Effect of Direct and Water-Mediated Interactions on the Identification of Hotspots in Biomolecular Complexes with Multiple Subsystems

Identification of important residues in biochemical complexes is often a crucial step for many problems in molecular biology and biochemistry. A method is proposed to identify hotspots in biomolecular complexes based on a new metric, derived from networks representing molecular subunits (residues, bridging solvent molecules, ligands etc.) connected by interactions. A singular value decomposition of the weighted adjacency matrix is used to construct a scalar rank for each subunit that reflects its importance in the residue interaction network. This metric is called the singular value centrality. In addition, a new formalism is proposed to account for water-mediated interactions in the ranking of residues. Interactions for a residue network can be provided by various computational methods. In this work interactions are obtained from full quantum-mechanical calculations of protein-protein complexes using the fragment molecular orbital method. The ranking results are shown to be in good agreement with earlier computational and experimental studies. The developed method can be used to gain a deeper insight into the role of subunits in complex biomolecular systems.

A Deep Learning-Driven Sampling Technique to Explore the Phase Space of an RNA Stem-Loop

The folding and unfolding of RNA stem-loops are critical biological processes; however, their computational studies are often hampered by the ruggedness of their folding landscape, necessitating long simulation times at the atomistic scale. Here, we adapted DeepDriveMD (DDMD), an advanced deep learning-driven sampling technique originally developed for protein folding, to address the challenges of RNA stem-loop folding. Although tempering- and order parameter-based techniques are commonly used for similar rare-event problems, the computational costs or the need for a priori knowledge about the system often present a challenge in their effective use. DDMD overcomes these challenges by adaptively learning from an ensemble of running MD simulations using generic contact maps as the raw input. DeepDriveMD enables on-the-fly learning of a low-dimensional latent representation and guides the simulation toward the undersampled regions while optimizing the resources to explore the relevant parts of the phase space. We showed that DDMD estimates the free energy landscape of the RNA stem-loop reasonably well at room temperature. Our simulation framework runs at a constant temperature without external biasing potential, hence preserving the information on transition rates, with a computational cost much lower than that of the simulations performed with external biasing potentials. We also introduced a reweighting strategy for obtaining unbiased free energy surfaces and presented a qualitative analysis of the latent space. This analysis showed that the latent space captures the relevant slow degrees of freedom for the RNA folding problem of interest. Finally, throughout the manuscript, we outlined how different parameters are selected and optimized to adapt DDMD for this system. We believe this compendium of decision-making processes will help new users adapt this technique for the rare-event sampling problems of their interest.

Dynamic structural twist in metal-organic frameworks enhances solar overall water splitting

Photocatalytic overall water splitting holds great promise for solar-to-hydrogen conversion. Maintaining charge separation is a major challenge but is key to unlocking this potential. Here we discovered a metal-organic framework (MOF) that shows suppressed charge recombination. This MOF features electronically insulated Zn2+ nodes and two chemically equivalent, yet crystallographically independent, linkers. These linkers behave as an electron donor-acceptor pair with non-overlapping band edges. Upon photoexcitation, the MOF undergoes a dynamic excited-state structural twist, inducing orbital rearrangements that forbid radiative relaxation and thereby promote a long-lived charge-separated state. As a result, the MOF achieves visible-light photocatalytic overall water splitting, in the presence of co-catalysts, with an apparent quantum efficiency of 3.09 ± 0.32% at 365 nm and shows little activity loss in 100 h of consecutive runs. Furthermore, the dynamic excited-state structural twist is also successfully extended to other photocatalysts. This strategy for suppressing charge recombination will be applicable to diverse photochemical processes beyond overall water splitting.

Recent advances in computational prediction of molecular properties in food chemistry

The combination of food chemistry and computational simulation has brought many impacts to food research, moving from experimental chemistry to computer chemistry. This paper will systematically review in detail the important role played by computational simulations in the development of the molecular structure of food, mainly from the atomic, molecular, and multicomponent dimension. It will also discuss how different computational chemistry models can be constructed and analyzed to obtain reliable conclusions. From the calculation principle to case analysis, this paper focuses on the selection and application of quantum mechanics, molecular mechanics and coarse-grained molecular dynamics in food chemistry research. Finally, experiments and computations of food chemistry are compared and summarized to obtain the best balance between them. The above review and outlook will provide an important reference for the intersection of food chemistry and computational chemistry, and is expected to provide innovative thinking for structural research in food chemistry.

MDverse, shedding light on the dark matter of molecular dynamics simulations

The rise of open science and the absence of a global dedicated data repository for molecular dynamics (MD) simulations has led to the accumulation of MD files in generalist data repositories, constituting the dark matter of MD - data that is technically accessible, but neither indexed, curated, or easily searchable. Leveraging an original search strategy, we found and indexed about 250,000 files and 2000 datasets from Zenodo, Figshare and Open Science Framework. With a focus on files produced by the Gromacs MD software, we illustrate the potential offered by the mining of publicly available MD data. We identified systems with specific molecular composition and were able to characterize essential parameters of MD simulation such as temperature and simulation length, and could identify model resolution, such as all-atom and coarse-grain. Based on this analysis, we inferred metadata to propose a search engine prototype to explore the MD data. To continue in this direction, we call on the community to pursue the effort of sharing MD data, and to report and standardize metadata to reuse this valuable matter.

