PKA17-A Coarse-Grain Grid-Based Methodology and Web-Based Software for Predicting Protein pK a Shifts.

We have developed and tested PKA17, a coarse-grain grid-based model for predicting protein pK a shifts. Our pK a predictor is currently deployed via a website interface. We have carried out parameter fitting using 442 Asp, Glu, His, Lys, and Arg residues for which experimental results are available in the literature. PROPKA software has been used for benchmarking. The average unsigned error and root-mean-square deviation (RMSD) have been found to be 0.628 and 0.831 pH units, respectively, for PKA17. The corresponding results with PROPKA are 0.761 and 1.063 units. We have assessed the robustness of the developed PKA17 methodology with a number of tests and have also explored the possibility of using a combination of PROPKA and PKA17 calculations in order to improve the accuracy of predicted pK a values for protein residues. We have also once again confirmed that protein acidity constants are influenced almost entirely by residues in the immediate spatial proximity of the ionizable amino acids. The resulting PKA17 software has been deployed online with a web-based interface at http://users.wpi.edu/~jpcvitkovic/pka_calc.html. © 2019 Wiley Periodicals, Inc.

Binding of Copper and Cisplatin to Atox1 Is Mediated by Glutathione through the Formation of Metal-Sulfur Clusters.

Copper is an essential nutrient required for many biological processes involved in primary metabolism, but free copper is toxic due to its ability to catalyze formation of free radicals. To prevent toxic effects, in the cell copper is bound to proteins and low molecular weight compounds, such as glutathione, at all times. The widely used chemotherapy agent cisplatin is known to bind to copper-transporting proteins, including copper chaperone Atox1. Cisplatin interactions with Atox1 and other copper transporters are linked to cancer resistance to platinum-based chemotherapy. Here we analyze the binding of copper and cisplatin to Atox1 in the presence of glutathione under redox conditions that mimic intracellular environment. We show that copper(I) and glutathione form large polymers with a molecular mass of approximately 8 kDa, which can transfer copper to Atox1. Cisplatin also can form polymers with glutathione, albeit at a slower rate. Analysis of simultaneous binding of copper and cisplatin to Atox1 under physiological conditions shows that both metals are bound to the protein through copper-sulfur-platinum bridges.

Developing multisite empirical force field models for Pt(II) and cisplatin.

We have developed empirical force field parameters for Pt(II) and cisplatin. Two force field frameworks were used-modified OPLS-AA and our second-order polarizable POSSIM. A seven-site model was used for the Pt(II) ion. The goal was to create transferable parameter sets compatible with the force field models for proteins and general organic compounds. A number of properties of the Pt(II) ion and its coordination compounds have been considered, including geometries and energies of the complexes, hydration free energy, and radial distribution functions in water. Comparison has been made with experimental and quantum mechanical results. We have demonstrated that both versions are generally capable of reproducing key properties of the system, but the second-order polarizable POSSIM formalism permits more accurate quantitative results to be obtained. For example, the energy of formation of cisplatin as calculated with the modified OPLS-AA exhibited an error of 9.9%, while the POSSIM error for the same quantity was 6.2%. The produced parameter sets are transferable and suitable to be used in protein-metal binding simulations in which position or even coordination of the ion does not have to be constrained using preexisting knowledge. © 2016 Wiley Periodicals, Inc.

Using polarizable POSSIM force field and fuzzy-border continuum solvent model to calculate pK(a) shifts of protein residues.

Our Fuzzy-Border (FB) continuum solvent model has been extended and modified to produce hydration parameters for small molecules using POlarizable Simulations Second-order Interaction Model (POSSIM) framework with an average error of 0.136 kcal/mol. It was then used to compute pKa shifts for carboxylic and basic residues of the turkey ovomucoid third domain (OMTKY3) protein. The average unsigned errors in the acid and base pKa values were 0.37 and 0.4 pH units, respectively, versus 0.58 and 0.7 pH units as calculated with a previous version of polarizable protein force field and Poisson Boltzmann continuum solvent. This POSSIM/FB result is produced with explicit refitting of the hydration parameters to the pKa values of the carboxylic and basic residues of the OMTKY3 protein; thus, the values of the acidity constants can be viewed as additional fitting target data. In addition to calculating pKa shifts for the OMTKY3 residues, we have studied aspartic acid residues of Rnase Sa. This was done without any further refitting of the parameters and agreement with the experimental pKa values is within an average unsigned error of 0.65 pH units. This result included the Asp79 residue that is buried and thus has a high experimental pKa value of 7.37 units. Thus, the presented model is capable or reproducing pKa results for residues in an environment that is significantly different from the solvated protein surface used in the fitting. Therefore, the POSSIM force field and the FB continuum solvent parameters have been demonstrated to be sufficiently robust and transferable. © 2016 Wiley Periodicals, Inc.

