Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

Refined Bonded Terms in Coarse-Grained Models for Intrinsically Disordered Proteins Improve Backbone Conformations

Coarse-grained models designed for intrinsically disordered proteins and regions (IDP/Rs) usually omit some bonded potentials (e.g., angular and dihedral potentials) as a conventional strategy to enhance backbone flexibility. However, a notable drawback of this approach is the generation of inaccurate backbone conformations. Here, we addressed this problem by introducing residue-specific angular, refined dihedral, and correction map (CMAP) potentials, derived based on the statistics from a customized coil database. These bonded potentials were integrated into the existing Mpipi model, resulting in a new model, denoted as the "Mpipi+" model. Results show that the Mpipi+ model can improve backbone conformations. More importantly, it can markedly improve the secondary structure propensity (SSP) based on the experimental chemical shift and, consequently, succeed in capturing transient secondary structures. Moreover, the Mpipi+ model preserves the liquid-liquid phase separation (LLPS) propensities of IDPs.

Phosphorylation of disordered proteins tunes local and global intramolecular interactions

Protein post-translational modifications, such as phosphorylation, are important regulatory signals for diverse cellular functions. In particular, intrinsically disordered protein regions (IDRs) are subject to phosphorylation as a means to modulate their interactions and functions. Toward understanding the relationship between phosphorylation in IDRs and specific functional outcomes, we must consider how phosphorylation affects the IDR conformational ensemble. Various experimental techniques are suited to interrogate the features of IDR ensembles; molecular simulations can provide complementary insights and even illuminate ensemble features that may be experimentally inaccessible. Therefore, we sought to expand the tools available to study phosphorylated IDRs by all-atom Monte Carlo simulations. To this end, we implemented parameters for phosphoserine (pSer) and phosphothreonine (pThr) into the OPLS version of the continuum solvent model, ABSINTH, and assessed their performance in all-atom simulations compared to published findings. We simulated short (< 20 residues) and long (> 80 residues) phospho-IDRs that, collectively, survey both local and global phosphorylation-induced changes to the ensemble. Our simulations of four well-studied phospho-IDRs show near-quantitative agreement with published findings for these systems via metrics including changes to radius of gyration, transient helicity, and persistence length. We also leveraged the inherent advantage of sequence control in molecular simulations to explore the conformational effects of diverse combinations of phospho-sites in two multi-phosphorylated IDRs. Our results support and expand on prior observations that connect phosphorylation to changes in the IDR conformational ensemble. Herein, we describe phosphorylation as a means to alter sequence chemistry, net charge and charge patterning, and intramolecular interactions, which can collectively modulate the local and global IDR ensemble features.

Thermodynamic modulation of gephyrin condensation by inhibitory synapse components

Phase separation drives compartmentalization of intracellular contents into various biomolecular condensates. Individual condensate components are thought to differentially contribute to the organization and function of condensates. However, how intermolecular interactions among constituent biomolecules modulate the phase behaviors of multicomponent condensates remains unclear. Here, we used core components of the inhibitory postsynaptic density (iPSD) as a model system to quantitatively probe how the network of intra- and intermolecular interactions defines the composition and cellular distribution of biomolecular condensates. We found that oligomerization-driven phase separation of gephyrin, an iPSD-specific scaffold, is critically modulated by an intrinsically disordered linker region exhibiting minimal homotypic attractions. Other iPSD components, such as neurotransmitter receptors, differentially promote gephyrin condensation through distinct binding modes and affinities. We further demonstrated that the local accumulation of scaffold-binding proteins at the cell membrane promotes the nucleation of gephyrin condensates in neurons. These results suggest that in multicomponent systems, the extent of scaffold condensation can be fine-tuned by scaffold-binding factors, a potential regulatory mechanism for self-organized compartmentalization in cells.

