Single-Molecule FRET Spectroscopy and the Polymer Physics of Unfolded and Intrinsically Disordered Proteins

Quantification of Distributions of Local Proton Concentrations in Heterogeneous Soft Matter and Non-Anfinsen Biomacromolecules

A new method to quantitatively analyze heterogeneous distributions of local proton densities around paramagnetic centers in unstructured and weakly structured biomacromolecules and soft matter is introduced, and its feasibility is demonstrated on aqueous solutions of stochastically spin-labeled polysaccharides. This method is based on the pulse EPR experiment ih-RIDME (intermolecular hyperfine relaxation-induced dipolar modulation enhancement). Global analysis of a series of RIDME traces allows for a mathematically stable transformation of the time-domain data to the distribution of local proton concentrations. Two pulse sequences are proposed and tested, which combine the ih-RIDME block and the double-electron-electron resonance (DEER) experiment. Such experiments can be potentially used to correlate the local proton concentration with the macromolecular chain conformation. We anticipate an application of this approach in studies of intrinsically disordered proteins, biomolecular aggregates, and biomolecular condensates.

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Pulsed-Interleaved-Excitation Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy

We report on pulsed-interleaved-excitation two-dimensional fluorescence lifetime correlation spectroscopy (PIE 2D FLCS) to study biomolecular structural dynamics with high sensitivity and high time resolution using Förster resonance energy transfer (FRET). PIE 2D FLCS is an extension of 2D FLCS, which is a unique single-molecule fluorescence method that uses fluorescence lifetime information to distinguish different fluorescence species in equilibrium and resolves their interconversion dynamics with a submicrosecond time resolution. Because 2D FLCS has used only a single-color excitation so far, it was difficult to distinguish a very low-FRET (or zero-FRET) species from only donor-labeled species. We overcome this difficulty by implementing the PIE scheme (i.e., alternate excitation of the donor and acceptor dyes using two temporally interleaved excitations with different colors) to 2D FLCS, realizing two-color excitation and two-color fluorescence detection in 2D FLCS. After proof-of-principle PIE 2D FLCS analysis on the photon data synthesized with Monte Carlo simulation, we apply PIE 2D FLCS to a DNA-hairpin sample and show that this method readily distinguishes four fluorescent species, i.e., high-FRET, low-FRET, and two single-dye-labeled species. In addition, we show that PIE 2D FLCS can also quantitatively evaluate the contributions of the donor-acceptor spectral crosstalk, which often appears as artifacts in FRET studies and degrades the information obtained.

HYPK: A marginally disordered protein sensitive to charge decoration

Intrinsically disordered proteins (IDPs) that lie close to the empirical boundary separating IDPs and folded proteins in Uversky's charge-hydropathy plot may behave as "marginal IDPs" and sensitively switch conformation upon changes in environment (temperature, crowding, and charge screening), sequence, or both. In our search for such a marginal IDP, we selected Huntingtin-interacting protein K (HYPK) near that boundary as a candidate; PKIα, also near that boundary, has lower secondary structure propensity; and Crk1, just across the boundary on the folded side, has higher secondary structure propensity. We used a qualitative Förster resonance energy transfer-based assay together with circular dichroism to simultaneously probe global and local conformation. HYPK shows several unique features indicating marginality: a cooperative transition in end-to-end distance with temperature, like Crk1 and folded proteins, but unlike PKIα; enhanced secondary structure upon crowding, in contrast to Crk1 and PKIα; and a cross-over from salt-induced expansion to compaction at high temperature, likely due to a structure-to-disorder transition not seen in Crk1 and PKIα. We then tested HYPK's sensitivity to charge patterning by designing charge-flipped variants including two specific sequences with identical amino acid composition that markedly differ in their predicted size and response to salt. The experimentally observed trends, also including mutants of PKIα, verify the predictions from sequence charge decoration metrics. Marginal proteins like HYPK show features of both folded and disordered proteins that make them sensitive to physicochemical perturbations and structural control by charge patterning.

Experimental methods to study the structure and dynamics of intrinsically disordered regions in proteins

Eukaryotic proteins often feature long stretches of amino acids that lack a well-defined three-dimensional structure and are referred to as intrinsically disordered proteins (IDPs) or regions (IDRs). Although these proteins challenge conventional structure-function paradigms, they play vital roles in cellular processes. Recent progress in experimental techniques, such as NMR spectroscopy, single molecule FRET, high speed AFM and SAXS, have provided valuable insights into the biophysical basis of IDP function. This review discusses the advancements made in these techniques particularly for the study of disordered regions in proteins. In NMR spectroscopy new strategies such as 13C detection, non-uniform sampling, segmental isotope labeling, and rapid data acquisition methods address the challenges posed by spectral overcrowding and low stability of IDPs. The importance of various NMR parameters, including chemical shifts, hydrogen exchange rates, and relaxation measurements, to reveal transient secondary structures within IDRs and IDPs are presented. Given the high flexibility of IDPs, the review outlines NMR methods for assessing their dynamics at both fast (ps-ns) and slow (μs-ms) timescales. IDPs exert their functions through interactions with other molecules such as proteins, DNA, or RNA. NMR-based titration experiments yield insights into the thermodynamics and kinetics of these interactions. Detailed study of IDPs requires multiple experimental techniques, and thus, several methods are described for studying disordered proteins, highlighting their respective advantages and limitations. The potential for integrating these complementary techniques, each offering unique perspectives, is explored to achieve a comprehensive understanding of IDPs.

