Sequence- and Temperature-Dependent Properties of Unfolded and Disordered Proteins from Atomistic Simulations

Temperature-Dependent Coarse-Grained Model for Simulations of Intrinsically Disordered Protein LCST and UCST Liquid-Liquid Phase Separations

Many intrinsically disordered proteins (IDPs) can undergo a liquid-liquid phase separation (LLPS) in water, depending on solution conditions (temperature, pH, and ionic strength). There are two types of LLPS that are controlled by temperature: those occurring above a lower critical solution temperature (LCST) and those occurring below an upper critical solution temperature (UCST). IDP coarse-grained (CG) models are particularly appropriate for investigating the physical and chemical factors that govern their LLPS and supramolecular organization. However, the development of CG models allowing simulations of both LCST and UCST behavior of temperature-sensitive IDPs is still in its infancy. In this context, we present here a novel temperature-dependent (TD) CG model for IDP simulations based on the MARTINI 3 force field. The model was developed by modifying the Lennard-Jones potentials between apolar or charged solute beads and water with a TD rescaling factor. It was parametrized to fit the TD potentials of mean force (PMF) between two apolar or two charged molecules computed using all-atom (AA) simulations. We show that the TD CG model is able to reproduce the experimentally known LLPS of both LCST and UCST low-complexity sequences and to estimate phase transition temperatures comparable to experimental measurements.

Deep generative modeling of temperature-dependent structural ensembles of proteins

Deep learning has revolutionized protein structure prediction, but capturing conformational ensembles and structural variability remains an open challenge. While molecular dynamics (MD) is the foundation method for simulating biomolecular dynamics, it is computationally expensive. Recently, deep learning models trained on MD have made progress in generating structural ensembles at reduced cost. However, they remain limited in modeling atomistic details and, crucially, incorporating the effect of environmental factors. Here, we present aSAM (atomistic structural autoencoder model), a latent diffusion model trained on MD to generate heavy atom protein ensembles. Unlike most methods, aSAM models atoms in a latent space, greatly facilitating accurate sampling of side chain and backbone torsion angle distributions. Additionally, we extended aSAM into the first reported transferable generator conditioned on temperature, named aSAMt. Trained on the large and open mdCATH dataset, aSAMt captures temperature-dependent ensemble properties and demonstrates generalization beyond training temperatures. By comparing aSAMt ensembles to long MD simulations of fast folding proteins, we find that high-temperature training enhances the ability of deep generators to explore energy landscapes. Finally, we also show that our MD-based aSAMt can already capture experimentally observed thermal behavior of proteins. Our work is a step towards generalizable ensemble generation to complement physics-based approaches.

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

The molecular basis for cellular function of intrinsically disordered protein regions

Intrinsically disordered protein regions exist in a collection of dynamic interconverting conformations that lack a stable 3D structure. These regions are structurally heterogeneous, ubiquitous and found across all kingdoms of life. Despite the absence of a defined 3D structure, disordered regions are essential for cellular processes ranging from transcriptional control and cell signalling to subcellular organization. Through their conformational malleability and adaptability, disordered regions extend the repertoire of macromolecular interactions and are readily tunable by their structural and chemical context, making them ideal responders to regulatory cues. Recent work has led to major advances in understanding the link between protein sequence and conformational behaviour in disordered regions, yet the link between sequence and molecular function is less well defined. Here we consider the biochemical and biophysical foundations that underlie how and why disordered regions can engage in productive cellular functions, provide examples of emerging concepts and discuss how protein disorder contributes to intracellular information processing and regulation of cellular function.

Modulating hierarchical self-assembly in thermoresponsive intrinsically disordered proteins through high-temperature incubation time

The cornerstone of structural biology is the unique relationship between protein sequence and the 3D structure at equilibrium. Although intrinsically disordered proteins (IDPs) do not fold into a specific 3D structure, breaking this paradigm, some IDPs exhibit large-scale organization, such as liquid-liquid phase separation. In such cases, the structural plasticity has the potential to form numerous self-assembled structures out of thermal equilibrium. Here, we report that high-temperature incubation time is a defining parameter for micro and nanoscale self-assembly of resilin-like IDPs. Interestingly, high-resolution scanning electron microscopy micrographs reveal that an extended incubation time leads to the formation of micron-size rods and ellipsoids that depend on the amino acid sequence. More surprisingly, a prolonged incubation time also induces amino acid composition-dependent formation of short-range nanoscale order, such as periodic lamellar nanostructures. We, therefore, suggest that regulating the period of high-temperature incubation, in the one-phase regime, can serve as a unique method of controlling the hierarchical self-assembly mechanism of structurally disordered proteins.