Recent advances in de novo computational design and redesign of intrinsically disordered proteins and intrinsically disordered protein regions

In the early 2000s, the concept of "unstructured biology" has emerged to be an important field in protein science by generating various new research directions. Many novel strategies and methods have been developed that are focused on effectively identifying/predicting intrinsically disordered proteins (IDPs) and intrinsically disordered protein regions (IDPRs), identifying their potential functions, disorder based drug design etc. Due to the range of functions of IDPs/IDPRs and their involvement in various debilitating diseases they are of contemporary interest to the scientific community. Recent researches are focused on designing/redesigning specific IDPs/IDPRs de novo. These de novo design/redesigns of IDPs/IDPRs are carried out by altering compositional biases and specific sequence patterning parameters. The main focus of these researches is to influence specific molecular functions, phase behavior, cellular phenotypes etc. In this review, we first provide the differences of natively folded and natively unfolded or IDPs with respect to their potential energy landscapes. Here, we provide current understandings on the different computational design strategies and methods that have been utilized in de novo design and redesigns of IDPs and IDPRs. Finally, we conclude the review by discussing the challenges that have been faced during the computational design/design attempts of IDPs/IDPRs.

Biophysical and Integrative Characterization of Protein Intrinsic Disorder as a Prime Target for Drug Discovery

Protein intrinsic disorder is increasingly recognized for its biological and disease-driven functions. However, it represents significant challenges for biophysical studies due to its high conformational flexibility. In addressing these challenges, we highlight the complementary and distinct capabilities of a range of experimental and computational methods and further describe integrative strategies available for combining these techniques. Integrative biophysics methods provide valuable insights into the sequence–structure–function relationship of disordered proteins, setting the stage for protein intrinsic disorder to become a promising target for drug discovery. Finally, we briefly summarize recent advances in the development of new small molecule inhibitors targeting the disordered N-terminal domains of three vital transcription factors.

From dilute to concentrated solutions of intrinsically disordered proteins: Interpretation and analysis of collected data

Intrinsically disordered proteins (IDPs) have a broad energy landscape and consequently sample many different conformations in solution. The innate flexibility of IDPs is exploited in their biological function, and in many instances allows a single IDP to regulate a range of processes in vivo. Due to their highly flexible nature, characterizing the structural properties of IDPs is not straightforward. Often solution-based methods such as Nuclear Magnetic Resonance (NMR), Förster Resonance Energy Transfer (FRET), and Small-Angle X-ray Scattering (SAXS) are used. SAXS is indeed a powerful technique to study the structural and conformational properties of IDPs in solution, and from the obtained SAXS spectra, information about the average size, shape, and extent of oligomerization can be determined. In this chapter, we will introduce model-free methods that can be used to interpret SAXS data and introduce methods that can be used to interpret SAXS data beyond analytical models, for example, by using atomistic and different levels of coarse-grained models in combination with molecular dynamics (MD) and Monte Carlo simulations.

Hydration Free Energies of Polypeptides from Popular Implicit Solvent Models versus All-Atom Simulation Results Based on Molecular Quasichemical Theory

Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT)─an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecular solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions and thus provides a convenient framework to investigate the assumptions in implicit solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit solvent models for polyglycine and polyalanine solutes covering a range of chain lengths and conformations. The hydration free energies or the differences in hydration free energies between conformers obtained from the implicit solvent models do not agree with explicit solvent results, with the deviations being largest for the group additive EEF1 and ABSINTH models. GB/SA does better in capturing the qualitative trends seen in explicit solvent results. Analysis founded on QCT reveals the critical importance of the cooperativity of hydration that is inherent in the hydrophilic and hydrophobic contributions to hydration─physics that is not well captured in additive models but somewhat better accounted for by means of a dielectric in the GB/SA approach.

pH Induced Switch in the Conformational Ensemble of Intrinsically Disordered Protein Prothymosin-α and Its Implications for Amyloid Fibril Formation

