Hamiltonian Switch Metropolis Monte Carlo Simulations for Improved Conformational Sampling of Intrinsically Disordered Regions Tethered to Ordered Domains of Proteins

Convergence-Adaptive Roundtrip Method Enables Rapid and Accurate FEP Calculations

The free energy perturbation (FEP) method is a powerful technique for accurate binding free energy calculations, which is crucial for identifying potent ligands with a high affinity in drug discovery. However, the widespread application of FEP is limited by the high computational cost required to achieve equilibrium sampling and the challenges in obtaining converged predictions. In this study, we present the convergence-adaptive roundtrip (CAR) method, which is an enhanced adaptive sampling approach, to address the key challenges in FEP calculations, including the precision-efficiency tradeoff, sampling efficiency, and convergence assessment. By employing on-the-fly convergence analysis to automatically adjust simulation times, enabling efficient traversal of the important phase space through rapid propagation of conformations between different states and eliminating the need for multiple parallel simulations, the CAR method increases convergence and minimizes computational overhead while maintaining calculation accuracy. The performance of the CAR method was evaluated through relative binding free energy (RBFE) calculations on benchmarks comprising four diverse protein-ligand systems. The results demonstrated a significant speedup of over 8-fold compared to conventional FEP methods while maintaining high accuracy. The overall R2 values of 0.65 and 0.56 were obtained using the combined-structure FEP approach and the single-step FEP approach, respectively, in conjunction with the CAR method. In-depth case studies further highlighted the superior performance of the CAR method in terms of convergence acceleration, improved predicted correlations, and reduced computational costs. The advancement of the CAR method makes it a highly effective approach, enhancing the applicability of FEP in drug discovery.

Machine Learning Generation of Dynamic Protein Conformational Ensembles

Machine learning has achieved remarkable success across a broad range of scientific and engineering disciplines, particularly its use for predicting native protein structures from sequence information alone. However, biomolecules are inherently dynamic, and there is a pressing need for accurate predictions of dynamic structural ensembles across multiple functional levels. These problems range from the relatively well-defined task of predicting conformational dynamics around the native state of a protein, which traditional molecular dynamics (MD) simulations are particularly adept at handling, to generating large-scale conformational transitions connecting distinct functional states of structured proteins or numerous marginally stable states within the dynamic ensembles of intrinsically disordered proteins. Machine learning has been increasingly applied to learn low-dimensional representations of protein conformational spaces, which can then be used to drive additional MD sampling or directly generate novel conformations. These methods promise to greatly reduce the computational cost of generating dynamic protein ensembles, compared to traditional MD simulations. In this review, we examine recent progress in machine learning approaches towards generative modeling of dynamic protein ensembles and emphasize the crucial importance of integrating advances in machine learning, structural data, and physical principles to achieve these ambitious goals.

Re-Balancing Replica Exchange with Solute Tempering for Sampling Dynamic Protein Conformations

Replica exchange with solute tempering (REST) is a highly effective variant of replica exchange for enhanced sampling in explicit solvent simulations of biomolecules. By scaling the Hamiltonian for a selected "solute" region of the system, REST effectively applies tempering only to the degrees of freedom of interest but not the rest of the system ("solvent"), allowing fewer replicas for covering the same temperature range. A key consideration of REST is how the solute-solvent interactions are scaled together with the solute-solute interactions. Here, we critically evaluate the performance of the latest REST2 protocol for sampling large-scale conformation fluctuations of intrinsically disordered proteins (IDPs). The results show that REST2 promotes artificial protein conformational collapse at high effective temperatures, which seems to be a designed feature originally to promote the sampling of reversible folding of small proteins. The collapse is particularly severe with larger IDPs, leading to replica segregation in the effective temperature space and hindering effective sampling of large-scale conformational changes. We propose that the scaling of the solute-solvent interactions can be treated as free parameters in REST, which can be tuned to control the solute conformational properties (e.g., chain expansion) at different effective temperatures and achieve more effective sampling. To this end, we derive a new REST3 protocol, where the strengths of the solute-solvent van der Waals interactions are recalibrated to reproduce the levels of protein chain expansion at high effective temperatures. The efficiency of REST3 is examined using two IDPs with nontrivial local and long-range structural features, including the p53 N-terminal domain and the kinase inducible transactivation domain of transcription factor CREB. The results suggest that REST3 leads to a much more efficient temperature random walk and improved sampling efficiency, which also further reduces the number of replicas required. Nonetheless, our analysis also reveals significant challenges of relying on tempering alone for sampling large-scale conformational fluctuations of disordered proteins. It is likely that more efficient sampling protocols will require incorporating more sophisticated Hamiltonian replica exchange schemes in addition to tempering.