Modulating Hierarchical Self-Assembly In Thermoresponsive Intrinsically Disordered Proteins Through High-Temperature Incubation Time

The cornerstone of structural biology is the unique relationship between protein sequence and the 3D structure at equilibrium. Although intrinsically disordered proteins (IDPs) do not fold into a specific 3D structure, breaking this paradigm, some IDPs exhibit large-scale organization, such as liquid-liquid phase separation. In such cases, the structural plasticity has the potential to form numerous self-assembled structures out of thermal equilibrium. Here, we report that high-temperature incubation time is a defining parameter for micro and nanoscale self-assembly of resilin-like IDPs. Interestingly, high-resolution scanning electron microscopy micrographs reveal that an extended incubation time leads to the formation of micron-size rods and ellipsoids that depend on the amino acid sequence. More surprisingly, a prolonged incubation time also induces amino acid composition-dependent formation of short-range nanoscale order, such as periodic lamellar nanostructures. We can correlate the lamellar structures to β-sheet formation and demonstrate similarities between the observed nanoscopic structural arrangement and spider silk. We, therefore, suggest that regulating the period of high-temperature incubation, in the one-phase regime, can serve as a unique method of controlling the hierarchical self-assembly mechanism of structurally disordered proteins.

In-situ PLL-g-PEG Functionalized Nanopore for Enhancing Protein Characterization

Single-molecule nanopore detection technology has revolutionized proteomics research by enabling highly sensitive and label-free detection of individual proteins. Herein, we designed a small, portable, and leak-free flowcell made of PMMA for nanopore experiments. In addition, we developed an in situ functionalizing PLL-g-PEG approach to produce non-sticky nanopores for measuring the volume of diseases-relevant biomarker, such as the Alpha-1 antitrypsin (AAT) protein. The in situ functionalization method allows continuous monitoring, ensuring adequate functionalization, which can be directly used for translocation experiments. The functionalized nanopores exhibit improved characteristics, including an increased nanopore lifetime and enhanced translocation events of the AAT proteins. Furthermore, we demonstrated the reduction in the translocation event's dwell time, along with an increase in current blockade amplitudes and translocation numbers under different voltage stimuli. The study also successfully measures the single AAT protein volume (253 nm3 ), which closely aligns with the previously reported hydrodynamic volume. The real-time in situ PLL-g-PEG functionalizing method and the developed nanopore flowcell hold great promise for various nanopores applications involving non-sticky single-molecule characterization.

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.

A synergy between site-specific and transient interactions drives the phase separation of a disordered, low-complexity domain

TAR DNA-binding protein 43 (TDP-43) is involved in key processes in RNA metabolism and is frequently implicated in many neurodegenerative diseases, including amyotrophic lateral sclerosis and frontotemporal dementia. The prion-like, disordered C-terminal domain (CTD) of TDP-43 is aggregation-prone, can undergo liquid-liquid phase separation (LLPS) in isolation, and is critical for phase separation (PS) of the full-length protein under physiological conditions. While a short conserved helical region (CR, spanning residues 319-341) promotes oligomerization and is essential for LLPS, aromatic residues in the flanking disordered regions (QN-rich, IDR1/2) are also found to play a critical role in PS and aggregation. Compared with other phase-separating proteins, TDP-43 CTD has a notably distinct sequence composition including many aliphatic residues such as methionine and leucine. Aliphatic residues were previously suggested to modulate the apparent viscosity of the resulting phases, but their direct contribution toward CTD phase separation has been relatively ignored. Using multiscale simulations coupled with in vitro saturation concentration (csat) measurements, we identified the importance of aromatic residues while also suggesting an essential role for aliphatic methionine residues in promoting single-chain compaction and LLPS. Surprisingly, NMR experiments showed that transient interactions involving phenylalanine and methionine residues in the disordered flanking regions can directly enhance site-specific, CR-mediated intermolecular association. Overall, our work highlights an underappreciated mode of biomolecular recognition, wherein both transient and site-specific hydrophobic interactions act synergistically to drive the oligomerization and phase separation of a disordered, low-complexity domain.

Combining Experiments and Simulations to Examine the Temperature-Dependent Behavior of a Disordered Protein

Intrinsically disordered proteins are a class of proteins that lack stable folded conformations and instead adopt a range of conformations that determine their biochemical functions. The temperature-dependent behavior of such disordered proteins is complex and can vary depending on the specific protein and environment. Here, we have used molecular dynamics simulations and previously published experimental data to investigate the temperature-dependent behavior of histatin 5, a 24-residue-long polypeptide. We examined the hypothesis that histatin 5 undergoes a loss of polyproline II (PPII) structure with increasing temperature, leading to more compact conformations. We found that the conformational ensembles generated by the simulations generally agree with small-angle X-ray scattering data for histatin 5, but show some discrepancies with the hydrodynamic radius as probed by pulsed-field gradient NMR spectroscopy, and with the secondary structure information derived from circular dichroism. We attempted to reconcile these differences by reweighting the conformational ensembles against the scattering and NMR data. By doing so, we were in part able to capture the temperature-dependent behavior of histatin 5 and to link the observed decrease in hydrodynamic radius with increasing temperature to a loss of PPII structure. We were, however, unable to achieve agreement with both the scattering and NMR data within experimental errors. We discuss different possible reasons for this including inaccuracies in the force field, differences in conditions of the NMR and scattering experiments, and issues related to the calculation of the hydrodynamic radius from conformational ensembles. Our study highlights the importance of integrating multiple types of experimental data when modeling conformational ensembles of disordered proteins and how environmental factors such as the temperature influence them.

