TIP3P Water Model Research Articles

Is the Conformational Ensemble of Alzheimer's Aβ10-40 Peptide Force Field Dependent?

By applying REMD simulations we have performed comparative analysis of the conformational ensembles of amino-truncated Aβ10-40 peptide produced with five force fields, which combine four protein parameterizations (CHARMM36, CHARMM22*, CHARMM22/cmap, and OPLS-AA) and two water models (standard and modified TIP3P). Aβ10-40 conformations were analyzed by computing secondary structure, backbone fluctuations, tertiary interactions, and radius of gyration. We have also calculated Aβ10-40 3JHNHα-coupling and RDC constants and compared them with their experimental counterparts obtained for the full-length Aβ1-40 peptide. Our study led us to several conclusions. First, all force fields predict that Aβ adopts unfolded structure dominated by turn and random coil conformations. Second, specific TIP3P water model does not dramatically affect secondary or tertiary Aβ10-40 structure, albeit standard TIP3P model favors slightly more compact states. Third, although the secondary structures observed in CHARMM36 and CHARMM22/cmap simulations are qualitatively similar, their tertiary interactions show little consistency. Fourth, two force fields, OPLS-AA and CHARMM22* have unique features setting them apart from CHARMM36 or CHARMM22/cmap. OPLS-AA reveals moderate β-structure propensity coupled with extensive, but weak long-range tertiary interactions leading to Aβ collapsed conformations. CHARMM22* exhibits moderate helix propensity and generates multiple exceptionally stable long- and short-range interactions. Our investigation suggests that among all force fields CHARMM22* differs the most from CHARMM36. Fifth, the analysis of 3JHNHα-coupling and RDC constants based on CHARMM36 force field with standard TIP3P model led us to an unexpected finding that in silico Aβ10-40 and experimental Aβ1-40 constants are generally in better agreement than these quantities computed and measured for identical peptides, such as Aβ1-40 or Aβ1-42. This observation suggests that the differences in the conformational ensembles of Aβ10-40 and Aβ1-40 are small and the former can be used as proxy of the full-length peptide. Based on this argument, we concluded that CHARMM36 force field with standard TIP3P model produces the most accurate representation of Aβ10-40 conformational ensemble.

Assessment and Optimization of Configurational-Bias Monte Carlo Particle Swap Strategies for Simulations of Water in the Gibbs Ensemble.

Particle swap moves between phases are usually the rate-limiting step for Gibbs ensemble Monte Carlo (GEMC) simulations of fluid phase equilibria at low reduced temperatures because the acceptance probabilities for these moves can become very low for molecules with articulated architecture and/or highly directional interactions. The configurational-bias Monte Carlo (CBMC) technique can greatly increase the acceptance probabilities, but the efficiency of the CBMC algorithm is influenced by multiple parameters. In this work we assess the performance of different CBMC strategies for GEMC simulations using the SPC/E and TIP4P water models at 283, 343, and 473 K, demonstrate that much higher acceptance probabilities can be achieved than previously reported in the literature, and make recommendations for CBMC strategies leading to optimal efficiency.

Developing force fields when experimental data is sparse: AMBER/GAFF-compatible parameters for inorganic and alkyl oxoanions.

We present a set of Lennard-Jones parameters for classical, all-atom models of acetate and various alkylated and non-alkylated forms of sulfate, sulfonate and phosphate ions, optimized to reproduce their interactions with water and with the physiologically relevant sodium, ammonium and methylammonium cations. The parameters are internally consistent and are fully compatible with the Generalized Amber Force Field (GAFF), the AMBER force field for proteins, the accompanying TIP3P water model and the sodium model of Joung and Cheatham. The parameters were developed primarily relying on experimental information - hydration free energies and solution activity derivatives at 0.5 m concentration - with ab initio, gas phase calculations being used for the cases where experimental information is missing. The ab initio parameterization scheme presented here is distinct from other approaches because it explicitly connects gas phase binding energies to intermolecular interactions in solution. We demonstrate that the original GAFF/AMBER parameters often overestimate anion-cation interactions, leading to an excessive number of contact ion pairs in solutions of carboxylate ions, and to aggregation in solutions of divalent ions. GAFF/AMBER parameters lead to excessive numbers of salt bridges in proteins and of contact ion pairs between sodium and acidic protein groups, issues that are resolved by using the optimized parameters presented here.

