Methods for Monte Carlo simulations of biomacromolecules

Expanding the molecular language of protein liquid-liquid phase separation

Understanding the relationship between a polypeptide sequence and its phase separation has important implications for analysing cellular function, treating disease and designing novel biomaterials. Several sequence features have been identified as drivers for protein liquid-liquid phase separation (LLPS), schematized as a 'molecular grammar' for LLPS. Here we further probe how sequence modulates phase separation and the material properties of the resulting condensates, targeting sequence features previously overlooked in the literature. We generate sequence variants of a repeat polypeptide with either no charged residues, high net charge, no glycine residues or devoid of aromatic or arginine residues. All but one of 12 variants exhibited LLPS, albeit to different extents, despite substantial differences in composition. Furthermore, we find that all the condensates formed behaved like viscous fluids, despite large differences in their viscosities. Our results support the model of multiple interactions between diverse residue pairs-not just a handful of residues-working in tandem to drive the phase separation and dynamics of condensates.

Molecular insights into the interaction between a disordered protein and a folded RNA

Intrinsically disordered protein regions (IDRs) are well-established as contributors to intermolecular interactions and the formation of biomolecular condensates. In particular, RNA-binding proteins (RBPs) often harbor IDRs in addition to folded RNA-binding domains that contribute to RBP function. To understand the dynamic interactions of an IDR-RNA complex, we characterized the RNA-binding features of a small (68 residues), positively charged IDR-containing protein, SERF. At high concentrations, SERF and RNA undergo charge-driven associative phase separation to form a protein- and RNA-rich dense phase. A key advantage of this model system is that this threshold for demixing is sufficiently high that we could use solution-state biophysical methods to interrogate the stoichiometric complexes of SERF with RNA in the one-phase regime. Herein, we describe our comprehensive characterization of SERF alone and in complex with a small fragment of the HIV-1 TAR RNA (TAR) with complementary biophysical methods and molecular simulations. We find that this binding event is not accompanied by the acquisition of structure by either molecule; however, we see evidence for a modest global compaction of the SERF ensemble when bound to RNA. This behavior likely reflects attenuated charge repulsion within SERF via binding to the polyanionic RNA and provides a rationale for the higher-order assembly of SERF in the context of RNA. We envision that the SERF-RNA system will lower the barrier to accessing the details that support IDR-RNA interactions and likewise deepen our understanding of the role of IDR-RNA contacts in complex formation and liquid-liquid phase separation.

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.

Understanding the Energy Landscape of Intrinsically Disordered Protein Ensembles

A substantial portion of various organisms' proteomes comprises intrinsically disordered proteins (IDPs) that lack a defined three-dimensional structure. These IDPs exhibit a diverse array of conformations, displaying remarkable spatiotemporal heterogeneity and exceptional conformational flexibility. Characterizing the structure or structural ensemble of IDPs presents significant conceptual and methodological challenges owing to the absence of a well-defined native structure. While databases such as the Protein Ensemble Database (PED) provide IDP ensembles obtained through a combination of experimental data and molecular modeling, the absence of reaction coordinates poses challenges in comprehensively understanding pertinent aspects of the system. In this study, we leverage the energy landscape visualization method (JCTC, 6482, 2019) to scrutinize four IDP ensembles sourced from PED. ELViM, a methodology that circumvents the need for a priori reaction coordinates, aids in analyzing the ensembles. The specific IDP ensembles investigated are as follows: two fragments of nucleoporin (NUL: 884-993 and NUS: 1313-1390), yeast sic 1 N-terminal (1-90), and the N-terminal SH3 domain of Drk (1-59). Utilizing ELViM enables the comprehensive validation of ensembles, facilitating the detection of potential inconsistencies in the sampling process. Additionally, it allows for identifying and characterizing the most prevalent conformations within an ensemble. Moreover, ELViM facilitates the comparative analysis of ensembles obtained under diverse conditions, thereby providing a powerful tool for investigating the functional mechanisms of IDPs.

Intra-condensate demixing of TDP-43 inside stress granules generates pathological aggregates

Cytosolic aggregation of the nuclear protein TDP-43 is associated with many neurodegenerative diseases, but the triggers for TDP-43 aggregation are still debated. Here, we demonstrate that TDP-43 aggregation requires a double event. One is up-concentration in stress granules beyond a threshold, and the other is oxidative stress. These two events collectively induce intra-condensate demixing, giving rise to a dynamic TDP-43 enriched phase within stress granules, which subsequently transitions into pathological aggregates. Mechanistically, intra-condensate demixing is triggered by local unfolding of the RRM1 domain for intermolecular disulfide bond formation and by increased hydrophobic patch interactions in the C-terminal domain. By engineering TDP-43 variants resistant to intra-condensate demixing, we successfully eliminate pathological TDP-43 aggregates in cells. We conclude that up-concentration inside condensates and simultaneous exposure to environmental stress could be a general pathway for protein aggregation, with intra-condensate demixing constituting a key intermediate step.

