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. 2025 Jun 26;129(27):6817–6827. doi: 10.1021/acs.jpcb.5c02360

Hydrophobicity in Intrinsically Disordered Protein Force Fields: Implications for Conformational Ensembles and Protein–Protein Interactions

Samuel Lobo †, Saeed Najafi ‡, M Scott Shell †,*, Joan-Emma Shea ‡,§,*
PMCID: PMC12257530  PMID: 40569578

Abstract

Intrinsically disordered proteins (IDPs) lack a stable 3D structure under physiological conditions, making them challenging to study and simulate. In this study, we compare the hydrophobicity and water–protein interactions of amino acids in three popular all-atom molecular dynamics (MD) force fields: amber03ws (a03ws), CHARMM36m (C36m), and a99SB-disp. Using the indirect umbrella sampling (INDUS) technique, we quantify the dewetting free energies of each amino acid in the force fields. Additionally, we analyze water structuring around the amino acids using the water triplet angle distribution and measure water diffusion in the hydration shells. Our results reveal that CHARMM36m has the lowest dewetting free energies, indicating higher amino acid hydrophobicity, while a99SB-disp exhibits the highest, suggesting lower hydrophobicity. Water diffusion is significantly slower in the hydration shells of a99SB-disp due to its unique water structuring (e.g., higher frequency of tetrahedral coordination), while there is much less of a water diffusion slowdown in a03ws and CHARMM36m. We show that these differences impact the behavior of an aggregation-prone tau fragment, jR2R3 P301L, in MD simulations. We find that CHARMM36m’s propensity for dimer formation is attributed to its lower dewetting free energies, whereas a99SB-disp’s higher-than-expected dimerization propensity is due to favorable, entropically driven changes in water structure upon peptide association. These findings underscore the importance of accurately modeling water–protein interactions for IDPs and protein–protein interactions as well as the sensitivity of these to the underlying force field. Our study suggests that dewetting free energies and water structuring metrics, such as the water triplet angle distribution, can be valuable for future force field development and for predicting phenomena related to water–protein interactions.

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Introduction

Intrinsically disordered proteins (IDPs) represent a significant fraction of the human proteome and are characterized by their lack of a stable structure. , This structural flexibility enables IDPs to play diverse functional roles, including cellular signaling, molecular recognition, and phase separation, but they are also being implicated in the progression of neurodegenerative diseases, cancers, and other pathologies. − IDPs’ dynamic nature can be challenging to study and interpret, and all-atom molecular dynamics (MD) simulations, particularly when coupled with enhanced sampling protocols, have emerged as useful tools to probe IDP structure and the underlying molecular mechanisms responsible for IDPs’ function or dysfunction. A critical element to the success of IDP MD simulations lies in an accurate parameterization not only of protein–protein interactions but, importantly, of water–protein interactions. Indeed, water–protein interactions must be carefully tuned in all-atom MD force fields to accurately replicate the behavior of IDPs observed in experiments, and slight differences in a water model or in water–protein interactions (e.g., force field) can lead to substantially different IDP behavior in a simulation. −

Prior to the past decade, MD force fields tended to produce ensembles for disordered proteins that were excessively compact because they had largely been developed to stabilize globular proteins. , Over the past decade, substantial advancements have been made to improve MD force fields for disordered proteins. − ,, In 2014, Best et al. developed the amber03ws force field by modifying the original amber03w force field to strengthen water–protein Lennard-Jones (LJ) interactions by 10%, thereby more accurately capturing the radii of gyration of IDPs. In 2017, Huang et al. developed the CHARMM36m force field by modifying CHARMM36, e.g., adjusting a LJ parameter in the water hydrogen atoms and altering the backbone torsions via the CMAP potential. In particular, in 2018, Robustelli et al. developed the a99SB-disp force field by modifying a99SB-ILDNe.g., optimizing torsion parameters, strengthening the water oxygen’s C6 dispersion term, and modifying LJ potentials between backbone carbonyl oxygens and backbone amide hydrogensand achieved state-of-the-art accuracy for disordered states while preserving accuracy for folded proteins. These force fields were mainly evaluated by their ability to reproduce NMR observables, such as chemical shifts and residual dipolar couplings, as well as radius of gyration data from SAXS or FRET experiments. Amber03ws, CHARMM36m, and a99SB-disp are popular choices for modeling disordered protein conformations, thermodynamics, and dynamics.

These three force fields, which we abbreviate to a03ws, C36m, and a99SBdisp, have some notable differences. C36m uses a 3-site water model (TIP3P), while a03ws and a99SBdisp employ 4-site water models (TIP4P-2005 and a modified TIP4P-D, respectively) that more accurately capture physical properties of water. , a03ws tends to destabilize folded proteins more than a99SBdisp and C36m, and it results in more nuclear Overhauser effect (NOE) violations. Meanwhile, C36m tends to overly collapse disordered proteins. Some researchers have alleviated the overstabilization of protein–protein interactions in C36m by replacing the TIP3P water model with a99SBdisp’s water model, and others have observed how amino acid hydropathy is dependent on the water model. It should be noted that a03ws, a99SBdisp, and C36m each had distinct development strategies and that even within the Amber family, the force fields are not simply sequential improvements of each other; Figure 3 of Lemkul (2020) shows a schematic of the historical development and relationships among protein force fields.

Much of the assessment of the accuracy of these protein–water-modified force fields for describing IDPs has focused thus far on their ability to describe monomer conformations. Far less emphasis has been placed on whether these IDP force fields are capable of correctly modeling the IDP–IDP association. It is important to note that many IDPs do not act as independent units but rather only play their functional roles once they have bound to a partner molecule (e.g., another IDP or a surface). Water–protein interactions can play as important a role in determining protein–protein association as in determining monomeric conformation, as a protein’s surface must dewet when forming a complex with another protein.

The association of proteins can have pathological ramifications, as in the case of the self-assembly of IDPs into toxic oligomers and fibrils during amyloid aggregation, which is implicated in many neurodegenerative diseases. In amyloid aggregation, many disordered monomers self-associate to form ordered filaments, and this is largely driven by water-mediated hydrophobic interactions and intermolecular hydrogen bonding. Disordered monomers are highly hydrated, while ordered amyloid filaments are largely dewetted. To gain a deeper understanding of amyloid aggregation mechanisms, it is essential to accurately model IDP–IDP association, which in turn requires the precise modeling of protein dewetting.

Considering the importance of accurately modeling protein dewetting and a lack of clarity in the literature about how IDP force fields perform in this regard, we aim in this work to quantify differences in amino acids’ dewetting free energies in each of these popular force fields. Additionally, we assess how such differences translate into association propensities and the resulting assemblies. Several other groups have investigated how the force field affects IDP–IDP association in oligomers of short peptides − and intra-IDP association of longer peptide monomers. − For instance, Man et al. and Carballo-Pacheco et al. compared the dimerization and oligomerization behavior of Aβ16–22 peptides across more than a dozen force fields, finding differences in oligomerization kinetics. , Notably, Cai et al. optimized peptide–peptide and peptide–solvent interactions to make the PACE-ASM force field that captures self-assembly of peptides, explicitly representing heavy atoms and amide hydrogens along with a coarse-grained water model.

We recently introduced a new hydrophobicity scale based on computed amino acid dewetting free energies from indirect umbrella sampling (INDUS) , calculations, and here we use this metric as a first step in assessing the hydrophobicity of a03ws, C36m, and a99SBdisp force fields. This quantitative measure of hydrophobicity, F dewet, captures context-dependent and cooperative effects in hydration behavior and directly measures both enthalpic and entropic contributions to amino acid hydration, making it an intuitive and physically grounded metric for analyzing hydrophobicity in molecular simulations.