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.

Designing Intracellular Compartments for Efficient Engineered Microbial Cell Factories

With the rapid development of synthetic biology, various kinds of microbial cell factories (MCFs) have been successfully constructed to produce high-value-added compounds. However, the complexity of metabolic regulation and pathway crosstalk always cause issues such as intermediate metabolite accumulation, byproduct generation, and metabolic burden in MCFs, resulting in low efficiencies and low yields of industrial biomanufacturing. Such issues could be solved by spatially rearranging the pathways using intracellular compartments. In this review, design strategies are summarized and discussed based on the types and characteristics of natural and artificial subcellular compartments. This review systematically presents information for the construction of efficient MCFs with intracellular compartments in terms of four aspects of design strategy goals: (1) improving local reactant concentration; (2) intercepting and isolating competing pathways; (3) providing specific reaction substances and environments; and (4) storing and accumulating products.

A General Picture of Cucurbit[8]uril Host–Guest Binding: Recalibrating Bonded Interactions

Atomic-level understanding of the dynamic feature of host–guest interactions remains a central challenge in supramolecular chemistry. The remarkable guest binding behavior of the Cucurbiturils family of supramolecular containers makes them promising drug carriers. Among Cucurbit[n]urils, Cucurbit[8]uril (CB8) has an intermediate portal size and cavity volume. It can exploit almost all host–guest recognition motifs formed by this host family. In our previous work, an extensive computational investigation of the binding of seven commonly abused and structurally diverse drugs to the CB8 host was performed, and a general dynamic binding picture of CB8-guest interactions was obtained. Further, two widely used fixed-charge models for drug-like molecules were investigated and compared in great detail, aiming at providing guidelines in choosing an appropriate charge scheme in host-guest modelling. Iterative refitting of atomic charges leads to improved binding thermodynamics and the best root-mean-squared deviation from the experimental reference is 2.6 kcal/mol. In this work, we focus on a thorough evaluation of the remaining parts of classical force fields, i.e., the bonded interactions. The widely used general Amber force fields are assessed and refitted with generalized force-matching to improve the intra-molecular conformational preference, and thus the description of inter-molecular host–guest interactions. The interaction pattern and binding thermodynamics show a significant dependence on the modelling parameters. The refitted system-specific parameter set improves the consistency of the modelling results and the experimental reference significantly. Finally, combining the previous charge-scheme comparison and the current force-field refitting, we provide general guidelines for the theoretical modelling of host–guest binding.

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.

Disordered proteins mitigate the temperature dependence of site-specific binding free energies

Biophysical characterization of protein-protein interactions involving disordered proteins is challenging. A common simplification is to measure the thermodynamics and kinetics of disordered site binding using peptides containing only the minimum residues necessary. We should not assume, however, that these few residues tell the whole story. Son of sevenless, a multidomain signaling protein from Drosophila melanogaster, is critical to the mitogen-activated protein kinase pathway, passing an external signal to Ras, which leads to cellular responses. The disordered 55 kDa C-terminal domain of Son of sevenless is an autoinhibitor that blocks guanidine exchange factor activity. Activation requires another protein, Downstream of receptor kinase (Drk), which contains two Src homology 3 domains. Here, we utilized NMR spectroscopy and isothermal titration calorimetry to quantify the thermodynamics and kinetics of the N-terminal Src homology 3 domain binding to the strongest sites incorporated into the flanking disordered sequences. Comparing these results to those for isolated peptides provides information about how the larger domain affects binding. The affinities of sites on the disordered domain are like those of the peptides at low temperatures but less sensitive to temperature. Our results, combined with observations showing that intrinsically disordered proteins become more compact with increasing temperature, suggest a mechanism for this effect.

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 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.

Comprehensive evaluation of end-point free energy techniques in carboxylated-pillar[6]arene host-guest binding: I. Standard procedure

Despite the massive application of end-point free energy methods in protein-ligand and protein-protein interactions, computational understandings about their performance in relatively simple and prototypical host-guest systems are limited. In this work, we present a comprehensive benchmark calculation with standard end-point free energy techniques in a recent host-guest dataset containing 13 host-guest pairs involving the carboxylated-pillar[6]arene host. We first assess the charge schemes for solutes by comparing the charge-produced electrostatics with many ab initio references, in order to obtain a preliminary albeit detailed view of the charge quality. Then, we focus on four modelling details of end-point free energy calculations, including the docking procedure for the generation of initial condition, the charge scheme for host and guest molecules, the water model used in explicit-solvent sampling, and the end-point methods for free energy estimation. The binding thermodynamics obtained with different modelling schemes are compared with experimental references, and some practical guidelines on maximizing the performance of end-point methods in practical host-guest systems are summarized. Further, we compare our simulation outcome with predictions in the grand challenge and discuss further developments to improve the prediction quality of end-point free energy methods. Overall, unlike the widely acknowledged applicability in protein-ligand binding, the standard end-point calculations cannot produce useful outcomes in host-guest binding and thus are not recommended unless alterations are performed.