FRETpredict: a Python package for FRET efficiency predictions using rotamer libraries

Förster resonance energy transfer (FRET) is a widely-used and versatile technique for the structural characterization of biomolecules. Here, we introduce FRETpredict, an easy-to-use Python software to predict FRET efficiencies from ensembles of protein conformations. FRETpredict uses a rotamer library approach to describe the FRET probes covalently bound to the protein. The software efficiently and flexibly operates on large conformational ensembles such as those generated by molecular dynamics simulations to facilitate the validation or refinement of molecular models and the interpretation of experimental data. We provide access to rotamer libraries for many commonly used dyes and linkers and describe a general methodology to generate new rotamer libraries for FRET probes. We demonstrate the performance and accuracy of the software for different types of systems: a rigid peptide (polyproline 11), an intrinsically disordered protein (ACTR), and three folded proteins (HiSiaP, SBD2, and MalE). FRETpredict is open source (GPLv3) and is available at github.com/KULL-Centre/FRETpredict and as a Python PyPI package at pypi.org/project/FRETpredict .

Direct prediction of intrinsically disordered protein conformational properties from sequence

Intrinsically disordered regions (IDRs) are ubiquitous across all domains of life and play a range of functional roles. While folded domains are generally well described by a stable three-dimensional structure, IDRs exist in a collection of interconverting states known as an ensemble. This structural heterogeneity means that IDRs are largely absent from the Protein Data Bank, contributing to a lack of computational approaches to predict ensemble conformational properties from sequence. Here we combine rational sequence design, large-scale molecular simulations and deep learning to develop ALBATROSS, a deep-learning model for predicting ensemble dimensions of IDRs, including the radius of gyration, end-to-end distance, polymer-scaling exponent and ensemble asphericity, directly from sequences at a proteome-wide scale. ALBATROSS is lightweight, easy to use and accessible as both a locally installable software package and a point-and-click-style interface via Google Colab notebooks. We first demonstrate the applicability of our predictors by examining the generalizability of sequence-ensemble relationships in IDRs. Then, we leverage the high-throughput nature of ALBATROSS to characterize the sequence-specific biophysical behavior of IDRs within and between proteomes.

The molecular basis for cellular function of intrinsically disordered protein regions

Intrinsically disordered protein regions exist in a collection of dynamic interconverting conformations that lack a stable 3D structure. These regions are structurally heterogeneous, ubiquitous and found across all kingdoms of life. Despite the absence of a defined 3D structure, disordered regions are essential for cellular processes ranging from transcriptional control and cell signalling to subcellular organization. Through their conformational malleability and adaptability, disordered regions extend the repertoire of macromolecular interactions and are readily tunable by their structural and chemical context, making them ideal responders to regulatory cues. Recent work has led to major advances in understanding the link between protein sequence and conformational behaviour in disordered regions, yet the link between sequence and molecular function is less well defined. Here we consider the biochemical and biophysical foundations that underlie how and why disordered regions can engage in productive cellular functions, provide examples of emerging concepts and discuss how protein disorder contributes to intracellular information processing and regulation of cellular function.

DNA binding redistributes activation domain ensemble and accessibility in pioneer factor Sox2

More than 1600 human transcription factors orchestrate the transcriptional machinery to control gene expression and cell fate. Their function is conveyed through intrinsically disordered regions (IDRs) containing activation or repression domains but lacking quantitative structural ensemble models prevents their mechanistic decoding. Here we integrate single-molecule FRET and NMR spectroscopy with molecular simulations showing that DNA binding can lead to complex changes in the IDR ensemble and accessibility. The C-terminal IDR of pioneer factor Sox2 is highly disordered but its conformational dynamics are guided by weak and dynamic charge interactions with the folded DNA binding domain. Both DNA and nucleosome binding induce major rearrangements in the IDR ensemble without affecting DNA binding affinity. Remarkably, interdomain interactions are redistributed in complex with DNA leading to variable exposure of two activation domains critical for transcription. Charged intramolecular interactions allowing for dynamic redistributions may be common in transcription factors and necessary for sensitive tuning of structural ensembles.

Magnetic tweezers characterization of the entropic elasticity of intrinsically disordered proteins and peptoids

Understanding the conformational behavior of biopolymers is essential to unlocking knowledge of their biophysical mechanisms and functional roles. Single-molecule force spectroscopy can provide a unique perspective on this by exploiting entropic elasticity to uncover key biopolymer structural parameters. A particularly powerful approach involves the use of magnetic tweezers, which can easily generate lower stretching forces (0.1-20 pN). For forces at the low end of this range, the elastic response of biopolymers is sensitive to excluded volume effects, and they can be described by Pincus blob elasticity model that allow robust extraction of the Flory polymer scaling exponent. Here, we detail protocols for the use of magnetic tweezers for force-extension measurements of intrinsically disordered proteins and peptoids. We also discuss procedures for fitting low-force elastic curves to the predictions of polymer physics models to extract key conformational parameters.