Transferable deep generative modeling of intrinsically disordered protein conformations

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

HYPK: A marginally disordered protein sensitive to charge decoration

Intrinsically disordered proteins (IDPs) that lie close to the empirical boundary separating IDPs and folded proteins in Uversky's charge-hydropathy plot may behave as "marginal IDPs" and sensitively switch conformation upon changes in environment (temperature, crowding, and charge screening), sequence, or both. In our search for such a marginal IDP, we selected Huntingtin-interacting protein K (HYPK) near that boundary as a candidate; PKIα, also near that boundary, has lower secondary structure propensity; and Crk1, just across the boundary on the folded side, has higher secondary structure propensity. We used a qualitative Förster resonance energy transfer-based assay together with circular dichroism to simultaneously probe global and local conformation. HYPK shows several unique features indicating marginality: a cooperative transition in end-to-end distance with temperature, like Crk1 and folded proteins, but unlike PKIα; enhanced secondary structure upon crowding, in contrast to Crk1 and PKIα; and a cross-over from salt-induced expansion to compaction at high temperature, likely due to a structure-to-disorder transition not seen in Crk1 and PKIα. We then tested HYPK's sensitivity to charge patterning by designing charge-flipped variants including two specific sequences with identical amino acid composition that markedly differ in their predicted size and response to salt. The experimentally observed trends, also including mutants of PKIα, verify the predictions from sequence charge decoration metrics. Marginal proteins like HYPK show features of both folded and disordered proteins that make them sensitive to physicochemical perturbations and structural control by charge patterning.

Disordered clock protein interactions and charge blocks turn an hourglass into a persistent circadian oscillator

Organismal physiology is widely regulated by the molecular circadian clock, a feedback loop composed of protein complexes whose members are enriched in intrinsically disordered regions. These regions can mediate protein-protein interactions via SLiMs, but the contribution of these disordered regions to clock protein interactions had not been elucidated. To determine the functionality of these disordered regions, we applied a synthetic peptide microarray approach to the disordered clock protein FRQ in Neurospora crassa. We identified residues required for FRQ's interaction with its partner protein FRH, the mutation of which demonstrated FRH is necessary for persistent clock oscillations but not repression of transcriptional activity. Additionally, the microarray demonstrated an enrichment of FRH binding to FRQ peptides with a net positive charge. We found that positively charged residues occurred in significant "blocks" within the amino acid sequence of FRQ and that ablation of one of these blocks affected both core clock timing and physiological clock output. Finally, we found positive charge clusters were a commonly shared molecular feature in repressive circadian clock proteins. Overall, our study suggests a mechanistic purpose for positive charge blocks and yielded insights into repressive arm protein roles in clock function.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Transferable deep generative modeling of intrinsically disordered protein conformations

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

Self-tuning Hamiltonian Monte Carlo for accelerated sampling

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters based on a local loss function that promotes the fast exploration of phase space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein commonly used as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a >100 fold speedup in the optimization of simulation parameters compared to a grid search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times.

Disrupting Dimeric β-Amyloid by Electric Fields

The early oligomers of the amyloid Aβ peptide are implicated in Alzheimer's disease, but their transient nature complicates the characterization of their structure and toxicity. Here, we investigate the stability of the minimal toxic species, i.e., β-amyloid dimers, in the presence of an oscillating electric field. We first use deep learning (AlphaFold-multimer) for generating initial models of Aβ42 dimers. The flexibility and secondary structure content of the models are then analyzed by multiple runs of molecular dynamics (MD). Structurally stable models are similar to ensemble representatives from microsecond-long MD sampling. Finally, we employ the validated model as the starting structure of MD simulations in the presence of an external oscillating electric field and observe a fast decay of β-sheet content at high field strengths. Control simulations using the helical dimer of the 42-residue leucine zipper peptide show higher structural stability than the Aβ42 dimer. The simulation results provide evidence that an external electric field (oscillating at 1 GHz) can disrupt amyloid oligomers which should be further investigated by experiments with brain organoids in vitro and eventually in vivo.