Integrative spatiotemporal modeling of biomolecular processes: application to the assembly of the Nuclear Pore Complex

Dynamic processes involving biomolecules are essential for the function of the cell. Here, we introduce an integrative method for computing models of these processes based on multiple heterogeneous sources of information, including time-resolved experimental data and physical models of dynamic processes. We first compute integrative structure models at fixed time points and then optimally select and connect these snapshots into a series of trajectories that optimize the likelihood of both the snapshots and transitions between them. The method is demonstrated by application to the assembly process of the human Nuclear Pore Complex in the context of the reforming nuclear envelope during mitotic cell division, based on live-cell correlated electron tomography, bulk fluorescence correlation spectroscopy-calibrated quantitative live imaging, and a structural model of the fully-assembled Nuclear Pore Complex. Modeling of the assembly process improves the model precision over static integrative structure modeling alone. The method is applicable to a wide range of time-dependent systems in cell biology, and is available to the broader scientific community through an implementation in the open source Integrative Modeling Platform software.

Rescaling protein-protein interactions improves Martini 3 for flexible proteins in solution

Multidomain proteins with flexible linkers and disordered regions play important roles in many cellular processes, but characterizing their conformational ensembles is difficult. We have previously shown that the coarse-grained model, Martini 3, produces too compact ensembles in solution, that may in part be remedied by strengthening protein-water interactions. Here, we show that decreasing the strength of protein-protein interactions leads to improved agreement with experimental data on a wide set of systems. We show that the 'symmetry' between rescaling protein-water and protein-protein interactions breaks down when studying interactions with or within membranes; rescaling protein-protein interactions better preserves the binding specificity of proteins with lipid membranes, whereas rescaling protein-water interactions preserves oligomerization of transmembrane helices. We conclude that decreasing the strength of protein-protein interactions improves the accuracy of Martini 3 for IDPs and multidomain proteins, both in solution and in the presence of a lipid membrane.

Advancing biomolecular simulation through exascale HPC, AI and quantum computing

Biomolecular simulation can act as both a digital microscope and a crystal ball; offering the potential for a deeper understanding of experimental observations whilst also presenting a forward-looking avenue for the in silico design and evaluation of hitherto unsynthesized compounds. Indeed, as the intricacy of our scientific inquiries has grown, so too has the computational prowess we seek to deploy in our pursuit of answers. As we enter the Exascale era, this mini-review surveys the computational landscape from both the point of view of the development of new and ever more powerful systems, and the simulations that are run on them. Moreover, as we stand on the cusp of a transformative phase in computational biology, this article offers a contemplative glance into the future, speculating on the profound implications of artificial intelligence and quantum computing for large-scale biomolecular simulations.

NMR and Single-Molecule FRET Insights into Fast Protein Motions and Their Relation to Function

Proteins often undergo large-scale conformational transitions, in which secondary and tertiary structure elements (loops, helices, and domains) change their structures or their positions with respect to each other. Simple considerations suggest that such dynamics should be relatively fast, but the functional cycles of many proteins are often relatively slow. Sophisticated experimental methods are starting to tackle this dichotomy and shed light on the contribution of large-scale conformational dynamics to protein function. In this review, we focus on the contribution of single-molecule Förster resonance energy transfer and nuclear magnetic resonance (NMR) spectroscopies to the study of conformational dynamics. We briefly describe the state of the art in each of these techniques and then point out their similarities and differences, as well as the relative strengths and weaknesses of each. Several case studies, in which the connection between fast conformational dynamics and slower function has been demonstrated, are then introduced and discussed. These examples include both enzymes and large protein machines, some of which have been studied by both NMR and fluorescence spectroscopies.

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small ligands is of fundamental importance for understanding molecular principles of chemotherapy and for designing new and more effective drugs. Due to the still high costs and to the several limitations of experimental techniques, it is most often desirable to predict these ligand-protein complexes in silico, particularly when screening for new putative drugs from databases of millions of compounds. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology aimed at generating bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites. Validation was performed on the enzyme adenylate kinase (ADK), a paradigmatic example of proteins that undergo very large conformational changes upon ligand binding. By only exploiting the unbound structure and the putative binding sites of the protein, we generated a significant fraction of bound-like structures, which employed in ensemble-docking calculations allowed to find native-like poses of substrates, inhibitors, and catalytically incompetent binders. Our protocol provides a general framework for the generation of bound-like conformations of flexible proteins that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening for difficult targets, prediction of the impact of amino acid mutations on structure and dynamics, and protein engineering.