Aggregation of intrinsically disordered proteins (IDPs) can lead to neurodegenerative diseases. Although there is experimental evidence that acidic pH promotes IDP monomer compaction leading to aggregation, the general mechanism is unclear. We studied the pH effect on the conformational ensemble of prothymosin-α (proTα), which is involved in multiple essential functions, and probed its role in aggregation using computer simulations. We show that compaction in the proTα dimension at low pH is due to the protein's collapse in the intermediate region (E41-D80) rich in glutamic acid residues, enhancing its β-sheet content. We observed by performing dimer simulations that the conformations with high β-sheet content could act as aggregation-prone (N*) states and nucleate the aggregation process. The simulations initiated using N* states form dimers within a microsecond time scale, whereas the non-N* states do not form dimers within this time scale. This study contributes to understanding the general principles of pH-induced IDP aggregation.

Solvent paramagnetic relaxation enhancement as a versatile method for studying structure and dynamics of biomolecular systems

Solvent paramagnetic relaxation enhancement (sPRE) is a versatile nuclear magnetic resonance (NMR)-based method that allows characterization of the structure and dynamics of biomolecular systems through providing quantitative experimental information on solvent accessibility of NMR-active nuclei. Addition of soluble paramagnetic probes to the solution of a biomolecule leads to paramagnetic relaxation enhancement in a concentration-dependent manner. Here we review recent progress in the sPRE-based characterization of structural and dynamic properties of biomolecules and their complexes, and aim to deliver a comprehensive illustration of a growing number of applications of the method to various biological systems. We discuss the physical principles of sPRE measurements and provide an overview of available co-solute paramagnetic probes. We then explore how sPRE, in combination with complementary biophysical techniques, can further advance biomolecular structure determination, identification of interaction surfaces within protein complexes, and probing of conformational changes and low-population transient states, as well as deliver insights into weak, nonspecific, and transient interactions between proteins and co-solutes. In addition, we present examples of how the incorporation of solvent paramagnetic probes can improve the sensitivity of NMR experiments and discuss the prospects of applying sPRE to NMR metabolomics, drug discovery, and the study of intrinsically disordered proteins.

Toward Accurate Coarse-Grained Simulations of Disordered Proteins and Their Dynamic Interactions

Intrinsically disordered proteins (IDPs) play crucial roles in cellular regulatory networks and are now recognized to often remain highly dynamic even in specific interactions and assemblies. Accurate description of these dynamic interactions is extremely challenging using atomistic simulations because of the prohibitive computational cost. Efficient coarse-grained approaches could offer an effective solution to overcome this bottleneck if they could provide an accurate description of key local and global properties of IDPs in both unbound and bound states. The recently developed hybrid-resolution (HyRes) protein model has been shown to be capable of providing a semiquantitative description of the secondary structure propensities of IDPs. Here, we show that greatly improved description of global structures and transient interactions can be achieved by introducing a solvent-accessible surface area-based implicit solvent term followed by reoptimization of effective interaction strengths. The new model, termed HyRes II, can semiquantitatively reproduce a wide range of local and global structural properties of a set of IDPs of various lengths and complexities. It can also distinguish the level of compaction between folded proteins and IDPs. In particular, applied to the disordered N-terminal transactivation domain (TAD) of tumor suppressor p53, HyRes II is able to recapitulate various nontrivial structural properties compared to experimental results, some of them to a level of accuracy that is almost comparable to results from atomistic explicit solvent simulations. Furthermore, we demonstrate that HyRes II can be used to simulate the dynamic interactions of TAD with the DNA-binding domain of p53, generating structural ensembles that are highly consistent with existing NMR data. We anticipate that HyRes II will provide an efficient and relatively reliable tool toward accurate coarse-grained simulations of dynamic protein interactions.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