POSSIM: Parameterizing Complete Second-Order Polarizable Force Field for Proteins.

Previously, we reported development of a fast polarizable force field and software named POSSIM (POlarizable Simulations with Second order Interaction Model). The second-order approximation permits the speed up of the polarizable component of the calculations by ca. an order of magnitude. We have now expanded the POSSIM framework to include a complete polarizable force field for proteins. Most of the parameter fitting was done to high-level quantum mechanical data. Conformational geometries and energies for dipeptides have been reproduced within average errors of ca. 0.5 kcal/mol for energies of the conformers (for the electrostatically neutral residues) and 9.7° for key dihedral angles. We have also validated this force field by running Monte Carlo simulations of collagen-like proteins in water. The resulting geometries were within 0.94 Å root-mean-square deviation (RMSD) from the experimental data. We have performed additional validation by studying conformational properties of three oligopeptides relevant in the context of N-glycoprotein secondary structure. These systems have been previously studied with combined experimental and computational methods, and both POSSIM and benchmark OPLS-AA simulations that we carried out produced geometries within ca. 0.9 Å RMSD of the literature structures. Thus, the performance of POSSIM in reproducing the structures is comparable with that of the widely used OPLS-AA force field. Furthermore, our fitting of the force field parameters for peptides and proteins has been streamlined compared with the previous generation of the complete polarizable force field and relied more on transferability of parameters for nonbonded interactions (including the electrostatic component). The resulting deviations from the quantum mechanical data are similar to those achieved with the previous generation; thus, the technique is robust, and the parameters are transferable. At the same time, the number of parameters used in this work was noticeably smaller than that of the previous generation of our complete polarizable force field for proteins; thus, the transferability of this set can be expected to be greater, and the danger of force field fitting artifacts is lower. Therefore, we believe that this force field can be successfully applied in a wide variety of applications to proteins and protein-ligand complexes.

Computational Studies of the Effect of Shock Waves on the Binding of Model Complexes.

We have simulated effects of a shock wave in water that would result from the collapse of a cavitation bubble on binding in model complexes. We have considered a benzene dimer, a pair of uracil molecules, a complex of fragments of the X-linked inhibitor of apoptosis and caspase-9, and a fragment of c-Myc oncoprotein in binding with its dimerization partner Max. The effect of the shock waves was simulated by adding a momentum to a slab of solvent water molecules and observing the system as the slab moved and caused changes. In the cases of the small molecular pairs, the passage of the shock waves lead to dissociation of the complexes. The behavior of the protein systems was more complex, yet significant disruption of the binding and geometry was also observed. In all the cases, the effects did not occur during the immediate impact of the high-momentum solvent molecules, but rather during the expansion of the compressed system that followed the passage of the waves. The rationale of the studies was in attempting to understand the strong effects that irradiation with a low-intensity ultrasound can have on biomolecular systems, because such ultrasound irradiation can cause cavitation bubbles to be produced and collapse, thus leading to local shock wave generation. The long-term objective is to contribute to future design of synergetic ultrasound and chemical drug strategy of protein inhibition.

Polarizable simulations with second order interaction model (POSSIM) force field: developing parameters for protein side-chain analogues.

A previously introduced polarizable simulations with second-order interaction model (POSSIM) force field has been extended to include parameters for small molecules serving as models for peptide and protein side-chains. Parameters have been fitted to permit reproducing many-body energies, gas-phase dimerization energies, and geometries and liquid-phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second-order approximation of the full-scale induced point dipole polarization formalism. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters are currently being used in further development of the POSSIM fast polarizable force field for proteins.

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first-order Fuzzy-Border continuum solvation model.

