Metadynamic metainference: Convergence towards force field independent structural ensembles of a disordered peptide

A conformational fingerprint for amyloidogenic light chains

Both immunoglobulin light-chain (LC) amyloidosis (AL) and multiple myeloma (MM) share the overproduction of a clonal LC. However, while LCs in MM remain soluble in circulation, AL LCs misfold into toxic-soluble species and amyloid fibrils that accumulate in organs, leading to distinct clinical manifestations. The significant sequence variability of LCs has hindered the understanding of the mechanisms driving LC aggregation. Nevertheless, emerging biochemical properties, including dimer stability, conformational dynamics, and proteolysis susceptibility, distinguish AL LCs from those in MM under native conditions. This study aimed to identify a2 conformational fingerprint distinguishing AL from MM LCs. Using small-angle X-ray scattering (SAXS) under native conditions, we analyzed four AL and two MM LCs. We observed that AL LCs exhibited a slightly larger radius of gyration and greater deviations from X-ray crystallography-determined or predicted structures, reflecting enhanced conformational dynamics. SAXS data, integrated with molecular dynamics simulations, revealed a conformational ensemble where LCs adopt multiple states, with variable and constant domains either bent or straight. AL LCs displayed a distinct, low-populated, straight conformation (termed H state), which maximized solvent accessibility at the interface between constant and variable domains. Hydrogen-deuterium exchange mass spectrometry experimentally validated this H state. These findings reconcile diverse experimental observations and provide a precise structural target for future drug design efforts.

Determining accurate conformational ensembles of intrinsically disordered proteins at atomic resolution

Determining accurate atomic resolution conformational ensembles of intrinsically disordered proteins (IDPs) is extremely challenging. Molecular dynamics (MD) simulations provide atomistic conformational ensembles of IDPs, but their accuracy is highly dependent on the quality of physical models, or force fields, used. Here, we demonstrate how to determine accurate atomic resolution conformational ensembles of IDPs by integrating all-atom MD simulations with experimental data from nuclear magnetic resonance (NMR) spectroscopy and small-angle x-ray scattering (SAXS) with a simple, robust and fully automated maximum entropy reweighting procedure. We demonstrate that when this approach is applied with sufficient experimental data, IDP ensembles derived from different MD force fields converge to highly similar conformational distributions. The maximum entropy reweighting procedure presented here facilitates the integration of MD simulations with extensive experimental datasets and enables the calculation of accurate, force-field independent atomic resolution conformational ensembles of IDPs.

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.

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.

Predicting chemical shifts with graph neural networks

Inferring molecular structure from Nuclear Magnetic Resonance (NMR) measurements requires an accurate forward model that can predict chemical shifts from 3D structure. Current forward models are limited to specific molecules like proteins and state-of-the-art models are not differentiable. Thus they cannot be used with gradient methods like biased molecular dynamics. Here we use graph neural networks (GNNs) for NMR chemical shift prediction. Our GNN can model chemical shifts accurately and capture important phenomena like hydrogen bonding induced downfield shift between multiple proteins, secondary structure effects, and predict shifts of organic molecules. Previous empirical NMR models of protein NMR have relied on careful feature engineering with domain expertise. These GNNs are trained from data alone with no feature engineering yet are as accurate and can work on arbitrary molecular structures. The models are also efficient, able to compute one million chemical shifts in about 5 seconds. This work enables a new category of NMR models that have multiple interacting types of macromolecules.

How to Determine Accurate Conformational Ensembles by Metadynamics Metainference: A Chignolin Study Case

The reliability and usefulness of molecular dynamics simulations of equilibrium processes rests on their statistical precision and their capability to generate conformational ensembles in agreement with available experimental knowledge. Metadynamics Metainference (M&M), coupling molecular dynamics with the enhanced sampling ability of Metadynamics and with the ability to integrate experimental information of Metainference, can in principle achieve both goals. Here we show that three different Metadynamics setups provide converged estimate of the populations of the three-states populated by a model peptide. Errors are estimated correctly by block averaging, but higher precision is obtained by performing independent replicates. One effect of Metadynamics is that of dramatically decreasing the number of effective frames resulting from the simulations and this is relevant for M&M where the number of replicas should be large enough to capture the conformational heterogeneity behind the experimental data. Our simulations allow also us to propose that monitoring the relative error associated with conformational averaging can help to determine the minimum number of replicas to be simulated in the context of M&M simulations. Altogether our data provides useful indication on how to generate sound conformational ensemble in agreement with experimental data.