A fast-slow method to treat solute dynamics in explicit solvent

Aiming to reduce the computational cost in the current explicit solvent molecular dynamics (MD) simulation, this paper proposes a fast-slow method for the fast MD simulation of biomolecules in explicit solvent. This fast-slow method divides the entire system into two parts: a core layer (typically solute or biomolecule) and a peripheral layer (typically solvent molecules). The core layer is treated using standard MD method but the peripheral layer is treated by a slower dynamics method to reduce the computational cost. We compared four different simulation models in testing calculations for several small proteins. These include gas-phase, implicit solvent, fast-slow explicit solvent and standard explicit solvent MD simulations. Our study shows that gas-phase and implicit solvent models do not provide a realistic solvent environment and fail to correctly produce reliable dynamic structures of proteins. On the other hand, the fast-slow method can essentially reproduce the same solvent effect as the standard explicit solvent model while gaining an order of magnitude in efficiency. This fast-slow method thus provides an efficient approach for accelerating the MD simulation of biomolecules in explicit solvent.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

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

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

Unifying coarse-grained force fields for folded and disordered proteins

Liquid-liquid phase separation drives the formation of biological condensates that play essential roles in transcriptional regulation and signal sensing. Computational modeling could provide high-resolution structural characterizations of these condensates and help uncover physicochemical interactions that dictate their stability. However, many protein molecules involved in phase separation often contain multiple ordered domains connected with flexible, structureless linkers. Simulating such proteins necessitates force fields with consistent accuracy for both folded and disordered proteins. We provide a critical review of existing coarse-grained force fields for disordered proteins and highlight the challenges in their application to folded proteins. After discussing existing algorithms for force field parameterization, we propose an optimization strategy that should lead to computer models with improved transferability across protein types.

When Order Meets Disorder: Modeling and Function of the Protein Interface in Fuzzy Complexes

The degree of proteins structural organization ranges from highly structured, compact folding to intrinsic disorder, where each degree of self-organization corresponds to specific functions: well-organized structural motifs in enzymes offer a proper environment for precisely positioned functional groups to participate in catalytic reactions; at the other end of the self-organization spectrum, intrinsically disordered proteins act as binding hubs via the formation of multiple, transient and often non-specific interactions. This review focusses on cases where structurally organized proteins or domains associate with highly disordered protein chains, leading to the formation of interfaces with varying degrees of fuzziness. We present a review of the computational methods developed to provide us with information on such fuzzy interfaces, and how they integrate experimental information. The discussion focusses on two specific cases, microtubules and homologous recombination nucleoprotein filaments, where a network of intrinsically disordered tails exerts regulatory function in recruiting partner macromolecules, proteins or DNA and tuning the atomic level association. Notably, we show how computational approaches such as molecular dynamics simulations can bring new knowledge to help bridging the gap between experimental analysis, that mostly concerns ensemble properties, and the behavior of individual disordered protein chains that contribute to regulation functions.

AlphaFold and Implications for Intrinsically Disordered Proteins

Accurate predictions of the three-dimensional structures of proteins from their amino acid sequences have come of age. AlphaFold, a deep learning-based approach to protein structure prediction, shows remarkable success in independent assessments of prediction accuracy. A significant epoch in structural bioinformatics was the structural annotation of over 98% of protein sequences in the human proteome. Interestingly, many predictions feature regions of very low confidence, and these regions largely overlap with intrinsically disordered regions (IDRs). That over 30% of regions within the proteome are disordered is congruent with estimates that have been made over the past two decades, as intense efforts have been undertaken to generalize the structure-function paradigm to include the importance of conformational heterogeneity and dynamics. With structural annotations from AlphaFold in hand, there is the temptation to draw inferences regarding the "structures" of IDRs and their interactomes. Here, we offer a cautionary note regarding the misinterpretations that might ensue and highlight efforts that provide concrete understanding of sequence-ensemble-function relationships of IDRs. This perspective is intended to emphasize the importance of IDRs in sequence-function relationships (SERs) and to highlight how one might go about extracting quantitative SERs to make sense of how IDRs function.