While hydrophobicity’s enthalpic component is more directly measurable from a force field, it is more challenging to quantify the entropic components of hydrophobicity. The water triplet distribution, also called the water 3-body angle distribution, provides a powerful tool to assess water structuring by quantifying the geometric arrangement of the water network around a protein. This metric captures the extent of local water ordering, which correlates directly with entropy changes during dewetting. Specifically, we quantify the tetrahedral water ordering in an amino acid’s hydration shell. The extent of tetrahedral ordering has been seen to correlate to water diffusion and therefore potentially impacts protein conformational dynamics as well.

We thus compare water structuring using the triplet angle distribution and examine hydration water diffusivity in each force field. In combination with quantifying differences in protein hydrophobicity and protein–water interactions, these collective results highlight how the biases of these force fields influence the monomer and dimer behavior of an aggregation-prone tau fragment. Finally, we discuss the implications for simulating amyloid aggregation and offer insights into future parameterization of IDP force fields.

Methods

INDUS Dewetting Free Energy Measurements

The indirect umbrella sampling (INDUS) simulations , were conducted using a modified version of Gromacs 2016.3, which includes biasing potentials on the coarse-grained number of water molecules (N v) within the hydration volume. This modified version was provided by the Patel group at the University of Pennsylvania. Here, to ensure at least two to three layers of water molecules in the hydration shell of the residue, the radius of the spherical probe volume (R v) attached to each heavy atom is set to R v = 0.55 nm. It is important to note that if R v is too large, the behavior of the hydration water may become less pertinent to the target residue, and the dewetting free energy signal could be diminished by the influence of bulk water. The Gaussian coarse-graining function employed in INDUS is parameterized with a standard deviation of σ = 0.01 nm and a truncation length of r c = 0.02 nm. The water dynamics is governed by the Hamiltonian: H = H 0 + 1/2 κ (N v – N*)2, where H 0 is the unbiased potential and the second term represents the harmonic biasing potential with strength κ = 10κ0, κ0 = (1/⟨δN v 2⟩).

The biased simulations are conducted for a total duration of 6 ns with the first 2 ns of each simulation discarded to allow the system to reach a steady state. The overlapping successive windows of N v (the instantaneous number of water molecules within the hydration volume), obtained from biased simulations at different N*, enable the estimation of the dehydration free energy. The dehydration free energy is calculated as the negative logarithm of the unbiased probability distribution of observing N water molecules within the hydration volume expressed as βF(N) = −ln P v(N). The P v(N) is determined using the unbinned weighted histogram analysis method (UWHAM). To accurately represent the dewetting feature, all calculated free energies are truncated before the hydration water reaches the vapor phase, where 20% of the water remains in the probe volume.

These simulations were performed in water. We note that the dewetting free energies differ based on the local environment context, as discussed by Najafi et al., and the relative dewetting free energies between amino acids may differ depending on the environment (e.g., solvent), as discussed by De Sancho & Lopez. Recent transfer-free-energy calculations in model condensates further underscore this environment dependence and reveal an interplay between protein- and water-mediated contributions to phase separation. Some alternative ways to quantify dewetting thermodynamics include comparing characteristics of solvation cavities and evaluating the hydration water’s response to increasing temperature.

Diffusion Measurements

The hydration water diffusion coefficient is calculated by determining the slope of the average mean square displacement (MSD) of the oxygen atoms in the hydration water over time (i.e., D = MSD/t at every 1.0 ps for 10 ps). The resulting diffusion coefficient provides a fundamental understanding of how the water molecules behave within the hydration shell, capturing the dynamic aspects of the hydration water.

Water Triplet Angle Distribution

Water oxygens are selected, either around the peptide (Figure E­(i), selecting within 4.25 Å of the peptide heavy atoms) or within a defined box (Figures E­(ii), S5, and S6). In a single frame of the simulation, waters are looped through, and all the angles between neighboring oxygens, within 3.5 Å, are tabulated. These angles are tabulated in each frame of the trajectory and histogrammed to make the water triplet distribution, also called the water 3-body angle distribution. This was originally described by Monroe and Shell. Relative tetrahedrality refers to the fraction of angles between 100 and 120° in the selection (e.g., around a peptide or within a box) divided by the fraction of angles between 100 and 120° in bulk water.

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(A) Depiction of the simulation setup with a small, capped peptide (valine-leucine-glycine with ACE and NME caps, gray sticks) diffusing within a teal box above a restrained jR2R3 P301L seed (purple). Flat-bottomed harmonic restraints prevent the chain’s center of mass from diffusing outside the teal box. (B) Free energy surface of the peptide as a function of its height above the seed at two temperatures, from umbrella sampling on the center of mass; shading denotes standard errors. (C) The docking free energy for each force field at two temperatures. a99SBdisp has a greater docking free energy at 325 K, indicating a significant entropic component of the docking process, likely due to water unstructuring upon docking. (D) Comparing the residence times (median and 90th percentile) of the peptide on the seed for each force field; a99SBdisp has longer residence times than the other force fields. (E­(i)) Comparing water tetrahedrality around the undocked and docked peptides for each force field. Relative tetrahedrality is the fraction of tetrahedral water angles (100° < θ < 120°) in the hydration shell divided by the fraction of tetrahedral water angles in bulk. (E­(ii)) Comparing water tetrahedrality in a larger box (i.e., within the dashed lines of panel A) when the peptide is undocked vs docked in each force field. Tetrahedral waters are released as the peptide’s hydration shell overlaps with the seed’s hydration shell upon binding, especially in a99SBdisp.

Replica Exchange Molecular Dynamics

jR2R3 P301L is a 19-residue fragment of tau: 295DNIKHVLGGGSVQIVYKPV313. Monomer and dimer ensembles were simulated in GROMACS (versions 2019.6 and 2021) by placing one or two copies of this peptide in a water box (rhombic dodecahedral box length 7 nm or higher) with the associated water model (TIP4P-2005s for a03ws, a99SBdisp water for a99SBdisp, and modified TIP3P for CHARMM36m) and chlorine ion(s) to neutralize the net charge of the system. 60 replicas were used, ranging from 300 to 455 K, and replica exchanges were attempted every 3 ps, achieving an average exchange probability of about 30%. 500–750 ns per replica was sampled for the monomers and dimers. The 300 K trajectory was used for analysis. See the Supporting Information for further details on the replica exchange setup and equilibration.

Restrained Molecular Dynamics

Simulations for Figures and S3–S7 were done in OpenMM. We used the Langevin Middle integrator, with a time step of 3 fs and a friction term of 2/ps. PME was used for Coulombic interactions; a nonbonded cutoff of 1.0 nm was used, and bonds with hydrogens were restrained. A Monte Carlo barostat was used to simulate the NPT ensemble with a temperature and pressure of 300 K and 1 atm, respectively. The alpha carbons that were resolved by cryo-EM (residues 295–311) were restrained with a force constant of 100 kJ/mol/nm2. Flat-bottomed harmonic restraints with a force constant of 1000 kJ/mol/nm2 were used to prevent the peptide from escaping the teal box (Figure A). The width of the teal box was 0.7 nm; the depth was 1.6 nm; and the maximum height was 1.8 nm above the top of the filament. The VLG peptide was capped with ACE and NME caps.

Umbrella Sampling

Twelve umbrellas were spaced from y = 1 Å to y = 12 Å, spaced by 1 Å, restraining the center of mass of the VLG peptide with a force constant of 400 kJ/mol/nm2 (E k = 1/2 k (y – y umbrella)2). Each umbrella was simulated for 50–300 ns to obtain more than 100 uncorrelated samples at each umbrella. Initial conformations were taken from the simulation without umbrella restraints. Uncorrelated samples were determined by integrating the autocorrelation function, using pymbar’s timeseries module. Pymbar was used to create the free energy surface, and bootstrapping was done to determine the 68% confidence interval in the free energy landscape.