Refinement of α-Synuclein Ensembles Against SAXS Data: Comparison of Force Fields and Methods

The inherent flexibility of intrinsically disordered proteins (IDPs) makes it difficult to interpret experimental data using structural models. On the other hand, molecular dynamics simulations of IDPs often suffer from force-field inaccuracies, and long simulation times or enhanced sampling methods are needed to obtain converged ensembles. Here, we apply metainference and Bayesian/Maximum Entropy reweighting approaches to integrate prior knowledge of the system with experimental data, while also dealing with various sources of errors and the inherent conformational heterogeneity of IDPs. We have measured new SAXS data on the protein α-synuclein, and integrate this with simulations performed using different force fields. We find that if the force field gives rise to ensembles that are much more compact than what is implied by the SAXS data it is difficult to recover a reasonable ensemble. On the other hand, we show that when the simulated ensemble is reasonable, we can obtain an ensemble that is consistent with the SAXS data, but also with NMR diffusion and paramagnetic relaxation enhancement data.

A kinetic ensemble of the Alzheimer's Aβ peptide

The conformational and thermodynamic properties of disordered proteins are commonly described in terms of structural ensembles and free energy landscapes. To provide information on the transition rates between the different states populated by these proteins, it would be desirable to generalize this description to kinetic ensembles. Approaches based on the theory of stochastic processes can be particularly suitable for this purpose. Here, we develop a Markov state model and apply it to determine a kinetic ensemble of Aβ42, a disordered peptide associated with Alzheimer's disease. Through the Google Compute Engine, we generated 315-µs all-atom molecular dynamics trajectories. Using a probabilistic-based definition of conformational states in a neural network approach, we found that Aβ42 is characterized by inter-state transitions on the microsecond timescale, exhibiting only fully unfolded or short-lived, partially folded states. Our results illustrate how kinetic ensembles provide effective information about the structure, thermodynamics and kinetics of disordered proteins.

Hybrid methods for combined experimental and computational determination of protein structure

Knowledge of protein structure is paramount to the understanding of biological function, developing new therapeutics, and making detailed mechanistic hypotheses. Therefore, methods to accurately elucidate three-dimensional structures of proteins are in high demand. While there are a few experimental techniques that can routinely provide high-resolution structures, such as x-ray crystallography, nuclear magnetic resonance (NMR), and cryo-EM, which have been developed to determine the structures of proteins, these techniques each have shortcomings and thus cannot be used in all cases. However, additionally, a large number of experimental techniques that provide some structural information, but not enough to assign atomic positions with high certainty have been developed. These methods offer sparse experimental data, which can also be noisy and inaccurate in some instances. In cases where it is not possible to determine the structure of a protein experimentally, computational structure prediction methods can be used as an alternative. Although computational methods can be performed without any experimental data in a large number of studies, inclusion of sparse experimental data into these prediction methods has yielded significant improvement. In this Perspective, we cover many of the successes of integrative modeling, computational modeling with experimental data, specifically for protein folding, protein-protein docking, and molecular dynamics simulations. We describe methods that incorporate sparse data from cryo-EM, NMR, mass spectrometry, electron paramagnetic resonance, small-angle x-ray scattering, Förster resonance energy transfer, and genetic sequence covariation. Finally, we highlight some of the major challenges in the field as well as possible future directions.