Advanced Sampling Methods for Multiscale Simulation of Disordered Proteins and Dynamic Interactions

Intrinsically disordered proteins (IDPs) are highly prevalent and play important roles in biology and human diseases. It is now also recognized that many IDPs remain dynamic even in specific complexes and functional assemblies. Computer simulations are essential for deriving a molecular description of the disordered protein ensembles and dynamic interactions for a mechanistic understanding of IDPs in biology, diseases, and therapeutics. Here, we provide an in-depth review of recent advances in the multi-scale simulation of disordered protein states, with a particular emphasis on the development and application of advanced sampling techniques for studying IDPs. These techniques are critical for adequate sampling of the manifold functionally relevant conformational spaces of IDPs. Together with dramatically improved protein force fields, these advanced simulation approaches have achieved substantial success and demonstrated significant promise towards the quantitative and predictive modeling of IDPs and their dynamic interactions. We will also discuss important challenges remaining in the atomistic simulation of larger systems and how various coarse-grained approaches may help to bridge the remaining gaps in the accessible time- and length-scales of IDP simulations.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Microbially Guided Discovery and Biosynthesis of Biologically Active Natural Products

The design of small molecules that inhibit disease-relevant proteins represents a longstanding challenge of medicinal chemistry. Here, we describe an approach for encoding this challenge-the inhibition of a human drug target-into a microbial host and using it to guide the discovery and biosynthesis of targeted, biologically active natural products. This approach identified two previously unknown terpenoid inhibitors of protein tyrosine phosphatase 1B (PTP1B), an elusive therapeutic target for the treatment of diabetes and cancer. Both inhibitors appear to target an allosteric site, which confers selectivity, and can inhibit PTP1B in living cells. A screen of 24 uncharacterized terpene synthases from a pool of 4464 genes uncovered additional hits, demonstrating a scalable discovery approach, and the incorporation of different PTPs into the microbial host yielded alternative PTP-specific detection systems. Findings illustrate the potential for using microbes to discover and build natural products that exhibit precisely defined biochemical activities yet possess unanticipated structures and/or binding sites.

Learning the protein language: Evolution, structure, and function

Language models have recently emerged as a powerful machine-learning approach for distilling information from massive protein sequence databases. From readily available sequence data alone, these models discover evolutionary, structural, and functional organization across protein space. Using language models, we can encode amino-acid sequences into distributed vector representations that capture their structural and functional properties, as well as evaluate the evolutionary fitness of sequence variants. We discuss recent advances in protein language modeling and their applications to downstream protein property prediction problems. We then consider how these models can be enriched with prior biological knowledge and introduce an approach for encoding protein structural knowledge into the learned representations. The knowledge distilled by these models allows us to improve downstream function prediction through transfer learning. Deep protein language models are revolutionizing protein biology. They suggest new ways to approach protein and therapeutic design. However, further developments are needed to encode strong biological priors into protein language models and to increase their accessibility to the broader community.

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent the ABSINTH (self-Assembly of Biomolecules Studied by an Implicit, Novel, Tunable Hamiltonian) implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA (atomic multipole optimized energetics for biomolecular applications) forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

Multivalent-Interaction-Driven Assembly of Discrete, Flexible, and Asymmetric Supramolecular Protein Nano-Prisms

Current approaches to design monodisperse protein assemblies require rigid, tight, and symmetric interactions between oligomeric protein units. Herein, we introduce a new multivalent-interaction-driven assembly strategy that allows flexible, spaced, and asymmetric assembly between protein oligomers. We discovered that two polygonal protein oligomers (ranging from triangle to hexagon) dominantly form a discrete and stable two-layered protein prism nanostructure via multivalent interactions between fused binding pairs. We demonstrated that protein nano-prisms with long flexible peptide linkers (over 80 amino acids) between protein oligomer layers could be discretely formed. Oligomers with different structures could also be monodispersely assembled into two-layered but asymmetric protein nano-prisms. Furthermore, producing higher-order architectures with multiple oligomer layers, for example, 3-layered nano-prisms or nanotubes, was also feasible.