Measuring Potentials between Atom Groups

OpenMM was used to measure the potential energies between atom groups. Seed-water potential energy (Figure S3) and peptide–peptide potential energy (Table S2) were measured by selecting groups in OpenMM. We referred to the “Computing Interaction Energies” OpenMM cookbook to measure these quantities. For the seed-water potential energy, we used a nonbonded cutoff of 1.2 nm and a switching distance of 1.0 nm while analyzing 500 frames of a trajectory. For peptide–peptide potential energy, only a single conformation was evaluated, and we used a 1.0 nm nonbonded cutoff.

Hydrogen Bonding, Clustering, Visualizations, 2D Free Energy Surface, and Other Analyses

Intermolecular hydrogen bonding analysis was conducted in GROMACS (“gmx hbond ... -n index.ndx” and selecting each dimer chain), using distance cutoffs of 3.5 Å and angle cutoffs of 30° for determining hydrogen bonds. Clusters were determined with the Daura algorithm with GROMACS (“gmx cluster ... -method gromos”), after selecting the full trajectory (e.g., Figure S2C) or part of a trajectory within certain marked cutoffs of collective variables (Figure C). VMD (Figure ) and ChimeraX (other figures) were used for visualizing conformations; the “hbond” command in ChimeraX was used to visualize hydrogen bonds (dashed lines in Figure C). The 2D energy landscapes in Figures C and S10 were generated by measuring the 2D probability density, taking a logarithm, scaling by Boltzmann’s constant and temperature, and applying Gaussian interpolation to smooth the landscape. MDAnalysis was also used to count waters (Figure B) and select atoms. Mdtraj was used to count contacts (Figure B,C)see Figure S8 for details on counting interchain-aligned PHF6 contacts.

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(A) Comparing a cluster from the C36m dimer ensemble to a dimer from the solved cryo-EM structure (see Figure A­(iii,iv)). I297, V306, and I308 form side chain contacts in both structures, and this also strongly resembles the same motif in the LNT filament (PDB #7P6A). (B) Comparing interchain-aligned PHF6 contacts in each force field, which is a key feature in all the tau filaments. PHF6 is residues 306–311 of tau. ∼22% of the C36m ensemble has more than 12 interchain-aligned PHF6 contacts, while the other force fields have <2%. 90% confidence intervals are shown. (C) A free energy landscape of C36m dimers along two collective variables: interchain-aligned PHF6 contacts and intrachain contacts. The top cluster from five regions (i–v) of this energy landscape is shown. Panel (A­(i)) shows the top cluster from region iv, while panel (C­(v)) shows the second cluster, which forms a compact dimer that appears in Figure A­(ii). PHF6 (residues 306–311) is pink, intramolecular hydrogen bonds are blue dashes, intermolecular hydrogen bonds are purple dashes, and well-aligned PHF6 hydrogen bonds are black dashes.

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(A) Depiction of the simulation setup for the INDUS procedure. The capped amino acids are placed far apart in a water box, and then waters are iteratively pushed out of the hydration volume (B), defined by the distances from the amino acids’ heavy atoms, to ultimately determine dewetting free energies. (C) Dewetting free energies per water of each amino acid in the three force fields. Amino acids are ordered based on their hydrophilicity in a03ws. (D) Comparing water diffusivity of the hydration waters relative to bulk water in each force field; note the stretched y-axis from 0.9 to 1.0. D bulk for a03ws, a99SBdisp, and C36m is 0.23, 0.19, and 0.58 Å2/ps, respectively.

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(A) jR2R3 P301L monomer (i) and dimer (ii) cluster and its hydration waters. (iv) Depiction of the cryo-EM structure of jR2R3 P301L, which consists of four strands, two of which form an internal side chain zipper. A dimer from the side chain zipper strand is depicted in (iii). (B) Comparing the distribution of hydration waters for monomers (left half of violins) and dimers (right half of violins) for each force field. For reference, the hydration waters of the compact cluster (A­(ii)) are indicated with a star, and the hydration waters of the cryo-EM dimer (A­(iii)) and filament (A­(iv)) are indicated with dashed lines. (C) Comparing the center-of-mass distance distribution between the two peptides in the dimer ensemble for each force field; shading denotes a 90% confidence interval. CHARMM36m has a strong propensity for the associated state (i.e., low center-of-mass distances), while a03ws has a stronger propensity for the disassociated state.

Results

Force Field Differences in Single Amino Acids

We begin by comparing the dewetting free energies of each of the 20 amino acids in the three force fields: a03ws, a99SBdisp, and C36m. We used the INDUS technique to bias hydration waters away from each amino acid and thereby quantify the free energetic cost associated with dewetting each amino acid in each force field, F dewet. Each amino acid was capped (with ACE and NME), restrained, and solvated (Figure A,B) before iteratively biasing waters away from the hydration shell (see Methods), defined for each amino acid as the volume within 5.5 Å of its heavy atoms, encompassing the first two layers of hydration waters. C36m’s amino acids have the lowest dewetting free energies (Figure C), indicating that less free energy is required to dewet (or expel the hydration waters); therefore, from this metric, C36m has the most hydrophobic amino acids of the three force fields. Given that C36m is known to overly structure IDPs, this behavior is expected. a99SBdisp produces the highest dewetting free energies (i.e., the least hydrophobicity) of the three force fields, while a03ws produces intermediate values. Thus, in terms of this dewetting free energy hydrophobicity metric, we rank the three force fields from least to most hydrophobic as a99SBdisp < a03ws < C36m.

Next, we studied the water diffusion coefficient, D, in the hydration shell of each amino acid. Notably, a99SBdisp has significantly slower water diffusion (normalized to the bulk water diffusion coefficient) in the hydration shells relative to a03ws and C36m. Specifically, a99SBdisp’s hydration water tends to diffuse 21–32% slower relative to bulk, while a03ws and C36m have only 2–7% slowdowns in the hydration shells. This force field variation in hydration water dynamics may be attributed to differences in protein–water affinity and water structuring, as discussed in our recent work: we found that water diffusion is not simply correlated to hydrophobicity but rather has a nonmonotonic relationship; water diffusion initially increases as hydrophobicity decreases but slows around charged residues due to their higher affinity for water. This nonmonotonic relationship can be seen for each force field in Figure D. The dewetting free energy data in Figure C and the water–protein enthalpy data in Figure S3 suggest that a99SBdisp has the strongest water–protein affinities, which likely contribute to the observed water diffusion slowdown in the hydration shells.

Force Field Differences in Peptides

After investigating water properties around lone amino acids for each force field, we turn to peptides and the effects of water–protein parameterization on IDP monomer conformation and protein–protein interactions. In particular, we are interested in how force field differences affect biological processes like amyloid aggregation, where water–protein and protein–protein interactions are strongly intertwined. During aggregation, a monomeric peptide must shed a significant portion of its hydration waters as it associates with other peptides to form oligomers and eventually amyloid filaments. Therefore, one might anticipate that a more hydrophobic force field (e.g., where amino acids have lower F dewet) would have a higher propensity for amyloid aggregation because it is energetically favorable for a peptide to shed its hydration waters. However, it is important to recognize that other factors, such as protein–protein interaction strengths and water structural differences in the monomeric and aggregated states, affect amyloid aggregation propensities and that considerations of hydrophobic scales alone may not be sufficient to predict oligomer formation propensity.