SOURSOP: A Python Package for the Analysis of Simulations of Intrinsically Disordered Proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite simulation analysis of unfolded regions of proteins (SOURSOP), an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 μs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 μs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

The analytical Flory random coil is a simple-to-use reference model for unfolded and disordered proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory Random Coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Nucleation of Biomolecular Condensates from Finite-Sized Simulations

The nucleation of protein condensates is a concentration-driven process of assembly. When modeled in the canonical ensemble, condensation is affected by finite-size effects. Here, we present a general and efficient route for obtaining ensemble properties of protein condensates in the macroscopic limit from finite-sized nucleation simulations. The approach is based on a theoretical description of droplet nucleation in the canonical ensemble and enables estimation of thermodynamic and kinetic parameters, such as the macroscopic equilibrium density of the dilute protein phase, the surface tension of the condensates, and nucleation free energy barriers. We apply the method to coarse-grained simulations of NDDX4 and FUS-LC, two phase-separating disordered proteins with different physicochemical characteristics. Our results show that NDDX4 condensate droplets, characterized by lower surface tension, higher solubility, and faster monomer exchange dynamics compared to those of FUS-LC, form with negligible nucleation barriers. In contrast, FUS-LC condensates form via an activated process over a wide range of concentrations.

Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model

Accuracy and transferability are the two highly desirable properties of molecular mechanical force fields. Compared with the extensively used point-charge additive force fields that apply fixed atom-centered point partial charges to model electrostatic interactions, polarizable force fields are thought to have the advantage of modeling the atomic polarization effects. Previous works have demonstrated the accuracy of the recently developed polarizable Gaussian multipole (pGM) models. In this work, we assessed the transferability of the electrostatic parameters of the pGM models with (pGM-perm) and without (pGM-ind) atomic permanent dipoles in terms of reproducing the electrostatic potentials surrounding molecules/oligomers absent from electrostatic parameterizations. Encouragingly, both the pGM-perm and pGM-ind models show significantly improved transferability than the additive model in the tests (1) from water monomer to water oligomer clusters; (2) across different conformations of amino acid dipeptides and tetrapeptides; (3) from amino acid tetrapeptides to longer polypeptides; and (4) from nucleobase monomers to Watson-Crick base pair dimers and tetramers. Furthermore, we demonstrated that the double-conformation fittings using amino acid tetrapeptides in the αR and β conformations can result in good transferability not only across different tetrapeptide conformations but also from tetrapeptides to polypeptides with lengths ranging from 1 to 20 repetitive residues for both the pGM-ind and pGM-perm models. In addition, the observation that the pGM-ind model has significantly better accuracy and transferability than the point-charge additive model, even though they have an identical number of parameters, strongly suggest the importance of intramolecular polarization effects. In summary, this and previous works together show that the pGM models possess both accuracy and transferability, which are expected to serve as foundations for the development of next-generation polarizable force fields for modeling various polarization-sensitive biological systems and processes.

Direct generation of protein conformational ensembles via machine learning

Dynamics and conformational sampling are essential for linking protein structure to biological function. While challenging to probe experimentally, computer simulations are widely used to describe protein dynamics, but at significant computational costs that continue to limit the systems that can be studied. Here, we demonstrate that machine learning can be trained with simulation data to directly generate physically realistic conformational ensembles of proteins without the need for any sampling and at negligible computational cost. As a proof-of-principle we train a generative adversarial network based on a transformer architecture with self-attention on coarse-grained simulations of intrinsically disordered peptides. The resulting model, idpGAN, can predict sequence-dependent coarse-grained ensembles for sequences that are not present in the training set demonstrating that transferability can be achieved beyond the limited training data. We also retrain idpGAN on atomistic simulation data to show that the approach can be extended in principle to higher-resolution conformational ensemble generation.

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.

Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model

A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.

Conformational buffering underlies functional selection in intrinsically disordered protein regions

Many disordered proteins conserve essential functions in the face of extensive sequence variation, making it challenging to identify the mechanisms responsible for functional selection. Here we identify the molecular mechanism of functional selection for the disordered adenovirus early gene 1A (E1A) protein. E1A competes with host factors to bind the retinoblastoma (Rb) protein, subverting cell cycle regulation. We show that two binding motifs tethered by a hypervariable disordered linker drive picomolar affinity Rb binding and host factor displacement. Compensatory changes in amino acid sequence composition and sequence length lead to conservation of optimal tethering across a large family of E1A linkers. We refer to this compensatory mechanism as conformational buffering. We also detect coevolution of the motifs and linker, which can preserve or eliminate the tethering mechanism. Conformational buffering and motif-linker coevolution explain robust functional encoding within hypervariable disordered linkers and could underlie functional selection of many disordered protein regions.