An ABSINTH-Based Protocol for Predicting Binding Affinities between Proteins and Small Molecules

The core task in computational drug discovery is to accurately predict binding free energies in receptor-ligand systems for large libraries of putative binders. Here, the ABSINTH implicit solvent model and force field are extended to describe small, organic molecules and their interactions with proteins. We show that an automatic pipeline based on partitioning arbitrary molecules into substructures corresponding to model compounds with known free energies of solvation can be combined with the CHARMM general force field into a method that is successful at the two important challenges a scoring function faces in virtual screening work flows: it ranks known binders with correlation values rivaling that of comparable state-of-the-art methods and it enriches true binders in a set of decoys. Our protocol introduces innovative modifications to common virtual screening workflows, notably the use of explicit ions as competitors and the integration over multiple protein and ligand species differing in their protonation states. We demonstrate the value of modifications to both the protocol and ABSINTH itself. We conclude by discussing the limitations of high-throughput implicit methods such as the one proposed here.

Influence of electrostatic forces on the association kinetics and conformational ensemble of an intrinsically disordered protein

Recent work has revealed that the association of a disordered region of a protein with a folded binding partner can occur as rapidly as association between two folded proteins. This is the case for the phosphatase calcineurin (CaN) and its association with its activator calmodulin. Calmodulin binds to the intrinsically disordered regulatory domain of CaN. Previous studies have shown that electrostatic steering can accelerate the binding of folded proteins with disordered ligands. Given that electrostatic forces are strong determinants of disordered protein ensembles, the relationship between electrostatics, conformational ensembles, and quaternary interactions is unclear. Here, we employ experimental approaches to explore the impact of electrostatic interactions on the association of calmodulin with the disordered regulatory region of CaN. We find that estimated association rate constants of calmodulin with our chosen calmodulin-substrates are within the diffusion-limited regime. The association rates are dependent on the ionic strength, indicating that favorable electrostatic forces increase the rate of association. Further, we show that charged amino acids outside the calmodulin-binding site modulate the binding rate. Conformational ensembles obtained from computer simulations suggest that electrostatic interactions within the regulatory domain might bias the conformational ensemble such that the calmodulin binding region is readily accessible. Given the prevalence of charged residues in disordered protein chains, our findings are likely relevant to many protein-protein interactions.

Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs, also known as stickers, is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter, such as temperature, that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single-chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low-complexity domains. We also leverage theories to compute sequence-specific percolation lines and thereby provide a thermodynamic framework for hardening transitions that have been observed for many biomolecular condensates.

Information theoretic measures for quantifying sequence-ensemble relationships of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) contribute to a multitude of functions. De novo design of IDPs should open the door to modulating functions and phenotypes controlled by these systems. Recent design efforts have focused on compositional biases and specific sequence patterns as the design features. Analysis of the impact of these designs on sequence-function relationships indicates that individual sequence/compositional parameters are insufficient for describing sequence-function relationships in IDPs. To remedy this problem, we have developed information theoretic measures for sequence–ensemble relationships (SERs) of IDPs. These measures rely on prior availability of statistically robust conformational ensembles derived from all atom simulations. We show that the measures we have developed are useful for comparing sequence-ensemble relationships even when sequence is poorly conserved. Based on our results, we propose that de novo designs of IDPs, guided by knowledge of their SERs, should provide improved insights into their sequence–ensemble–function relationships.

Targeting Intrinsically Disordered Proteins through Dynamic Interactions

Intrinsically disordered proteins (IDPs) are over-represented in major disease pathways and have attracted significant interest in understanding if and how they may be targeted using small molecules for therapeutic purposes. While most existing studies have focused on extending the traditional structure-centric drug design strategies and emphasized exploring pre-existing structure features of IDPs for specific binding, several examples have also emerged to suggest that small molecules could achieve specificity in binding IDPs and affect their function through dynamic and transient interactions. These dynamic interactions can modulate the disordered conformational ensemble and often lead to modest compaction to shield functionally important interaction sites. Much work remains to be done on further elucidation of the molecular basis of the dynamic small molecule-IDP interaction and determining how it can be exploited for targeting IDPs in practice. These efforts will rely critically on an integrated experimental and computational framework for disordered protein ensemble characterization. In particular, exciting advances have been made in recent years in enhanced sampling techniques, Graphic Processing Unit (GPU)-computing, and protein force field optimization, which have now allowed rigorous physics-based atomistic simulations to generate reliable structure ensembles for nontrivial IDPs of modest sizes. Such de novo atomistic simulations will play crucial roles in exploring the exciting opportunity of targeting IDPs through dynamic interactions.