To disentangle the factors that dictate IDP assembly, we investigate a 19-amino acid tau fragment jR2R3 P301L, which spans residues 295–313 at the junction of the R2 and R3 repeat domains of tau and includes a familial mutation (P301L) that is linked to neurodegenerative disease. The jR2R3 P301L tau fragment assembles into paired helical filaments and can seed full-length tau in cells. , A recent high-resolution cryo-EM structure of jR2R3 P301L revealed that it assembles into a 4-stranded filament with pseudo 21 screw symmetry (see Figure A­(iv)). In this structure, the main strand forms side chain zippers that resemble the “LNT” filament found in the brains of individuals with the neurodegenerative disease Limbic-predominant Neuronal inclusion body 4R Tauopathy (LNT). Here, we first compare how water interacts with the jR2R3 P301L peptide in each force field and investigate how the water–protein interactions affect the peptide’s conformational ensemble. Next, we evaluated water structural and dynamic differences as the peptide associates with a filament in each force field.

We simulate the monomeric and dimeric conformational ensembles of the tau fragment jR2R3 P301L in each force field using replica exchange molecular dynamics (see Methods). While all three force fields appear to have similar levels of monomer hydration (∼208–210 hydration waters on average) and similar monomer conformation ensembles (Figure S1), C36m appears to be more hydrophobic based on the dimer simulations, with a greater propensity to shed hydration waters compared to a03ws and a99SBdisp (Figure B). C36m dimers have an average of ∼167 hydration waters per monomer, while a03ws and a99SBdisp have ∼203 and ∼185, respectively. For reference, a filament of jR2R3 has ∼59 hydration waters per monomer based on modeling its cryo-EM structure.

Dimer simulations show that in C36m, the two monomers rarely dissociate, as indicated by the center-of-mass distance distribution and intermolecular hydrogen bond counts (Figures C and S2). In contrast, in a03ws, the two monomers rarely associate, while in a99SBdisp, both the associated and dissociated states are frequently sampled. C36m’s higher dimerization propensity can be explained by its lower dewetting free energies (see Figure C), as less free energy is needed to remove waters as the peptides dimerize in C36m. However, a99SBdisp has a higher dimerization propensity than a03ws, despite the higher hydrophobicity of a03ws in amino acid F dewet calculations, highlighting how hydrophobicity alone does not fully account for assembly behavior. Two potential explanations for a99SBdisp’s higher-than-expected dimerization propensity are (1) a99SBdisp has stronger peptide–peptide interactions than a03ws, and (2) a99SBdisp has more favorable changes in water structure upon association than a03ws. To evaluate the first explanation, we measure the interpeptide potential energy for dimer conformations (i.e., the compact dimer and the cryo-EM dimer in Figure A­(ii,iii)) and observe that a99SBdisp exhibits weaker peptide–peptide interactions than a03ws for each conformation (Table S2). Therefore, peptide–peptide interactions (i.e., explanation #1) likely cannot explain a99SBdisp’s higher-than-expected dimerization propensity.

Next, we characterize water structure changes and solvent entropy to potentially explain why a99SBdisp had a higher dimerization propensity than a03ws. To control for conformational differences resulting from the use of different force fields, we simulate the association and dissociation of a small peptide with a restrained seed of jR2R3 P301L. Specifically, we simulate a restrained seed consisting of five monomers from one strand of the cryo-EM filament structure and allow a small, capped 300VLG302 peptide to freely dock and undock on the side of the seed. The simulation setup is depicted in Figure A, in which the teal box is where the small peptide is allowed to diffuse freely (using flat-bottom harmonic restraints). We assess water structure both around the peptide and globally using the water triplet angle distribution, and we compare the docked peptide state to that when it is far away. Interestingly, we find that tetrahedral water structuring (i.e., the population of 100–120° angles) is notably higher around the small peptide in a99SBdisp vs in a03ws: water is ∼7.9% more tetrahedral than bulk water in a99SBdisp, while it is only ∼5.5% more tetrahedral than bulk in a03ws (Figure E­(i)). Additionally, water tetrahedrality increases by ∼1.2 percentage points in a99SBdisp around the peptide when it is docked but increases by ∼0.7 percentage points in a03ws. Previous research has shown that changes in tetrahedral water angles of this magnitude have been associated with significant changes in water properties. ,,,

When the small peptide is far from the seed, the population of tetrahedral water structures around either the peptide or the seed (i.e., two hydration shells) is largest. When the peptide docks onto the seed, the two hydration shells merge, leading to the release of these ordered hydration waters, which then rejoin the less tetrahedral bulk water. We quantify this release of ordered waters by measuring the water triplet angle distribution globally (i.e., in the larger dashed box), as shown in Figure A. We find that a99SBdisp has a greater release of ordered, tetrahedral waters upon docking than a03ws or C36m (Figure E­(ii)). We hypothesize that this release of ordered waters generates an entropic driving force that can promote aggregation and protein–protein interactions more broadly.

Along with this global decrease in tetrahedral waters upon docking, a99SBdisp also shows a global increase in icosahedral waters (i.e., forming 60–65° angles) upon docking; see Figure S4. As the ordered, tetrahedral hydration shells fuse in a99SBdisp, many waters transition from tetrahedral arrangements to icosahedral arrangements. Waters form icosahedral angles when in closely packed arrangements, and these low-volume arrangements are likely to be higher in entropy. Robinson Brown et al. found similar trade-offs between tetrahedral and icosahedral water triplet angle populations in a wide range of aqueous systems with solutes of varying hydrophobicity.

We then evaluate whether the pronounced release of ordered tetrahedral waters upon binding in a99SBdisp truly serves as an entropic driving force for protein association. To do this, we measured the free energy of docking, ΔG dock, at two temperatures, using umbrella sampling to bias the center of mass of the small peptide (depicted as sticks in Figure A) above the restrained seed (colored purple in Figure A). Specifically, we defined the free energy minimum around y = 2 Å as the docked state and the maximum around y = 7.5 Å as the undocked state. Interestingly, the docking free energy becomes more negative at a higher temperature in a99SBdisp (Figure B), indicating a significant entropic component to the docking free energy. In contrast, there is no major entropic contribution in the other two force fields (Figure C). This suggests that the large release of ordered waters upon binding in a99SBdisp does serve as an entropic driving force for protein association; this entropic effect was observable, with just ∼15 waters being released by the small peptide upon docking.

Next, we compare protein association dynamics in each force field and find that a99SBdisp has the slowest dynamics, while C36m has the fastest. Specifically, we compare the residence times of the small peptide on the seed (see Figure A,D) and see notable differences in association and dissociation kinetics. Here, we consider y < 3 Å to be the start of the peptide’s residence (i.e., docked) and y < 9 Å to be the end (i.e., undocked). The median residence time for a99SBdisp is ∼14 ns, while it is ∼7 and ∼4 ns for a03ws and C36m, respectively. The 90th percentile residence time for a99SBdisp is ∼63 ns, while it is ∼23 and ∼24 ns for a03ws and C36m, respectively. This difference in protein association dynamics is likely related to differences in the water structure around the protein in each force field. In a99SBdisp, the peptide is surrounded by significantly more tetrahedral water relative to bulk, whereas C36m shows minimal difference in water structuring relative to bulk (Figure E). Tetrahedral water structuring is associated with slower water diffusion and slower solute dynamics, as Jiao et al. and Robinson Brown et al. demonstrated. , The increased water structuring around amino acids in a99SBdisp seems to explain both the slower kinetics of the small peptide associating and dissociating from the seed (Figure D) and the slower water diffusion around amino acids (Figure D).

We additionally look at water structure around other regions of the restrained jR2R3 P301L seed and observe that a99SBdisp produces the farthest-reaching solvent structural correlations, with notable effects even 2–3 Å away (Figure S6B,D­(ii)). In contrast, C36m has the shortest-reaching solvent restructuring effects, which were nearly negligible even 1–2 Å away (Figure S6B,D­(iii)). C36m displays insignificant tetrahedral water structuring around the seed (Figure S6B,D­(iii)), unlike a99SBdisp and a03ws, perhaps due to C36m’s 3-point water model, which less accurately captures the geometry of water hydrogen bonding. Finally, all three force fields have notable increases in ∼50° water angles, characterized as close-packed by van Lehn et al., within 1 Å of the peptide. This ∼50° effect is especially pronounced at C36m and very slight in a99SBdisp.