Antibody binding modulates the dynamics of the membrane-bound prion protein

Misfolding of the cellular prion protein (PrP^C) is associated with lethal neurodegeneration. PrP^C consists of a flexible tail (residues 23-123) and a globular domain (residues 124-231) whose C-terminal end is anchored to the cell membrane. The neurotoxic antibody POM1 and the innocuous antibody POM6 recognize the globular domain. Experimental evidence indicates that POM1 binding to PrP^C emulates the influence on PrP^C of the misfolded prion protein (PrP^Sc) while the binding of POM6 has the opposite biological response. Little is known about the potential interactions between flexible tail, globular domain, and the membrane. Here, we used atomistic simulations to investigate how these interactions are modulated by the binding of the Fab fragments of POM1 and POM6 to PrP^C and by interstitial sequence truncations to the flexible tail. The simulations show that the binding of the antibodies restricts the range of orientations of the globular domain with respect to the membrane and decreases the distance between tail and membrane. Five of the six sequence truncations influence only marginally this distance and the contact patterns between tail and globular domain. The only exception is a truncation coupled to a charge inversion mutation of four N-terminal residues, which increases the distance of the flexible tail from the membrane. The interactions of the flexible tail and globular domain are modulated differently by the two antibodies.

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy

Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π-π and hybrid cation-π/π-π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in-vitro phase diagrams; Mpipi predictions agree well with experiment on both fronts. Moreover, it can account for protein-RNA interactions, correctly predicts the multiphase behaviour of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental LLPS trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.

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

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

Targeted modulation of protein liquid-liquid phase separation by evolution of amino-acid sequence

Rationally and efficiently modifying the amino-acid sequence of proteins to control their ability to undergo liquid-liquid phase separation (LLPS) on demand is not only highly desirable, but can also help to elucidate which protein features are important for LLPS. Here, we propose a computational method that couples a genetic algorithm to a sequence-dependent coarse-grained protein model to evolve the amino-acid sequences of phase-separating intrinsically disordered protein regions (IDRs), and purposely enhance or inhibit their capacity to phase-separate. We validate the predicted critical solution temperatures of the mutated sequences with ABSINTH, a more accurate all-atom model. We apply the algorithm to the phase-separating IDRs of three naturally occurring proteins, namely FUS, hnRNPA1 and LAF1, as prototypes of regions that exist in cells and undergo homotypic LLPS driven by different types of intermolecular interaction, and we find that the evolution of amino-acid sequences towards enhanced LLPS is driven in these three cases, among other factors, by an increase in the average size of the amino acids. However, the direction of change in the molecular driving forces that enhance LLPS (such as hydrophobicity, aromaticity and charge) depends on the initial amino-acid sequence. Finally, we show that the evolution of amino-acid sequences to modulate LLPS is strongly coupled to the make-up of the medium (e.g. the presence or absence of RNA), which may have significant implications for our understanding of phase separation within the many-component mixtures of biological systems.

Proteomic and functional mapping of cardiac NaV1.5 channel phosphorylation sites

Phosphorylation of the voltage-gated Na⁺ (Na_V) channel Na_V1.5 regulates cardiac excitability, yet the phosphorylation sites regulating its function and the underlying mechanisms remain largely unknown. Using a systematic, quantitative phosphoproteomic approach, we analyzed Na_V1.5 channel complexes purified from nonfailing and failing mouse left ventricles, and we identified 42 phosphorylation sites on Na_V1.5. Most sites are clustered, and three of these clusters are highly phosphorylated. Analyses of phosphosilent and phosphomimetic Na_V1.5 mutants revealed the roles of three phosphosites in regulating Na_V1.5 channel expression and gating. The phosphorylated serines S664 and S667 regulate the voltage dependence of channel activation in a cumulative manner, whereas the nearby S671, the phosphorylation of which is increased in failing hearts, regulates cell surface Na_V1.5 expression and peak Na⁺ current. No additional roles could be assigned to the other clusters of phosphosites. Taken together, our results demonstrate that ventricular Na_V1.5 is highly phosphorylated and that the phosphorylation-dependent regulation of Na_V1.5 channels is highly complex, site specific, and dynamic.