Non-affine deformation analysis and 3D packing defects: A new way to probe membrane heterogeneity in molecular simulations

Here, we discuss a new framework developed over the last 5 years in our group to probe nanoscale membrane heterogeneity. The framework is based on the idea of characterizing lateral heterogeneity through non-affine deformation (NAD) measurements, transverse heterogeneity through three dimensional (3D) lipid packing defects, and using these approaches to formalize the seemingly trivial correlation between lateral organization and lipid packing in biological membranes. We find that measurements from NAD analysis, a prescription which is borrowed from Physics of glasses and granular material, can faithfully distinguish between liquid-ordered and disordered phases in membranes at molecular length scales and, can also be used to identify phase boundaries with high precision. Concomitantly, 3D-packing defects can not only distinguish between the two co-existing fluid phases based on their molecular scale packing (or membrane free volume), but also provide a route to connect the membrane domains to their functionality, such as exploring the molecular origins of inter-leaflet domain registration and peptide partitioning. The correlation between lateral membrane order and transverse packing presents novel molecular design-level features that can explain functions such as protein/peptide partitioning and small-molecule permeation dynamics in complex and heterogeneous membranes with high-fidelity. The framework allows us to explore the nature of lateral organization and molecular packing as a manifestation of intricate molecular interactions among a chemically rich variety of lipids and other molecules in a membrane with complex membrane composition and asymmetry across leaflets.

Transferable deep generative modeling of intrinsically disordered protein conformations

Intrinsically disordered proteins have dynamic structures through which they play key biological roles. The elucidation of their conformational ensembles is a challenging problem requiring an integrated use of computational and experimental methods. Molecular simulations are a valuable computational strategy for constructing structural ensembles of disordered proteins but are highly resource-intensive. Recently, machine learning approaches based on deep generative models that learn from simulation data have emerged as an efficient alternative for generating structural ensembles. However, such methods currently suffer from limited transferability when modeling sequences and conformations absent in the training data. Here, we develop a novel generative model that achieves high levels of transferability for intrinsically disordered protein ensembles. The approach, named idpSAM, is a latent diffusion model based on transformer neural networks. It combines an autoencoder to learn a representation of protein geometry and a diffusion model to sample novel conformations in the encoded space. IdpSAM was trained on a large dataset of simulations of disordered protein regions performed with the ABSINTH implicit solvent model. Thanks to the expressiveness of its neural networks and its training stability, idpSAM faithfully captures 3D structural ensembles of test sequences with no similarity in the training set. Our study also demonstrates the potential for generating full conformational ensembles from datasets with limited sampling and underscores the importance of training set size for generalization. We believe that idpSAM represents a significant progress in transferable protein ensemble modeling through machine learning.

Mechanistic Insight into the Mechanical Unfolding of the Integral Membrane Diacylglycerol Kinase

The essential forces stabilizing membrane proteins and governing their folding and unfolding are difficult to decipher. Single-molecule atomic force spectroscopy mechanically unfolds individual membrane proteins and quantifies their dynamics and energetics. However, it remains challenging to structurally assign unfolding intermediates precisely and to deduce dominant interactions between specific residues that facilitate either the localized stabilization of these intermediates or the global assembly of membrane proteins. Here, we performed force spectroscopy experiments and multiscale molecular dynamics simulations to study the unfolding pathway of diacylglycerol kinase (DGK), a small trimeric multispan transmembrane enzyme. The remarkable agreement between experiments and simulations allowed precise structural assignment and interaction analysis of unfolding intermediates, bypassing existing limitations on structural mapping, and thus provided mechanistic explanations for the formation of these states. DGK unfolding was found to proceed with structural segments varying in size that do not correlate with its secondary structure. We identified intermolecular side-chain packing interactions as one of the major contributions to the stability of unfolding intermediates. Mutagenesis creating packing defects induced a dramatic decrease in the mechano-stability of corresponding intermediates and also in the thermo-stability of DGK trimer, in good agreement with predictions from simulations. Hence, the molecular determinants of the mechano- and thermo-stability of a membrane protein can be identified at residue resolution. The accurate structural assignment established and microscopic mechanism revealed in this work may substantially expand the scope of single-molecule studies of membrane proteins.

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.

Structural and physical basis for the elasticity of elastin

Elastin function is to endow vertebrate tissues with elasticity so that they can adapt to local mechanical constraints. The hydrophobicity and insolubility of the mature elastin polymer have hampered studies of its molecular organisation and structure-elasticity relationships. Nevertheless, a growing number of studies from a broad range of disciplines have provided invaluable insights, and several structural models of elastin have been proposed. However, many questions remain regarding how the primary sequence of elastin (and the soluble precursor tropoelastin) governs the molecular structure, its organisation into a polymeric network, and the mechanical properties of the resulting material. The elasticity of elastin is known to be largely entropic in origin, a property that is understood to arise from both its disordered molecular structure and its hydrophobic character. Despite a high degree of hydrophobicity, elastin does not form compact, water-excluding domains and remains highly disordered. However, elastin contains both stable and labile secondary structure elements. Current models of elastin structure and function are drawn from data collected on tropoelastin and on elastin-like peptides (ELPs) but at the tissue level, elasticity is only achieved after polymerisation of the mature elastin. In tissues, the reticulation of tropoelastin chains in water defines the polymer elastin that bears elasticity. Similarly, ELPs require polymerisation to become elastic. There is considerable interest in elastin especially in the biomaterials and cosmetic fields where ELPs are widely used. This review aims to provide an up-to-date survey of/perspective on current knowledge about the interplay between elastin structure, solvation, and entropic elasticity.