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.

Generation of Quantum Configurational Ensembles Using Approximate Potentials

Conformational analysis is of paramount importance in drug design: it is crucial to determine pharmacological properties, understand molecular recognition processes, and characterize the conformations of ligands when unbound. Molecular Mechanics (MM) simulation methods, such as Monte Carlo (MC) and molecular dynamics (MD), are usually employed to generate ensembles of structures due to their ability to extensively sample the conformational space of molecules. The accuracy of these MM-based schemes strongly depends on the functional form of the force field (FF) and its parametrization, components that often hinder their performance. High-level methods, such as ab initio MD, provide reliable structural information but are still too computationally expensive to allow for extensive sampling. Therefore, to overcome these limitations, we present a multilevel MC method that is capable of generating quantum configurational ensembles while keeping the computational cost at a minimum. We show that FF reparametrization is an efficient route to generate FFs that reproduce QM results more closely, which, in turn, can be used as low-cost models to achieve the gold standard QM accuracy. We demonstrate that the MC acceptance rate is strongly correlated with various phase space overlap measurements and that it constitutes a robust metric to evaluate the similarity between the MM and QM levels of theory. As a more advanced application, we present a self-parametrizing version of the algorithm, which combines sampling and FF parametrization in one scheme, and apply the methodology to generate the QM/MM distribution of a ligand in aqueous solution.

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.

Cancer-Associated Mutations Perturb the Disordered Ensemble and Interactions of the Intrinsically Disordered p53 Transactivation Domain

Intrinsically disordered proteins (IDPs) are key components of regulatory networks that control crucial aspects of cell decision making. The intrinsically disordered transactivation domain (TAD) of tumor suppressor p53 mediates its interactions with multiple regulatory pathways to control the p53 homeostasis during the cellular response to genotoxic stress. Many cancer-associated mutations have been discovered in p53-TAD, but their structural and functional consequences are poorly understood. Here, by combining atomistic simulations, NMR spectroscopy, and binding assays, we demonstrate that cancer-associated mutations can significantly perturb the balance of p53 interactions with key activation and degradation regulators. Importantly, the four mutations studied in this work do not all directly disrupt the known interaction interfaces. Instead, at least three of these mutations likely modulate the disordered state of p53-TAD to perturb its interactions with regulators. Specifically, NMR and simulation analysis together suggest that these mutations can modulate the level of conformational expansion as well as rigidity of the disordered state. Our work suggests that the disordered conformational ensemble of p53-TAD can serve as a central conduit in regulating the response to various cellular stimuli at the protein-protein interaction level. Understanding how the disordered state of IDPs may be modulated by regulatory signals and/or disease associated perturbations will be essential in the studies on the role of IDPs in biology and diseases.

The diversity of molecular interactions involving intrinsically disordered proteins: A molecular modeling perspective

Intrinsically Disordered Proteins and Regions (IDPs/IDRs) are key components of a multitude of biological processes. Conformational malleability enables IDPs/IDRs to perform very specialized functions that cannot be accomplished by globular proteins. The functional role for most of these proteins is related to the recognition of other biomolecules to regulate biological processes or as a part of signaling pathways. Depending on the extent of disorder, the number of interacting sites and the type of partner, very different architectures for the resulting assemblies are possible. More recently, molecular condensates with liquid-like properties composed of multiple copies of IDPs and nucleic acids have been proven to regulate key processes in eukaryotic cells. The structural and kinetic details of disordered biomolecular complexes are difficult to unveil experimentally due to their inherent conformational heterogeneity. Computational approaches, alone or in combination with experimental data, have emerged as unavoidable tools to understand the functional mechanisms of this elusive type of assemblies. The level of description used, all-atom or coarse-grained, strongly depends on the size of the molecular systems and on the timescale of the investigated mechanism. In this mini-review, we describe the most relevant architectures found for molecular interactions involving IDPs/IDRs and the computational strategies applied for their investigation.