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87–0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82–0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65–0.99 and 0.76–0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953–0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes.

Base sequence specificity of counterion binding to DNA: what can MD simulations tell us?

Nucleic acids are highly charged biopolymers whose secondary structure is strongly dependent on electrostatic interactions. Solvent molecules and ions are also believed to play an important role in mediating and directing both sequence recognition and interactions with other molecules, such as proteins and a variety of ligands. Therefore, to fully understand the biological functions of DNA, it is necessary to understand the interactions with the surrounding counterions. It is well known that monovalent counterions can bind to the minor groove of DNA with consecutive sequences of four, or more, adenine and thymine (A-tracts) with relatively long residence times. However, much less is known about their binding to the backbone and to the major groove. In this work, we used molecular dynamics simulations to both investigate the interactions between the backbone and major groove of DNA and one of its physiological counterions (Na+) and evaluate the relationship between these interactions and the nucleotide sequence. Three dodecamers, namely CGAAAATTTTCG, CGCTCTAGAGCG, and CGCGAATTCGCG, were simulated using the Toukan–Rahman flexible SPC water model and Smith and Dang parameters for Na+, revealing a significant sequence dependence on the ion binding to both backbone and major groove. In the absence of experimental data on the atomistic details of the studied interactions, the reliability of the results was evaluated performing the simulations with additional sets of potential parameters for ions and solvent, namely the Ȧqvist or the Joung and Cheatham ion parameters and the TIP3P water model. This allowed us to evaluate the results by verifying which features are preserved independently from the parameters adopted.

Water self-diffusivity confined in graphene nanogap using molecular dynamics simulations

Fundamental understanding of water confined in graphene is crucial to optimally design and operate sustainable energy, water desalination, and bio-medical systems. However, the current understanding predominantly remains in the static properties near the graphene surfaces. In this paper, a key water transport property, i.e., self-diffusivity, is examined under confinement by various graphene nanogap sizes (Lz = 0.7–4.17 nm), using molecular dynamics simulations with various graphene-water interatomic potentials (Simple Point Charge (SPC/E) and TIP3P water models). It is found that the water self-diffusivity nearly linearly decreases as the graphene-water interatomic potential energy increases at a given nanogap size. It also decreases as the graphene nanogap size decreases down to Lz = 1.34 nm; however, it shows the peak water self-diffusivity at Lz = 0.8 nm and then continues to decrease. The peak water self-diffusivity is related to the significant change of the overlapping surface force, and associated, nonlinear local water density distribution. The in-plane water self-diffusivity is higher up to nearly an order of magnitude than that of the out-of-plane due to the geometrical confinement effect by the graphene nanogap. The obtained results provide a roadmap to fundamentally understand the water transport properties in the graphene geometries and surface interactions.

Wetting and nanodroplet contact angle of the clay 2:1 surface: The case of Na-montmorillonite (001)

Molecular dynamics simulation method is performed to study the wetting and contact angle between a water nanodroplet and a surface of Na-montmorillonite (Na-MMT). The nanodroplet of 256, 500 and 1000 water molecules, based on SPC and TIP4P water models, is handled by means of Monte Carlo and Molecular Dynamics simulation methods The spreading of water molecules on Na-MMT’s surface is not uniform. In fact, the contact line is not perfectly circlar; it depends on the distribution of cations on clay’s surface. The average contact angle of air/water/clay corresponds to 25° for all cases of nanodroplets studied here, which reveals that Na-MMT is definitely hydrophilic. In the nanodroplet, most of water molecules remain at a distance between 3.5 and ∼4Å to the clay’s surface. However, at the edge of nanodroplet, water molecules are caught by the clay’s surface oxygen and thus enter into the 0–3Å zone, which blocks the spreading of nanodroplet.