An analytical theory to describe sequence-specific inter-residue distance profiles for polyampholytes and intrinsically disordered proteins

Intrinsically Disordered Proteins (IDPs), unlike folded proteins, lack a unique folded structure and rapidly interconvert among ensembles of disordered states. However, they have specific conformational properties when averaged over their ensembles of disordered states. It is critical to develop a theoretical formalism to predict these ensemble average conformational properties that are encoded in the IDP sequence (the specific order in which amino acids/residues are linked). We present a general heteropolymer theory that analytically computes the ensemble average distance profiles (⟨R_ij ²⟩) between any two (i, j) monomers (amino acids for IDPs) as a function of the sequence. Information rich distance profiles provide a detailed description of the IDP in contrast to typical metrics such as scaling exponents, radius of gyration, or end-to-end distance. This generalized formalism supersedes homopolymer-like models or models that are built only on the composition of amino acids but ignore sequence details. The prediction of these distance profiles for highly charged polyampholytes and naturally occurring IDPs unmasks salient features that are hidden in the sequence. Moreover, the model reveals strategies to modulate the entire distance map to achieve local or global swelling/compaction by subtle changes/modifications-such as phosphorylation, a biologically relevant process-in specific hotspots in the sequence. Sequence-specific distance profiles and their modulation have been benchmarked against all-atom simulations. Our new formalism also predicts residue-pair specific coil-globule transitions. The analytical nature of the theory will facilitate design of new sequences to achieve specific target distance profiles with broad applications in synthetic biology and polymer science.

RNA-Induced Conformational Switching and Clustering of G3BP Drive Stress Granule Assembly by Condensation

Stressed cells shut down translation, release mRNA molecules from polysomes, and form stress granules (SGs) via a network of interactions that involve G3BP. Here we focus on the mechanistic underpinnings of SG assembly. We show that, under non-stress conditions, G3BP adopts a compact auto-inhibited state stabilized by electrostatic intramolecular interactions between the intrinsically disordered acidic tracts and the positively charged arginine-rich region. Upon release from polysomes, unfolded mRNAs outcompete G3BP auto-inhibitory interactions, engendering a conformational transition that facilitates clustering of G3BP through protein-RNA interactions. Subsequent physical crosslinking of G3BP clusters drives RNA molecules into networked RNA/protein condensates. We show that G3BP condensates impede RNA entanglement and recruit additional client proteins that promote SG maturation or induce a liquid-to-solid transition that may underlie disease. We propose that condensation coupled to conformational rearrangements and heterotypic multivalent interactions may be a general principle underlying RNP granule assembly.

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Under non-stressed conditions, G3BP adopts a compact auto-inhibited state

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Conformational expansion of G3BP increases the interaction valences

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G3BP clusters crosslink RNA to assemble stress granules upon cellular stress

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G3BP condensates prevent RNA entanglement

High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.

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.

Computing, Analyzing, and Comparing the Radius of Gyration and Hydrodynamic Radius in Conformational Ensembles of Intrinsically Disordered Proteins

The level of compaction of an intrinsically disordered protein may affect both its physical and biological properties, and can be probed via different types of biophysical experiments. Small-angle X-ray scattering (SAXS) probe the radius of gyration (R_g) whereas pulsed-field-gradient nuclear magnetic resonance (NMR) diffusion, fluorescence correlation spectroscopy, and dynamic light scattering experiments can be used to determine the hydrodynamic radius (R_h). Here we show how to calculate R_g and R_h from a computationally generated conformational ensemble of an intrinsically disordered protein. We further describe how to use a Bayesian/Maximum Entropy procedure to integrate data from SAXS and NMR diffusion experiments, so as to derive conformational ensembles in agreement with those experiments.

Probing the Basis of α-Synuclein Aggregation by Comparing Simulations to Single-Molecule Experiments

Intrinsically disordered proteins often play an important role in protein aggregation. However, it is challenging to determine the structures and interactions that drive the early stages of aggregation because they are transient and obscured in a heterogeneous mixture of disordered states. Even computational methods are limited because the lack of ordered structure makes it difficult to ensure that the relevant conformations are sampled. We address these challenges by integrating atomistic simulations with high-resolution single-molecule measurements reported previously, using the measurements to help discern which parts of the disordered ensemble of structures in the simulations are most probable while using the simulations to identify residues and interactions that are important for oligomer stability. This approach was applied to α-synuclein, an intrinsically disordered protein that aggregates in the context of Parkinson's disease. We simulated single-molecule pulling experiments on dimers, the minimal oligomer, and compared them to force spectroscopy measurements. Force-extension curves were simulated starting from a set of 66 structures with substantial structured content selected from the ensemble of dimer structures generated at zero force via Monte Carlo simulations. The pattern of contour length changes as the structures unfolded through intermediate states was compared to the results from optical trapping measurements on the same dimer to discern likely structures occurring in the measurements. Simulated pulling curves were generally consistent with experimental data but with a larger number of transient intermediates. We identified an ensemble of β-rich dimer structures consistent with the experimental data from which dimer interfaces could be deduced. These results suggest specific druggable targets in the structural motifs of α-synuclein that may help prevent the earliest steps of oligomerization.