Structural Proteomics Methods to Interrogate the Conformations and Dynamics of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and regions of intrinsic disorder (IDRs) are abundant in proteomes and are essential for many biological processes. Thus, they are often implicated in disease mechanisms, including neurodegeneration and cancer. The flexible nature of IDPs and IDRs provides many advantages, including (but not limited to) overcoming steric restrictions in binding, facilitating posttranslational modifications, and achieving high binding specificity with low affinity. IDPs adopt a heterogeneous structural ensemble, in contrast to typical folded proteins, making it challenging to interrogate their structure using conventional tools. Structural mass spectrometry (MS) methods are playing an increasingly important role in characterizing the structure and function of IDPs and IDRs, enabled by advances in the design of instrumentation and the development of new workflows, including in native MS, ion mobility MS, top-down MS, hydrogen-deuterium exchange MS, crosslinking MS, and covalent labeling. Here, we describe the advantages of these methods that make them ideal to study IDPs and highlight recent applications where these tools have underpinned new insights into IDP structure and function that would be difficult to elucidate using other methods.

Microstructural Capture of Living Ultrathin Polymer Brush Evolution via Kinetic Simulation Studies

Performing dynamic off-lattice multicanonical Monte Carlo simulations, we study the statics, dynamics, and scission-recombination kinetics of a self-assembled in situ-polymerized polydisperse living polymer brush (LPB), designed by surface-initiated living polymerization. The living brush is initially grown from a two-dimensional substrate by end-monomer polymerization-depolymerization reactions through seeding of initiator arrays on the grafting plane which come in contact with a solution of nonbonded monomers under good solvent conditions. The polydispersity is shown to significantly deviate from the Flory-Schulz type for low temperatures because of pronounced diffusion limitation effects on the rate of the equilibration reaction. The self-avoiding chains take up fairly compact structures of typical size R_g(N) ∼ N^ν in rigorously two-dimensional (d = 2) melt, with ν being the inverse fractal dimension (ν = 1/d). The Kratky description of the intramolecular structure factor F(q), in keeping with the concept of generalized Porod scattering from compact particles with fractal contour, discloses a robust nonmonotonic fashion with q^dF(q) ∼ (qR_g)^-3/4 in the intermediate-q regime. It is found that the kinetics of LPB growth, given by the variation of the mean chain length, follows a power law ⟨N(t)⟩ ∝ t^1/3 with elapsed time after the onset of polymerization, whereby the instantaneous molecular weight distribution (MWD) of the chains c(N) retains its functional form. The variation of ⟨N(t)⟩ during quenches of the LPB to different temperatures T can be described by a single master curve in units of dimensionless time t/τ_∞, where τ_∞ is the typical (final temperature T^∞-dependent) relaxation time which is found to scale as τ_∞ ∝ ⟨N(t = ∞)⟩⁵ with the ultimate average length of the chains. The equilibrium monomer density profile ϕ(z) of the LPB varies as ϕ(z) ∝ ϕ^-α with the concentration of segments ϕ in the system and the probability distribution c(N) of chain lengths N in the brush layer scales as c(N) ∝ N^-τ. The computed exponents α ≈ 0.64 and τ ≈ 1.70 are in good agreement with those predicted within the context of the Diffusion-Limited Aggregation theory, α = 2/3 and τ = 7/4.

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.

A Unified De Novo Approach for Predicting the Structures of Ordered and Disordered Proteins

As recognition of the abundance and relevance of intrinsically disordered proteins (IDPs) continues to grow, demand increases for methods that can rapidly predict the conformational ensembles populated by these proteins. To date, IDP simulations have largely been dominated by molecular dynamics (MD) simulations, which require significant compute times and/or complex hardware. Recent developments in MD have afforded methods capable of simulating both ordered and disordered proteins, yet to date, accurate fold prediction from a sequence has been dominated by Monte Carlo (MC)-based methods such as Rosetta. To overcome the limitations of current approaches in IDP simulation using Rosetta while maintaining its utility for modeling folded domains, we developed PyRosetta-based algorithms that allow for the accurate de novo prediction of proteins across all degrees of foldedness along with structural ensembles of disordered proteins. Our simulations have accuracy comparable to state-of-the-art MD with vastly reduced computational demands.