The small impact of various partial charge distributions in ground and excited state on the computational Stokes shift of 1-methyl-6-oxyquinolinium betaine in diverse water models.

The influence of the partial charge distribution obtained from quantum mechanics of the solute 1-methyl-6-oxyquinolinium betaine in the ground- and first excited state on the time-dependent Stokes shift is studied via molecular dynamics computer simulation. Furthermore, the effect of the employed solvent model - here the non-polarizable SPC, TIP4P and TIP4P/2005 and the polarizable SWM4 water model - on the solvation dynamics of the system is investigated. The use of different functionals and calculation methods influences the partial charge distribution and the magnitude of the dipole moment of the solute, but not the orientation of the dipole moment. Simulations based on the calculated charge distributions show nearly the same relaxation behavior. Approximating the whole solute molecule by a dipole results in the same relaxation behavior, but lower solvation energies, indicating that the time scale of the Stokes shift does not depend on peculiarities of the solute. However, the SPC and TIP4P water models show too fast dynamics which can be ascribed to a too large diffusion coefficient and too low viscosity. The calculated diffusion coefficient and viscosity for the SWM4 and TIP4P/2005 models coincide well with experimental values and the corresponding relaxation behavior is comparable to experimental values. Furthermore we found that for a quantitative description of the Stokes shift of the applied system at least two solvation shells around the solute have to be taken into account.

Sensitivity of Protein Glass Transition to the Choice of Water Model.

The sensitivity of protein glass transition temperature and dynamics of Trp-cage miniprotein to the choice of water models have been investigated by performing molecular dynamics simulations at different temperatures between 130 and 300 K using mTIP3P, TIP4P, and TIP4P-Ew water models with the CHARMM22 force field. Analysis of the structure of the protein and the ordering of the hydration shell water molecules revealed correlated dynamic crossovers of the protein and its hydration water. It is demonstrated that the parametrization of different water models is robust enough to probe the onset temperatures for the two dynamic crossovers of the peptide: the first one around 150 K which is attributed to active methyl group rotations and the second one around 200-230 K specifically pertaining to glass transition of the protein. The behavior of the protein has been found to be qualitatively similar to the three water models employed, while the structural ordering and number of hydration shell waters vary significantly among the 3-site and 4-site water models. The changes in the probability density map of methyl hydrogens of the protein with temperature also show sensitivity to the choice of water model.

The SAMPL5 host-guest challenge: computing binding free energies andenthalpies from explicit solvent simulations by the attach-pull-release (APR) method.

The absolute binding free energies and binding enthalpies of twelve host-guest systems in the SAMPL5 blind challenge were computed using our attach-pull-release (APR) approach. This method has previously shown good correlations between experimental and calculated binding data in retrospective studies of cucurbit[7]uril (CB7) and β-cyclodextrin (βCD) systems. In the present work, the computed binding free energies for host octa acid (OA or OAH) and tetra-endo-methyl octa-acid (TEMOA or OAMe) with guests are in good agreement with prospective experimental data, with a coefficient of determination (R2) of 0.8 and root-mean-squared error of 1.7kcal/mol using the TIP3P water model. The binding enthalpy calculations achieve moderate correlations, with R2 of 0.5 and RMSE of 2.5kcal/mol, for TIP3P water. Calculations using the newly developed OPC water model also show good performance. Furthermore, the present calculations semi-quantitatively capture the experimental trend of enthalpy-entropy compensation observed, and successfully predict guests with the strongest and weakest binding affinity. The most populated binding poses of all twelve systems, based on clustering analysis of 750ns molecular dynamics (MD) trajectories, were extracted and analyzed. Computational methods using MD simulations and explicit solvent models in a rigorous statistical thermodynamic framework, like APR, can generate reasonable predictions of binding thermodynamics. Especially with continuing improvement in simulation force fields, such methods hold the promise of making substantial contributions to hit identification and lead optimization in the drug discovery process.