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.

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.

Solution Ensemble of the C-Terminal Domain from the Transcription Factor Pdx1 Resembles an Excluded Volume Polymer

The pancreatic and duodenal homeobox 1 (Pdx1) is an essential pancreatic transcription factor. The C-terminal intrinsically disordered domain of Pdx1 (Pdx1-C) has a heavily biased amino acid composition; most notably, 18 of 83 residues are proline, including a hexaproline cluster near the middle of the chain. For these reasons, Pdx1-C is an attractive target for structure characterization, given the availability of suitable methods. To determine the solution ensembles of disordered proteins, we have developed a suite of ¹³C direct-detect NMR experiments that provide high spectral quality, even in the presence of strong proline enrichment. Here, we have extended our suite of NMR experiments to include four new pulse programs designed to record backbone residual dipolar couplings in a ¹³C,¹⁵N-CON detection format. Using our NMR strategy, in combination with small-angle X-ray scattering measurements and Monte Carlo simulations, we have determined that Pdx1-C is extended in solution, with a radius of gyration and internal scaling similar to that of an excluded volume polymer, and a subtle tendency toward a collapsed structure to the N-terminal side of the hexaproline sequence. This structure leaves Pdx1-C exposed for interactions with trans-regulatory co-factors that contribute with Pdx1 to transcription control in the cell.

Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins

We present an analytical theory to compute conformations of heteropolymers-applicable to describe disordered proteins-as a function of temperature and charge sequence. The theory describes coil-globule transition for a given protein sequence when temperature is varied and has been benchmarked against the all-atom Monte Carlo simulation (using CAMPARI) of intrinsically disordered proteins (IDPs). In addition, the model quantitatively shows how subtle alterations of charge placement in the primary sequence-while maintaining the same charge composition-can lead to significant changes in conformation, even as drastic as a coil (swelled above a purely random coil) to globule (collapsed below a random coil) and vice versa. The theory provides insights on how to control (enhance or suppress) these changes by tuning the temperature (or solution condition) and charge decoration. As an application, we predict the distribution of conformations (at room temperature) of all naturally occurring IDPs in the DisProt database and notice significant size variation even among IDPs with a similar composition of positive and negative charges. Based on this, we provide a new diagram-of-states delineating the sequence-conformation relation for proteins in the DisProt database. Next, we study the effect of post-translational modification, e.g., phosphorylation, on IDP conformations. Modifications as little as two-site phosphorylation can significantly alter the size of an IDP with everything else being constant (temperature, salt concentration, etc.). However, not all possible modification sites have the same effect on protein conformations; there are certain "hot spots" that can cause maximal change in conformation. The location of these "hot spots" in the parent sequence can readily be identified by using a sequence charge decoration metric originally introduced by Sawle and Ghosh. The ability of our model to predict conformations (both expanded and collapsed states) of IDPs at a high-throughput level can provide valuable insights into the different mechanisms by which phosphorylation/charge mutation controls IDP function.

The Rational Discovery of a Tau Aggregation Inhibitor

Intrinsically disordered proteins play vital roles in biology, and their dysfunction contributes to many major disease states. These proteins remain challenging targets for rational ligand discovery or drug design because they are highly dynamic and fluctuate through a diverse set of conformations, frustrating structure-based approaches. To meet this challenge, we have developed protocols to efficiently identify active small molecule ligands of disordered proteins. Our approach utilizes enhanced sampling molecular dynamics and conformational analysis approaches optimized for disordered targets, coupled with computational docking and machine learning-based screens of compound libraries. By applying this protocol to an amyloid-forming segment of microtubule-associated protein tau, we successfully identified novel, chemically diverse tau ligands, including an inhibitor that delays the aggregation reaction in vitro without affecting the amount of aggregate formed at the steady state. Our results indicate that we have expanded the toolkit of protein aggregation inhibitors into new areas of chemical space and demonstrate the feasibility of our ligand discovery strategy.