Fine structures of intrinsically disordered proteins

We report simulation studies of 33 single intrinsically disordered proteins (IDPs) using coarse-grained bead-spring models where interactions among different amino acids are introduced through a hydropathy matrix and additional screened Coulomb interaction for the charged amino acid beads. Our simulation studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLoS Comput. Biol. 14, e1005941 (2018); Tesei et al. Proc. Natl. Acad. Sci. U. S. A. 118, e2111696118 (2021)] and the comparison with the existing experimental data indicate an optimal interaction parameter ϵ = 0.1 and 0.2 kcal/mol for the HPS1 and HPS2 hydropathy scales. We use these best-fit parameters to investigate both the universal aspects as well as the fine structures of the individual IDPs by introducing additional characteristics. (i) First, we investigate the polymer-specific scaling relations of the IDPs in comparison to the universal scaling relations [Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers. By studying the scaled end-to-end distances ⟨RN2⟩/(2Lℓp) and the scaled transverse fluctuations l̃⊥2=⟨l⊥2⟩/L, we demonstrate that IDPs are broadly characterized with a Flory exponent of ν ≃ 0.56 with the conclusion that conformations of the IDPs interpolate between Gaussian and self-avoiding random walk chains. Then, we introduce (ii) Wilson charge index (W) that captures the essential features of charge interactions and distribution in the sequence space and (iii) a skewness index (S) that captures the finer shape variation of the gyration radii distributions as a function of the net charge per residue and charge asymmetry parameter. Finally, our study of the (iv) variation of ⟨Rg⟩ as a function of salt concentration provides another important metric to bring out finer characteristics of the IDPs, which may carry relevant information for the origin of life.

Single-molecule-binding studies of antivirals targeting the hepatitis C virus core protein

IMPORTANCE

The hepatitis C virus is associated with nearly 300,000 deaths annually. At the core of the virus is an RNA-protein complex called the nucleocapsid, which consists of the viral genome and many copies of the core protein. Because the assembly of the nucleocapsid is a critical step in viral replication, a considerable amount of effort has been devoted to identifying antiviral therapeutics that can bind to the core protein and disrupt assembly. Although several candidates have been identified, little is known about how they interact with the core protein or how those interactions alter the structure and thus the function of this viral protein. Our work biochemically characterizes several of these binding interactions, highlighting both similarities and differences as well as strengths and weaknesses. These insights bolster the notion that this viral protein is a viable target for novel therapeutics and will help to guide future developments of these candidate antivirals.

Pincus blob elasticity in an intrinsically disordered protein

Understanding the dynamic structure of intrinsically disordered proteins (IDPs) is important to deciphering their biological functions. Here, we exploit precision entropic elasticity measurements to infer the conformational behavior of a model IDP construct formed from the disordered tail of the neurofilament low molecular weight protein. The IDP construct notably displays a low-force power-law elastic regime, consistent with the Pincus blob model, which allows direct extraction of the Flory exponent, [Formula: see text], from the force-extension relationship. We find [Formula: see text] increases with added denaturant, transitioning from a nearly ideal chain to a swollen chain in a manner quantitatively consistent with measurements of IDP dimensions from other experimental techniques. We suggest that measurements of entropic elasticity could be broadly useful in the study of IDP structure.

Nuclear magnetic resonance/single molecule fluorescence combinations to study dynamic protein systems

Many proteins require different structural states or conformations for function, and intrinsically disordered proteins, i.e. proteins without stable three-dimensional structure, are certainly an extreme. Single molecule fluorescence and nuclear magnetic resonance (NMR) spectroscopy are both exceptionally well suited to decipher and describe these states and their interconversion. Different time scales, from picoseconds to several milliseconds, can be addressed by both techniques. The length scales probed and the sample requirements (e.g. concentration, molecular weight, sample complexity) are, however, vastly different, making NMR and single molecule fluorescence an excellent combination for integrated studies. Here, we review recently undertaken approaches for the combined use of NMR and single molecule fluorescence to study protein dynamics.

Intrinsically disordered regions in TRPV2 mediate protein-protein interactions

Transient receptor potential (TRP) ion channels are gated by diverse intra- and extracellular stimuli leading to cation inflow (Na+, Ca2+) regulating many cellular processes and initiating organismic somatosensation. Structures of most TRP channels have been solved. However, structural and sequence analysis showed that ~30% of the TRP channel sequences, mainly the N- and C-termini, are intrinsically disordered regions (IDRs). Unfortunately, very little is known about IDR 'structure', dynamics and function, though it has been shown that they are essential for native channel function. Here, we imaged TRPV2 channels in membranes using high-speed atomic force microscopy (HS-AFM). The dynamic single molecule imaging capability of HS-AFM allowed us to visualize IDRs and revealed that N-terminal IDRs were involved in intermolecular interactions. Our work provides evidence about the 'structure' of the TRPV2 IDRs, and that the IDRs may mediate protein-protein interactions.

Time-resolved burst variance analysis

Quantifying biomolecular dynamics has become a major task of single-molecule fluorescence spectroscopy methods. In single-molecule Förster resonance energy transfer (smFRET), kinetic information is extracted from the stream of photons emitted by attached donor and acceptor fluorophores. Here, we describe a time-resolved version of burst variance analysis that can quantify kinetic rates at microsecond to millisecond timescales in smFRET experiments of diffusing molecules. Bursts are partitioned into segments with a fixed number of photons. The FRET variance is computed from these segments and compared with the variance expected from shot noise. By systematically varying the segment size, dynamics at different timescales can be captured. We provide a theoretical framework to extract kinetic rates from the decay of the FRET variance with increasing segment size. Compared to other methods such as filtered fluorescence correlation spectroscopy, recurrence analysis of single particles, and two-dimensional lifetime correlation spectroscopy, fewer photons are needed to obtain reliable timescale estimates, which reduces the required measurement time.