Protein ensemble modeling and analysis with MMMx

Proteins, especially of eukaryotes, often have disordered domains and may contain multiple folded domains whose relative spatial arrangement is distributed. The MMMx ensemble modeling and analysis toolbox (https://github.com/gjeschke/MMMx) can support the design of experiments to characterize the distributed structure of such proteins, starting from AlphaFold2 predictions or folded domain structures. Weak order can be analyzed with reference to a random coil model or to peptide chains that match the residue-specific Ramachandran angle distribution of the loop regions and are otherwise unrestrained. The deviation of the mean square end-to-end distance of chain sections from their average over sections of the same sequence length reveals localized compaction or expansion of the chain. The shape sampled by disordered chains is visualized by superposition in the principal axes frame of their inertia tensor. Ensembles of different sizes and with weighted conformers can be compared based on a similarity parameter that abstracts from the ensemble width.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Transferable deep generative modeling of intrinsically disordered protein conformations

Intrinsically disordered proteins have dynamic structures through which they play key biological roles. The elucidation of their conformational ensembles is a challenging problem requiring an integrated use of computational and experimental methods. Molecular simulations are a valuable computational strategy for constructing structural ensembles of disordered proteins but are highly resource-intensive. Recently, machine learning approaches based on deep generative models that learn from simulation data have emerged as an efficient alternative for generating structural ensembles. However, such methods currently suffer from limited transferability when modeling sequences and conformations absent in the training data. Here, we develop a novel generative model that achieves high levels of transferability for intrinsically disordered protein ensembles. The approach, named idpSAM, is a latent diffusion model based on transformer neural networks. It combines an autoencoder to learn a representation of protein geometry and a diffusion model to sample novel conformations in the encoded space. IdpSAM was trained on a large dataset of simulations of disordered protein regions performed with the ABSINTH implicit solvent model. Thanks to the expressiveness of its neural networks and its training stability, idpSAM faithfully captures 3D structural ensembles of test sequences with no similarity in the training set. Our study also demonstrates the potential for generating full conformational ensembles from datasets with limited sampling and underscores the importance of training set size for generalization. We believe that idpSAM represents a significant progress in transferable protein ensemble modeling through machine learning.

Single-Molecule FRET at 10 MHz Count Rates

A bottleneck in many studies utilizing single-molecule Förster resonance energy transfer is the attainable photon count rate, as it determines the temporal resolution of the experiment. As many biologically relevant processes occur on time scales that are hardly accessible with currently achievable photon count rates, there has been considerable effort to find strategies to increase the stability and brightness of fluorescent dyes. Here, we use DNA nanoantennas to drastically increase the achievable photon count rates and observe fast biomolecular dynamics in the small volume between two plasmonic nanoparticles. As a proof of concept, we observe the coupled folding and binding of two intrinsically disordered proteins, which form transient encounter complexes with lifetimes on the order of 100 μs. To test the limits of our approach, we also investigated the hybridization of a short single-stranded DNA to its complementary counterpart, revealing a transition path time of 17 μs at photon count rates of around 10 MHz, which is an order-of-magnitude improvement compared to the state of the art. Concomitantly, the photostability was increased, enabling many seconds long megahertz fluorescence time traces. Due to the modular nature of the DNA origami method, this platform can be adapted to a broad range of biomolecules, providing a promising approach to study previously unobservable ultrafast biophysical processes.

Energy, water, and protein folding: A molecular dynamics-based quantitative inventory of molecular interactions and forces that make proteins stable

Protein folding energetics can be determined experimentally on a case-by-case basis but it is not understood in sufficient detail to provide deep control in protein design. The fundamentals of protein stability have been outlined by calorimetry, protein engineering, and biophysical modeling, but these approaches still face great difficulty in elucidating the specific contributions of the intervening molecules and physical interactions. Recently, we have shown that the enthalpy and heat capacity changes associated to the protein folding reaction can be calculated within experimental error using molecular dynamics simulations of native protein structures and their corresponding unfolded ensembles. Analyzing in depth molecular dynamics simulations of four model proteins (CI2, barnase, SNase, and apoflavodoxin), we dissect here the energy contributions to ΔH (a key component of protein stability) made by the molecular players (polypeptide and solvent molecules) and physical interactions (electrostatic, van der Waals, and bonded) involved. Although the proteins analyzed differ in length, isoelectric point and fold class, their folding energetics is governed by the same quantitative pattern. Relative to the unfolded ensemble, the native conformations are enthalpically stabilized by comparable contributions from protein-protein and solvent-solvent interactions, and almost equally destabilized by interactions between protein and solvent molecules. The native protein surface seems to interact better with water than the unfolded one, but this is outweighed by the unfolded surface being larger. From the perspective of physical interactions, the native conformations are stabilized by van de Waals and Coulomb interactions and destabilized by conformational strain arising from bonded interactions. Also common to the four proteins, the sign of the heat capacity change is set by interactions between protein and solvent molecules or, from the alternative perspective, by Coulomb interactions.