We have computed pK(a) values for 11 substituted phenol compounds using the continuum Fuzzy-Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides, and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pK(a) values of propanoic and butanoic acids within about 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed-position grid points. Second, it uses either second- or first-order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of using the first-order technique. This approximation places the presented methodology between the Generalized Born and Poisson-Boltzmann continuum solvation models with respect to their accuracy of reproducing the many-body effects in modeling a continuum solvent.

Importance of electrostatic polarizability in calculating cysteine acidity constants and copper(I) binding energy of Bacillus subtilis CopZ.

CopZ is a copper chaperone from Bacillus subtilis. It is an important part of Cu(I) trafficking. We have calculated pK(a) values for the CXXC motif of this protein, which is responsible for the Cu(I) binding, and the Cu(I) binding constants. Polarizable and fixed-charges formalisms were used, and solvation parameters for the both models have been refitted. We had to partially redevelop parameters for the protonated and deprotonated cysteine residues. We have discovered that the polarizable force field (PFF) is qualitatively superior and allows a uniformly better level of energetic results. The PFF pK(a) values for cysteine are within about 0.8-2.8 pH units of the experimental data, while the fixed-charges OPLS formalism yields errors of up to tens of units. The PFF magnitude of the copper binding energy is about 10 kcal/mol or 50% higher than the experimental value, while the using the refitted OPLS parameters leads to an overall positive binding energy, thus predicting no thermodynamically stable complex. At the same time, the agreement of the polarizable S···Cu(I) distances with the experimental results is within 0.08 Å range, and the nonpolarizable calculations lead to an error of about 0.4 Å. Moreover, the accuracy of the PFF has been achieved without any explicit fitting to either pK(a) or CopZ···Cu(I) binding energies. We believe that this makes our polarizable technique a choice method in reproducing protein-copper binding and further supports the notion that explicit treatment of electrostatic polarization is crucial in many biologically relevant studies, especially ion binding and transport.

Effects of lysine substitution on stability of polyalanine alpha-helix.

We have studied stability of polyalanine alpha-helices with lysine residues added at C-and N-termini in gas-phase and aqueous solution. Monte Carlo simulations with the fixed-charges OPLS-AA and our polarizable POSSIM force fields were carried out. The results of the simulations confirm previously observed phenomena of the helix being stable with the LYS residue on the C-terminus and losing its helical structure if the charged LYS residue is located at the N-terminus of the polypeptide in gas-hase. Both OPLS-AA and POSSIM force fields performed essentially similarly, thus validity of the both for reproducing and predicting structures of such polypeptides has been confirmed. We have also studied the effect of replacing the normal N- and C-termini with methyl capping (this approach is often used in computational studies). Our results have demonstrated that the structure and stability of the polypeptides do not depend significantly on such a substitution although details of the resulting structure may change. The liquid-state simulations produced stable alpha-helixes regardless of the position of the protonated lysine residue. Overall, we have validated our polarizable POSSIM force field and the techniques used in the simulations, since the change of the helix structure as a function of the position of the LYS residue depends on a fine balance of energy contributions, and our methodology reproduced this balance well.

Polarizable Simulations with Second order Interaction Model (POSSIM) force field: Developing parameters for alanine peptides and protein backbone.

A previously introduced POSSIM (POlarizable Simulations with Second order Interaction Model) force field has been extended to include parameters for alanine peptides and protein backbones. New features were introduced into the fitting protocol, as compared to the previous generation of the polarizable force field for proteins. A reduced amount of quantum mechanical data was employed in fitting the electrostatic parameters. Transferability of the electrostatics between our recently developed NMA model and the protein backbone was confirmed. Binding energy and geometry for complexes of alanine dipeptide with a water molecule were estimated and found in a good agreement with high-level quantum mechanical results (for example, the intermolecular distances agreeing within ca. 0.06Å). Following the previously devised procedure, we calculated average errors in alanine di- and tetra-peptide conformational energies and backbone angles and found the agreement to be adequate (for example, the alanine tetrapeptide extended-globular conformational energy gap was calculated to be 3.09 kcal/mol quantim mechanically and 3.14 kcal/mol with the POSSIM force field). However, we have now also included simulation of a simple alpha-helix in both gas-phase and water as the ultimate test of the backbone conformational behavior. The resulting alanine and protein backbone force field is currently being employed in further development of the POSSIM fast polarizable force field for proteins.