Small-molecule sequestration of amyloid-β as a drug discovery strategy for Alzheimer's disease

Disordered proteins are challenging therapeutic targets, and no drug is currently in clinical use that modifies the properties of their monomeric states. Here, we identify a small molecule (10074-G5) capable of binding and sequestering the intrinsically disordered amyloid-β (Aβ) peptide in its monomeric, soluble state. Our analysis reveals that this compound interacts with Aβ and inhibits both the primary and secondary nucleation pathways in its aggregation process. We characterize this interaction using biophysical experiments and integrative structural ensemble determination methods. We observe that this molecule increases the conformational entropy of monomeric Aβ while decreasing its hydrophobic surface area. We also show that it rescues a Caenorhabditis elegans model of Aβ-associated toxicity, consistent with the mechanism of action identified from the in silico and in vitro studies. These results illustrate the strategy of stabilizing the monomeric states of disordered proteins with small molecules to alter their behavior for therapeutic purposes.

Refining All-Atom Protein Force Fields for Polar-Rich, Prion-like, Low-Complexity Intrinsically Disordered Proteins

Significant efforts in the past decade have given us highly accurate all-atom protein force fields for molecular dynamics (MD) simulations of folded and disordered proteins. These simulations, complemented with experimental data, provide new insights into molecular interactions that underlie the physical properties of proteins, especially for intrinsically disordered proteins (IDPs) for which defining the heterogeneous structural ensemble is hugely challenging by experiments alone. Consequently, the accuracy of these protein force fields is of utmost importance to ensure reliable simulated conformational data. Here, we first assess the accuracy of current state-of-the-art force fields for IDPs (ff99SBws and ff03ws) applied to disordered proteins of low amino acid sequence complexity that can undergo liquid-liquid phase separation. On the basis of a detailed comparison of NMR chemical shifts between simulation and experiment on several IDPs, we find that regions surrounding specific polar residues result in simulated ensembles with exaggerated helicity when compared to experiment. To resolve this discrepancy, we introduce residue-specific modifications to the backbone torsion potential of three residues (Ser, Thr, and Gln) in the ff99SBws force field. The modified force field, ff99SBws-STQ, provides a more accurate representation of helical structure propensity in these LC domains without compromising faithful representation of helicity in a region with distinct sequence composition. Our refinement strategy also suggests a path forward for integrating experimental data in the assessment of residue-specific deficiencies in the current physics-based force fields and improves these force fields further for their broader applicability.

The dynamics of linear polyubiquitin

Polyubiquitin chains are flexible multidomain proteins, whose conformational dynamics enable them to regulate multiple biological pathways. Their dynamic is determined by the linkage between ubiquitins and by the number of ubiquitin units. Characterizing polyubiquitin behavior as a function of their length is hampered because of increasing system size and conformational variability. Here, we introduce a new approach to efficiently integrating small-angle x-ray scattering with simulations allowing us to accurately characterize the dynamics of linear di-, tri-, and tetraubiquitin in the free state as well as of diubiquitin in complex with NEMO, a central regulator in the NF-κB pathway. Our results show that the behavior of the diubiquitin subunits is independent of the presence of additional ubiquitin modules and that the dynamics of polyubiquitins with different lengths follow a simple model. Together with experimental data from multiple biophysical techniques, we then rationalize the 2:1 NEMO:polyubiquitin binding.

Structure and Dynamics in the ATG8 Family From Experimental to Computational Techniques

Autophagy is a conserved and essential intracellular mechanism for the removal of damaged components. Since autophagy deregulation is linked to different kinds of pathologies, it is fundamental to gain knowledge on the fine molecular and structural details related to the core proteins of the autophagy machinery. Among these, the family of human ATG8 proteins plays a central role in recruiting other proteins to the different membrane structures involved in the autophagic pathway. Several experimental structures are available for the members of the ATG8 family alone or in complex with their different biological partners, including disordered regions of proteins containing a short linear motif called LC3 interacting motif. Recently, the first structural details of the interaction of ATG8 proteins with biological membranes came into light. The availability of structural data for human ATG8 proteins has been paving the way for studies on their structure-function-dynamic relationship using biomolecular simulations. Experimental and computational structural biology can help to address several outstanding questions on the mechanism of human ATG8 proteins, including their specificity toward different interactors, their association with membranes, the heterogeneity of their conformational ensemble, and their regulation by post-translational modifications. We here summarize the main results collected so far and discuss the future perspectives within the field and the knowledge gaps. Our review can serve as a roadmap for future structural and dynamics studies of the ATG8 family members in health and disease.