3D animation as a tool for integrative modeling of dynamic molecular mechanisms

As the scientific community accumulates diverse data describing how molecular mechanisms occur, creating and sharing visual models that integrate the richness of this information has become increasingly important to help us explore, refine, and communicate our hypotheses. Three-dimensional (3D) animation is a powerful tool to capture dynamic hypotheses that are otherwise difficult or impossible to visualize using traditional 2D illustration techniques. This perspective discusses the current and future roles that 3D animation can play in the research sphere.

Drug discovery: In silico dry data can bypass biological wet data?

The recent and extraordinary increase in computer power, along with the availability of efficient algorithms based on artificial intelligence, has prompted a large number of inexperienced scientists to challenge the complex and yet competitive world of drug discovery, by pretending to identify new hits through the sole use of computer aided drug design (CADD). Does the golden era of dry data run the risk of overshadowing the importance of wet data and, in doing so, forget that in silico and biological data need each other in successful preclinical drug discovery programmes?

Bonds and bytes: The odyssey of structural biology

Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of structural biology, no single method comprehensively reveals the behavior of biological systems across various spatiotemporal scales. Instead, we have a versatile toolkit of techniques, each contributing a piece to the overall puzzle. Integrative structural biology combines different techniques to create accurate and precise multi-scale models that expand our understanding of complex biological systems. This review outlines recent advancements in computational and experimental methods in structural biology, with special focus on recent Artificial Intelligence techniques, emphasizes integrative approaches that combine different types of data for precise spatiotemporal modeling, and provides an outlook into future directions of this field.

Picosecond Dynamics of a Small Molecule in Its Bound State with an Intrinsically Disordered Protein

Intrinsically disordered proteins (IDPs) are highly dynamic biomolecules that rapidly interconvert among many structural conformations. These dynamic biomolecules are involved in cancers, neurodegeneration, cardiovascular illnesses, and viral infections. Despite their enormous therapeutic potential, IDPs have generally been considered undruggable because of their lack of classical long-lived binding pockets for small molecules. Currently, only a few instances are known where small molecules have been observed to interact with IDPs, and this situation is further exacerbated by the limited sensitivity of experimental techniques to detect such binding events. Here, using experimental nuclear magnetic resonance (NMR) spectroscopy 19F transverse spin-relaxation measurements, we discovered that a small molecule, 5-fluoroindole, interacts with the disordered domains of non-structural protein 5A from hepatitis C virus with a Kd of 260 ± 110 μM. Our analysis also allowed us to determine the rotational correlation times (τc) for the free and bound states of 5-fluoroindole. In the free state, we observed a rotational correlation time of 27.0 ± 1.3 ps, whereas in the bound state, τc only increased to 46 ± 10 ps. Our findings imply that it is possible for small molecules to engage with IDPs in exceptionally dynamic ways, in sharp contrast to the rigid binding modes typically exhibited when small molecules bind to well-defined binding pockets within structured proteins.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

DP/MM: A Hybrid Model for Zinc-Protein Interactions in Molecular Dynamics

Zinc-containing proteins are vital for many biological processes, yet accurately modeling them using classical force fields is hindered by complicated polarization and charge transfer effects. This study introduces DP/MM, a hybrid force field scheme that utilizes a deep potential model to correct the atomic forces of zinc ions and their coordinated atoms, elevating them from MM to QM levels of accuracy. Trained on the difference between MM and QM atomic forces across diverse zinc coordination groups, the DP/MM model faithfully reproduces structural characteristics of zinc coordination during simulations, such as the tetrahedral coordination of Cys4 and Cys3His1 groups. Furthermore, DP/MM allows water exchange in the zinc coordination environment. With its unique blend of accuracy, efficiency, flexibility, and transferability, DP/MM serves as a valuable tool for studying structures and dynamics of zinc-containing proteins and also represents a pioneering approach in the evolving landscape of machine learning potentials for molecular modeling.