Electrostatic polarization is crucial in reproducing Cu(I) interaction energies and hydration.

We have explored the suitability of fixed-charges and polarizable force fields for modeling interactions of the monovalent Cu(I) ion. Parameters for this ion have been tested and refitted within the fixed-charges OPLS-AA and polarizable force field (PFF) frameworks. While this ion plays an important role in many protein interactions, the attention to it in developing empirical force fields is limited. Our PFF parameters for the copper ion worked very well for the Cu(I) interactions with water, while both the original OPLS2005 and our refitted OPLS versions moderately underestimated the copper-water interaction energy. However, the greatest problem in using the nonpolarizable fixed-charges OPLS force field was observed while calculating interaction energies and distances for Cu(I)-benzene complexes. The OPLS2005 model underestimates the interaction energy by a factor of 4. Refitting the OPLS parameters reduced this underestimation to a factor of 2.2-2.4, but only at a cost of distorting the complex geometry. At the same time, the polarizable calculations had an error of about 4%. Moreover, we then used the PFF and nonpolarizable refitted OPLS models for finding free energy of hydration for copper ion via molecular dynamics simulations. While the OPLS calculations lead to a 22% error in the solvation energy, the PFF result was off by only 1.8%. This was achieved with no refitting of the parameters but simply by employing the model developed for the Cu(I) interaction with a single water molecule. We believe that the presented results not only lead to a conclusion about a qualitatively greater suitability of polarizable force fields for simulating molecular interactions with ions but also attest to the excellent level of transferability of PFF parameters.

Quality of random number generators significantly affects results of Monte Carlo simulations for organic and biological systems.

We have simulated pure liquid butane, methanol, and hydrated alanine polypeptide with the Monte Carlo technique using three kinds of random number generators (RNG's)-the standard Linear Congruential Generator (LCG), a modification of the LCG with additional randomization used in the BOSS software, and the "Mersenne Twister" generator by Matsumoto and Nishimura. While using the latter two RNG's leads to reasonably similar physical features, the LCG produces significant different results. For the pure fluids, a noticeable expansion occurs. Using the original LCG on butane yields, a molecular volume of 171.4 Å(3) per molecule compared to about 163.6-163.9 Å(3) for the other two generators, a deviation of about 5%. For methanol, the LCG produces an average volume of 86.3 Å(3) per molecule, which is about 24% higher than the 68.8-70.2 Å(3) obtained with the RNG's in BOSS and the generator by Matsumoto and Nishimura. In case of the hydrated tridecaalanine peptide, the volume and energy tend to be noticeably greater with the LCG than with the BOSS (modified LCG) RNG's. For the simulated hydrated extended conformation of tridecaalanine, the difference in volume reached about 87%. The uniformity and periodicity of the generators do not seem to play the crucial role in these phenomena. We conclude that, it is important to test a RNG's by modeling a system such as the pure liquid methanol with a well-established force field before routinely employing it in Monte Carlo simulations.

Reproducing basic pKa values for turkey ovomucoid third domain using a polarizable force field.

We have extended our previous studies of calculating acidity constants for the acidic residues found in the turkey ovomucoid third domain protein (OMTKY3) by determining the relative pKa values for the basic residues (Lys13, Arg21, Lys29, Lys34, His52, and Lys55). A polarizable force field (PFF) was employed. The values of the pKa were found by direct comparison of energies of solvated protonated and deprotonated forms of the protein. Poisson-Boltzmann (PBF) and surface generalized Born (SGB) continuum solvation models represent the hydration, and a nonpolarizable fixed-charge OPLS-AA force field was used for comparison. Our results indicate that (i) the pKa values of the basic residues can be found in close agreement with the experimental values when a PFF is used in conjunction with the PBF solvation model, (ii) it is sufficient to take into the account only the residues which are in close proximity (hydrogen bonded) to the residue in question, and (iii) the PBF solvation model is superior to the SGB solvation model for these pKa calculations. The average error with the PBF/PFF model is only 0.7 pH unit, compared with 2.2 and 6.1 units for the PBF/OPLS and SGB/OPLS, respectively. The maximum deviation of the PBF/PFF results from the experimental values is 1.7 pH units compared with 6.0 pH units for the PBF/OPLS. Moreover, the best results were obtained while using an advanced nonpolar energy calculation scheme. The overall conclusion is that this methodology and force field are suitable for the accurate assessment of pKa shifts for both acidic and basic protein residues.