A Practical Guide to the Simultaneous Determination of Protein Structure and Dynamics Using Metainference

Accurate protein structural ensembles can be determined with metainference, a Bayesian inference method that integrates experimental information with prior knowledge of the system and deals with all sources of uncertainty and errors as well as with system heterogeneity. Furthermore, metainference can be implemented using the metadynamics approach, which enables the computational study of complex biological systems requiring extensive conformational sampling. In this chapter, we provide a step-by-step guide to perform and analyse metadynamic metainference simulations using the ISDB module of the open-source PLUMED library, as well as a series of practical tips to avoid common mistakes. Specifically, we will guide the reader in the process of learning how to model the structural ensemble of a small disordered peptide by combining state-of-the-art molecular mechanics force fields with nuclear magnetic resonance data, including chemical shifts, scalar couplings and residual dipolar couplings.

Determination of Protein Structural Ensembles by Hybrid-Resolution SAXS Restrained Molecular Dynamics

Small-angle X-ray scattering (SAXS) experiments provide low-resolution but valuable information about the dynamics of biomolecular systems, which could be ideally integrated into molecular dynamics (MD) simulations to accurately determine conformational ensembles of flexible proteins. The applicability of this strategy is hampered by the high computational cost required to calculate scattering intensities from three-dimensional structures. We previously presented a hybrid resolution method that makes atomistic SAXS-restrained MD simulation feasible by adopting a coarse-grained approach to efficiently back-calculate scattering intensities; here, we extend this technique, applying it in the framework of metainference with the aim to investigate the dynamical behavior of flexible biomolecules. The efficacy of the method is assessed on the K63-diubiquitin, showing that the inclusion of SAXS restraints is effective in generating a reliable conformational ensemble, improving the agreement with independent experimental data.

Hierarchical Ensembles of Intrinsically Disordered Proteins at Atomic Resolution in Molecular Dynamics Simulations

Intrinsically disordered proteins (IDPs) constitute a large fraction of the human proteome and are critical in the regulation of cellular processes. A detailed understanding of the conformational dynamics of IDPs could help to elucidate their roles in health and disease. However, the inherent flexibility of IDPs makes structural studies and their interpretation challenging. Molecular dynamics (MD) simulations could address this challenge in principle, but inaccuracies in the simulation models and the need for long simulations have stymied progress. To overcome these limitations, we adopt a hierarchical approach that builds on the "flexible-meccano" model reported by Bernadó et al. (J. Am. Chem. Soc. 2005, 127, 17968-17969). First, we exhaustively sample small IDP fragments in all-atom simulations to capture their local structures. Then, we assemble the fragments into full-length IDPs to explore the stereochemically possible global structures of IDPs. The resulting ensembles of three-dimensional structures of full-length IDPs are highly diverse, much more so than in standard MD simulation. For the paradigmatic IDP α-synuclein, our ensemble captures both the local structure, as probed by nuclear magnetic resonance spectroscopy, and its overall dimension, as obtained from small-angle X-ray scattering in solution. By generating representative and meaningful starting ensembles, we can begin to exploit the massive parallelism afforded by current and future high-performance computing resources for atomic-resolution characterization of IDPs.