Molecular Dynamics Simulation Study of Parallel Telomeric DNA Quadruplexes at Different Ionic Strengths: Evaluation of Water and Ion Models.

Most molecular dynamics (MD) simulations of DNA quadruplexes have been performed under minimal salt conditions using the Åqvist potential parameters for the cation with the TIP3P water model. Recently, this combination of parameters has been reported to be problematic for the stability of quadruplex DNA, especially caused by the ion interactions inside or near the quadruplex channel. Here, we verify how the choice of ion parameters and water model can affect the quadruplex structural stability and the interactions with the ions outside the channel. We have performed a series of MD simulations of the human full-parallel telomeric quadruplex by neutralizing its negative charge with K(+) ions. Three combinations of different cation potential parameters and water models have been used: (a) Åqvist ion parameters, TIP3P water model; (b) Joung and Cheatham ion parameters, TIP3P water model; and (c) Joung and Cheatham ion parameters, TIP4Pew water model. For the combinations (b) and (c), the effect of the ionic strength has been evaluated by adding increasing amounts of KCl salt (50, 100, and 200 mM). Two independent simulations using the Åqvist parameters with the TIP3P model show that this combination is clearly less suited for the studied quadruplex with K(+) as counterions. In both simulations, one ion escapes from the channel, followed by significant deformation of the structure, leading to deviating conformation compared to that in the reference crystallographic data. For the other combinations of ion and water potentials, no tendency is observed for the channel ions to escape from the quadruplex channel. In addition, the internal mobility of the three loops, torsion angles, and counterion affinity have been investigated at varied salt concentrations. In summary, the selection of ion and water models is crucial as it can affect both the structure and dynamics as well as the interactions of the quadruplex with its counterions. The results obtained with the TIP4Pew model are found to be closest to the experimental data at all of the studied ion concentrations.

Charges of TIP4P water model for mixed quantum/classical calculations of OH stretching frequency in liquid water

Charges of TIP4P water model for mixed quantum/classical calculations of OH stretching frequency in liquid water

Solvated and generalised Born calculations differences using GPU CUDA and multi-CPU simulations of an antifreeze protein with AMBER

While there has been an increase in the number of biomolecular computational studies employing graphics processing units (GPU), results describing their use with the molecular dynamics package AMBER with the CUDA implementation are scarce. No information is available comparing MD methodologies pmemd.cuda, pmemd.mpi or sander.mpi, available in AMBER, for generalised Born (GB) simulations or with solvated systems. As part of our current studies with antifreeze proteins (AFP), and for the previous reasons, we present details of our experience comparing performance of MD simulations at varied temperatures between multi-CPU runs using sander.mpi, pmemd.mpi and pmemd.cuda with the AFP from the fish ocean pout (1KDF). We found extremely small differences in total energies between multi-CPU and GPU CUDA implementations of AMBER12 in 1ns production simulations of the solvated system using the TIP3P water model. Additionally, GPU computations achieved typical one order of magnitude speedups when using mixed precision but were similar to CPU speeds when computing with double precision. However, we found that GB calculations were highly sensitive to the choice of initial GB parametrisation regardless of the type of methodology, with substantial differences in total energies.

Osmotic Pressure Simulations of Amino Acids and Peptides Highlight Potential Routes to Protein Force Field Parameterization.

Recent molecular dynamics (MD) simulations of proteins have suggested that common force fields overestimate the strength of amino acid interactions in aqueous solution. In an attempt to determine the causes of these effects, we have measured the osmotic coefficients of a number of amino acids using the AMBER ff99SB-ILDN force field with two popular water models, and compared the results with available experimental data. With TIP4P-Ew water, interactions between aliphatic residues agree well with experiment, but interactions of the polar residues serine and threonine are found to be excessively attractive. For all tested amino acids, the osmotic coefficients are lower when the TIP3P water model is used. Additional simulations performed on charged amino acids indicate that the osmotic coefficients are strongly dependent on the parameters assigned to the salt ions, with a reparameterization of the sodium/carboxylate interaction reported by the Aksimentiev group significantly improving description of the osmotic coefficient for glutamate. For five neutral amino acids, we also demonstrate a decrease in solute-solute attractions using the recently reported TIP4P-D water model and using the KBFF force field. Finally, we show that for four two-residue peptides improved agreement with experiment can be achieved by rederiving the partial charges for each peptide.