Polarizable Simulations with Second order Interaction Model - force field and software for fast polarizable calculations: Parameters for small model systems and free energy calculations.

We are presenting POSSIM (POlarizable Simulations with Second order Interaction Model) - a software package and a set of parameters designed for molecular simulations. The key feature of POSSIM is that the electrostatic polarization is taken into account using a previously introduced fast formalism. This permits cutting computational cost of using the explicit polarization by about an order of magnitude. In this article, parameters for water, methane, ethane, propane, butane, methanol and NMA are introduced. These molecules are viewed as model systems for protein simulations. We have achieved our goal of ca. 0.5 kcal/mol accuracy for gas-phase dimerization energies and no more than 2% deviations in liquid state heats of vaporization and densities. Moreover, free energies of hydration of the polarizable methane, ethane and methanol have been calculated using the statistical perturbation theory. These calculations are a model for calculating protein pKa shifts and ligand binding affinities. The free energies of hydration were found to be 2.12 kcal/mol, 1.80 kcal/mol and -4.95 kcal/mol for methane, ethane and methanol, respectively. The experimentally determined literature values are 1.91 kcal/mol, 1.83 kcal/mol and -5.11 kcal/mol. The POSSIM average error in these absolute free energies of hydration is only about 0.13 kcal/mol. Using the statistical perturbation theory with polarizable force fields is not widespread, and we believe that this work opens road to further development of the POSSIM force field and its applications for obtaining accurate energies in protein-related computer modeling.

Computational Studies of the X-Linked Inhibitor of Apoptosis Complex Formation with Caspase-9 and a Small Antagonist.

Apoptosis is self-programmed cell death. The X-linked inhibitor of apoptosis (XIAP) is known to inhibit caspase proteins, the key players in apoptosis. When this happens, the cells become cancerous as they cannot die naturally. XIAP inhibitors are often overexpressed in cancer tissue. Presented in this article are the results of simulations of XIAP-caspase and XIAP-antagonist complexes. It has been previously established experimentally that low intensity ultrasound promotes apoptosis and increases the therapeutic effect of some XIAP-caspase interaction antagonists. The resulting calculated complex formation energies produced in this work were used with a simple multiscale model as an example of applying such energetic results for estimating the effects of ultrasound on these complexes. The microscopic simulations have been carried out with molecular mechanics employing an all-atom description of the molecules with the OPLS-AA and polarizable force field (PFF) formalisms. It has been determined that the interaction energies in the XIAP-caspase-9 pair with both OPLS and PFF are roughly the same and in the 30-40 kcal/mol range, while PFF predicts a higher magnitude of energy of the XIAP-antagonist complex formation (ca. 100 kcal/mol vs ca. 40 kcal/mol), thus probably being more adequate in reproducing the inhibition abilities of this low molecular weight antagonist. The presented study of the ultrasound effect leads to the conclusion that it is most likely based on the cavitation accompanying the ultrasound irradiation of the cells and not on a simple frequency resonance, as was suggested by some authors.

Electrostatic polarization is crucial for reproducing pKa shifts of carboxylic residues in Turkey ovomucoid third domain.

We have computed pKa shifts for carboxylic residues of the serine protease inhibitor turkey ovomucoid third domain (residues Asp7, Glu10, Glu19, Asp27, and Glu43). Both polarizable and nonpolarizable empirical force fields were employed. Hydration was represented by the surface generalized Born and Poisson-Boltzmann continuum model. The calculations were carried out in the most physically straightforward fashion, by directly comparing energies of the protonated and deprotonated protein forms, without any additional parameter fitting or adjustment. Our studies have demonstrated that (i) the Poisson-Boltzmann solvation model is more than adequate in reproducing pKa shifts, most likely due to its intrinsically many-body formalism; (ii) explicit treatment of electrostatic polarization included in our polarizable force field (PFF) calculations appears to be crucial in reproducing the acidity constant shifts. The average error of the PFF results was found to be as low as 0.58 pKa units, with the best fixed-charges average deviation being 3.28 units. Therefore, the pKa shifts phenomena and the governing electrostatics are clearly many-body controlled in their intrinsic nature; (iii) our results confirm previously reported conclusions that pKa shifts for protein residues are controlled by the immediate environment of the residues in question, as opposed to long-range interactions in proteins. We are confident that our confirmation of the importance of explicit inclusion of polarization in empirical force fields for protein studies will be useful far beyond the immediate goal of accurate calculation of acidity constants.

