. Tight coordination of the motions of the pump is required to couple the two spatially distant processes of ion binding and ATP hydrolysis. Here, we review our current understanding of the structural dynamics of P-type ATPases, focusing primarily on Ca2+ pumps. We integrate different types of information that report on structural dynamics, primarily time-resolved fluorescence experiments including single-molecule Förster resonance energy transfer and molecular dynamics simulations, and interpret them in the framework provided by the numerous crystal structures of sarco/endoplasmic reticulum Ca2+-ATPase. We discuss the challenges in characterizing the dynamics of membrane pumps, and the likely impact of new technologies on the field.

Dynamic conformational flexibility and molecular interactions of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are highly flexible and undergo disorder to order transition upon binding. They are highly abundant in human proteomes and play critical roles in cell signaling and regulatory processes. This review mainly focuses on the dynamics of disordered proteins including their conformational heterogeneity, protein-protein interactions, and the phase transition of biomolecular condensates that are central to various biological functions. Besides, the role of RNA-mediated chaperones in protein folding and stability of IDPs were also discussed. Finally, we explored the dynamic binding interface of IDPs as novel therapeutic targets and the effect of small molecules on their interactions.

Transition path dynamics in the binding of intrinsically disordered proteins: A simulation study

Association of proteins and other biopolymers is a ubiquitous process in living systems. Recent single-molecule measurements probe the dynamics of association in unprecedented detail by measuring the properties of association transition paths, i.e., short segments of molecular trajectories between the time the proteins are close enough to interact and the formation of the final complex. Interpretation of such measurements requires adequate models for describing the dynamics of experimental observables. In an effort to develop such models, here we report a simulation study of the association dynamics of two oppositely charged, disordered polymers. We mimic experimental measurements by monitoring intermonomer distances, which we treat as "experimental reaction coordinates." While the dynamics of the distance between the centers of mass of the molecules is found to be memoryless and diffusive, the dynamics of the experimental reaction coordinates displays significant memory and can be described by a generalized Langevin equation with a memory kernel. We compute the most commonly measured property of transition paths, the distribution of the transition path time, and show that, despite the non-Markovianity of the underlying dynamics, it is well approximated as one-dimensional diffusion in the potential of mean force provided that an apparent value of the diffusion coefficient is used. This apparent value is intermediate between the slow (low frequency) and fast (high frequency) limits of the memory kernel. We have further studied how the mean transition path time depends on the ionic strength and found only weak dependence despite strong electrostatic attraction between the polymers.

Single-molecule FRET methods to study the dynamics of proteins at work

Feynman commented that "Everything that living things do can be understood in terms of the jiggling and wiggling of atoms". Proteins can jiggle and wiggle large structural elements such as domains and subunits as part of their functional cycles. Single-molecule fluorescence resonance energy transfer (smFRET) is an excellent tool to study conformational dynamics and decipher coordinated large-scale motions within proteins. smFRET methods introduced in recent years are geared toward understanding the time scales and amplitudes of function-related motions. This review discusses the methodology for obtaining and analyzing smFRET temporal trajectories that provide direct dynamic information on transitions between conformational states. It also introduces correlation methods that are useful for characterizing intramolecular motions. This arsenal of techniques has been used to study multiple molecular systems, from membrane proteins through molecular chaperones, and we examine some of these studies here. Recent exciting methodological novelties permit revealing very fast, submillisecond dynamics, whose relevance to protein function is yet to be fully grasped.

