Precision DEER Distances from Spin-Label Ensemble Refinement

Encoding prior knowledge in ensemble refinement

The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we propose how to set the exchange rate a priori to properly balance this trade-off. We focus on gentle ensemble refinement, where the difference between the potential energy surfaces of the reference and refined models is small on a thermal scale. By relating the variance of this energy difference to the Kullback-Leibler divergence between the respective Boltzmann distributions, one can encode prior knowledge about energy uncertainties, i.e., force-field errors, in the exchange rate. The energy uncertainty is defined in the space of observables and depends on their type and number and on the thermodynamic state. We highlight the relation of gentle refinement to free energy perturbation theory. A balanced encoding of prior knowledge increases the quality and transparency of ensemble refinement. Our findings extend to non-Boltzmann distributions, where the uncertainty in energy becomes an uncertainty in information.

Hierarchical Assembly of Single-Stranded RNA

Single-stranded RNA (ssRNA) plays a major role in the flow of genetic information-most notably, in the form of messenger RNA (mRNA)-and in the regulation of biological processes. The highly dynamic nature of chains of unpaired nucleobases challenges structural characterizations of ssRNA by experiments or molecular dynamics (MD) simulations alike. Here, we use hierarchical chain growth (HCG) to construct ensembles of ssRNA chains. HCG assembles the structures of protein and nucleic acid chains from fragment libraries created by MD simulations. Applied to homo- and heteropolymeric ssRNAs of different lengths, we find that HCG produces structural ensembles that overall are in good agreement with diverse experiments, including nuclear magnetic resonance (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET). The agreement can be further improved by ensemble refinement using Bayesian inference of ensembles (BioEn). HCG can also be used to assemble RNA structures that combine base-paired and base-unpaired regions, as illustrated for the 5' untranslated region (UTR) of SARS-CoV-2 RNA.

chiLife: An open-source Python package for in silico spin labeling and integrative protein modeling

Here we introduce chiLife, a Python package for site-directed spin label (SDSL) modeling for electron paramagnetic resonance (EPR) spectroscopy, in particular double electron-electron resonance (DEER). It is based on in silico attachment of rotamer ensemble representations of spin labels to protein structures. chiLife enables the development of custom protein analysis and modeling pipelines using SDSL EPR experimental data. It allows the user to add custom spin labels, scoring functions and spin label modeling methods. chiLife is designed with integration into third-party software in mind, to take advantage of the diverse and rapidly expanding set of molecular modeling tools available with a Python interface. This article describes the main design principles of chiLife and presents a series of examples.

Structural ensembles of disordered proteins from hierarchical chain growth and simulation

Disordered proteins and nucleic acids play key roles in cellular function and disease. Here, we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. While atomistic molecular dynamics (MD) simulation has seen a lot of improvement in recent years, large-scale computing resources and careful validation are required to simulate full-length disordered biopolymers in solution. As a computationally efficient alternative, hierarchical chain growth (HCG) combines pre-sampled chain fragments in a statistically reproducible manner into ensembles of full-length atomically detailed biomolecular structures. Experimental data can be integrated during and after chain assembly. Applications to the neurodegeneration-linked proteins α-synuclein, tau, and TDP-43, including as condensate, illustrate the use of HCG. We conclude by highlighting the emerging connections to AI-based structural modeling including AlphaFold2.

Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure

The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

Intrinsically disordered proteins (IDPs) and multidomain proteins with flexible linkers show a high level of structural heterogeneity and are best described by ensembles consisting of multiple conformations with associated thermodynamic weights. Determining conformational ensembles usually involves the integration of biophysical experiments and computational models. In this review, we discuss current approaches to determine conformational ensembles of IDPs and multidomain proteins, including the choice of biophysical experiments, computational models used to sample protein conformations, models to calculate experimental observables from protein structure, and methods to refine ensembles against experimental data. We also provide examples of recent applications of integrative conformational ensemble determination to study IDPs and multidomain proteins and suggest future directions for research in the field.

Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å Cα RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.