CHARMM TIP3P Water Model Suppresses Peptide Folding by Solvating the Unfolded State.

The accuracy of molecular dynamics simulations depends on the underlying force field, defined by the form and parametrization of the interparticle potential functions and the water model. The treatment of the solvent is crucial in molecular dynamics force fields, as hydrophobic interactions and hydrogen bonding are important molecular forces. The widely used CHARMM force field was originally parametrized using a modified version of the TIP3P water model (mTIP3P), including Lennard-Jones interactions between hydrogens and oxygens. The latest version, CHARMM36, was optimized using the standard TIP3P water model (sTIP3P) for proteins, while mTIP3P is still being used for lipids. Our replica exchange molecular dynamics simulations on dynamic peptides show that the CHARMM36 force field with mTIP3P water yields less realistic folding than with sTIP3P water. Analysis of the dimensions and hydrogen bonding of the unfolded state reveals that the peptides are more solvated and extended in mTIP3P, due to a higher solvation energy of the peptide in this water model. We recommend using CHARMM36 with sTIP3P when simulating peptides, folded proteins, and natively unfolded proteins, but combinations of proteins with lipids would require a reparametrization to make their water models compatible.

Coarse-Grained Model for Water Involving a Virtual Site.

In this work, we propose a new coarse-grained (CG) model for water by combining the features of two popular CG water models (BMW and MARTINI models) as well as by adopting a topology similar to that of the TIP4P water model. In this CG model, a CG unit, representing four real water molecules, consists of a virtual site, two positively charged particles, and a van der Waals (vdW) interaction center. Distance constraint is applied to the bonds formed between the vdW interaction center and the positively charged particles. The virtual site, which carries a negative charge, is determined by the locations of the two positively charged particles and the vdW interaction center. For the new CG model of water, we coined the name "CAVS" (charge is attached to a virtual site) due to the involvment of the virtual site. After being tested in molecular dynamic (MD) simulations of bulk water at various time steps, under different temperatures and in different salt (NaCl) concentrations, the CAVS model offers encouraging predictions for some bulk properties of water (such as density, dielectric constant, etc.) when compared to experimental ones.

Comparison of hydration behavior and conformational preferences of the Trp-cage mini-protein in different rigid-body water models.

The secondary structure conformational properties and hydration shell metrics of the Trp-cage mini-protein are examined in the folded and unfolded ensembles in mTIP3P, TIP4P, and TIP4P-Ew water models with the CHARMM22 force-field using molecular dynamics simulations at 250 K. Upon changing the water model, the conformational order metrics of the peptide show significant differences in the unfolded rather than in the folded ensemble. The unfolding temperatures for Trp-cage are observed to be around 460, 470, and 430 K in mTIP3P, TIP4P, and TIP4P-Ew, respectively. Upon comparing the results with a previous study on a 16-residue β-hairpin fragment of the 2GB1 protein, the same set of conformational order metrics are found to be insufficient in describing the free energy landscape of peptides having a distinct native secondary structure. However, the hydration shell properties of the peptide have been found to be independent of the sequence of the peptide and it changes in conformation upon unfolding. Our calculations reveal that for a particular water model, the secondary structure preferences in the unfolded ensembles of the two peptides are qualitatively different. The unfolded structures of Trp-cage prefer extended and compact structures in TIP4P-Ew and mTIP3P water, respectively, whereas the β-hairpin peptide prefers extended unfolded structures in mTIP3P. The conformational preferences of the unfolded peptide in a given water model have been found to depend on the peptide sequence, where the binding energies of the water molecules around the polar residues in the unfolded conformations show sensitivity to the multipole moments of the water models. The significance of an accurate description of peptide-solvent interactions in the parametrization of biomolecular force-fields, to obtain an accurate description of conformational preferences, in particular in the unfolded ensembles of proteins, is highlighted.