After exploring the differences in water structuring and dimerization propensities among the force fields, we now turn our attention to the implications of these findings for oligomer formation. C36m’s dimer ensemble (from the REMD simulation) featured a prominent cluster that resembled the solved cryo-EM filament structure. As shown in Figure A, both the cluster from REMD and the solved cryo-EM structure have prominent side chain contacts between I297, V306, and I308 that point inward and induce a C-shaped turn. We hypothesize this C36m dimer cluster may be an oligomer on the pathway to filament formation.

Only C36m has a significant population of dimers that resembled an amyloid filament (Figures C and S10). All solved amyloid structures from tauopathies show amino acids 306–311 forming parallel β-sheets; this key sequence motif is known as PHF6. Approximately 22% of C36m’s dimer ensemble had more than 12 aligned PHF6 contacts (see Figure S8 for the definition of these contacts), while only ∼1.3% and ∼0.1% of a99SBdisp and a03ws ensembles, respectively, have more than 12 aligned PHF6 contacts (Figure B).

We hypothesize that many intrachain contacts can compete with these interchain PHF6 contacts, so we construct a 2D free energy landscape along these two metrics (Figures C and S10). We find a few free energy minima on the pathway to the oligomer assembly, some of which we depict in Figure C. The most favorable assembly path to the filament-like conformation (iv) involves first reducing intrachain contacts and then forming aligned, interchain PHF6 contacts. One cluster (v) forms many aligned PHF6 contacts and many intrachain contacts, but this does not appear to be a common path from monomers to dimers that resemble the cryo-EM structure. This cluster (v) has many hydrogen bonds but does not have the free hydrogen bonding sites on PHF6 (pink) that must be available for the oligomer to grow into a filament, and notably, this cluster also lacks the intrachain side chain zipper.

Discussion and Conclusion

To correctly capture the behavior of intrinsically disordered proteins, it is essential to model water–protein interactions and water–water interactions accurately as IDP conformational ensembles are particularly sensitive to these interactions. Molecular dynamics force fields vary in their water models, hydration water structuring, bulk water structuring, and water–protein affinities, and these distinctions can lead to large differences in hydrophobicity, entropic response, protein kinetics, and protein–protein interactions. This study reveals significant differences in hydrophobicity and water–protein interactions in the three popular force fields for intrinsically disordered proteins (IDPs): a03ws, a99SBdisp, and CHARMM36m (C36m).

Water–protein interaction differences in these three force fields lead to distinct behaviors of the known amyloid-forming tau fragment jR2R3 P301L. C36m exhibits the strongest propensity for dimer formation (Figure C) driven by its lower dewetting free energies (Figure C). Meanwhile, a99SBdisp exhibits a greater dimer formation propensity than a03ws, apparently related to its enhanced tetrahedral water structuring, which appears to entropically drive dimerization (Figure B,C,E). a99SBdisp features significantly slower water dynamics in the peptide’s hydration shell relative to bulk water (Figure D), and it has slower protein association dynamics (Figure D) due to its increased water tetrahedral population. C36m notably uses a three-site water model (TIP3P), which likely contributes to a reduced water structuring response around proteins, while a03ws and a99SBdisp use four-site models (TIP4P-2005s and a modified TIP4P-D, respectively) with increased water structuring responses, especially in a99SBdisp. Previously, researchers have compared tetrahedral water structuring for various water models in the bulk phase versus at a hydrophobic surface, and they also observed a greater tetrahedral water structuring difference for TIP4P than TIP3P. A systematic study of each force field’s amino acid parameters with each of the three water models in future work could disentangle the relative effects of protein and water interactions.

Hydrophobicity and water structure are especially important in modeling the amyloid formation of IDPs. When forming an amyloid filament, a peptide must shed a significant portion of its hydration waters, nearly 70% of them in the case of the tau fragment studied here, and this process is influenced by the dewetting free energies in each force field. C36m’s lower dewetting free energies facilitate aggregation by reducing the energetic cost of displacing hydration waters. In contrast, the higher dewetting free energies in a99SBdisp and a03ws are associated with a higher resistance to water removal, thereby reducing their aggregation propensities. However, a99SBdisp has favorable water structuring that can entropically drive aggregation, as many structured waters are released upon peptide stacking. This mechanism, where structured hydration waters shells fuse and release water, increases a99SBdisp’s aggregation propensity moderately. While IDP force field development efforts have focused primarily on adjusting protein–protein and protein–water interactions, our work suggests adjusting water–water interaction parameters that affect water structuring near the protein surface (i.e., within 3 Å) could be a way to tune IDP force fields. In particular, water tetrahedrality from the water triplet angle distribution and dewetting free energy from INDUS may be useful metrics to monitor when fine-tuning force fields.

Interestingly, C36m REMD simulations of a tau fragment dimer produced conformations with a strong resemblance to its fibril structure from cryo-EM (Figure A), supporting the idea that fibril commensurate structures are present as “excited state” conformations in the monomeric and early oligomeric structural pool. − This C36m structure, which has many interchain-aligned contacts between its amyloidogenic segment (PHF6), was observed to a much lesser extent in a99SBdisp and a03ws REMD simulations (Figure S10). This structure’s stability is likely due to C36m’s high hydrophobicity (see Figure C). While Robustelli et al. showed that C36m produces overly compact IDP monomer ensembles, this same force field appears useful for reproducing experimental amyloid structures. This highlights the challenge of developing a force field that is suitable for simulating monomeric and oligomeric structures. Indeed, efforts to produce extended conformations by strengthening water–protein interactions in force fields led to improved radii of gyration and end-to-end distances for protein monomeric ensembles. However, dimer formation requires expelling water, and strong protein–water interactions make this a challenge, emphasizing how a force field adjustment that can correct one problem can inadvertently create another one.

a99SBdisp is an example of a force field for which increasing protein–water interactions yielded more accurate monomer conformational ensembles than a03ws and C36m for monomer ensembles; however, these stronger interactions and increased tetrahedral water structuring lead it to display slower kinetics. Such slower kinetics are computationally costly when modeling interprotein interactions, e.g., in amyloid aggregation. The slower kinetics may more accurately reflect the natural dynamics of protein association and dissociation, but they also pose a significant limitation for observing aggregation within attainable simulation time scales. Unlike a99SBdisp, C36m and a03ws seem to have faster protein kinetics (Figure D); C36m has particularly fast protein kinetics, likely due to its quickly diffusing TIP3P water model (see Figure caption), for which bulk water diffuses about twice as fast as experimental values.

Force fields for globular proteins have been seen to produce reasonable structures for dimers and higher oligomers while producing clearly overstructured monomer conformations. − The reason that globular protein force fields work well for protein aggregation, particularly for describing fibrils, − may be because the protein aggregation process has similar driving forces as protein folding, with protein–protein interactions satisfied via inter- versus intrapeptide contacts.

While our focus here was on how these hydrophobicity and water-structuring properties affect amyloid aggregation, they are also essential for modeling protein–protein interactions more broadly. Additionally, these dewetting free energy scales from INDUS may be useful for predicting binding affinities. Generally, we hypothesize that dewetting free energies and water structure can serve as valuable predictors for other phenomena that depend on water–protein interactions such as binding affinities, solubilities, viscosities, phase transition behavior, and enzymatic activities.

