The emerging role of physical modeling in the future of structure determination

MELD-Adapt: On-the-Fly Belief Updating in Integrative Molecular Dynamics

Integrative structural biology synergizes experimental data with computational methods to elucidate the structures and interactions within biomolecules, a task that becomes critical in the absence of high-resolution structural data. A challenging step for integrating the data is knowing the expected accuracy or belief in the dataset. We previously showed that the Modeling Employing Limited Data (MELD) approach succeeds at predicting structures and finding the best interpretation of the data when the initial belief is equal to or slightly lower than the real value. However, the initial belief might be unknown to the user, as it depends on both the technique and the system of study. Here we introduce MELD-Adapt, designed to dynamically evaluate and infer the reliability of input data while at the same time finding the best interpretation of the data and the structures compatible with it. We demonstrate the utility of this method across different systems, particularly emphasizing its capability to correct initial assumptions and identify the correct fraction of data to produce reliable structural models. The approach is tested with two benchmark sets: the folding of 12 proteins with coarse physical insights and the binding of peptides with varying affinities to the extraterminal domain using chemical shift perturbation data. We find that subtle differences in data structure (e.g., locally clustered or globally distributed), starting belief, and force field preferences can have an impact on the predictions, limiting the possibility of a transferable protocol across all systems and data types. Nonetheless, we find a wide range of initial setup conditions that will lead to successful sampling and identification of native states, leading to a robust pipeline. Furthermore, disagreements about how much data is enforced and satisfied rapidly serve to identify incorrect setup conditions.

Appraisal of blob-Based Approaches in the Prediction of Protein Folding Times

A series of reports published in the last 3 years has illustrated that a blob-based model (BBM) can predict the folding time of proteins from their primary amino acid (aa) sequence based on three simple rules established to characterize the long-range backbone dynamics (LRBD) of racemic polypeptides. The sole use of LRBD to predict protein folding times with the BBM represents a radical departure from all other prediction methods currently applied to determine protein folding times, which rely instead on parameters such as the structure content, folding kinetics, chain length, amino acid properties, or contact topography of proteins. Furthermore, the built-in modularity of the BBM enables the parametrization and inclusion of new phenomena affecting the LRBD of polypeptides, while its conceptual simplicity makes it an interesting new mathematical tool for studying protein folding. However, its novelty implies that its relationship with many other methods used to predict protein folding times has not been well researched. Consequently, the purpose of this report is to uncover the physical phenomena encountered during protein folding that are best described by the BBM through the identification of parameters that have been recognized over the years as being strong predictors for protein folding, such as protein size, topology, structural class, and folding kinetics. This was accomplished by determining the parameters most strongly correlated with the folding times predicted by the BBM. While the BBM in its present form appears to be a good indicator of the folding times of the vast majority of the 195 proteins considered so far, this report finds that it excels for moderately large proteins that are primarily composed of locally formed structural motifs such as α-helices or for proteins that fold in multiple steps. Altogether, these observations based on the use of the BBM support the notion that proteins fold the way they do because the LRBD of polypeptides is mostly driven by the local interactions experienced between aa's within reach of one another.

Hybrid computational methods combining experimental information with molecular dynamics

A goal of structural biology is to understand how macromolecules carry out their biological roles by identifying their metastable states, mechanisms of action, pathways leading to conformational changes, and the thermodynamic and kinetic relationships between those states. Integrative modeling brings structural insights into systems where traditional structure determination approaches cannot help. We focus on the synergies and challenges of integrative modeling combining experimental data with molecular dynamics simulations.

Pyrene Excimer Formation (PEF) and Its Application to the Study of Polypeptide Dynamics

This Perspective describes how the fluorescence blob model (FBM) has been developed and applied over the past 30 years to characterize the long-range backbone dynamics (LRBD) of polymers in solution. In these experiments, the polymers are randomly labeled with the dye pyrene, which forms an excimer upon the encounter between an excited and a ground-state pyrenyl label inside a finite subvolume of the polymer coil referred to as a blob representing the volume probed by the excited pyrene. By compartmentalizing the polymer coil into a cluster of identical blobs, FBM analysis of the fluorescence decays acquired with the polymers yields the number N_blob of structural units inside a blob. Since a flexible or rigid backbone will result in an N_blob that is either large or small, N_blob can be used as a measure of the flexibility of a given polymer. After having established that these experiments based on pyrene excimer formation (PEF) yielded quantitative information about the LRBD of a variety of polymers in solution, control experiments were carried out to characterize the effects that different molecular variables, such as the side-chain size (SCS) of a structural unit or the length of the linker connecting pyrene to the polymeric backbone, had on the parameters retrieved with the FBM. At this point, the FBM was applied to study the LRBD of polypeptides prepared from racemic mixtures of amino acids (aa's). These studies led to the establishment of simple rules that could be developed into mathematical equations to describe the LRBD of polypeptides. The N_blob values retrieved from the FBM analysis of the fluorescence decays acquired with the pyrene-labeled polypeptides could then be employed to predict the total conformational search time (τ_tcs) of any polypeptide based on their sequence. Strong correlations were found between the predicted τ_tcs and the experimental folding times of 145 proteins. The good quality of these correlations suggests that the blob-based approach described in this report might represent an interesting mathematical means for studying protein folding.