Helical Polyampholyte Sequences Have Unique Thermodynamic Properties

Helices are the most common structural pattern observed in structured proteins. Polypeptide sequences that form helices in isolation have been identified and extensively studied. These are generally rich in alanine, the amino acid with strongest helical propensity. Insertion of charged or polar amino acids has been shown to be necessary to make alanine-rich peptides soluble and sometimes even increase the helicity of the peptides. More recently sequences that contain mostly charged residues (E-R/K rich) have been found in naturally occurring proteins that are highly helical, soluble, and extended regardless their length. Artificial sequences composed mostly or exclusively of charged amino acids have been designed that are also highly helical, depending on the specific pattern of oppositely charged residues. Here we explore the thermodynamic properties of a number of 16-residue long peptides with varying helical propensity by performing equilibrium simulations over a broad range of temperatures. We observe quantitative differences in the peptides' helical propensities that can be related to qualitative differences in the free energy landscape, depending on the ampholytic patterns in the sequence. The results provide hints on how the specific physical properties of naturally occurring long sequences with similar patterns of charged residues may relate to their biological function.

Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation. Using typical values of the short-range mean-field parameters derived from all-atom Monte Carlo simulations (at zero salt), we predict the conformational changes as a function of salt concentration. We notice that conformational transitions in response to changes in ionic strength strongly depend on sequence specific charge patterning. For example, globule to coil transition can be observed upon increasing salt concentration, in stark contrast to uniformly charged polyelectrolyte theories based on net charge only. In addition, it is possible to observe non-monotonic behavior with salt as well. Drastic differences in salt-induced conformational transitions is also evident between two doubly phosphorylated sequences-derived from the same wild type sequence-that only differ in the site of phosphorylation. Similar effects are also predicted between two sequences derived from the same parent sequence differing by a single site mutation where a negative charge is replaced by a positive charge. These effects are purely a result of charge decoration and can only be understood in terms of metrics based on specific placement of charges, and cannot be explained by models based on charge composition alone. Identifying sequences and hot spots within sequences-for post translational modification or charge mutation-using our high-throughput theory will yield fundamental insights into design and biological regulation mediated by phosphorylation and/or local changes in salt concentration.

Protein-Ligand Interaction Energy-Based Entropy Calculations: Fundamental Challenges For Flexible Systems

Entropy calculations represent one of the most challenging steps in obtaining the binding free energy in biomolecular systems. A novel computationally effective approach (IE) was recently proposed to calculate the entropy based on the computation of protein-ligand interaction energy directly from molecular dynamics (MD) simulations. We present a study focused on the application of this method to flexible molecular systems and compare its performance with well-established normal mode (NM) and quasiharmonic (QH) entropy calculation approaches. Our results demonstrated that the IE method is intended for calculating entropy change for binding partners in fixed conformations, as by the original definition of IE, and is not applicable to the molecular complexes in which the interacting partners undergo significant conformational changes during the binding process.

Measuring NDC80 binding reveals the molecular basis of tension-dependent kinetochore-microtubule attachments

Proper kinetochore-microtubule attachments, mediated by the NDC80 complex, are required for error-free chromosome segregation. Erroneous attachments are corrected by the tension dependence of kinetochore-microtubule interactions. Here, we present a method, based on fluorescence lifetime imaging microscopy and Förster resonance energy transfer, to quantitatively measure the fraction of NDC80 complexes bound to microtubules at individual kinetochores in living human cells. We found that NDC80 binding is modulated in a chromosome autonomous fashion over prometaphase and metaphase, and is predominantly regulated by centromere tension. We show that this tension dependency requires phosphorylation of the N-terminal tail of Hec1, a component of the NDC80 complex, and the proper localization of Aurora B kinase, which modulates NDC80 binding. Our results lead to a mathematical model of the molecular basis of tension-dependent NDC80 binding to kinetochore microtubules in vivo.

When a cell divides, each new cell that forms needs to contain a complete set of DNA, which is stored in structures called chromosomes. So first, the chromosomes duplicate, and the two copies are held together. A protein structure known as a kinetochore then forms on each copy of the chromosome. The kinetochores act as a pair of hands that pull the chromosome copies apart and toward opposite sides of the dividing cell. They do this by grabbing protein ‘ropes’ called microtubules that extend toward the chromosomes from each side of the cell.