Our comparative analysis of a03ws, a99SBdisp, and CHARMM36m force fields highlights the crucial role of hydrophobicity and water structure in IDPs. The distinct water–protein interactions, e.g., water structuring, in each force field resulted in different behavior of a tau fragment jR2R3 P301L. Specifically, we see differences in monomer and dimer hydration, dimerization propensity, kinetics, water structuring, and entropically driven protein association. We found that measuring dewetting free energies and water structure (via INDUS and the water triplet angle distribution) provides valuable insight, which may be broadly applicable for predicting other properties related to water–protein interactions. Our study highlights the importance of knowing how force fields were optimized and the ramifications of these optimization choices when selecting a force field for a specific research goal.

Supplementary Material

jp5c02360_si_001.pdf (1.4MB, pdf)

Acknowledgments

We are grateful to Amish Patel for providing a copy of the INDUS code. Simulations were performed using resources of the Extreme Science and Engineering Discovery Environment, which is supported by the NSF grant ACI-1548562 (project TG MCA05S027 using the Purdue Anvil Cluster and Texas Applied Computing Center Stampede2 Cluster) and the computational facilities purchased with funds from the National Science Foundation (CNS-1725797) and administered by the Center for Scientific Computing (CSC). The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center (MRSEC; NSF DMR 2308708) at UC Santa Barbara. S.L. acknowledges support from the University of California Graduate Opportunity Fellowship and NIH Grant 5R01AG056058-09. J.-E.S. acknowledges support from the NSF (MCB-1716956). M.S.S. gratefully acknowledges funding support from the NSF through award no. CHEM-1800344. We acknowledge support from the W. M. Keck Foundation, the NIH grants R01-GM118560-01A, and the NSF grant NSF-ANR MCB/PHY 2423885.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.5c02360.

  • Amino-acid dewetting free energies; complete REMD simulation protocol; intermonomer potential energies; monomer/dimer energy landscapes; hydrogen-bond and contact analyses; water-structure and density profiles; and 2D free-energy surfaces (PDF)

The authors declare no competing financial interest.

Published as part of The Journal of Physical Chemistry B special issue “Athanassios Z. Panagiotopoulos Festschrift”.