Features of molecular recognition of intrinsically disordered proteins via coupled folding and binding

The sequence-structure-function paradigm of proteins has been revolutionized by the discovery of intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs). In contrast to traditional ordered proteins, IDPs/IDRs are unstructured under physiological conditions. The absence of well-defined three-dimensional structures in the free state of IDPs/IDRs is fundamental to their function. Folding upon binding is an important mode of molecular recognition for IDPs/IDRs. While great efforts have been devoted to investigating the complex structures and binding kinetics and affinities, our knowledge on the binding mechanisms of IDPs/IDRs remains very limited. Here, we review recent advances on the binding mechanisms of IDPs/IDRs. The structures and kinetic parameters of IDPs/IDRs can vary greatly, and the binding mechanisms can be highly dependent on the structural properties of IDPs/IDRs. IDPs/IDRs can employ various combinations of conformational selection and induced fit in a binding process, which can be templated by the target and/or encoded by the IDP/IDR. Further studies should provide deeper insights into the molecular recognition of IDPs/IDRs and enable the rational design of IDP/IDR binding mechanisms in the future.

Polymer effects modulate binding affinities in disordered proteins

Structural disorder is widespread in regulatory protein networks. Weak and transient interactions render disordered proteins particularly sensitive to fluctuations in solution conditions such as ion and crowder concentrations. How this sensitivity alters folding coupled binding reactions, however, has not been fully understood. Here, we demonstrate that salt jointly modulates polymer properties and binding affinities of 5 disordered proteins from a transcription factor network. A combination of single-molecule Förster resonance energy transfer experiments, polymer theory, and molecular simulations shows that all 5 proteins expand with increasing ionic strengths due to Debye-Hückel charge screening. Simultaneously, pairwise affinities between the proteins increase by an order of magnitude within physiological salt limits. A quantitative analysis shows that 50% of the affinity increase can be explained by changes in the disordered state. Disordered state properties therefore have a functional relevance even if these states are not directly involved in biological functions. Numerical solutions of coupled binding equilibria with our results show that networks of homologous disordered proteins can function surprisingly robustly in fluctuating cellular environments, despite the sensitivity of its individual proteins.

Probing microscopic conformational dynamics in folding reactions by measuring transition paths

Transition paths comprise those parts of a folding trajectory where the molecule passes through the high-energy transition states separating folded and unfolded conformations. The transition states determine the folding kinetics and mechanism but are difficult to observe because of their brief duration. Single-molecule experiments have in recent years begun to characterize transition paths in folding reactions, allowing the microscopic conformational dynamics that occur as a molecule traverses the energy barriers to be probed directly. Here we review single-molecule fluorescence and force spectroscopy measurements of transition-path properties, including the time taken to traverse the paths, the local velocity along them, the path shapes, and the variability within these measurements reflecting differences between individual barrier crossings. We discuss how these measurements have been related to theories of folding as diffusion over an energy landscape to deduce properties such as the diffusion coefficient, and how they are being combined with simulations to obtain enhanced atomistic understanding of folding. The richly detailed information available from transition path measurements holds great promise for improved understanding of microscopic mechanisms in folding.

Brownian Dynamics Simulations of Biological Molecules

Brownian dynamics (BD) is a technique for carrying out computer simulations of physical systems that are driven by thermal fluctuations. Biological systems at the macromolecular and cellular level, while falling in the gap between well-established atomic-level models and continuum models, are especially suitable for such simulations. We present a brief history, examples of important biological processes that are driven by thermal motion, and those that have been profitably studied by BD. We also present some of the challenges facing developers of algorithms and software, especially in the attempt to simulate larger systems more accurately and for longer times.

Coupled Binding and Helix Formation Monitored by Synchrotron-Radiation Circular Dichroism

Intrinsically disordered proteins organize interaction networks in the cell in many regulation and signaling processes. These proteins often gain structure upon binding to their target proteins in multistep reactions involving the formation of both secondary and tertiary structure. To understand the interactions of disordered proteins, we need to understand the mechanisms of these coupled folding and binding reactions. We studied helix formation in the binding of the molten globule-like nuclear coactivator binding domain and the disordered interaction domain from activator of thyroid hormone and retinoid receptors. We demonstrate that helix formation in a rapid binding reaction can be followed by stopped-flow synchrotron-radiation circular dichroism (CD) spectroscopy and describe the design of such a beamline. Fluorescence-monitored binding experiments of activator of thyroid hormone and retinoid receptors and nuclear coactivator binding domain display several kinetic phases, including one concentration-independent phase, which is consistent with an intermediate stabilized at high ionic strength. Time-resolved CD experiments show that almost all helicity is formed upon initial association of the proteins or separated from the encounter complex by only a small energy barrier. Through simulation of mechanistic models, we show that the intermediate observed at high ionic strength likely involves a structural rearrangement with minor overall changes in helicity. Our experiments provide a benchmark for simulations of coupled binding reactions and demonstrate the feasibility of using synchrotron-radiation CD for mechanistic studies of protein-protein interactions.