Cellulose Nanofibrils and Mechanism of their Mineralization in Biomimetic Synthesis of Hydroxyapatite/Native Bacterial Cellulose Nanocomposites: Molecular Dynamics Simulations.

Molecular dynamics (MD) simulation of a nanofibril of native bacterial cellulose (BC) in solutions of mineral ions is presented. The supersaturated calcium-phosphate (CP) solution with the ionic composition of hydroxyapatite and CaCl2 solutions with the concentrations below, equal to, and above the solubility limits are simulated. The influence of solvation models (TIP3P and TIP4P-ew water models) on structural characteristics of the simulated nanofibril and on the crystal nucleation process is assessed. The structural characteristics of cellulose nanofibrils (in particular, of the surface layer) are found to be nearly independent of the solvation models used in the simulation and on the presence of ions in the solutions. It is shown that ionic clusters are formed in the solution rather than on the fibril surface. The cluster sizes are slightly different for the two water models. The effect of the ion-ion interaction parameters on the results is discussed. The main conclusion is that the activity of hydroxyl groups on the BC fibril surface is not high enough to cause adsorption of Ca(2+) ions from the solution. Therefore, the nucleation of CP crystals takes place initially in solution, and then the crystallites formed can be adsorbed on BC nanofibril surfaces.

Fluctuations and local ice structure in model supercooled water.

Large-scale simulations (up to 32,000 molecules) are used to analyze local structures and fluctuations for the TIP4P/2005 and TIP5P water models, under deeply supercooled conditions, near previously proposed liquid-liquid critical points. Bulk freezing does not occur in our simulations, but correlations between molecules with local ice-like structure (ice-like molecules) are strong and long ranged (∼4 nm), exceeding the shortest dimension of smaller simulation cells at the lowest temperatures considered. Correlations between ice-like molecules decay slowly at low temperature, on the order of a hundred nanoseconds. Local ice-like structure is strongly correlated with highly tetrahedral liquid structure at all times, both structures contribute to density fluctuations, and to the associated anomalous scattering. For the TIP4P/2005 and TIP5P models, we show that the apparent spontaneous liquid-liquid phase separations, recently reported [T. Yagasaki, M. Matsumoto, and H. Tanaka, Phys. Rev. E 89, 020301 (2014)] for small rectangular simulation cells below the proposed critical points, exhibit strong system size dependence and do not occur at all in the largest systems we consider. Furthermore, in the smaller rectangular systems where layers of different densities do occur, we find that the appearance of a region of low density is always accompanied simultaneously by an excess of local ice density, with no separation in time. Our results suggest that the density differences observed in direct simulations for the two models considered here are likely due to long-range correlations between ice-like molecules and do not provide strong evidence of liquid-liquid phase separation.

Theoretical Studies of Interactions between O-Phosphorylated and Standard Amino-Acid Side-Chain Models in Water.

Phosphorylation is a common post-translational modification of the amino-acid side chains (serine, tyrosine, and threonine) that contain hydroxyl groups. The transfer of the negatively charged phosphate group from an ATP molecule to such amino-acid side chains leads to changes in the local conformations of proteins and the pattern of interactions with other amino-acid side-chains. A convenient characteristic of the side chain-side chain interactions in the context of an aqueous environment is the potential of mean force (PMF) in water. A series of umbrella-sampling molecular dynamic (MD) simulations with the AMBER force field were carried out for pairs of O-phosphorylated serine (pSer), threonine (pThr), and tyrosine, (pTyr) with natural amino acids in a TIP3P water model as a solvent at 298 K. The weighted-histogram analysis method was used to calculate the four-dimensional potentials of mean force. The results demonstrate that the positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the relative orientation depend on the character of the interacting pairs. More distinct minima are observed for oppositely charged pairs such as, e.g., O-phosphorylated side-chains and positively charged ones, such as the side-chains of lysine and arginine.