References

  1. Quaglia F., Mészáros B., Salladini E., Hatos A., Pancsa R., Chemes L. B., Pajkos M., Lazar T., Peña-Díaz S., Santos J.. et al. DisProt in 2022: Improved Quality and Accessibility of Protein Intrinsic Disorder Annotation. Nucleic Acids Res. 2022;50(D1):D480–D487. doi: 10.1093/nar/gkab1082. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Tompa P.. Intrinsically Unstructured Proteins. Trends Biochem. Sci. 2002;27(10):527–533. doi: 10.1016/S0968-0004(02)02169-2. [DOI] [PubMed] [Google Scholar]
  3. Iakoucheva L. M., Brown C. J., Lawson J. D., Obradović Z., Dunker A. K.. Intrinsic Disorder in Cell-Signaling and Cancer-Associated Proteins. J. Mol. Biol. 2002;323(3):573–584. doi: 10.1016/S0022-2836(02)00969-5. [DOI] [PubMed] [Google Scholar]
  4. Yang J., Gao M., Xiong J., Su Z., Huang Y.. Features of Molecular Recognition of Intrinsically Disordered Proteins via Coupled Folding and Binding. Protein Sci. 2019;28(11):1952–1965. doi: 10.1002/pro.3718. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Darling A. L., Zaslavsky B. Y., Uversky V. N.. Intrinsic Disorder-Based Emergence in Cellular Biology: Physiological and Pathological Liquid-Liquid Phase Transitions in Cells. Polymers. 2019;11(6):990. doi: 10.3390/polym11060990. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Uversky V. N.. Intrinsically Disordered Proteins in Overcrowded Milieu: Membrane-Less Organelles, Phase Separation, and Intrinsic Disorder. Curr. Opin. Struct. Biol. 2017;44:18–30. doi: 10.1016/j.sbi.2016.10.015. [DOI] [PubMed] [Google Scholar]
  7. Trivedi R., Nagarajaram H. A.. Intrinsically Disordered Proteins: An Overview. Int. J. Mol. Sci. 2022;23(22):14050. doi: 10.3390/ijms232214050. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Stelzl L. S., Pietrek L. M., Holla A., Oroz J., Sikora M., Köfinger J., Schuler B., Zweckstetter M., Hummer G.. Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure. JACS Au. 2022;2(3):673–686. doi: 10.1021/jacsau.1c00536. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Calabresi P., Mechelli A., Natale G., Volpicelli-Daley L., Di Lazzaro G., Ghiglieri V.. Alpha-Synuclein in Parkinson’s Disease and Other Synucleinopathies: From Overt Neurodegeneration Back to Early Synaptic Dysfunction. Cell Death Dis. 2023;14(3):176. doi: 10.1038/s41419-023-05672-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Best R. B., Zheng W., Mittal J.. Balanced Protein–Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association. J. Chem. Theory Comput. 2014;10(11):5113–5124. doi: 10.1021/ct500569b. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Huang J., Rauscher S., Nawrocki G., Ran T., Feig M., de Groot B. L., Grubmüller H., MacKerell A. D.. CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins. Nat. Methods. 2017;14(1):71–73. doi: 10.1038/nmeth.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Robustelli P., Piana S., Shaw D. E.. Developing a Molecular Dynamics Force Field for Both Folded and Disordered Protein States. Proc. Natl. Acad. Sci. U.S.A. 2018;115(21):E4758–E4766. doi: 10.1073/pnas.1800690115. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Beauchamp K. A., Lin Y.-S., Das R., Pande V. S.. Are Protein Force Fields Getting Better? A Systematic Benchmark on 524 Diverse NMR Measurements. J. Chem. Theory Comput. 2012;8(4):1409–1414. doi: 10.1021/ct2007814. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Lindorff-Larsen K., Maragakis P., Piana S., Eastwood M. P., Dror R. O., Shaw D. E.. Systematic Validation of Protein Force Fields against Experimental Data. PLoS One. 2012;7(2):e32131. doi: 10.1371/journal.pone.0032131. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Nerenberg P. S., Jo B., So C., Tripathy A., Head-Gordon T.. Optimizing Solute-Water van Der Waals Interactions to Reproduce Solvation Free Energies. J. Phys. Chem. B. 2012;116(15):4524–4534. doi: 10.1021/jp2118373. [DOI] [PubMed] [Google Scholar]
  16. Lindorff-Larsen K., Piana S., Palmo K., Maragakis P., Klepeis J. L., Dror R. O., Shaw D. E.. Improved Side-Chain Torsion Potentials for the Amber ff99SB Protein Force Field. Proteins. 2010;78(8):1950–1958. doi: 10.1002/prot.22711. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Abascal J. L. F., Vega C.. A General Purpose Model for the Condensed Phases of Water: TIP4P/2005. J. Chem. Phys. 2005;123(23):234505. doi: 10.1063/1.2121687. [DOI] [PubMed] [Google Scholar]
  18. Piana S., Donchev A. G., Robustelli P., Shaw D. E.. Water Dispersion Interactions Strongly Influence Simulated Structural Properties of Disordered Protein States. J. Phys. Chem. B. 2015;119(16):5113–5123. doi: 10.1021/jp508971m. [DOI] [PubMed] [Google Scholar]
  19. Gong X., Zhang Y., Chen J.. Likely Overstabilization of Charge–Charge Interactions in CHARMM36m­(w): A Case for a99SB-Disp Water. J. Phys. Chem. B. 2024;128(47):11554–11564. doi: 10.1021/acs.jpcb.4c04777. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Qin X., Ji J., Chakraborty S., Nangia S.. Extending the PARCH Scale: Assessing Hydropathy of Proteins across Multiple Water Models. J. Chem. Inf. Model. 2025;65(6):2999–3009. doi: 10.1021/acs.jcim.4c02415. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Lemkul J. A.. Pairwise-additive and polarizable atomistic force fields for molecular dynamics simulations of proteins. Prog. Mol. Biol. Transl. Sci. 2020;170:1–71. doi: 10.1016/bs.pmbts.2019.12.009. [DOI] [PubMed] [Google Scholar]
  22. Taylor A. I. P., Staniforth R. A.. General Principles Underpinning Amyloid Structure. Front. Neurosci. 2022;16:878869. doi: 10.3389/fnins.2022.878869. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Carballo-Pacheco M., Ismail A. E., Strodel B.. On the Applicability of Force Fields To Study the Aggregation of Amyloidogenic Peptides Using Molecular Dynamics Simulations. J. Chem. Theory Comput. 2018;14(11):6063–6075. doi: 10.1021/acs.jctc.8b00579. [DOI] [PubMed] [Google Scholar]
  24. Man V. H., He X., Derreumaux P., Ji B., Xie X.-Q., Nguyen P. H., Wang J.. Effects of All-Atom Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of Aβ16–22 Dimer. J. Chem. Theory Comput. 2019;15(2):1440–1452. doi: 10.1021/acs.jctc.8b01107. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Nguyen P. H., Li M. S., Derreumaux P.. Effects of All-Atom Force Fields on Amyloid Oligomerization: Replica Exchange Molecular Dynamics Simulations of the Aβ16–22 Dimer and Trimer. Phys. Chem. Chem. Phys. 2011;13(20):9778. doi: 10.1039/c1cp20323a. [DOI] [PubMed] [Google Scholar]
  26. Samantray S., Yin F., Kav B., Strodel B.. Different Force Fields Give Rise to Different Amyloid Aggregation Pathways in Molecular Dynamics Simulations. J. Chem. Inf. Model. 2020;60(12):6462–6475. doi: 10.1021/acs.jcim.0c01063. [DOI] [PubMed] [Google Scholar]
  27. Man V. H., He X., Gao J., Wang J.. Effects of All-Atom Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of PHF6 Peptide of Tau Protein. J. Chem. Theory Comput. 2021;17(10):6458–6471. doi: 10.1021/acs.jctc.1c00028. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Li Y., Peng X.. Comparison of the Force Fields on Monomeric and Fibrillar PHF6 of Tau Protein. Biophys. Chem. 2021;277:106631. doi: 10.1016/j.bpc.2021.106631. [DOI] [PubMed] [Google Scholar]
  29. Wu K. Y., Doan D., Medrano M., Chang C. A.. Modeling Structural Interconversion in Alzheimers’ Amyloid Beta Peptide with Classical and Intrinsically Disordered Protein Force Fields. J. Biomol. Struct. Dyn. 2022;40(20):10005–10022. doi: 10.1080/07391102.2021.1939163. [DOI] [PubMed] [Google Scholar]
  30. Weber O. C., Uversky V. N.. How Accurate Are Your Simulations? Effects of Confined Aqueous Volume and AMBER FF99SB and CHARMM22/CMAP Force Field Parameters on Structural Ensembles of Intrinsically Disordered Proteins: Amyloid-β42 in Water. Intrinsically Disord. Proteins. 2017;5(1):e1377813. doi: 10.1080/21690707.2017.1377813. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Caliskan M., Mandaci S. Y., Uversky V. N., Coskuner-Weber O.. Secondary Structure Dependence of Amyloid-β(1–40) on Simulation Techniques and Force Field Parameters. Chem. Biol. Drug Des. 2021;97(5):1100–1108. doi: 10.1111/cbdd.13830. [DOI] [PubMed] [Google Scholar]
  32. He X., Man V. H., Gao J., Wang J.. Effects of All-Atom and Coarse-Grained Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of a Tau K18 Monomer. J. Chem. Inf. Model. 2024;64(23):8880–8891. doi: 10.1021/acs.jcim.4c01448. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Cai X., Han W.. Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide–Peptide and Peptide–Solvent Interactions. J. Chem. Inf. Model. 2022;62(11):2744–2760. doi: 10.1021/acs.jcim.2c00066. [DOI] [PubMed] [Google Scholar]