Biochemical and biophysical comparison of human and mouse beta-2 microglobulin reveals the molecular determinants of low amyloid propensity

The molecular bases of amyloid aggregation propensity are still poorly understood, especially for proteins that display a stable folded native structure. A prototypic example is human beta-2 microglobulin (β2m), which, when accumulated in patients, gives rise to dialysis-related amyloidosis. Interestingly, although the physiologic concentration of β2m in mice is five times higher than that found in human patients, no amyloid deposits are observed in mice. Moreover, murine β2m (mβ2m) not only displays a lower amyloid propensity both in vivo and in vitro but also inhibits the aggregation of human β2m in vitro. Here, we compared human and mβ2m for their aggregation propensity, ability to form soluble oligomers, stability, three-dimensional structure and dynamics. Our results indicate that mβ2m low-aggregation propensity is due to two concomitant aspects: the low-aggregation propensity of its primary sequence combined with the absence of high-energy amyloid-competent conformations under native conditions. The identification of the specific properties determining the low-aggregation propensity of mouse β2m will help delineate the molecular risk factors which cause a folded protein to aggregate.

Martini bead form factors for nucleic acids and their application in the refinement of protein–nucleic acid complexes against SAXS data

The use of small-angle X-ray scattering (SAXS) in combination with molecular dynamics simulation is hampered by its heavy computational cost. The calculation of SAXS from atomic structures can be speeded up by using a coarse-grain representation of the structure. Following the work of Niebling, Björling & Westenhoff [J. Appl. Cryst. (2014), 47, 1190–1198], the Martini bead form factors for nucleic acids have been derived and then implemented, together with those previously determined for proteins, in the publicly available PLUMED library. A hybrid multi-resolution strategy has also been implemented to perform SAXS restrained simulations at atomic resolution by calculating the virtual positions of the Martini beads on the fly and using them for the calculation of SAXS. The accuracy and efficiency of the method are demonstrated by refining the structure of two protein–nucleic acid complexes. Instrumental for this result is the use of metainference, which allows the consideration and alleviation of the approximations at play in the present SAXS calculations.

Is protein context responsible for peptide-mediated interactions?

Many cell signaling pathways are orchestrated by the weak, transient, and reversible peptide-mediated interactions (PMIs). Here, the role of protein context in contributing to the stability and specificity of PMIs is investigated systematically.

Nature of the Pre-Chemistry Ensemble in Mitogen-Activated Protein Kinases

In spite of the availability of a significant amount of structural detail on docking interactions involving mitogen-activated protein kinases (MAPKs) and their substrates, the mechanism by which the disordered phospho-acceptor on the substrate transiently interacts with the kinase catalytic elements and is phosphorylated, often with high efficiency, remains poorly understood. Here, this dynamic interaction is analyzed in the context of available biophysical and biochemical data for ERK2, an archetypal MAPK. A hypothesis about the nature of the ternary complex involving a MAPK, its substrate, and ATP immediately prior to the chemical step (the pre-chemistry complex) is proposed. It is postulated that the solution ensemble (the pre-chemistry ensemble) representing the pre-chemistry complex comprises several conformations that are linked by dynamics on multiple timescales. These individual conformations possess different intrinsic abilities to proceed through the chemical step. The overall rate of chemistry is therefore related to the microscopic nature of the pre-chemistry ensemble, its constituent conformational microstates, and their intrinsic abilities to yield a phosphorylated product. While characterizing these microstates within the pre-chemistry ensemble in atomic or near-atomic detail is an extremely challenging proposition, recent developments in hybrid methodologies that employ computational approaches driven by experimental data appear to provide the most promising path forward toward achieving this goal.

The Antibody Light-Chain Linker Regulates Domain Orientation and Amyloidogenicity

The antibody light chain (LC) consists of two domains and is essential for antigen binding in mature immunoglobulins. The two domains are connected by a highly conserved linker that comprises the structurally important Arg108 residue. In antibody light chain (AL) amyloidosis, a severe protein amyloid disease, the LC and its N-terminal variable domain (V_L) convert to fibrils deposited in the tissues causing organ failure. Understanding the factors shaping the architecture of the LC is important for basic science, biotechnology and for deciphering the principles that lead to fibril formation. In this study, we examined the structure and properties of LC variants with a mutated or extended linker. We show that under destabilizing conditions, the linker modulates the amyloidogenicity of the LC. The fibril formation propensity of LC linker variants and their susceptibility to proteolysis directly correlate implying an interplay between the two LC domains. Using NMR and residual dipolar coupling-based simulations, we found that the linker residue Arg108 is a key factor regulating the relative orientation of the V_L and C_L domains, keeping them in a bent and dense, but still flexible conformation. Thus, inter-domain contacts and the relative orientation of V_L and C_L to each other are of major importance for maintaining the structural integrity of the full-length LC.