Visualizing single-molecule conformational transition and binding dynamics of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play crucial roles in cellular processes and hold promise as drug targets. However, the dynamic nature of IDPs remains poorly understood. Here, we construct a single-molecule electrical nanocircuit based on silicon nanowire field-effect transistors (SiNW-FETs) and functionalize it with an individual disordered c-Myc bHLH-LZ domain to enable label-free, in situ, and long-term measurements at the single-molecule level. We use the device to study c-Myc interaction with Max and/or small molecule inhibitors. We observe the self-folding/unfolding process of c-Myc and reveal its interaction mechanism with Max and inhibitors through ultrasensitive real-time monitoring. We capture a relatively stable encounter intermediate ensemble of c-Myc during its transition from the unbound state to the fully folded state. The c-Myc/Max and c-Myc/inhibitor dissociation constants derived are consistent with other ensemble experiments. These proof-of-concept results provide an understanding of the IDP-binding/folding mechanism and represent a promising nanotechnology for IDP conformation/interaction studies and drug discovery.

SOURSOP: A Python Package for the Analysis of Simulations of Intrinsically Disordered Proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite simulation analysis of unfolded regions of proteins (SOURSOP), an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

Novel mechanisms of MITF regulation and melanoma predisposition identified in a mouse suppressor screen

MITF, a basic-Helix-Loop-Helix Zipper (bHLHZip) transcription factor, plays vital roles in melanocyte development and functions as an oncogene. To explore MITF regulation and its role in melanoma, we conducted a genetic screen for suppressors of the Mitf-associated pigmentation phenotype. An intragenic Mitf mutation was identified, leading to termination of MITF at the K316 SUMOylation site and loss of the C-end intrinsically disordered region (IDR). The resulting protein is more nuclear but less stable than wild-type MITF and retains DNA-binding ability. Interestingly, as a dimer, it can translocate wild-type and mutant MITF partners into the nucleus, improving its own stability and ensuring an active nuclear MITF supply. Interactions between K316 SUMOylation and S409 phosphorylation sites across monomers largely explain the observed effects. Notably, the recurrent melanoma-associated E318K mutation in MITF, which affects K316 SUMOylation, also alters protein regulation in concert with S409, unraveling a novel regulatory mechanism with unexpected disease insights.

Protein aggregation and neurodegenerative disease: Structural outlook for the novel therapeutics

Before the controversial approval of humanized monoclonal antibody lecanemab, which binds to the soluble amyloid-β protofibrils, all the treatments available earlier, for Alzheimer's disease (AD) were symptomatic. The researchers are still struggling to find a breakthrough in AD therapeutic medicine, which is partially attributable to lack in understanding of the structural information associated with the intrinsically disordered proteins and amyloids. One of the major challenges in this area of research is to understand the structural diversity of intrinsically disordered proteins under in vitro conditions. Therefore, in this review, we have summarized the in vitro applications of biophysical methods, which are aimed to shed some light on the heterogeneity, pathogenicity, structures and mechanisms of the intrinsically disordered protein aggregates associated with proteinopathies including AD. This review will also rationalize some of the strategies in modulating disease-relevant pathogenic protein entities by small molecules using structural biology approaches and biophysical characterization. We have also highlighted tools and techniques to simulate the in vivo conditions for native and cytotoxic tau/amyloids assemblies, urge new chemical approaches to replicate tau/amyloids assemblies similar to those in vivo conditions, in addition to designing novel potential drugs.

Single-molecule FRET and molecular diffusion analysis characterize stable oligomers of amyloid-β 42 of extremely low population

Soluble oligomers produced during protein aggregation have been thought to be toxic species causing various diseases. Characterization of these oligomers is difficult because oligomers are a heterogeneous mixture, which is not readily separable, and may appear transiently during aggregation. Single-molecule spectroscopy can provide valuable information by detecting individual oligomers, but there have been various problems in determining the size and concentration of oligomers. In this work, we develop and use a method that analyzes single-molecule fluorescence burst data of freely diffusing molecules in solution based on molecular diffusion theory and maximum likelihood method. We demonstrate that the photon count rate, diffusion time, population, and Förster resonance energy transfer (FRET) efficiency can be accurately determined from simulated data and the experimental data of a known oligomerization system, the tetramerization domain of p53. We used this method to characterize the oligomers of the 42-residue amyloid-β (Aβ42) peptide. Combining peptide incubation in a plate reader and single-molecule free-diffusion experiments allows for the detection of stable oligomers appearing at various stages of aggregation. We find that the average size of these oligomers is 70-mer and their overall population is very low, less than 1 nM, in the early and middle stages of aggregation of 1 µM Aβ42 peptide. Based on their average size and long diffusion time, we predict the oligomers have a highly elongated rod-like shape.