Development of nano-delivery systems for loaded bioactive compounds: using molecular dynamics simulations

Over the past decade, a remarkable surge in the development of functional nano-delivery systems loaded with bioactive compounds for healthcare has been witnessed. Notably, the demanding requirements of high solubility, prolonged circulation, high tissue penetration capability, and strong targeting ability of nanocarriers have posed interdisciplinary research challenges to the community. While extensive experimental studies have been conducted to understand the construction of nano-delivery systems and their metabolic behavior in vivo, less is known about these molecular mechanisms and kinetic pathways during their metabolic process in vivo, and lacking effective means for high-throughput screening. Molecular dynamics (MD) simulation techniques provide a reliable tool for investigating the design of nano-delivery carriers encapsulating these functional ingredients, elucidating the synthesis, translocation, and delivery of nanocarriers. This review introduces the basic MD principles, discusses how to apply MD simulation to design nanocarriers, evaluates the ability of nanocarriers to adhere to or cross gastrointestinal mucosa, and regulates plasma proteins in vivo. Moreover, we presented the critical role of MD simulation in developing delivery systems for precise nutrition and prospects for the future. This review aims to provide insights into the implications of MD simulation techniques for designing and optimizing nano-delivery systems in the healthcare food industry.

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

Atomistic molecular simulations of Aβ-Zn conformational ensembles

The amyloid-forming Aβ peptide is able to interact with metal cations to form very stable complexes that influence fibril formation and contribute to the onset of Alzheimer's disease. Multiple structures of peptides derived from Aβ in complex with different metals have been resolved experimentally to provide an atomic-level description of the metal-protein interactions. However, Aβ is intrinsically disordered, and hence more amenable to an ensemble description. Molecular dynamics simulations can now reach the timescales needed to generate ensembles for these type of complexes. However, this requires accurate force fields both for the protein and the protein-metal interactions. Here we use state-of-the-art methods to generate force field parameters for the Zn(II) cations in a set of complexes formed by different Aβ variants and combine them with the Amber99SB*-ILDN optimized force field. Upon comparison of NMR experiments with the simulation results, further optimized with a Bayesian/Maximum entropy approach, we provide an accurate description of the molecular ensembles for most Aβ-metal complexes. We find that the resulting conformational ensembles are more heterogeneous than the NMR models deposited in the Protein Data Bank.

Lessons Learned from Multiobjective Automatic Optimizations of Classical Three-Site Rigid Water Models Using Microscopic and Macroscopic Target Experimental Observables

The development of accurate water models is of primary importance for molecular simulations. Despite their intrinsic approximations, three-site rigid water models are still ubiquitously used to simulate a variety of molecular systems. Automatic optimization approaches have been recently used to iteratively refine three-site water models to fit macroscopic (average) thermodynamic properties, providing state-of-the-art three-site models that still present some deviations from the liquid water properties. Here, we show the results obtained by automatically optimizing three-site rigid water models to fit a combination of microscopic and macroscopic experimental observables. We use Swarm-CG, a multiobjective particle-swarm-optimization algorithm, for training the models to reproduce the experimental radial distribution functions of liquid water at various temperatures (rich in microscopic-level information on, e.g., the local orientation and interactions of the water molecules). We systematically analyze the agreement of these models with experimental observables and the effect of adding macroscopic information to the training set. Our results demonstrate how adding microscopic-rich information in the training of water models allows one to achieve state-of-the-art accuracy in an efficient way. Limitations in the approach and in the approximated description of water in these three-site models are also discussed, providing a demonstrative case useful for the optimization of approximated molecular models, in general.

Addressing Challenges of Macrocyclic Conformational Sampling in Polar and Apolar Solvents: Lessons for Chameleonicity

We evaluated a workflow to reliably sample the conformational space of a set of 47 peptidic macrocycles. Starting from SMILES strings, we use accelerated molecular dynamics simulations to overcome high energy barriers, in particular, the cis-trans isomerization of peptide bonds. We find that our approach performs very well in polar solvents like water and dimethyl sulfoxide. Interestingly, the protonation state of a secondary amine in the ring only slightly influences the conformational ensembles of our test systems. For several of the macrocycles, determining the conformational distribution in chloroform turns out to be considerably more challenging. Especially, the choice of partial charges crucially influences the ensembles in chloroform. We address these challenges by modifying initial structures and the choice of partial charges. Our results suggest that special care has to be taken to understand the configurational distribution in apolar solvents, which is a key step toward a reliable prediction of membrane permeation of macrocycles and their chameleonic properties.

Large-scale data-driven and physics-based models offer insights into the relationships among the structures, dynamics, and functions of chromosomes

The organized three-dimensional chromosome architecture in the cell nucleus provides scaffolding for precise regulation of gene expression. When the cell changes its identity in the cell-fate decision-making process, extensive rearrangements of chromosome structures occur accompanied by large-scale adaptations of gene expression, underscoring the importance of chromosome dynamics in shaping genome function. Over the last two decades, rapid development of experimental methods has provided unprecedented data to characterize the hierarchical structures and dynamic properties of chromosomes. In parallel, these enormous data offer valuable opportunities for developing quantitative computational models. Here, we review a variety of large-scale polymer models developed to investigate the structures and dynamics of chromosomes. Different from the underlying modeling strategies, these approaches can be classified into data-driven ('top-down') and physics-based ('bottom-up') categories. We discuss their contributions to offering valuable insights into the relationships among the structures, dynamics, and functions of chromosomes and propose the perspective of developing data integration approaches from different experimental technologies and multidisciplinary theoretical/simulation methods combined with different modeling strategies.