  34. Najafi S., Lobo S., Shell M. S., Shea J.-E.. Context Dependency of Hydrophobicity in Intrinsically Disordered Proteins: Insights from a New Dewetting Free Energy-Based Hydrophobicity Scale. J. Phys. Chem. B. 2025;129(7):1904–1915. doi: 10.1021/acs.jpcb.4c06399. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Patel A. J., Varilly P., Chandler D.. Fluctuations of Water near Extended Hydrophobic and Hydrophilic Surfaces. J. Phys. Chem. B. 2010;114(4):1632–1637. doi: 10.1021/jp909048f. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Patel A. J., Varilly P., Chandler D., Garde S.. Quantifying Density Fluctuations in Volumes of All Shapes and Sizes Using Indirect Umbrella Sampling. J. Stat. Phys. 2011;145(2):265–275. doi: 10.1007/s10955-011-0269-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Monroe J. I., Shell M. S.. Decoding Signatures of Structure, Bulk Thermodynamics, and Solvation in Three-Body Angle Distributions of Rigid Water Models. J. Chem. Phys. 2019;151(9):094501. doi: 10.1063/1.5111545. [DOI] [PubMed] [Google Scholar]
  38. Robinson Brown D. C., Webber T. R., Jiao S., Rivera Mirabal D. M., Han S., Shell M. S.. Relationships between Molecular Structural Order Parameters and Equilibrium Water Dynamics in Aqueous Mixtures. J. Phys. Chem. B. 2023;127(20):4577–4594. doi: 10.1021/acs.jpcb.3c00826. [DOI] [PubMed] [Google Scholar]
  39. Zhang B. W., Xia J., Tan Z., Levy R. M.. A Stochastic Solution to the Unbinned WHAM Equations. J. Phys. Chem. Lett. 2015;6(19):3834–3840. doi: 10.1021/acs.jpclett.5b01771. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. De Sancho D., López X.. Crossover in Aromatic Amino Acid Interaction Strength: Tyrosine vs Phenylalanine in Biomolecular Condensates. eLife. 2025;14:RP104950. doi: 10.7554/eLife.104950.1. [DOI] [Google Scholar]
  41. Rekhi S., Mittal J.. Amino Acid Transfer Free Energies Reveal Thermodynamic Driving Forces in Biomolecular Condensate Formation. bioRxiv. 2024 doi: 10.1101/2024.12.01.625774. [DOI] [Google Scholar]
  42. Azizi K., Laio A., Hassanali A.. Solvation Thermodynamics from Cavity Shapes of Amino Acids. PNAS Nexus. 2023;2(8):pgad239. doi: 10.1093/pnasnexus/pgad239. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Ji J., Carpentier B., Chakraborty A., Nangia S.. An Affordable Topography-Based Protocol for Assigning a Residue’s Character on a Hydropathy (PARCH) Scale. J. Chem. Theory Comput. 2024;20(4):1656–1672. doi: 10.1021/acs.jctc.3c00106. [DOI] [PMC free article] [PubMed] [Google Scholar]
  44. Shirts M. R., Chodera J. D.. Statistically Optimal Analysis of Samples from Multiple Equilibrium States. J. Chem. Phys. 2008;129(12):124105. doi: 10.1063/1.2978177. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. Mirra S. S., Murrell J. R., Gearing M., Spillantini M. G., Goedert M., Crowther R. A., Levey A. I., Jones R., Green J., Shoffner J. M.. et al. Tau Pathology in a Family with Dementia and a P301L Mutation in Tau. J. Neuropathol. Exp. Neurol. 1999;58(4):335–345. doi: 10.1097/00005072-199904000-00004. [DOI] [PubMed] [Google Scholar]
  46. Longhini A. P., DuBose A., Lobo S., Vijayan V., Bai Y., Rivera E. K., Sala-Jarque J., Nikitina A., Carrettiero D. C., Unger M. T.. et al. Precision Proteoform Design for 4R Tau Isoform Selective Templated Aggregation. Proc. Natl. Acad. Sci. U.S.A. 2024;121(15):e2320456121. doi: 10.1073/pnas.2320456121. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Vigers M. P., Lobo S., Najafi S., Dubose A., Tsay K., Ganguly P., Longhini A. P., Jin Y., Buratto S. K., Kosik K. S.. et al. Tau P301L Mutation Promotes Core 4R Tauopathy Fibril Fold through Near-Surface Water Structuring and Conformational Rearrangement. bioRxiv. 2023 doi: 10.1101/2023.11.28.568818. [DOI] [Google Scholar]
  48. Shi Y., Zhang W., Yang Y., Murzin A. G., Falcon B., Kotecha A., van Beers M., Tarutani A., Kametani F., Garringer H. J.. et al. Structure-Based Classification of Tauopathies. Nature. 2021;598(7880):359–363. doi: 10.1038/s41586-021-03911-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Sugita Y., Okamoto Y.. Replica-Exchange Molecular Dynamics Method for Protein Folding. Chem. Phys. Lett. 1999;314(1):141–151. doi: 10.1016/S0009-2614(99)01123-9. [DOI] [Google Scholar]
  50. Jiao S., Robinson Brown D. C., Shell M. S.. Relationships between Water’s Structure and Solute Affinity at Polypeptoid Brush Surfaces. Langmuir. 2024;40(1):761–771. doi: 10.1021/acs.langmuir.3c02971. [DOI] [PubMed] [Google Scholar]
  51. Jiao S., Rivera Mirabal D. M., DeStefano A. J., Segalman R. A., Han S., Shell M. S.. Sequence Modulates Polypeptoid Hydration Water Structure and Dynamics. Biomacromolecules. 2022;23(4):1745–1756. doi: 10.1021/acs.biomac.1c01687. [DOI] [PubMed] [Google Scholar]
  52. Dallin B. C., Kelkar A. S., Van Lehn R. C.. Structural Features of Interfacial Water Predict the Hydrophobicity of Chemically Heterogeneous Surfaces. Chem. Sci. 2023;14(5):1308–1319. doi: 10.1039/D2SC02856E. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Harrach M. F., Drossel B.. Structure and Dynamics of TIP3P, TIP4P, and TIP5P Water near Smooth and Atomistic Walls of Different Hydroaffinity. J. Chem. Phys. 2014;140(17):174501. doi: 10.1063/1.4872239. [DOI] [PubMed] [Google Scholar]
  54. Nguyen P. H., Ramamoorthy A., Sahoo B. R., Zheng J., Faller P., Straub J. E., Dominguez L., Shea J.-E., Dokholyan N. V., De Simone A.. et al. Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer’s Disease, Parkinson’s Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis. Chem. Rev. 2021;121(4):2545–2647. doi: 10.1021/acs.chemrev.0c01122. [DOI] [PMC free article] [PubMed] [Google Scholar]
  55. Straub J. E., Thirumalai D.. Principles Governing Oligomer Formation in Amyloidogenic Peptides. Curr. Opin. Struct. Biol. 2010;20(2):187–195. doi: 10.1016/j.sbi.2009.12.017. [DOI] [PMC free article] [PubMed] [Google Scholar]
  56. Carballo-Pacheco M., Strodel B.. Advances in the Simulation of Protein Aggregation at the Atomistic Scale. J. Phys. Chem. B. 2016;120(12):2991–2999. doi: 10.1021/acs.jpcb.6b00059. [DOI] [PubMed] [Google Scholar]
  57. Shea J.-E., Best R. B., Mittal J.. Physics-Based Computational and Theoretical Approaches to Intrinsically Disordered Proteins. Curr. Opin. Struct. Biol. 2021;67:219–225. doi: 10.1016/j.sbi.2020.12.012. [DOI] [PMC free article] [PubMed] [Google Scholar]
  58. Chakraborty D., Straub J. E., Thirumalai D.. Energy Landscapes of Aβ Monomers Are Sculpted in Accordance with Ostwald’s Rule of Stages. Sci. Adv. 2023;9(12):eadd6921. doi: 10.1126/sciadv.add6921. [DOI] [PMC free article] [PubMed] [Google Scholar]
  59. Gonzalez M. A., Zaragoza A., Lynch C. I., Sansom M. S. P., Valeriani C.. Influence of Water Models on Water Movement through AQP1. J. Chem. Phys. 2021;155(15):154502. doi: 10.1063/5.0063986. [DOI] [PubMed] [Google Scholar]
  60. Larini L., Gessel M. M., LaPointe N. E., Do T. D., Bowers M. T., Feinstein S. C., Shea J.-E.. Initiation of Assembly of Tau(273–284) and Its ΔK280 Mutant: An Experimental and Computational Study. Phys. Chem. Chem. Phys. 2013;15(23):8916. doi: 10.1039/c3cp00063j. [DOI] [PMC free article] [PubMed] [Google Scholar]
  61. Ganguly P., Do T. D., Larini L., LaPointe N. E., Sercel A. J., Shade M. F., Feinstein S. C., Bowers M. T., Shea J.-E.. Tau Assembly: The Dominant Role of PHF6 (VQIVYK) in Microtubule Binding Region Repeat R3. J. Phys. Chem. B. 2015;119(13):4582–4593. doi: 10.1021/acs.jpcb.5b00175. [DOI] [PMC free article] [PubMed] [Google Scholar]
  62. Bellesia G., Shea J.-E.. What Determines the Structure and Stability of KFFE Monomers, Dimers, and Protofibrils? Biophys. J. 2009;96(3):875–886. doi: 10.1016/j.bpj.2008.10.040. [DOI] [PMC free article] [PubMed] [Google Scholar]
  63. Derreumaux P., Man V. H., Wang J., Nguyen P. H.. Tau R3–R4 Domain Dimer of the Wild Type and Phosphorylated Ser356 Sequences. I. In Solution by Atomistic Simulations. J. Phys. Chem. B. 2020;124(15):2975–2983. doi: 10.1021/acs.jpcb.0c00574. [DOI] [PubMed] [Google Scholar]
  64. Wu C., Bowers M. T., Shea J.-E.. Molecular Structures of Quiescently Grown and Brain-Derived Polymorphic Fibrils of the Alzheimer Amyloid Aβ9–40 Peptide: A Comparison to Agitated Fibrils. PLoS Comput. Biol. 2010;6(3):e1000693. doi: 10.1371/journal.pcbi.1000693. [DOI] [PMC free article] [PubMed] [Google Scholar]
  65. Buchete N.-V., Tycko R., Hummer G.. Molecular Dynamics Simulations of Alzheimer’s β-Amyloid Protofilaments. J. Mol. Biol. 2005;353(4):804–821. doi: 10.1016/j.jmb.2005.08.066. [DOI] [PubMed] [Google Scholar]
  66. Zheng J., Jang H., Ma B., Tsai C.-J., Nussinov R.. Modeling the Alzheimer Aβ17–42 Fibril Architecture: Tight Intermolecular Sheet-Sheet Association and Intramolecular Hydrated Cavities. Biophys. J. 2007;93(9):3046–3057. doi: 10.1529/biophysj.107.110700. [DOI] [PMC free article] [PubMed] [Google Scholar]
  67. Miller Y., Ma B., Nussinov R.. Zinc Ions Promote Alzheimer Aβ Aggregation via Population Shift of Polymorphic States. Proc. Natl. Acad. Sci. U.S.A. 2010;107(21):9490–9495. doi: 10.1073/pnas.0913114107. [DOI] [PMC free article] [PubMed] [Google Scholar]

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