Extreme dynamics in a biomolecular condensate

Proteins and nucleic acids can phase-separate in the cell to form concentrated biomolecular condensates^1-4. The functions of condensates span many length scales: they modulate interactions and chemical reactions at the molecular scale⁵, organize biochemical processes at the mesoscale⁶ and compartmentalize cells⁴. Understanding the underlying mechanisms of these processes will require detailed knowledge of the rich dynamics across these scales⁷. The mesoscopic dynamics of biomolecular condensates have been extensively characterized⁸, but their behaviour at the molecular scale has remained more elusive. Here, as an example of biomolecular phase separation, we study complex coacervates of two highly and oppositely charged disordered human proteins⁹. Their dense phase is 1,000 times more concentrated than the dilute phase, and the resulting percolated interaction network¹⁰ leads to a bulk viscosity 300 times greater than that of water. However, single-molecule spectroscopy optimized for measurements within individual droplets reveals that at the molecular scale, the disordered proteins remain exceedingly dynamic, with their chain configurations interconverting on submicrosecond timescales. Massive all-atom molecular dynamics simulations reproduce the experimental observations and explain this apparent discrepancy: the underlying interactions between individual charged side chains are short-lived and exchange on a pico- to nanosecond timescale. Our results indicate that, despite the high macroscopic viscosity of phase-separated systems, local biomolecular rearrangements required for efficient reactions at the molecular scale can remain rapid.

Analysis of photon trajectories from diffusing single molecules

In single-molecule free diffusion experiments, molecules spend most of the time outside a laser spot and generate bursts of photons when they diffuse through the focal spot. Only these bursts contain meaningful information and, therefore, are selected using physically reasonable criteria. The analysis of the bursts must take into account the precise way they were chosen. We present new methods that allow one to accurately determine the brightness and diffusivity of individual molecule species from the photon arrival times of selected bursts. We derive analytical expressions for the distribution of inter-photon times (with and without burst selection), the distribution of the number of photons in a burst, and the distribution of photons in a burst with recorded arrival times. The theory accurately treats the bias introduced due to the burst selection criteria. We use a Maximum Likelihood (ML) method to find the molecule's photon count rate and diffusion coefficient from three kinds of data, i.e., the bursts of photons with recorded arrival times (burstML), inter-photon times in bursts (iptML), and the numbers of photon counts in a burst (pcML). The performance of these new methods is tested on simulated photon trajectories and on an experimental system, the fluorophore Atto 488.

The Analytical Flory Random Coil Is a Simple-to-Use Reference Model for Unfolded and Disordered Proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory random coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google Colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Probing the conformational dynamics of thiol-isomerases using non-canonical amino acids and single-molecule FRET

Disulfide bonds drive protein correct folding, prevent protein aggregation, and stabilize three-dimensional structures of proteins and their assemblies. Dysregulation of this activity leads to several disorders, including cancer, neurodegeneration, and thrombosis. A family of 20+ enzymes, called thiol-isomerases (TIs), oversee this process in the endoplasmic reticulum of human cells to ensure efficacy and accuracy. While the biophysical and biochemical properties of cysteine residues are well-defined, our structural knowledge of how TIs select, interact and process their substrates remains poorly understood. How TIs structurally and functionally respond to changes in redox environment and other post-translational modifications remain unclear, too. We recently developed a workflow for site-specific incorporation of non-canonical amino acids into protein disulfide isomerase (PDI), the prototypical member of TIs. Combined with click chemistry, this strategy enabled us to perform single-molecule biophysical studies of PDI under various solution conditions. This paper details protocols and discusses challenges in performing these experiments. We expect this approach, combined with other emerging technologies in single-molecule biophysics and structural biology, to facilitate the exploration of the mechanisms by which TIs carry out their fascinating but poorly understood roles in humans, especially in the context of thrombosis.

Structural Preferences Shape the Entropic Force of Disordered Protein Ensembles

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and exist in a dynamic conformational ensemble instead of a native, well-folded structure. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in these ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function. But how the magnitude of this force depends on IDR sequence remains unexplored. Here, we use all-atom simulations to analyze how structural preferences in IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force: compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate the IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 μs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 μs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

Interaction of the tau fibrils with the neuronal membrane

Tau proteins are recently gaining a lot of interest due to their active role in causing a range of tauopathies. Molecular mechanisms underlying the tau interaction with the neuronal membrane are hitherto unknown and difficult to characterize using experimental methods. Using the cryo-EM structure of the tau-fibrils we have used atomistic molecular dynamics simulation to model the tau fibril and neuronal membrane interaction using explicit solvation. The dynamics and structural characteristics of the tau fibril with the neuronal membrane are compared to the tau fibril in the aqueous phase to corroborate the effect of the neuronal membrane in the tau structure. Tau fibrils have been modelled using CHARMM-36m force field and the six component neuronal membrane composition is taken from the earlier simulation results. The timescale conceivable in our molecular dynamics simulations is of the order of microseconds which captures the onset of the interaction of the tau fibrils with the neuronal membrane. This interaction is found to impact the tau pathogenesis that finally causes neuronal toxicity. Our study initiates the understanding of tau conformational ensemble in the presence of neuronal membrane and sheds the light on the significant tau-membrane interactions.

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.