Predicting Conformational Properties of Intrinsically Disordered Proteins from Sequence

Intrinsically disordered proteins (IDPs) can adopt a range of conformations from globules to swollen coils. This large range of conformational preferences for different IDPs raises the question of how conformational preferences are encoded by sequence. Global compositional features of a sequence such as the fraction of charged residues and the net charge per residue engender certain conformational biases. However, more specific sequence features such as the patterning of oppositely charged residues, expansion driving residues, or residues that can undergo posttranslational modifications can also influence the conformational ensembles of an IDP. Here, we outline how to calculate important global compositional features and patterning metrics that can be used to classify IDPs into different conformational classes and predict relative changes in conformation for sequences with the same amino acid composition. Although increased effort has been devoted to determining conformational properties of IDPs in recent years, quantitative predictions of conformation directly from sequence remain difficult and often inaccurate. Thus, if quantitative predictions of conformational properties are desired, then sequence-specific simulations must be performed.

Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach

The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the distance geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent geometry and may have benefits from the recent development of residue-specific force-fields.

Accuracy of protein-level disorder predictions

Experimental annotations of intrinsic disorder are available for 0.1% of 147 000 000 of currently sequenced proteins. Over 60 sequence-based disorder predictors were developed to help bridge this gap. Current benchmarks of these methods assess predictive performance on datasets of proteins; however, predictions are often interpreted for individual proteins. We demonstrate that the protein-level predictive performance varies substantially from the dataset-level benchmarks. Thus, we perform first-of-its-kind protein-level assessment for 13 popular disorder predictors using 6200 disorder-annotated proteins. We show that the protein-level distributions are substantially skewed toward high predictive quality while having long tails of poor predictions. Consequently, between 57% and 75% proteins secure higher predictive performance than the currently used dataset-level assessment suggests, but as many as 30% of proteins that are located in the long tails suffer low predictive performance. These proteins typically have relatively high amounts of disorder, in contrast to the mostly structured proteins that are predicted accurately by all 13 methods. Interestingly, each predictor provides the most accurate results for some number of proteins, while the best-performing at the dataset-level method is in fact the best for only about 30% of proteins. Moreover, the majority of proteins are predicted more accurately than the dataset-level performance of the most accurate tool by at least four disorder predictors. While these results suggests that disorder predictors outperform their current benchmark performance for the majority of proteins and that they complement each other, novel tools that accurately identify the hard-to-predict proteins and that make accurate predictions for these proteins are needed.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Covalently-assembled single-chain protein nanostructures with ultra-high stability

Protein nanostructures with precisely defined geometries have many potential applications in catalysis, sensing, signal processing, and drug delivery. While many de novo protein nanostructures have been assembled via non-covalent intramolecular and intermolecular interactions, a largely unexplored strategy is to construct nanostructures by covalently linking multiple individually folded proteins through site-specific ligations. Here, we report the synthesis of single-chain protein nanostructures with triangular and square shapes made using multiple copies of a three-helix bundle protein and split intein chemistry. Coarse-grained simulations confirm the experimentally observed flexibility of these nanostructures, which is optimized to produce triangular structures with high regularity. These single-chain nanostructures also display ultra-high thermostability, resist denaturation by chaotropes and organic solvents, and have applicability as scaffolds for assembling materials with nanometer resolution. Our results show that site-specific covalent ligation can be used to assemble individually folded proteins into single-chain nanostructures with bespoke architectures and high stabilities.

De novo protein nanostructures are typically assembled via top-down approaches. Here, the authors developed a bottom-up approach, using split inteins to ligate multiple copies of a three-helix bundle to create 2D triangular and square-shaped structures with high stability.