DEER-PREdict: Software for efficient calculation of spin-labeling EPR and NMR data from conformational ensembles

Owing to their plasticity, intrinsically disordered and multidomain proteins require descriptions based on multiple conformations, thus calling for techniques and analysis tools that are capable of dealing with conformational ensembles rather than a single protein structure. Here, we introduce DEER-PREdict, a software program to predict Double Electron-Electron Resonance distance distributions as well as Paramagnetic Relaxation Enhancement rates from ensembles of protein conformations. DEER-PREdict uses an established rotamer library approach to describe the paramagnetic probes which are bound covalently to the protein.DEER-PREdict has been designed to operate efficiently on large conformational ensembles, such as those generated by molecular dynamics simulation, to facilitate the validation or refinement of molecular models as well as the interpretation of experimental data. The performance and accuracy of the software is demonstrated with experimentally characterized protein systems: HIV-1 protease, T4 Lysozyme and Acyl-CoA-binding protein. DEER-PREdict is open source (GPLv3) and available at github.com/KULL-Centre/DEERpredict and as a Python PyPI package pypi.org/project/DEERPREdict.

Cu2+-based distance measurements by pulsed EPR provide distance constraints for DNA backbone conformations in solution

Electron paramagnetic resonance (EPR) has become an important tool to probe conformational changes in nucleic acids. An array of EPR labels for nucleic acids are available, but they often come at the cost of long tethers, are dependent on the presence of a particular nucleotide or can be placed only at the termini. Site directed incorporation of Cu2+-chelated to a ligand, 2,2'dipicolylamine (DPA) is potentially an attractive strategy for site-specific, nucleotide independent Cu2+-labelling in DNA. To fully understand the potential of this label, we undertook a systematic and detailed analysis of the Cu2+-DPA motif using EPR and molecular dynamics (MD) simulations. We used continuous wave EPR experiments to characterize Cu2+ binding to DPA as well as optimize Cu2+ loading conditions. We performed double electron-electron resonance (DEER) experiments at two frequencies to elucidate orientational selectivity effects. Furthermore, comparison of DEER and MD simulated distance distributions reveal a remarkable agreement in the most probable distances. The results illustrate the efficacy of the Cu2+-DPA in reporting on DNA backbone conformations for sufficiently long base pair separations. This labelling strategy can serve as an important tool for probing conformational changes in DNA upon interaction with other macromolecules.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

High-resolution EPR distance measurements on RNA and DNA with the non-covalent Ǵ spin label

Pulsed electron paramagnetic resonance (EPR) experiments, among them most prominently pulsed electron-electron double resonance experiments (PELDOR/DEER), resolve the conformational dynamics of nucleic acids with high resolution. The wide application of these powerful experiments is limited by the synthetic complexity of some of the best-performing spin labels. The recently developed $\bf\acute{G}$ (G-spin) label, an isoindoline-nitroxide derivative of guanine, can be incorporated non-covalently into DNA and RNA duplexes via Watson-Crick base pairing in an abasic site. We used PELDOR and molecular dynamics (MD) simulations to characterize $\bf\acute{G}$, obtaining excellent agreement between experiments and time traces calculated from MD simulations of RNA and DNA double helices with explicitly modeled $\bf\acute{G}$ bound in two abasic sites. The MD simulations reveal stable hydrogen bonds between the spin labels and the paired cytosines. The abasic sites do not significantly perturb the helical structure. $\bf\acute{G}$ remains rigidly bound to helical RNA and DNA. The distance distributions between the two bound $\bf\acute{G}$ labels are not substantially broadened by spin-label motions in the abasic site and agree well between experiment and MD. $\bf\acute{G}$ and similar non-covalently attached spin labels promise high-quality distance and orientation information, also of complexes of nucleic acids and proteins.

Integrating Molecular Simulation and Experimental Data: A Bayesian/Maximum Entropy Reweighting Approach

We describe a Bayesian/Maximum entropy (BME) procedure and software to construct a conformational ensemble of a biomolecular system by integrating molecular simulations and experimental data. First, an initial conformational ensemble is constructed using, for example, Molecular Dynamics or Monte Carlo simulations. Due to potential inaccuracies in the model and finite sampling effects, properties predicted from simulations may not agree with experimental data. In BME we use the experimental data to refine the simulation so that the new conformational ensemble has the following properties: (1) the calculated averages are close to the experimental values taking uncertainty into account and (2) it maximizes the relative Shannon entropy with respect to the original simulation ensemble. The output of this procedure is a set of optimized weights that can be used to calculate other properties and distributions of these. Here, we provide a practical guide on how to obtain and use such weights, how to choose adjustable parameters and discuss shortcomings of the method.