Fast Motions Dominate Dynamics of Intrinsically Disordered Tau Protein at High Temperatures

Reorientational dynamics of intrinsically disordered proteins (IDPs) contain multiple motions often clustered around three motional modes: ultrafast librational motions of amide groups, fast local backbone conformational fluctuations and slow chain segmental motions. This dynamic picture is mainly based on ¹⁵ N NMR relaxation studies of IDPs at relatively low temperatures where the amide-water proton exchange rates are sufficiently small. Less is known, however, about the dynamics of IDPs at more physiological temperatures. Here, we investigate protein dynamics in a 441-residue long IDP, tau protein, in the temperature range from 0-25 °C, using ¹⁵ N NMR relaxation rates and spectral density analysis. While at these temperatures relaxation rates are still better described in terms of amide group librational motions, local backbone dynamics and chain segmental motions, the temperature-dependent trend of spectral densities suggests that the timescales of fast backbone conformational fluctuations and slower chain segmental motions might become inseparable at higher temperatures. Our data demonstrate the remarkable dynamic plasticity of this prototypical IDP and highlight the need for dynamic studies of IDPs at multiple temperatures.

Relaxation dynamics measure the aggregation propensity of amyloid-β and its mutants

Atomistic molecular dynamics simulations are employed to investigate the global and segmental relaxation dynamics of the amyloid-β protein and its causative and protective mutants. Amyloid-β exhibits significant global/local dynamics that span a broad range of length and time scales due to its intrinsically disordered nature. The relaxation dynamics of the amyloid-β protein and its mutants is quantitatively correlated with its experimentally measured aggregation propensity. The protective mutant has slower relaxation dynamics, whereas the causative mutants exhibit faster global dynamics compared with that of the wild-type amyloid-β. The local dynamics of the amyloid-β protein or its mutants is governed by a complex interplay of the charge, hydrophobicity, and change in the molecular mass of the mutated residue.

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.

The analytical Flory random coil is a simple-to-use reference model for unfolded and disordered proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory Random Coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

SOURSOP: A Python package for the analysis of simulations of intrinsically disordered proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite SOURSOP, an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

FRETpredict: A Python package for FRET efficiency predictions using rotamer libraries

Here, we introduce FRETpredict, a Python software program to predict FRET efficiencies from ensembles of protein conformations. FRETpredict uses an established Rotamer Library Approach to describe the FRET probes covalently bound to the protein. The software efficiently operates on large conformational ensembles such as those generated by molecular dynamics simulations to facilitate the validation or refinement of molecular models and the interpretation of experimental data. We demonstrate the performance and accuracy of the software for different types of systems: a relatively structured peptide (polyproline 11), an intrinsically disordered protein (ACTR), and three folded proteins (HiSiaP, SBD2, and MalE). We also describe a general approach to generate new rotamer libraries for FRET probes of interest. FRETpredict is open source (GPLv3) and is available at github.com/KULL-Centre/FRETpredict and as a Python PyPI package at pypi.org/project/FRETpredict.

Structural preferences shape the entropic force of disordered protein ensembles

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and instead of a native, well-folded structure exist in a dynamic conformational ensemble. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in IDR ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function, but how the magnitude of this force depends on the IDR sequence remains unexplored. Here we use all-atom simulations to analyze how structural preferences encoded in dozens of IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force and that compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

Effects of Sequence Composition, Patterning and Hydrodynamics on the Conformation and Dynamics of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) perform diverse functions in cellular organization, transport and signaling. Unlike the well-defined structures of the classical natively folded proteins, IDPs and IDRs dynamically span large conformational and structural ensembles. This dynamic disorder impedes the study of the relationship between the amino acid sequences of the IDPs and their spatial structures and dynamics, with different experimental techniques often offering seemingly contradictory results. Although experimental and theoretical evidence indicates that some IDP properties can be understood based on their average biophysical properties and amino acid composition, other aspects of IDP function are dictated by the specifics of the amino acid sequence. We investigate the effects of several key variables on the dimensions and the dynamics of IDPs using coarse-grained polymer models. We focus on the sequence "patchiness" informed by the sequence and biophysical properties of different classes of IDPs-and in particular FG nucleoporins of the nuclear pore complex (NPC). We show that the sequence composition and patterning are well reflected in the global conformational variables such as the radius of gyration and hydrodynamic radius, while the end-to-end distance and dynamics are highly sequence-specific. We find that in good solvent conditions highly heterogeneous sequences of IDPs can be well mapped onto averaged minimal polymer models for the purpose of prediction of the IDPs dimensions and dynamic relaxation times. The coarse-grained simulations are in a good agreement with the results of atomistic MD. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for the further applications of mesoscopic models of FG nucleoporins and IDPs more broadly.

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.

Illuminating Intrinsically Disordered Proteins with Integrative Structural Biology

Intense study of intrinsically disordered proteins (IDPs) did not begin in earnest until the late 1990s when a few groups, working independently, convinced the community that these 'weird' proteins could have important functions. Over the past two decades, it has become clear that IDPs play critical roles in a multitude of biological phenomena with prominent examples including coordination in signaling hubs, enabling gene regulation, and regulating ion channels, just to name a few. One contributing factor that delayed appreciation of IDP functional significance is the experimental difficulty in characterizing their dynamic conformations. The combined application of multiple methods, termed integrative structural biology, has emerged as an essential approach to understanding IDP phenomena. Here, we review some of the recent applications of the integrative structural biology philosophy to study IDPs.