Residual Structures and Transient Long-Range Interactions of p53 Transactivation Domain: Assessment of Explicit Solvent Protein Force Fields

Molecular dynamics simulations using physics-based atomistic force fields have been increasingly used to characterize the heterogeneous structural ensembles of intrinsically disordered proteins (IDPs). To evaluate the accuracy of the latest atomistic explicit-solvent force fields in modeling larger IDPs with nontrivial structural features, we focus on the 61-residue N-terminal transactivation domain (TAD) of tumor suppressor p53, an important protein in cancer biology that has been extensively studied, and abundant experimental data is available for evaluation of simulated ensembles. We performed extensive replica exchange with solute tempering simulations, in excess of 1.0 μs/replica, to generate disordered structural ensembles of p53-TAD using six latest explicit solvent protein force fields. Multiple local and long-range structural properties, including chain dimension, residual secondary structures, and transient long-range contacts, were analyzed and compared against available experimental data. The results show that IDPs such as p53-TAD remain highly challenging for atomistic simulations due to conformational complexity and difficulty in achieving adequate convergence. Structural ensembles of p53-TAD generated using various force fields differ significantly from each other. The a99SB-disp force field demonstrates the best agreement with experimental data at all levels and proves to be suitable for simulating unbound p53-TAD and how its conformational properties may be modulated by phosphorylation and other cellular signals or cancer-associated mutations. Feasibility of such detailed structural characterization is a key step toward establishing the sequence-disordered ensemble-function-disease relationship of p53 and other biologically important IDPs.

Recent Advances in Computational Protocols Addressing Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDP) are abundant in the human genome and have recently emerged as major therapeutic targets for various diseases. Unlike traditional proteins that adopt a definitive structure, IDPs in free solution are disordered and exist as an ensemble of conformations. This enables the IDPs to signal through multiple signaling pathways and serve as scaffolds for multi-protein complexes. The challenge in studying IDPs experimentally stems from their disordered nature. Nuclear magnetic resonance (NMR), circular dichroism, small angle X-ray scattering, and single molecule Förster resonance energy transfer (FRET) can give the local structural information and overall dimension of IDPs, but seldom provide a unified picture of the whole protein. To understand the conformational dynamics of IDPs and how their structural ensembles recognize multiple binding partners and small molecule inhibitors, knowledge-based and physics-based sampling techniques are utilized in-silico, guided by experimental structural data. However, efficient sampling of the IDP conformational ensemble requires traversing the numerous degrees of freedom in the IDP energy landscape, as well as force-fields that accurately model the protein and solvent interactions. In this review, we have provided an overview of the current state of computational methods for studying IDP structure and dynamics and discussed the major challenges faced in this field.

Experimentally Derived and Computationally Optimized Backbone Conformational Statistics for Blocked Amino Acids

Experimentally derived, amino acid specific backbone dihedral angle distributions are invaluable for modeling data-driven conformational equilibria of proteins and for enabling quantitative assessments of the accuracies of molecular mechanics force fields. The protein coil library that is extracted from analysis of high-resolution structures of proteins has served as a useful proxy for quantifying intrinsic and context-dependent conformational distributions of amino acids. However, data that go into coil libraries will have hidden biases, and ad hoc procedures must be used to remove these biases. Here, we combine high-resolution biased information from protein structural databases with unbiased low-resolution information from spectroscopic measurements of blocked amino acids to obtain experimentally derived and computationally optimized coil-library landscapes for each of the 20 naturally occurring amino acids. Quantitative descriptions of conformational distributions require parsing of data into conformational basins with defined envelopes, centers, and statistical weights. We develop and deploy a numerical method to extract conformational basins. The weights of conformational basins are optimized to reproduce quantitative inferences drawn from spectroscopic experiments for blocked amino acids. The optimized distributions serve as touchstones for assessments of intrinsic conformational preferences and for quantitative comparisons of molecular mechanics force fields.