Accurate prediction of absolute acidity constants in water with a polarizable force field: substituted phenols, methanol, and imidazole.

Validity of a force field with explicit treatment of electrostatic polarization in a form of inducible point dipoles for computing acidity constants was tested by calculating absolute pK(a) values of substituted phenols, methanol, and imidazole in water with the molecular dynamics technique. The last two systems were selected as tyrosine and histidine side-chain analogues, respectively. The solvent was represented by an explicit polarizable water model. Similar calculations were also performed with a modified OPLS-AA nonpolarizable force field. The resulting pK(a) values were compared with available experimental data. While the nonpolarizable force field yields errors of about 5 units in the absolute pK(a) values for the phenols and methanol, the polarizable force field produces the acidity constant values within a ca. 0.8 units accuracy. For the case of imidazole, the fixed-charges force field was capable of reproducing the experimental value of pK(a) (6.4 versus the experimental 7.0 units), but only at a cost of dramatically underestimating dimerization energy for the imidazolium-water complex. At the same time, the polarizable force field yields an even more accurate result of pK(a) = 6.96 without any sacrifice of the accuracy in the dimerization energy. It has also been demonstrated that application of Ewald summation for the long-range electrostatics is important, and substitution of a simple cutoff procedure with Born correction for ions can lead to underestimation of absolute pK(a) values by more than 5 units. The accuracy of the absolute acidity constants computed with the polarizable force field is very encouraging and opens road for further tests on more diverse organic molecules sets, as well as on proteins.

Accurate determination of pyridine-poly(amidoamine) dendrimer absolute binding constants with the OPLS-AA force field and direct integration of radial distribution functions.

OPLS-AA force field and direct integration of intermolecular radial distribution functions (RDF) were employed to calculate absolute binding constants of pyridine molecules to amino group (NH2) and amide group hydrogen atoms in and first generation poly(amidoamine) dendrimers in chloroform. The average errors in the absolute and relative association constants, as predicted with the calculations, are 14.1% and 10.8%, respectively, which translate into ca. 0.08 and 0.06 kcal/mol errors in the absolute and relative binding free energies. We believe that this level of accuracy proves the applicability of the OPLS-AA, force field, in combination with the direct RDF integration, to reproducing and predicting absolute intermolecular association constants of low magnitudes (ca. 0.2-2.0 range).

Pseudospectral Local Second-Order Møller-Plesset Methods for Computation of Hydrogen Bonding Energies of Molecular Pairs.

We present a methodology for computing the binding energy of molecular dimers based on extrapolation of pseudospectral local second-order Moller-Plesset (MP2), or PS-LMP2, energies to the basis set limit. The extrapolation protocol is based on carrying out PS-LMP2 calculations with the Dunning cc-pVTZ (-f) and cc-pVQZ (-g) basis sets and then using a simple two-parameter function to compute the final basis set limit results. The function is parametrized to ultralarge basis set MP2 calculations for 5 molecular pairs taken from the literature and then tested by calculating results for a set of formamide dimers for which such calculations have also been carried out. The results agree to within ca. 0.2 kcal/mol with the conventional MP2 large basis set calculations. A specialized, but relatively simple, protocol is described for eliminating noise due to overcompleteness of the basis set. Timing results are presented for the LMP2 calculations, and comparisons are made with the LMP2 methodology of the QChem program. CPU time required by each of the methods scales as N(3), where N is the number of the basis functions, with the PS-LMP2 approach displaying a 2- to 3-fold advantage in the prefactor. We also discuss one set of test cases for which the PS-LMP2 results disagree with those obtained from an alternative type of MP2 calculation, N-methyl acetamide (NMA) dimers, and show that the results for liquid-state simulations using polarizable parameters derived by fitting to the PS-LMP2 binding energies appear to produce better results when compared with experimental data. The convergence issues associated with the alternative MP2 formulation remain to be investigated.