Unravelling the microscopic characteristics of intrinsically disordered proteins upon liquid–liquid phase separation

Biomolecular condensate formation via liquid–liquid phase separation (LLPS) has emerged as a ubiquitous mechanism underlying the spatiotemporal organization of biomolecules in the cell. These membraneless condensates form and disperse dynamically in response to environmental stimuli. Growing evidence indicates that the liquid-like condensates not only play functional physiological roles but are also implicated in a wide range of human diseases. As a major component of biomolecular condensates, intrinsically disordered proteins (IDPs) are intimately involved in the LLPS process. During the last decade, great efforts have been made on the macroscopic characterization of the physicochemical properties and biological functions of liquid condensates both in vitro and in the cellular context. However, characterization of the conformations and interactions at the molecular level within phase-separated condensates is still at an early stage. In the present review, we summarize recent biophysical studies investigating the intramolecular conformational changes of IDPs upon LLPS and the intermolecular clustering of proteins undergoing LLPS, with a particular focus on single-molecule fluorescence detection. We also discuss how these microscopic features are linked to the macroscopic phase transitions that are relevant to the physiological and pathological roles of the condensates.

Molecular Origin of Internal Friction in Intrinsically Disordered Proteins

Protein folding and dynamics are controlled by an interplay of thermal and viscosity effects. The effect of viscous drag through the solvent molecules is described by the classic Kramers theory in the high friction limit, which considers the dampening of the reactant molecules in the solution and quantifies the dependence of the reaction rate on the frictional drag. In addition to the external energy dissipation originating from the surrounding solvent molecules, there is an additional mode of internal energy dissipative force operative within the polypeptide chain reflecting the internal resistance of the chain to its conformational alterations. This dry, solvent-independent intrinsic frictional drag is termed internal friction. In the case of natively folded proteins, the physical origin of internal friction is primarily attributed to the intrachain interactions or other nonnative interactions in their compact states. However, the molecular origin of internal friction in intrinsically disordered proteins (IDPs) remains elusive.In this Account, we address this fundamental issue: what are the principal drivers of viscosity-independent (dry) friction in highly solvated, expanded, conformationally flexible, rapidly fluctuating IDPs that do not possess persistent intrachain interactions? IDPs exhibit diffusive conformational dynamics that is predominantly dominated by the segmental motion of the backbone arising due to the dihedral rotations in the Ramachandran Φ-Ψ space. The physical origin of friction in a complex biopolymeric system such as IDPs can be described by classic polymer models, namely, Rouse/Zimm models with internal friction. These one-dimensional models do not invoke torsional fluctuation components. Kuhn's classic description includes the connection between internal friction and microscopic dihedral hopping. Based on our time-resolved fluorescence anisotropy results, we describe that the sequence-dependent, collective, short-range backbone dihedral rotations govern localized internal friction in an archetypal IDP, namely, α-synuclein. The highly sensitive, residue-specific fluorescence depolarization kinetics offers a potent methodology to characterize and quantify the directional decorrelation engendered due to the short-range dihedral relaxation of the polypeptide backbone in the dihedral space. We utilized this characteristic relaxation time scale as our dynamic readout to quantify the site-specific frictional component. Our linear viscosity-dependent model of torsional relaxation time scale furnished a finite nonzero time constant at the zero solvent viscosity representing the solvent-independent internal friction. These results unveil the effect of the degree of dihedral restraining parameter on the internal friction component by showing that a restrained proline residue imparts higher torsional stiffness in the chain segments and, therefore, exhibits higher internal friction. This Account sheds light on the molecular underpinning of the sequence-specific internal friction in IDPs and will be of interest to unmask the role of internal friction in a diverse range of biomolecular processes involving binding-induced folding, allosteric interaction, protein misfolding and aggregation, and biomolecular condensation via phase separation.

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.

Guide to studying intrinsically disordered proteins by high-speed atomic force microscopy

Intrinsically disordered proteins (IDPs) are partially or entirely disordered. Their intrinsically disordered regions (IDRs) dynamically explore a wide range of structural space by their highly flexible nature. Due to this distinct feature largely different from structured proteins, conventional structural analyses relying on ensemble averaging is unsuitable for characterizing the dynamic structure of IDPs. Therefore, single-molecule measurement tools have been desired in IDP studies. High-speed atomic force microscopy (HS-AFM) is a unique tool that allows us to directly visualize single biomolecules at 2-3 nm lateral and ∼ 0.1 nm vertical spatial resolution, and at sub-100 ms temporal resolution under near physiological conditions, without any chemical labeling. HS-AFM has been successfully used not only to characterize the shape and motion of IDP molecules but also to visualize their function-related dynamics. In this article, after reviewing the principle and current performances of HS-AFM, we describe experimental considerations in the HS-AFM imaging of IDPs and methods to quantify molecular features from captured images. Finally, we outline recent HS-AFM imaging studies of IDPs.