Clustering and cross-linking of the wheat storage protein α-gliadin: A combined experimental and theoretical approach

Our aim was to understand mechanisms for clustering and cross-linking of gliadins, a wheat seed storage protein type, monomeric in native state, but incorporated in network while processed. The mechanisms were studied utilizing spectroscopy and high-performance liquid chromatography on a gliadin-rich fraction, in vitro produced α-gliadins, and synthetic gliadin peptides, and by coarse-grained modelling, Monte Carlo simulations and prediction algorithms. In solution, gliadins with α-helix structures (dip at 205 nm in CD) were primarily present as monomeric molecules and clusters of gliadins (peaks at 650- and 700-s on SE-HPLC). At drying, large polymers (R_g 90.3 nm by DLS) were formed and β-sheets increased (14% by FTIR). Trained algorithms predicted aggregation areas at amino acids 115-140, 150-179, and 250-268, and induction of liquid-liquid phase separation at P- and Poly-Q-sequences (Score = 1). Simulations showed that gliadins formed polymers by tail-to-tail or a hydrophobic core (Kratky plots and R_ee = 35 and 60 for C- and N-terminal). Thus, the N-terminal formed clusters while the C-terminal formed aggregates by disulphide and lanthionine bonds, with favoured hydrophobic clustering of similar/exact peptide sections (synthetic peptide mixtures on SE-HPLC). Mechanisms of clustering and cross-linking of the gliadins presented here, contribute ability to tailor processing results, using these proteins.

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

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

Rules of Physical Mathematics Govern Intrinsically Disordered Proteins

In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Molecular interactions contributing to FUS SYGQ LC-RGG phase separation and co-partitioning with RNA polymerase II heptads

The RNA-binding protein FUS (Fused in Sarcoma) mediates phase separation in biomolecular condensates and functions in transcription by clustering with RNA polymerase II. Specific contact residues and interaction modes formed by FUS and the C-terminal heptad repeats of RNA polymerase II (CTD) have been suggested but not probed directly. Here we show how RGG domains contribute to phase separation with the FUS N-terminal low-complexity domain (SYGQ LC) and RNA polymerase II CTD. Using NMR spectroscopy and molecular simulations, we demonstrate that many residue types, not solely arginine-tyrosine pairs, form condensed-phase contacts via several interaction modes including, but not only sp2-π and cation-π interactions. In phases also containing RNA polymerase II CTD, many residue types form contacts, including both cation-π and hydrogen-bonding interactions formed by the conserved human CTD lysines. Hence, our data suggest a surprisingly broad array of residue types and modes explain co-phase separation of FUS and RNA polymerase II.

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Folded domain charge properties influence the conformational behavior of disordered tails

Intrinsically disordered proteins and protein regions (IDRs) make up around 30% of the human proteome where they play essential roles in dictating and regulating many core biological processes. While IDRs are often studied as isolated domains, in naturally occurring proteins most IDRs are found adjacent to folded domains, where they exist as either N- or C-terminal tails or as linkers connecting two folded domains. Prior work has shown that charge properties of IDRs can influence their conformational behavior, both in isolation and in the context of folded domains. In contrast, the converse scenario is less well-explored: how do the charge properties of folded domains influence IDR conformational behavior? To answer this question, we combined a large-scale structural bioinformatics analysis with all-atom implicit solvent simulations of both rationally designed and naturally occurring proteins. Our results reveal three key takeaways. Firstly, the relative position and accessibility of charged residues across the surface of a folded domain can dictate IDR conformational behavior, overriding expectations based on net surface charge properties. Secondly, naturally occurring proteins possess multiple charge patches that are physically accessible to local IDRs. Finally, even modest changes in the local electrostatic environment of a folded domain can substantially modulate IDR-folded domain interactions. Taken together, our results suggest that folded domain surfaces can act as local determinants of IDR conformational behavior.

•

Intrinsically disordered regions (IDRs) are mostly found adjacent to folded domains.

•

Here we propose that the folded domain surface properties influence IDR behavior.

•

We combine all-atom simulations and sequence design of IDRs and folded domains.

•

IDR conformational behavior is determined by a complex combination of factors.

•

Folded domains can substantially alter IDR conformational biases.