Kinetochores grip the microtubule ropes more tightly when the connection is under greater tension. This helps the kinetochores to remain attached to the microtubules that will separate the chromosome copies while releasing the microtubules that would pull both copies to the same side. Previous research has shown that hundreds of finger-like structures made out of a protein group called NDC80 extend from each kinetochore ‘hand’ and attach to the microtubules. What remains a mystery is whether and how the NDC80 fingers grip the microtubules more tightly when tension is greater in cells.

Yoo et al. developed a technique for counting how many of the available NDC80 fingers of a single kinetochore are attached to microtubules within a living human cell. The new technique combines genetic engineering, fluorescence imaging and statistical methods to quantify the attachment of NDC80 to microtubules over time and space.

Yoo et al. found that more NDC80 bound to microtubules when there was greater tension. This relationship between binding and tension depends on an enzyme called Aurora B, which modifies the tip of each NDC80 finger and consequently changes the binding of NDC80 to microtubules. Yoo et al. further showed that Aurora B needs to be properly placed between two kinetochore hands to make NDC80-microtubule binding dependent on tension. Without this tension dependency, chromosomes could segregate unevenly into the newly formed cells – a problem that can lead to cancer, infertility and birth defects. The results presented by Yoo et al. therefore expand our understanding of how these diseases originate and may eventually help researchers to develop new treatments for them.

Composition-related structural transition of random peptides: insight into the boundary between intrinsically disordered proteins and folded proteins

Previous studies based on bioinformatics showed that there is a sharp distinction of structural features and residue composition between the intrinsically disordered proteins and the folded proteins. What induces such a composition-related structural transition? How do various kinds of interactions work in such processes? In this work, we investigate these problems based on a survey on peptides randomly composed of charged residues (including glutamic acids and lysines) and the residues with different hydrophobicity, such as alanines, glycines, or phenylalanines. Based on simulations using all-atom model and replica-exchange Monte Carlo method, a coil-globule transition is observed for each peptide. The corresponding transition temperature is found to be dependent on the contents of the hydrophobic and charged residues. For several cases, when the mean hydrophobicity is larger than a certain threshold, the transition temperature is higher than the room temperature, and vise versa. These thresholds of hydrophobicity and net charge are quantitatively consistent with the border line observed from the study of bioinformatics. These results outline the basic physical reasons for the compositional distinction between the intrinsically disordered proteins and the folded proteins. Furthermore, the contributions of various interactions to the structural variation of peptides are analyzed based on the contact statistics and the charge-pattern dependence of the gyration radii of the peptides. Our observations imply that the hydrophobicity contributes essentially to such composition-related transitions. Thus, we achieve a better understanding on composition-structure relation of the natural proteins and the underlying physics.

Enhanced Monte Carlo Methods for Modeling Proteins Including Computation of Absolute Free Energies of Binding

The generation of a complete ensemble of geometrical configurations is required to obtain reliable estimations of absolute binding free energies by alchemical free energy methods. Molecular dynamics (MD) is the most popular sampling method, but the representation of large biomolecular systems may be incomplete owing to energetic barriers that impede efficient sampling of the configurational space. Monte Carlo (MC) methods can possibly overcome this issue by adapting the attempted movement sizes to facilitate transitions between alternative local-energy minima. In this study, we present an MC statistical mechanics algorithm to explore the protein-ligand conformational space with emphasis on the motions of the protein backbone and side chains. The parameters for each MC move type were optimized to better reproduce conformational distributions of 18 dipeptides and the well-studied T4-lysozyme L99A protein. Next, the performance of the improved MC algorithms was evaluated by computing absolute free energies of binding for L99A lysozyme with benzene and seven analogs. Results for benzene with L99A lysozyme from MD and the optimized MC protocol were found to agree within 0.6 kcal/mol, while a mean unsigned error of 1.2 kcal/mol between MC results and experiment was obtained for the seven benzene analogs. Significant advantages in computation speed are also reported with MC over MD for similar extents of configurational sampling.

Segmenting Proteins into Tripeptides to Enhance Conformational Sampling with Monte Carlo Methods

This paper presents an approach to enhance conformational sampling of proteins employing stochastic algorithms such as Monte Carlo (MC) methods. The approach is based on a mechanistic representation of proteins and on the application of methods originating from robotics. We outline the general ideas of our approach and detail how it can be applied to construct several MC move classes, all operating on a shared representation of the molecule and using a single mathematical solver. We showcase these sampling techniques on several types of proteins. Results show that combining several move classes, which can be easily implemented thanks to the proposed approach, significantly improves sampling efficiency.