Biomolecular NMR spectroscopy in the era of artificial intelligence

Biomolecular nuclear magnetic resonance (NMR) spectroscopy and artificial intelligence (AI) have a burgeoning synergy. Deep learning-based structural predictors have forever changed structural biology, yet these tools currently face limitations in accurately characterizing protein dynamics, allostery, and conformational heterogeneity. We begin by highlighting the unique abilities of biomolecular NMR spectroscopy to complement AI-based structural predictions toward addressing these knowledge gaps. We then highlight the direct integration of deep learning approaches into biomolecular NMR methods. AI-based tools can dramatically improve the acquisition and analysis of NMR spectra, enhancing the accuracy and reliability of NMR measurements, thus streamlining experimental processes. Additionally, deep learning enables the development of novel types of NMR experiments that were previously unattainable, expanding the scope and potential of biomolecular NMR spectroscopy. Ultimately, a combination of AI and NMR promises to further revolutionize structural biology on several levels, advance our understanding of complex biomolecular systems, and accelerate drug discovery efforts.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Specifying conformational heterogeneity of multi-domain proteins at atomic resolution

The conformational landscape of multi-domain proteins is inherently linked to their specific functions. This also holds for polyubiquitin chains that are assembled by two or more ubiquitin domains connected by a flexible linker thus showing a large interdomain mobility. However, molecular recognition and signal transduction are associated with particular conformational substates that are populated in solution. Here, we apply high-resolution NMR spectroscopy in combination with dual-scale MD simulations to explore the conformational space of K6-, K29-, and K33-linked diubiquitin molecules. The conformational ensembles are evaluated utilizing a paramagnetic cosolute reporting on solvent exposure plus a set of complementary NMR parameters. This approach unravels a conformational heterogeneity of diubiquitins and explains the diversity of structural models that have been determined for K6-, K29-, and K33-linked diubiquitins in free and ligand-bound states so far. We propose a general application of the approach developed here to demystify multi-domain proteins occurring in nature.

Protein dynamics detected by magic-angle spinning relaxation dispersion NMR

Magic-angle spinning (MAS) nuclear magnetic resonance (NMR) is establishing itself as a powerful method for the characterization of protein dynamics at the atomic scale. We discuss here how R1ρ MAS relaxation dispersion NMR can explore microsecond-to-millisecond motions. Progress in instrumentation, isotope labeling, and pulse sequence design has paved the way for quantitative analyses of even rare structural fluctuations. In addition to isotropic chemical-shift fluctuations exploited in solution-state NMR relaxation dispersion experiments, MAS NMR has a wider arsenal of observables, allowing to see motions even if the exchanging states do not differ in their chemical shifts. We demonstrate the potential of the technique for probing motions in challenging large enzymes, membrane proteins, and protein assemblies.

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.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

Conformational heterogeneity and probability distributions from single-particle cryo-electron microscopy

Single-particle cryo-electron microscopy (cryo-EM) is a technique that takes projection images of biomolecules frozen at cryogenic temperatures. A major advantage of this technique is its ability to image single biomolecules in heterogeneous conformations. While this poses a challenge for data analysis, recent algorithmic advances have enabled the recovery of heterogeneous conformations from the noisy imaging data. Here, we review methods for the reconstruction and heterogeneity analysis of cryo-EM images, ranging from linear-transformation-based methods to nonlinear deep generative models. We overview the dimensionality-reduction techniques used in heterogeneous 3D reconstruction methods and specify what information each method can infer from the data. Then, we review the methods that use cryo-EM images to estimate probability distributions over conformations in reduced subspaces or predefined by atomistic simulations. We conclude with the ongoing challenges for the cryo-EM community.

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

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.

Atomistic simulations of the Escherichia coli ribosome provide selection criteria for translationally active substrates

As genetic code expansion advances beyond L-α-amino acids to backbone modifications and new polymerization chemistries, delineating what substrates the ribosome can accommodate remains a challenge. The Escherichia coli ribosome tolerates non-L-α-amino acids in vitro, but few structural insights that explain how are available, and the boundary conditions for efficient bond formation are so far unknown. Here we determine a high-resolution cryogenic electron microscopy structure of the E. coli ribosome containing α-amino acid monomers and use metadynamics simulations to define energy surface minima and understand incorporation efficiencies. Reactive monomers across diverse structural classes favour a conformational space where the aminoacyl-tRNA nucleophile is <4 Å from the peptidyl-tRNA carbonyl with a Bürgi-Dunitz angle of 76-115°. Monomers with free energy minima that fall outside this conformational space do not react efficiently. This insight should accelerate the in vivo and in vitro ribosomal synthesis of sequence-defined, non-peptide heterooligomers.