Salt-Dependent Conformational Changes of Intrinsically Disordered Proteins

The flexible structure of an intrinsically disordered protein (IDP) is known to be perturbed by salt concentrations, which can be understood by electrostatic screening on charged amino acids. However, an IDP usually contains more uncharged residues that are influenced by the salting-out effect. Here we have parametrized the salting-out effect into a coarse-grained model using a set of Förster resonance energy transfer data and verified with experimental salt-dependent liquid-liquid phase separation (LLPS) of 17 proteins. The new model can correctly capture the behavior of 6 more sequences, resulting in a total of 13 when varying salt concentrations. Together with a survey of more than 500 IDP sequences, we conclude that the salting-out effect, which was considered to be secondary to electrostatic screening, is important for IDP sequences with moderately charged residues at physiological salt concentrations. The presented scheme is generally applicable to other computational models for capturing salt-dependent IDP conformations.

Liquid-Liquid Phase Separation of Tau Protein Is Encoded at the Monomeric Level

Liquid-liquid phase separation (LLPS) is involved in both physiological and pathological processes. The intrinsically disordered protein Tau and its K18 construct can undergo LLPS in a distinct temperature-dependent manner, and the LLPS of Tau protein can initiate Tau aggregation. However, the underlying mechanism driving Tau LLPS remains largely elusive. To understand the temperature-dependent LLPS behavior of Tau at the monomeric level, we explored the conformational ensemble of Tau at different temperatures by performing all-atom replica-exchange molecular dynamic simulation on K18 monomer with an accumulated simulation time of 26.4 μs. Our simulation demonstrates that the compactness, β-structure propensity, and intramolecular interaction of K18 monomer exhibit nonlinear temperature-dependent behavior. ²⁹⁵DNIKHV³⁰⁰/³²⁶GNIHHK³³¹/³³⁷VEVKSE³⁴² make significant contributions to the temperature dependence of the β propensity of K18 monomer, while the two fibril-nucleating cores display relatively high β propensity at all temperatures. At a specific temperature, K18 monomer adopts the most collapsed state with exposed sites for both persistent and transient interactions. Given that more collapsed polypeptide chains were reported to be more prone to phase separate, our results suggest that K18 monomer inherently possesses conformational characteristics favoring LLPS. Our simulation predicts the importance of ²⁹⁵DNIKHV³⁰⁰/³²⁶GNIHHK³³¹/³³⁷VEVKSE³⁴² to the temperature-dependent conformational properties of K18, which is corroborated by CD spectra, turbidity assays, and DIC microscopy. Taken together, we offer a computational and experimental approach to comprehend the structural basis for LLPS by amyloidal building blocks.

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.

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

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

Model for disordered proteins with strongly sequence-dependent liquid phase behavior

Phase separation of intrinsically disordered proteins is important for the formation of membraneless organelles or biomolecular condensates, which play key roles in the regulation of biochemical processes within cells. In this work, we investigated the phase separation of different sequences of a coarse-grained model for intrinsically disordered proteins and discovered a surprisingly rich phase behavior. We studied both the fraction of total hydrophobic parts and the distribution of hydrophobic parts. Not surprisingly, sequences with larger hydrophobic fractions showed conventional liquid-liquid phase separation. The location of the critical point was systematically influenced by the terminal beads of the sequence due to changes in interfacial composition and tension. For sequences with lower hydrophobicity, we observed not only conventional liquid-liquid phase separation but also re-entrant phase behavior in which the liquid phase density decreases at lower temperatures. For some sequences, we observed the formation of open phases consisting of aggregates, rather than a normal liquid. These aggregates had overall lower densities than the conventional liquid phases and exhibited complex geometries with large interconnected string-like or membrane-like clusters. Our findings suggest that minor alterations in the ordering of residues may lead to large changes in the phase behavior of the protein, a fact of significant potential relevance for biology.

SAMPL7 TrimerTrip host-guest binding poses and binding affinities from spherical-coordinates-biased simulations

Host-guest binding remains a major challenge in modern computational modelling. The newest 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge contains a new series of host-guest systems. The TrimerTrip host binds to 16 structurally diverse guests. Previously, we have successfully employed the spherical coordinates as the collective variables coupled with the enhanced sampling technique metadynamics to enhance the sampling of the binding/unbinding event, search for possible binding poses and calculate the binding affinities in all three host-guest binding cases of the 6th SAMPL challenge. In this work, we report a retrospective study on the TrimerTrip host-guest systems by employing the same protocol to investigate the TrimerTrip host in the SAMPL7 challenge. As no binding pose is provided by the SAMPL7 host, our simulations initiate from randomly selected configurations and are proceeded long enough to obtain converged free energy estimates and search for possible binding poses. The calculated binding affinities are in good agreement with the experimental reference, and the obtained binding poses serve as a nice starting point for end-point or alchemical free energy calculations. Note that as the work is performed after the close of the SAMPL7 challenge, we do not participate in the challenge and the results are not formally submitted to the SAMPL7 challenge.