Simultaneous Assignment and Structure Determination of Proteins From Sparsely Labeled NMR Datasets

Sparsely labeled NMR samples provide opportunities to study larger biomolecular assemblies than is traditionally done by NMR. This requires new computational tools that can handle the sparsity and ambiguity in the NMR datasets. The MELD (modeling employing limited data) Bayesian approach was assessed to be the best performing in predicting structures from sparsely labeled NMR data in the 13th edition of the Critical Assessment of Structure Prediction (CASP) event—and limitations of the methodology were also noted. In this report, we evaluate the nature and difficulty in modeling unassigned sparsely labeled NMR datasets and report on an improved methodological pipeline leading to higher-accuracy predictions. We benchmark our methodology against the NMR datasets provided by CASP 13.

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

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

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

Structure-guided rational design of the substrate specificity and catalytic activity of an enzyme

The quest for an enzyme with desired property is high for biocatalyic production of valuable products in industrial biotechnology. Synthetic biology and metabolic engineering also increasingly require an enzyme with unusual property in terms of substrate spectrum and catalytic activity for the construction of novel circuits and pathways. Structure-guided enzyme engineering has demonstrated a prominent utility and potential in generating such an enzyme, even though some limitations still remain. In this chapter, we present some issues regarding the implementation of the structural information to enzyme engineering, and exemplify the structure-guided rational approach to the design of an enzyme with desired functionality such as substrate specificity and catalytic efficiency.

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.

Applications of Molecular Dynamics Simulation in Structure Prediction of Peptides and Proteins

Compared with rapid accumulation of protein sequences from high-throughput DNA sequencing, obtaining experimental 3D structures of proteins is still much more difficult, making protein structure prediction (PSP) potentially very useful. Currently, a vast majority of PSP efforts are based on data mining of known sequences, structures and their relationships (informatics-based). However, if closely related template is not available, these methods are usually much less reliable than experiments. They may also be problematic in predicting the structures of naturally occurring or designed peptides. On the other hand, physics-based methods including molecular dynamics (MD) can utilize our understanding of detailed atomic interactions determining biomolecular structures. In this mini-review, we show that all-atom MD can predict structures of cyclic peptides and other peptide foldamers with accuracy similar to experiments. Then, some notable successes in reproducing experimental 3D structures of small proteins through MD simulations (some with replica-exchange) of the folding were summarized. We also describe advancements of MD-based refinement of structure models, and the integration of limited experimental or bioinformatics data into MD-based structure modeling.

High Accuracy Protein Structures from Minimal Sparse Paramagnetic Solid-State NMR Restraints

There is a pressing need for new computational tools to integrate data from diverse experimental approaches in structural biology. We present a strategy that combines sparse paramagnetic solid-state NMR restraints with physics-based atomistic simulations. Our approach explicitly accounts for uncertainty in the interpretation of experimental data through the use of a semi-quantitative mapping between the data and the restraint energy that is calibrated by extensive simulations. We apply our approach to solid-state NMR data for the model protein GB1 labeled with Cu²⁺ -EDTA at six different sites. We are able to determine the structure to 0.9 Å accuracy within a single day of computation on a GPU cluster. We further show that in some cases, the data from only a single paramagnetic tag are sufficient for accurate folding.

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.

Computational Structural Biology: Successes, Future Directions, and Challenges

Computational biology has made powerful advances. Among these, trends in human health have been uncovered through heterogeneous 'big data' integration, and disease-associated genes were identified and classified. Along a different front, the dynamic organization of chromatin is being elucidated to gain insight into the fundamental question of genome regulation. Powerful conformational sampling methods have also been developed to yield a detailed molecular view of cellular processes. when combining these methods with the advancements in the modeling of supramolecular assemblies, including those at the membrane, we are finally able to get a glimpse into how cells' actions are regulated. Perhaps most intriguingly, a major thrust is on to decipher the mystery of how the brain is coded. Here, we aim to provide a broad, yet concise, sketch of modern aspects of computational biology, with a special focus on computational structural biology. We attempt to forecast the areas that computational structural biology will embrace in the future and the challenges that it may face. We skirt details, highlight successes, note failures, and map directions.

Weighing-up protein dynamics: the combination of native mass spectrometry and molecular dynamics simulations

Structural dynamics underpin biological function at the molecular level, yet many biophysical and structural biology approaches give only a static or averaged view of proteins. Native mass spectrometry yields spectra of the many states and interactions in the structural ensemble, but its spatial resolution is limited. Conversely, molecular dynamics simulations are innately high-resolution, but have a limited capacity for exploring all structural possibilities. The two techniques hence differ fundamentally in the information they provide, returning data that reflect different length scales and time scales, making them natural bedfellows. Here we discuss how the combination of native mass spectrometry with molecular dynamics simulations is enabling unprecedented insights into a range of biological questions by interrogating the motions of proteins, their assemblies, and interactions.