Effect of Charge Distribution on the Dynamics of Polyampholytic Disordered Proteins

The stability and physiological function of many biomolecular coacervates depend on the structure and dynamics of intrinsically disordered proteins (IDPs) that typically contain a significant fraction of charged residues. Although the effect of relative arrangement of charged residues on IDP conformation is a well-studied problem, the associated changes in dynamics are far less understood. In this work, we systematically interrogate the effects of charge distribution on the chain-level and segmental dynamics of polyampholytic IDPs in dilute solutions. We study a coarse-grained model polyampholyte consisting of an equal fraction of two oppositely charged residues (glutamic acid and lysine) that undergoes a transition from an ideal chain-like conformation for uniformly charge-patterned sequences to a semi-compact conformation for highly charge-segregated sequences. Changes in the chain-level dynamics with increasing charge segregation correlate with changes in conformation. The chain-level and segmental dynamics conform to simple homopolymer models for uniformly charge-patterned sequences but deviate with increasing charge segregation, both in the presence and absence of hydrodynamic interactions. We discuss the significance of these findings, obtained for a model polyampholyte, in the context of a charge-rich intrinsically disordered region of the naturally occurring protein LAF-1. Our findings have important implications for understanding the effects of charge patterning on the dynamics of polyampholytic IDPs in dilute conditions using polymer scaling theories.

Developing Bonded Potentials for a Coarse-Grained Model of Intrinsically Disordered Proteins

Recent advances in residue-level coarse-grained (CG) computational models have enabled molecular-level insights into biological condensates of intrinsically disordered proteins (IDPs), shedding light on the sequence determinants of their phase separation. The existing CG models that treat protein chains as flexible molecules connected via harmonic bonds cannot populate common secondary-structure elements. Here, we present a CG dihedral angle potential between four neighboring beads centered at Cα atoms to faithfully capture the transient helical structures of IDPs. In order to parameterize and validate our new model, we propose Cα-based helix assignment rules based on dihedral angles that succeed in reproducing the atomistic helicity results of a polyalanine peptide and folded proteins. We then introduce sequence-dependent dihedral angle potential parameters (εd) and use experimentally available helical propensities of naturally occurring 20 amino acids to find their optimal values. The single-chain helical propensities from the CG simulations for commonly studied prion-like IDPs are in excellent agreement with the NMR-based α-helix fraction, demonstrating that the new HPS-SS model can accurately produce structural features of IDPs. Furthermore, this model can be easily implemented for large-scale assembly simulations due to its simplicity.

Far-field lithography through saturated resonance energy transfer

A method based on resonance energy transfer in a donor-acceptor pair is proposed for writing three-dimensional features in the far field. The saturation of the energy transfer between the donor-acceptor pair induces a nonlinear intensity response in the radical population. This optical nonlinearity can enable three-dimensional nanofabrication without requiring the use of the ultrafast excitation that is compulsory for non-resonant multiphoton excitation. Addition of a second, spatially shaped beam can enable nanopatterning far below the diffraction limit.

Reduction of protein disulfide isomerase results in open conformations and stimulates dynamic exchange between structural ensembles

Human protein disulfide isomerase (PDI) is an essential redox-regulated enzyme required for oxidative protein folding. It comprises four thioredoxin domains, two catalytically active (a, a’) and two inactive (b, b’), organized to form a flexible abb’a’ U-shape. Snapshots of unbound oxidized and reduced PDI have been obtained by X-ray crystallography. Yet, how PDI’s structure changes in response to the redox environment and inhibitor binding remains controversial. Here, we used multiparameter confocal single-molecule FRET to track the movements of the two catalytic domains with high temporal resolution. We found that at equilibrium, PDI visits three structurally distinct conformational ensembles, two “open” (O₁ and O₂) and one “closed” (C). We show that the redox environment dictates the time spent in each ensemble and the rate at which they exchange. While oxidized PDI samples O₁, O₂, and C more evenly and in a slower fashion, reduced PDI predominantly populates O₁ and O₂ and exchanges between them more rapidly, on the submillisecond timescale. These findings were not expected based on crystallographic data. Using mutational analyses, we further demonstrate that the R300-W396 cation-π interaction and active site cysteines dictate, in unexpected ways, how the catalytic domains relocate. Finally, we show that irreversible inhibitors targeting the active sites of reduced PDI did not abolish these protein dynamics but rather shifted the equilibrium toward the closed ensemble. This work introduces a new structural framework that challenges current views of PDI dynamics, helps rationalize its multifaceted role in biology, and should be considered when designing PDI-targeted therapeutics.

The optimal docking strength for reversibly tethered kinases

Many kinases use reversible docking interactions to augment the specificity of their catalytic domains. Such docking interactions are often structurally independent of the catalytic domain, which allow for a flexible combination of modules in evolution and in bioengineering. The affinity of docking interactions spans several orders of magnitude. This led us to ask how the affinity of the docking interaction affects enzymatic activity and how to pick the optimal interaction module to complement a given substrate. Here, we develop equations that predict the optimal binding strength of a kinase docking interaction and validate it using numerical simulations and steady-state phosphorylation kinetics for tethered protein kinase A. We show that a kinase-substrate pair has an optimum docking strength that depends on their enzymatic constants, the tether architecture, the substrate concentration, and the kinetics of the docking interactions. We show that a reversible tether enhances phosphorylation rates most when 1) the docking strength is intermediate, 2) the substrate is nonoptimal, 3) the substrate concentration is low, 4) the docking interaction has rapid exchange kinetics, and 5) the tether optimizes the effective concentration of the intramolecular reaction. This work serves as a framework for interpreting mutations in kinase docking interactions and as a design guide for engineering enzyme scaffolds.