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.

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model

Intrinsically disordered proteins (IDPs) play an important role in an array of biological processes but present a number of fundamental challenges for computational modeling. Recently, simple polymer models have regained popularity for interpreting the experimental characterization of IDPs. Homopolymer theory provides a strong foundation for understanding generic features of phenomena ranging from single-chain conformational dynamics to the properties of entangled polymer melts, but is difficult to extend to the copolymer context. This challenge is magnified for proteins due to the variety of competing interactions and large deviations in side-chain properties. In this work, we apply a simple physics-based coarse-grained model for describing largely disordered conformational ensembles of peptides, based on the premise that sampling sterically forbidden conformations can compromise the faithful description of both static and dynamical properties. The Hamiltonian of the employed model can be easily adjusted to investigate the impact of distinct interactions and sequence specificity on the randomness of the resulting conformational ensemble. In particular, starting with a bead–spring-like model and then adding more detailed interactions one by one, we construct a hierarchical set of models and perform a detailed comparison of their properties. Our analysis clarifies the role of generic attractions, electrostatics, and side-chain sterics, while providing a foundation for developing efficient models for IDPs that retain an accurate description of the hierarchy of conformational dynamics, which is nontrivially influenced by interactions with surrounding proteins and solvent molecules.

Biomolecular Phase Separation: From Molecular Driving Forces to Macroscopic Properties

Biological phase separation is known to be important for cellular organization, which has recently been extended to a new class of biomolecules that form liquid-like droplets coexisting with the surrounding cellular or extracellular environment. These droplets are termed membraneless organelles, as they lack a dividing lipid membrane, and are formed through liquid-liquid phase separation (LLPS). Elucidating the molecular determinants of phase separation is a critical challenge for the field, as we are still at the early stages of understanding how cells may promote and regulate functions that are driven by LLPS. In this review, we discuss the role that disorder, perturbations to molecular interactions resulting from sequence, posttranslational modifications, and various regulatory stimuli play on protein LLPS, with a particular focus on insights that may be obtained from simulation and theory. We finally discuss how these molecular driving forces alter multicomponent phase separation and selectivity.

Emerging consensus on the collapse of unfolded and intrinsically disordered proteins in water

Establishing the degree of collapse of unfolded or disordered proteins is a fundamental problem in biophysics, because of its relation to protein folding and to the function of intrinsically disordered proteins. However, until recently, different experiments gave qualitatively different results on collapse and there were large discrepancies between experiments and all-atom simulations. New methodology introduced in the past three years has helped to resolve the differences between experiments, and improvements in simulations have closed the gap between experiment and simulation. These advances have led to an emerging consensus on the collapse of disordered proteins in water.

SAMPL6 host-guest binding affinities and binding poses from spherical-coordinates-biased simulations

Host-guest binding is a challenging problem in computer simulation. The prediction of binding affinities between hosts and guests is an important part of the statistical assessment of the modeling of proteins and ligands (SAMPL) challenges. In this work, the volume-based variant of well-tempered metadynamics is employed to calculate the binding affinities of the host-guest systems in the SAMPL6 challenge. By biasing the spherical coordinates describing the relative position of the host and the guest, the initial-configuration-induced bias vanishes and all possible binding poses are explored. The agreement between the predictions and the experimental results and the observation of new binding poses indicate that the volume-based technique serves as a nice candidate for the calculation of binding free energies and the search of the binding poses.

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.

Computational investigation of retro-isomer equilibrium structures: Intrinsically disordered, foldable, and cyclic peptides

We use all-atom modeling and advanced-sampling molecular dynamics simulations to investigate quantitatively the effect of peptide bond directionality on the equilibrium structures of four linear (two foldable, two disordered) and two cyclic peptides. We find that the retro forms of cyclic and foldable linear peptides adopt distinctively different conformations compared to their parents. While the retro form of a linear intrinsically disordered peptide with transient secondary structure fails to reproduce a secondary structure content similar to that of its parent, the retro form of a shorter disordered linear peptide shows only minor differences compared to its parent.

Thermodynamics of Helix formation in small peptides of varying lengthin vacuo, implicit solvent and explicit solvent: Comparison between AMBER force fields