CHARMM-GUI DEER facilitator for spin-pair distance distribution calculations and preparation of restrained-ensemble molecular dynamics simulations

The double electron-electron resonance (DEER) is a powerful structural biology technique to obtain distance information in the range of 18 to 80 å by measuring the dipolar coupling between two unpaired electron spins. The distance distributions obtained from the experiment provide valuable structural information about the protein in its native environment that can be exploited using restrained ensemble molecular dynamics (reMD) simulations. We present a new tool DEER Facilitator in CHARMM-GUI that consists of two modules Spin-Pair Distributor and reMD Prepper to setup simulations that utilize information from DEER experiments. Spin-Pair Distributor provides a web-based interface to calculate the spin-pair distance distribution of labeled sites in a protein using MD simulations. The calculated distribution can be used to guide the selection of the labeling sites in experiments as well as validate different protein structure models. reMD Prepper facilities the setup of reMD simulations using different types of spin labels in four different environments including vacuum, solution, micelle, and bilayer. The applications of these two modules are demonstrated with several test cases. Spin-Pair Distributor and reMD Prepper are available at http://www.charmm-gui.org/input/deer and http://www.charmm-gui.org/input/deerre. DEER Facilitator is expected to facilitate advanced biomolecular modeling and simulation, thereby leading to an improved understanding of the structure and dynamics of complex biomolecular systems based on experimental DEER data. © 2019 Wiley Periodicals, Inc.

Efficient Ensemble Refinement by Reweighting

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

Structural basis for functional interactions in dimers of SLC26 transporters

The SLC26 family of transporters maintains anion equilibria in all kingdoms of life. The family shares a 7 + 7 transmembrane segments inverted repeat architecture with the SLC4 and SLC23 families, but holds a regulatory STAS domain in addition. While the only experimental SLC26 structure is monomeric, SLC26 proteins form structural and functional dimers in the lipid membrane. Here we resolve the structure of an SLC26 dimer embedded in a lipid membrane and characterize its functional relevance by combining PELDOR/DEER distance measurements and biochemical studies with MD simulations and spin-label ensemble refinement. Our structural model reveals a unique interface different from the SLC4 and SLC23 families. The functionally relevant STAS domain is no prerequisite for dimerization. Characterization of heterodimers indicates that protomers in the dimer functionally interact. The combined structural and functional data define the framework for a mechanistic understanding of functional cooperativity in SLC26 dimers.

Inferring Structural Ensembles of Flexible and Dynamic Macromolecules Using Bayesian, Maximum Entropy, and Minimal-Ensemble Refinement Methods

The flexible and dynamic nature of biomolecules and biomolecular complexes is essential for many cellular functions in living organisms but poses a challenge for experimental methods to determine high-resolution structural models. To meet this challenge, experiments are combined with molecular simulations. The latter propose models for structural ensembles, and the experimental data can be used to steer these simulations and to select ensembles that most likely underlie the experimental data. Here, we explain in detail how the "Bayesian Inference Of ENsembles" (BioEn) method can be used to refine such ensembles using a wide range of experimental data. The "Ensemble Refinement of SAXS" (EROS) method is a special case of BioEn, inspired by the Gull-Daniell formulation of maximum entropy image processing and focused originally on X-ray solution scattering experiments (SAXS) and then extended to integrative structural modeling. We also briefly sketch the "minimum ensemble method," a maximum-parsimony refinement method that seeks to represent an ensemble with a minimal number of representative structures.

Assessing protein conformational landscapes: integration of DEER data in Maximum Occurrence analysis

The properties of the conformational landscape of a biomolecule are of capital importance to understand its function. It is widely accepted that a statistical ensemble is far more representative than a single structure, especially for proteins with disordered regions. While experimental data provide the most important handle on the conformational variability that the system is experiencing, they usually report on either time or ensemble averages. Since the available conformations largely outnumber the (independent) available experimental data, the latter can be equally well reproduced by a variety of ensembles. We have proposed the Maximum Occurrence (MaxOcc) approach to provide an upper bound of the statistical weight of each conformation. This method is expected to converge towards the true statistical weights by increasing the number of independent experimental datasets. In this paper we explore the ability of DEER (Double Electron Electron Resonance) data, which report on the distance distribution between two spin labels attached to a biomolecule, to restrain the MaxOcc values and its complementarity to previously introduced experimental techniques such as NMR and Small-Angle X-ray Scattering. We here present the case of Ca2+ bound calmodulin (CaM) as a test case and show that DEER data impose a sizeable reduction of the conformational space described by high MaxOcc conformations.