Biophysical experiments and biomolecular simulations: A perfect match?

A fundamental challenge in biological research is achieving an atomic-level description and mechanistic understanding of the function of biomolecules. Techniques for biomolecular simulations have undergone substantial developments, and their accuracy and scope have expanded considerably. Progress has been made through an increasingly tight integration of experiments and simulations, with experiments being used to refine simulations and simulations used to interpret experiments. Here we review the underpinnings of this progress, including methods for more efficient conformational sampling, accuracy of the physical models used, and theoretical approaches to integrate experiments and simulations. These developments are enabling detailed studies of complex biomolecular assemblies.

Molecular dynamics ensemble refinement of the heterogeneous native state of NCBD using chemical shifts and NOEs

Many proteins display complex dynamical properties that are often intimately linked to their biological functions. As the native state of a protein is best described as an ensemble of conformations, it is important to be able to generate models of native state ensembles with high accuracy. Due to limitations in sampling efficiency and force field accuracy it is, however, challenging to obtain accurate ensembles of protein conformations by the use of molecular simulations alone. Here we show that dynamic ensemble refinement, which combines an accurate atomistic force field with commonly available nuclear magnetic resonance (NMR) chemical shifts and NOEs, can provide a detailed and accurate description of the conformational ensemble of the native state of a highly dynamic protein. As both NOEs and chemical shifts are averaged on timescales up to milliseconds, the resulting ensembles reflect the structural heterogeneity that goes beyond that probed, e.g., by NMR relaxation order parameters. We selected the small protein domain NCBD as object of our study since this protein, which has been characterized experimentally in substantial detail, displays a rich and complex dynamical behaviour. In particular, the protein has been described as having a molten-globule like structure, but with a relatively rigid core. Our approach allowed us to describe the conformational dynamics of NCBD in solution, and to probe the structural heterogeneity resulting from both short- and long-timescale dynamics by the calculation of order parameters on different time scales. These results illustrate the usefulness of our approach since they show that NCBD is rather rigid on the nanosecond timescale, but interconverts within a broader ensemble on longer timescales, thus enabling the derivation of a coherent set of conclusions from various NMR experiments on this protein, which could otherwise appear in contradiction with each other.

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.

Computational Exploration of Conformational Transitions in Protein Drug Targets

Protein drug targets vary from highly structured to completely disordered; either way dynamics governs function. Hence, understanding the dynamical aspects of how protein targets function can enable improved interventions with drug molecules. Computational approaches offer highly detailed structural models of protein dynamics which are becoming more predictive as model quality and sampling power improve. However, the most advanced and popular models still have errors owing to imperfect parameter sets and often cannot access longer timescales of many crucial biological processes. Experimental approaches offer more certainty but can struggle to detect and measure lightly populated conformations of target proteins and subtle allostery. An emerging solution is to integrate available experimental data into advanced molecular simulations. In the future, molecular simulation in combination with experimental data may be able to offer detailed models of important drug targets such that improved functional mechanisms or selectivity can be accessed.

Force field development and simulations of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in many physiological processes such as signal transduction and transcriptional regulation. Computer simulations that are based on empirical force fields have been increasingly used to understand the biophysics of disordered proteins. In this review, we focus on recent improvement of protein force fields, including polarizable force fields, concerning their accuracy in modeling intrinsically disordered proteins. Some recent benchmarks and applications of these force fields are also overviewed.