Helix formation is of great significance in protein folding. The helix-forming tendencies of amino acids are accumulated along the sequence to determine the helix-forming tendency of peptides. Computer simulation can be used to model this process in atomic details and give structural insights. In the current work, we employ equilibrate-state free energy simulation to systematically study the folding/unfolding thermodynamics of a series of mutated peptides. Two AMBER force fields including AMBER99SB and AMBER14SB are compared. The new 14SB force field uses refitted torsion parameters compared with 99SB and they share the same atomic charge scheme. We find that in vacuo the helix formation is mutation dependent, which reflects the different helix propensities of different amino acids. In general, there are helix formers, helix indifferent groups and helix breakers. The helical structure becomes more favored when the length of the sequence becomes longer, which arises from the formation of additional backbone hydrogen bonds in the lengthened sequence. Therefore, the helix indifferent groups and helix breakers will become helix formers in long sequences. Also, protonation-dependent helix formation is observed for ionizable groups. In 14SB, the helical structures are more stable than in 99SB and differences can be observed in their grouping schemes, especially in the helix indifferent group. In solvents, all mutations are helix indifferent due to protein–solvent interactions. The decrease in the number of backbone hydrogen bonds is the same with the increase in the number of protein–water hydrogen bonds. The 14SB in explicit solvent is able to capture the free energy minima in the helical state while 14SB in implicit solvent, 99SB in explicit solvent and 99SB in implicit solvent cannot. The helix propensities calculated under 14SB agree with the corresponding experimental values, while the 99SB results obviously deviate from the references. Hence, implicit solvent models are unable to correctly describe the thermodynamics even for the simple helix formation in isolated peptides. Well-developed force fields and explicit solvents are needed to correctly describe the protein dynamics. Aside from the free energy, differences in conformational ensemble under different force fields in different solvent models are observed. The numbers of hydrogen bonds formed under different force fields agree and they are mostly determined by the solvent model.

Temperature-Controlled Liquid-Liquid Phase Separation of Disordered Proteins

The liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) is a commonly observed phenomenon within the cell, and such condensates are also highly attractive for applications in biomaterials and drug delivery. A better understanding of the sequence-dependent thermoresponsive behavior is of immense interest as it will aid in the design of protein sequences with desirable properties and in the understanding of cellular response to heat stress. In this work, we use a transferable coarse-grained model to directly probe the sequence-dependent thermoresponsive phase behavior of IDPs. To achieve this goal, we develop a unique knowledge-based amino acid potential that accounts for the temperature-dependent effects on solvent-mediated interactions for different types of amino acids. Remarkably, we are able to distinguish between more than 35 IDPs with upper or lower critical solution temperatures at experimental conditions, thus providing direct evidence that incorporating the temperature-dependent solvent-mediated interactions to IDP assemblies can capture the difference in the shape of the resulting phase diagrams. Given the success of the model in predicting experimental behavior, we use it as a high-throughput screening framework to scan through millions of disordered sequences to characterize the composition dependence of protein phase separation.

Evolution of All-Atom Protein Force Fields to Improve Local and Global Properties

Experimental studies on intrinsically disordered and unfolded proteins have shown that in isolation they typically have low populations of secondary structure and exhibit distance scalings suggesting that they are at near-theta-solvent conditions. Until recently, however, all-atom force fields failed to reproduce these fundamental properties of intrinsically disordered proteins (IDPs). Recent improvements by refining against ensemble-averaged experimental observables for polypeptides in aqueous solution have addressed deficiencies including secondary structure bias, global conformational properties, and thermodynamic parameters of biophysical reactions such as folding and collapse. To date, studies utilizing these improved all-atom force fields have mostly been limited to a small set of unfolded or disordered proteins. Here, we present data generated for a diverse library of unfolded or disordered proteins using three progressively improved generations of Amber03 force fields, and we explore how global and local properties are affected by each successive change in the force field. We find that the most recent force field refinements significantly improve the agreement of the global properties such as radii of gyration and end-to-end distances with experimental estimates. However, these global properties are largely independent of the local secondary structure propensity. This result stresses the need to validate force fields with reference to a combination of experimental data providing information about both local and global structure formation.

General Purpose Water Model Can Improve Atomistic Simulations of Intrinsically Disordered Proteins

Unconstrained atomistic simulations of intrinsically disordered proteins and peptides (IDP) remain a challenge: widely used, "general purpose" water models tend to favor overly compact structures relative to experiment. Here we have performed a total of 93 μs of unrestrained MD simulations to explore, in the context of IDPs, a recently developed "general-purpose" 4-point rigid water model OPC, which describes liquid state of water close to experiment. We demonstrate that OPC, together with a popular AMBER force field ff99SB, offers a noticeable improvement over TIP3P in producing more realistic structural ensembles of three common IDPs benchmarks: 55-residue apo N-terminal zinc-binding domain of HIV-1 integrase ("protein IN"), amyloid β-peptide (Aβ₄₂) (residues 1-42), and 26-reside H4 histone tail. As a negative control, computed folding profile of a regular globular miniprotein (CLN025) in OPC water is in appreciably better agreement with experiment than that obtained in TIP3P, which tends to overstabilize the compact native state relative to the extended conformations. We employed Aβ₄₂ peptide to investigate the possible influence of the solvent box size on simulation outcomes. We advocate a cautious approach for simulations of IDPs: we suggest that the solvent box size should be at least four times the radius of gyration of the random coil corresponding to the IDP. The computed free energy landscape of protein IN in OPC resembles a shallow "tub" - conformations with substantially different degrees of compactness that are within 2 k_B T of each other. Conformations with very different secondary structure content coexist within 1 k_B T of the global free energy minimum. States with higher free energy tend to have less secondary structure. Computed low helical content of the protein has virtually no correlation with its degree of compactness, which calls into question the possibility of using the helicity as a metric for assessing performance of water models for IDPs, when the helicity is low. Predicted radius of gyration ( R _g) of H4 histone tail in OPC water falls in-between that of a typical globular protein and a fully denatured protein of the same size; the predicted R _g is consistent with two independent predictions. In contrast, H4 tail in TIP3P water is as compact as the corresponding globular protein. The computed free energy landscape of H4 tail in OPC is relatively flat over a significant range of compactness, which, we argue, is consistent with its biological function as facilitator of internucleosome interactions.