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.

Specific Conformational Dynamics and Expansion Underpin a Multi-Step Mechanism for Specific Binding of p27 with Cdk2/Cyclin A

The protein p27, a prominent regulatory protein in eukaryotes and an intrinsically disordered protein (IDP), regulates cell division by causing cell cycle arrest when bound in ternary complex with cyclin-dependent kinase (Cdk2) and cyclins (e.g., Cdk2/Cyclin A). We present an integrative study of p27 and its binding to Cdk2/Cyclin A complex by performing single-molecule multiparameter fluorescence spectroscopy, stopped-flow experiments, and molecular dynamics simulations. Our results suggest that unbound p27 adopts a compact conformation and undergoes conformational dynamics across several orders of magnitude in time (nano-to milliseconds), reflecting a multi-step mechanism for binding Cdk2/Cyclin A. Mutagenesis studies reveal that the region D1 in p27 plays a significant role in mediating the association kinetics, undergoing conformational rearrangement upon initial binding. Additionally, FRET experiments indicate an expansion of p27 throughout binding. The detected local and long-range structural dynamics suggest that p27 exhibits a limited binding surface in the unbound form, and stochastic conformational changes in D1 facilitate initial binding to Cdk2/Cyclin A complex. Furthermore, the post-kinase inhibitory domain (post-KID) region of p27 exchanges between distinct conformational ensembles: an extended regime exhibiting worm-like chain behavior, and a compact ensemble, which may protect p27 against nonspecific interactions. In summary, the binding interaction involves three steps: (i) D1 initiates binding, (ii) p27 wraps around Cdk2/Cyclin A and D2 binds, and (iii) the fully-formed fuzzy ternary complex is formed concomitantly with an extension of the post-KID region. An understanding of how the IDP nature of p27 underpins its functional interactions with Cdk2/Cyclin A provides insight into the complex binding mechanisms of IDPs and their regulatory mechanisms.

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.

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

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

Layered nested Markov chain Monte Carlo

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many-body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded-volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. The proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Tuning the Flexibility of Glycine-Serine Linkers To Allow Rational Design of Multidomain Proteins

Flexible polypeptide linkers composed of glycine and serine are important components of engineered multidomain proteins. We have previously shown that the conformational properties of Gly-Gly-Ser repeat linkers can be quantitatively understood by comparing experimentally determined Förster resonance energy transfer (FRET) efficiencies of ECFP-linker-EYFP proteins to theoretical FRET efficiencies calculated using wormlike chain and Gaussian chain models. Here we extend this analysis to include linkers with different glycine contents. We determined the FRET efficiencies of ECFP-linker-EYFP proteins with linkers ranging in length from 25 to 73 amino acids and with glycine contents of 33.3% (GSSGSS), 16.7% (GSSSSSS), and 0% (SSSSSSS). The FRET efficiency decreased with an increasing linker length and was overall lower for linkers with less glycine. Modeling the linkers using the WLC model revealed that the experimentally observed FRET efficiencies were consistent with persistence lengths of 4.5, 4.8, and 6.2 Å for the GSSGSS, GSSSSS, and SSSSSS linkers, respectively. The observed increase in linker stiffness with reduced glycine content is much less pronounced than that predicted by a classical model developed by Flory and co-workers. We discuss possible reasons for this discrepancy as well as implications for using the stiffer linkers to control the effective concentrations of connected domains in engineered multidomain proteins.