Combining Molecular Dynamics Simulations and Biophysical Characterization to Investigate Protein-Specific Excipient Effects on Reteplase during Freeze Drying

We performed molecular dynamics simulations of Reteplase in the presence of different excipients to study the stabilizing mechanisms and to identify the role of excipients during freeze drying. To simulate the freeze-drying process, we divided the process into five distinct steps: (i) protein-excipient formulations at room temperature, (ii) the ice-growth process, (iii)-(iv) the partially solvated and fully dried formulations, and (v) the reconstitution. Furthermore, coarse-grained (CG) simulations were employed to explore the protein-aggregation process in the presence of arginine. By using a coarse-grained representation, we could observe the collective behavior and interactions between protein molecules during the aggregation process. The CG simulations revealed that the presence of arginine prevented intermolecular interactions of the catalytic domain of Reteplase, thus reducing the aggregation propensity. This suggests that arginine played a stabilizing role by interacting with protein-specific regions. From the freeze-drying simulations, we could identify several protein-specific events: (i) collapse of the domain structure, (ii) recovery of the drying-induced damages during reconstitution, and (iii) stabilization of the local aggregation-prone region via direct interactions with excipients. Complementary to the simulations, we employed nanoDSF, size-exclusion chromatography, and CD spectroscopy to investigate the effect of the freeze-drying process on the protein structure and stability.

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.

Comparison of On-the-Fly Probability Enhanced Sampling and Parallel Tempering Combined with Metadynamics for Atomistic Simulations of RNA Tetraloop Folding

Atomistic simulations with reliable models are extremely useful in providing exquisitely detailed pictures of biomolecular phenomena that are not always accessible to experiments. One such biomolecular phenomenon is RNA folding, which often requires exhaustive simulations with combined advanced sampling techniques. In this work, we employed the multithermal-multiumbrella on-the-fly probability enhanced sampling (MM-OPES) technique and compared it against combined parallel tempering and metadynamics simulations. We found that MM-OPES simulations were successful in reproducing the free energy surfaces from combined parallel tempering and metadynamics simulations. Importantly, we also investigated a wide range of temperature sets (minimum and maximum temperatures) for MM-OPES simulations in order to identify some guidelines for deciding the temperature limits for an accurate and efficient exploration of the free energy landscapes. We found that most temperature sets yielded almost the same accuracy in reproducing the free energy surface at the ambient conditions as long as (i) the maximum temperature is reasonably high, (ii) the temperature at which we run the simulation is reasonably high (in our simulations, running temperature is defined as [minimum temperature + maximum temperature]/2), and (iii) the effective sample size at the temperature of interest is statistically reasonable. In terms of the computational cost, all MM-OPES simulations were nearly 4 times less costly than the combined parallel tempering and metadynamics simulations. We concluded that the demanding combined parallel tempering and metadynamics simulations can safely be replaced with approximately 4 times less costly MM-OPES simulations (with carefully selected temperature limits) to obtain the same information.

Learning to evolve structural ensembles of unfolded and disordered proteins using experimental solution data

The structural characterization of proteins with a disorder requires a computational approach backed by experiments to model their diverse and dynamic structural ensembles. The selection of conformational ensembles consistent with solution experiments of disordered proteins highly depends on the initial pool of conformers, with currently available tools limited by conformational sampling. We have developed a Generative Recurrent Neural Network (GRNN) that uses supervised learning to bias the probability distributions of torsions to take advantage of experimental data types such as nuclear magnetic resonance J-couplings, nuclear Overhauser effects, and paramagnetic resonance enhancements. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between experimental data and probabilistic selection of torsions from learned distributions provides an alternative to existing approaches that simply reweight conformers of a static structural pool for disordered proteins. Instead, the biased GRNN, DynamICE, learns to physically change the conformations of the underlying pool of the disordered protein to those that better agree with experiments.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.

Machine learned coarse-grained protein force-fields: Are we there yet?

The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges.

Efficient Interrogation of the Kinetic Barriers Demarcating Catalytic States of a Tyrosine Kinase with Optimal Physical Descriptors and Mixture Models

Computer simulations are increasingly used to access thermo-kinetic information underlying structural transformation of protein kinases. Such information are necessary to probe their roles in disease progression and interactions with drug targets. However, the investigations are frequently challenged by forbiddingly high computational expense, and by the lack of standard protocols for the design of low dimensional physical descriptors that encode system features important for transitions. Here, we consider the demarcating characteristics of the different states of Abelson tyrosine kinase associated with distinct catalytic activity to construct a set of physically meaningful, orthogonal collective variables that preserve the slow modes of the system. Independent sampling of each metastable state is followed by the estimation of global partition function along the appropriate physical descriptors using the modified Expectation Maximized Molecular Dynamics method. The resultant free energy barriers are in excellent agreement with experimentally known rate-limiting dynamics and activation energy computed with conventional enhanced sampling methods. We discuss possible directions for further development and applications.

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.