Simulation methods for liquid-liquid phase separation of disordered proteins

Liquid-liquid phase separation of intrinsically disordered proteins (IDPs) and other biomolecules is a highly complex but robust process used by living systems. Drawing inspiration from biology, phase separating proteins have been successfully utilized for promising applications in fields of materials design and drug delivery. These protein-based materials are advantageous due to the ability to finely tune their stimulus-responsive phase behavior and material properties, and the ability to encode biologically active motifs directly into the sequence. The number of possible protein sequences is virtually endless, which makes sequence-based design a rather daunting task, but also attractive due to the amount of control coming from exploration of this variable space. The use of computational methods in this field of research have come to the aid in several aspects, including interpreting experimental results, identifying important structural features and molecular mechanisms capable of explaining the phase behavior, and ultimately providing predictive frameworks for rational design of protein sequences. Here we provide an overview of computational studies focused on phase separating biomolecules and the tools that are available to researchers interested in this topic.

Thermodynamically driven assemblies and liquid-liquid phase separations in biology

The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical origin of such organization is not fully understood, and even though it is clear that cells and organisms cannot maintain their integrity without consuming energy, there is growing evidence that individual assembly processes can be thermodynamically driven and occur spontaneously due to changes in thermodynamic variables such as intermolecular interactions and concentration. Understanding the phase separation in vivo requires a multidisciplinary approach, integrating the theory and physics of phase separation with experimental and computational techniques. This paper aims at providing a brief overview of the physics of phase separation and its biological implications, with a particular focus on the assembly of membraneless organelles. We discuss the underlying physical principles of phase separation from its thermodynamics to its kinetics. We also overview the wide range of methods utilized for experimental verification and characterization of phase separation of membraneless organelles, as well as the utility of molecular simulations rooted in thermodynamics and statistical physics in understanding the governing principles of thermodynamically driven biological self-assembly processes.

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.

Relation between single-molecule properties and phase behavior of intrinsically disordered proteins

Proteins that undergo liquid-liquid phase separation (LLPS) have been shown to play a critical role in many physiological functions through formation of condensed liquid-like assemblies that function as membraneless organelles within biological systems. To understand how different proteins may contribute differently to these assemblies and their functions, it is important to understand the molecular driving forces of phase separation and characterize their phase boundaries and material properties. Experimental studies have shown that intrinsically disordered regions of these proteins are a major driving force, as many of them undergo LLPS in isolation. Previous work on polymer solution phase behavior suggests a potential correspondence between intramolecular and intermolecular interactions that can be leveraged to discover relationships between single-molecule properties and phase boundaries. Here, we take advantage of a recently developed coarse-grained framework to calculate the θ temperature [Formula: see text], the Boyle temperature [Formula: see text], and the critical temperature [Formula: see text] for 20 diverse protein sequences, and we show that these three properties are highly correlated. We also highlight that these correlations are not specific to our model or simulation methodology by comparing between different pairwise potentials and with data from other work. We, therefore, suggest that smaller simulations or experiments to determine [Formula: see text] or [Formula: see text] can provide useful insights into the corresponding phase behavior.

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.

Temperature-induced collapse of a disordered peptide observed by three sampling methods in molecular dynamics simulations

The conformational ensembles of a disordered peptide, polyglutamine Q15, over a wide temperature range were sampled using multiple replicates of conventional molecular dynamics (cMD) simulations as well as two enhanced sampling methods, temperature replica exchange (TREMD) and replica exchange with solute tempering (REST). The radius of gyration, asphericity, secondary structure, and hydrogen bonding patterns were used for the comparison of the sampling methods. Overall, the three sampling methods generated similar conformational ensembles, with progressive collapse at higher temperatures. Although accumulating the longest simulation time (90 μs), cMD at room temperature missed a small subspace that was sampled by both TREMD and REST. This subspace was high in α-helical content and separated from the main conformational space by an energy barrier. REST used less simulation time than TREMD (36 μs versus 42 μs), and this gap is expected to widen significantly for larger disordered proteins. We conclude that REST is the method of choice for conformational sampling of intrinsically disordered proteins.