Intrinsically disordered linkers determine the interplay between phase separation and gelation in multivalent proteins

Phase transitions of linear multivalent proteins control the reversible formation of many intracellular membraneless bodies. Specific non-covalent crosslinks involving domains/motifs lead to system-spanning networks referred to as gels. Gelation transitions can occur with or without phase separation. In gelation driven by phase separation multivalent proteins and their ligands condense into dense droplets, and gels form within droplets. System spanning networks can also form without a condensation or demixing of proteins into droplets. Gelation driven by phase separation requires lower protein concentrations, and seems to be the biologically preferred mechanism for forming membraneless bodies. Here, we use coarse-grained computer simulations and the theory of associative polymers to uncover the physical properties of intrinsically disordered linkers that determine the extent to which gelation of linear multivalent proteins is driven by phase separation. Our findings are relevant for understanding how sequence-encoded information in disordered linkers influences phase transitions of multivalent proteins.

Our cells contain a variety of structures called organelles that perform specific roles within a cell. Some organelles are surrounded by a membrane, while others float inside the cell as spherical droplets made of proteins. These proteins contain several sticky regions, which are connected by flexible linker proteins. It is thought that the level of stickiness and the number of sticky regions, or domains, determine whether a protein will form a membraneless organelle. Often, proteins with similar sticky domains have different linkers, and until now, it was assumed that the linkers do not have any other purpose than stringing the domains together.

To test this further, Harmon et al. used a combination of computer simulations and physics-based theory. In these simulations, the domains were kept the same, but the properties of linkers were changed to see if this would influence how the membraneless organelles are formed.

The results showed that depending on the physical properties of the linkers, the proteins could huddle together and form dense spherical gel-like droplets similar to the membraneless organelles, or form open non-spherical gels. When the linkers were short, the proteins do not easily form droplets. Linkers that were sufficiently long but too bulky, lead to non-spherical gels. Compact linkers, however, enabled proteins to huddle and form spherical gels. The spherical droplet-spanning gels required much less protein compared to the open non-spherical gels.

This suggests that proteins important for forming membraneless organelles can be distinguished from those that are not based on the properties of their linkers – even when their domains are similar.

These findings further scientists’ knowledge of how specific types of proteins form membraneless organelles and will help to understand how membraneless organelles control many key aspects of how a cell works.

On the Helix Propensity in Generalized Born Solvent Descriptions of Modeling the Dark Proteome

Intrinsically disordered proteins that populate the so-called “Dark Proteome” offer challenging benchmarks of atomistic simulation methods to accurately model conformational transitions on a multidimensional energy landscape. This work explores the application of parallel tempering with implicit solvent models as a computational framework to capture the conformational ensemble of an intrinsically disordered peptide derived from the Ebola virus protein VP35. A recent X-ray crystallographic study reported a protein-peptide interface where the VP35 peptide underwent a folding transition from a disordered form to a helix-β-turn-helix topological fold upon molecular association with the Ebola protein NP. An assessment is provided of the accuracy of two generalized Born solvent models (GBMV2 and GBSW2) using the CHARMM force field and applied with temperature-based replica exchange dynamics to calculate the disorder propensity of the peptide and its probability density of states in a continuum solvent. A further comparison is presented of applying an explicit/implicit solvent hybrid replica exchange simulation of the peptide to determine the effect of modeling water interactions at the all-atom resolution.

Bayesian inference of protein ensembles from SAXS data

The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble.

The Ramachandran Number: An Order Parameter for Protein Geometry

Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as α-helices and β-sheets. Secondary structure is characterized by the local rotational state of the protein backbone, quantified by two dihedral angles called ϕ and ψ. Particular types of secondary structure can generally be described by a single (diffuse) location on a two-dimensional plot drawn in the space of the angles ϕ and ψ, called a Ramachandran plot. By contrast, a recently-discovered nanomaterial made from peptoids, structural isomers of peptides, displays a secondary-structure motif corresponding to two regions on the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to describe such ‘higher-order’ secondary structure in a compact way we introduce here a means of describing regions on the Ramachandran plot in terms of a single Ramachandran number, R, which is a structurally meaningful combination of ϕ and ψ. We show that the potential applications of R are numerous: it can be used to describe the geometric content of protein structures, and can be used to draw diagrams that reveal, at a glance, the frequency of occurrence of regular secondary structures and disordered regions in large protein datasets. We propose that R might be used as an order parameter for protein geometry for a wide range of applications.