Single-molecule fluorescence studies of intrinsically disordered proteins and liquid phase separation

Intrinsically disordered proteins (IDPs) are ubiquitous in proteomes and serve in a range of cellular functions including signaling, regulation, transport and enzyme function. IDP misfunction and aggregation are also associated with several diseases including neurodegenerative diseases and cancer. During the past decade, single-molecule methods have become popular for detailed biophysical and structural studies of these complex proteins. This work has included recent applications to cellular liquid-liquid phase separation (LLPS), relevant for functional dynamics of membraneless organelles such as the nucleolus and stress granules. In this concise review, we cover the conceptual motivations for development and application of single-molecule fluorescence methods for such IDP studies. We follow with a few key examples of systems and biophysical problems that have been addressed, and conclude with thoughts for emerging and future directions.

Exact Solutions for Distributions of First-Passage, Direct-Transit, and Looping Times in Symmetric Cusp Potential Barriers and Wells

For a particle diffusing in one dimension, the distribution of its first-passage time from point a to point b is determined by the durations of the particle trajectories that start from point a and are terminated as soon as they touch point b for the first time. Any such trajectory consists of looping and direct-transit segments. The latter is the final part of the trajectory that leaves point a and goes to point b without returning to point a. The rest of the trajectory is the looping segment that makes numerous loops which begin and end at the same point a without touching point b. In this article we discuss general relations between the first-passage time distribution and those for the durations of the two segments. These general relations allow us to find exact solutions for the Laplace transforms of the distributions of the first-passage, direct-transit, and looping times for transitions between two points separated by a symmetric cusp potential barrier or well of arbitrary height and depth, respectively. The obtained Laplace transforms are inverted numerically, leading to nontrivial dependences of the resulting distributions on the barrier height and the well depth.

Designed Mutations Alter the Binding Pathways of an Intrinsically Disordered Protein

Many cellular functions, including signaling and regulation, are carried out by intrinsically disordered proteins (IDPs) binding to their targets. Experimental and computational studies have now significantly advanced our understanding of these binding processes. In particular, IDPs that become structured upon binding typically follow a dock-and-coalesce mechanism, whereby the docking of one IDP segment initiates the process, followed by on-target coalescence of remaining IDP segments. Multiple dock-and-coalesce pathways may exist, but one may dominate, by relying on electrostatic attraction and molecular flexibility for fast docking and fast coalescing, respectively. Here we critically test this mechanistic understanding by designing mutations that alter the dominant pathway. This achievement marks an important step toward precisely manipulating IDP functions.

Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding

Conformational memory in single-molecule dynamics has attracted recent attention and, in particular, has been invoked as a possible explanation of some of the intriguing properties of transition paths observed in single-molecule force spectroscopy (SMFS) studies. Here we study one candidate for a non-Markovian model that can account for conformational memory, the generalized Langevin equation with a friction force that depends not only on the instantaneous velocity but also on the velocities in the past. The memory in this model is determined by a time-dependent friction memory kernel. We propose a method for extracting this kernel directly from an experimental signal and illustrate its feasibility by applying it to a generalized Rouse model of a SMFS experiment, where the memory kernel is known exactly. Using the same model, we further study how memory affects various statistical properties of transition paths observed in SMFS experiments and evaluate the performance of recent approximate analytical theories of non-Markovian dynamics of barrier crossing. We argue that the same type of analysis can be applied to recent single-molecule observations of transition paths in protein and DNA folding.