Cryptic sequence features within the disordered protein p27Kip1 regulate cell cycle signaling

Peptide motifs embedded within intrinsically disordered regions (IDRs) of proteins are often the sites of posttranslational modifications that control cell-signaling pathways. How do IDR sequences modulate the functionalities of motifs? We answer this question using the polyampholytic C-terminal IDR of the cell cycle inhibitory protein p27(Kip1) (p27). Phosphorylation of Thr-187 (T187) within the p27 IDR controls entry into S phase of the cell division cycle. Additionally, the conformational properties of polyampholytic sequences are predicted to be influenced by the linear patterning of oppositely charged residues. Therefore, we designed sequence variants of the p27 IDR to alter charge patterning outside the primary substrate motif containing T187. Computer simulations and biophysical measurements confirm predictions regarding the impact of charge patterning on the global dimensions of IDRs. Through functional studies, we uncover cryptic sequence features within the p27 IDR that influence the efficiency of T187 phosphorylation. Specifically, we find a positive correlation between T187 phosphorylation efficiency and the weighted net charge per residue of an auxiliary motif. We also find that accumulation of positive charges within the auxiliary motif can diminish the efficiency of T187 phosphorylation because this increases the likelihood of long-range intra-IDR interactions that involve both the primary and auxiliary motifs and inhibit their contributions to function. Importantly, our findings suggest that the cryptic sequence features of the WT p27 IDR negatively regulate T187 phosphorylation signaling. Our approaches provide a generalizable strategy for uncovering the influence of sequence contexts on the functionalities of primary motifs in other IDRs.

Phase separation in biology; functional organization of a higher order

Inside eukaryotic cells, macromolecules are partitioned into membrane-bounded compartments and, within these, some are further organized into non-membrane-bounded structures termed membrane-less organelles. The latter structures are comprised of heterogeneous mixtures of proteins and nucleic acids and assemble through a phase separation phenomenon similar to polymer condensation. Membrane-less organelles are dynamic structures maintained through multivalent interactions that mediate diverse biological processes, many involved in RNA metabolism. They rapidly exchange components with the cellular milieu and their properties are readily altered in response to environmental cues, often implicating membrane-less organelles in responses to stress signaling. In this review, we discuss: (1) the functional roles of membrane-less organelles, (2) unifying structural and mechanistic principles that underlie their assembly and disassembly, and (3) established and emerging methods used in structural investigations of membrane-less organelles.

Conserved interdomain linker promotes phase separation of the multivalent adaptor protein Nck

The organization of membranes, the cytosol, and the nucleus of eukaryotic cells can be controlled through phase separation of lipids, proteins, and nucleic acids. Collective interactions of multivalent molecules mediated by modular binding domains can induce gelation and phase separation in several cytosolic and membrane-associated systems. The adaptor protein Nck has three SRC-homology 3 (SH3) domains that bind multiple proline-rich segments in the actin regulatory protein neuronal Wiskott-Aldrich syndrome protein (N-WASP) and an SH2 domain that binds to multiple phosphotyrosine sites in the adhesion protein nephrin, leading to phase separation. Here, we show that the 50-residue linker between the first two SH3 domains of Nck enhances phase separation of Nck/N-WASP/nephrin assemblies. Two linear motifs within this element, as well as its overall positively charged character, are important for this effect. The linker increases the driving force for self-assembly of Nck, likely through weak interactions with the second SH3 domain, and this effect appears to promote phase separation. The linker sequence is highly conserved, suggesting that the sequence determinants of the driving forces for phase separation may be generally important to Nck functions. Our studies demonstrate that linker regions between modular domains can contribute to the driving forces for self-assembly and phase separation of multivalent proteins.

A coarse-grained model for polyglutamine aggregation modulated by amphipathic flanking sequences

The aggregation of proteins with expanded polyglutamine (polyQ) tracts is directly relevant to the formation of neuronal intranuclear inclusions in Huntington's disease. In vitro studies have uncovered the effects of flanking sequences as modulators of the driving forces and mechanisms of polyQ aggregation in sequence segments associated with HD. Specifically, a seventeen-residue amphipathic stretch (N17) that is directly N-terminal to the polyQ tract in huntingtin decreases the overall solubility, destabilizes nonfibrillar aggregates, and accelerates fibril formation. Published results from atomistic simulations showed that the N17 module reduces the frequency of intermolecular association. Our reanalysis of these simulation results demonstrates that the N17 module also reduces interchain entanglements between polyQ domains. These two effects, which are observed on the smallest lengthscales, are incorporated into phenomenological pair potentials and used in coarse-grained Brownian dynamics simulations to investigate their impact on large-scale aggregation. We analyze the results from Brownian dynamics simulations using the framework of diffusion-limited cluster aggregation. When entanglements prevail, which is true in the absence of N17, small spherical clusters and large linear aggregates form on distinct timescales, in accord with in vitro experiments. Conversely, when entanglements are quenched and a barrier to intermolecular associations is introduced, both of which are attributable to N17, the timescales for forming small species and large linear aggregates become similar. Therefore, the combination of a reduction of interchain entanglements through homopolymeric polyQ and barriers to intermolecular associations appears to be sufficient for providing a minimalist phenomenological rationalization of in vitro observations regarding the effects of N17 on polyQ aggregation.

Modulation of the disordered conformational ensembles of the p53 transactivation domain by cancer-associated mutations

Intrinsically disordered proteins (IDPs) are frequently associated with human diseases such as cancers, and about one-fourth of disease-associated missense mutations have been mapped into predicted disordered regions. Understanding how these mutations affect the structure-function relationship of IDPs is a formidable task that requires detailed characterization of the disordered conformational ensembles. Implicit solvent coupled with enhanced sampling has been proposed to provide a balance between accuracy and efficiency necessary for systematic and comparative assessments of the effects of mutations as well as post-translational modifications on IDP structure and interaction. Here, we utilize a recently developed replica exchange with guided annealing enhanced sampling technique to calculate well-converged atomistic conformational ensembles of the intrinsically disordered transactivation domain (TAD) of tumor suppressor p53 and several cancer-associated mutants in implicit solvent. The simulations are critically assessed by quantitative comparisons with several types of experimental data that provide structural information on both secondary and tertiary levels. The results show that the calculated ensembles reproduce local structural features of wild-type p53-TAD and the effects of K24N mutation quantitatively. On the tertiary level, the simulated ensembles are overly compact, even though they appear to recapitulate the overall features of transient long-range contacts qualitatively. A key finding is that, while p53-TAD and its cancer mutants sample a similar set of conformational states, cancer mutants could introduce both local and long-range structural modulations to potentially perturb the balance of p53 binding to various regulatory proteins and further alter how this balance is regulated by multisite phosphorylation of p53-TAD. The current study clearly demonstrates the promise of atomistic simulations for detailed characterization of IDP conformations, and at the same time reveals important limitations in the current implicit solvent protein force field that must be sufficiently addressed for reliable description of long-range structural features of the disordered ensembles.

Tumor suppressor p53 is the most frequently mutated protein in human cancers. Clinical studies have suggested that the type of p53 mutation can be linked to cancer prognosis, response to drug treatment, and patient survival. It is thus crucial to understand the molecular basis of p53 inactivation by various types of mutations, so as to understand the biological outcomes and assess potential cancer intervention strategies. Here, we utilize a recently developed replica exchange with guided annealing enhanced sampling technique to calculate well-converged atomistic conformational ensembles of the intrinsically disordered transactivation domain (TAD) of tumor suppressor p53 and several cancer-associated mutants in an implicit solvent protein force field. The calculated ensembles are in quantitative agreement with several types of existing NMR data on the wild-type protein and the K24N mutant. The results suggest that, while all sequences sample a similar set of conformational substates, cancer mutants could introduce both local and long-range structural modulations and in turn perturb the balance of p53 binding to various regulatory proteins and further alter how this balance is regulated by multisite phosphorylation of p53-TAD. The study also reveals important limitations in implicit solvent for simulations of disordered proteins like p53-TAD.

Relating sequence encoded information to form and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) showcase the importance of conformational plasticity and heterogeneity in protein function. We summarize recent advances that connect information encoded in IDP sequences to their conformational properties and functions. We focus on insights obtained through a combination of atomistic simulations and biophysical measurements that are synthesized into a coherent framework using polymer physics theories.