Molecular recognition in proteins. Simulation analysis of substrate binding by a tyrosyl-tRNA synthetase mutant

Interplay of substrate polymorphism and conformational plasticity of Plasmodium tyrosyl-tRNA synthetase

Aminoacyl-tRNA synthetases are an indispensable component of ribosomal protein translational machinery and Plasmodium Tyrosyl-tRNA synthetase (PfTyrRS) is a validated drug target. This manuscript illustrates the dynamic conformational landscape of PfTyrRS in the context of substrate binding. Molecular dynamics simulations of PfTyrRS in the presence and absence of ligand show conformational heterogeneity for both the protein and the bound ligand. Diverse conformations for the evolutionarily conserved ATP binding motif (KMSKS) have been observed in both apo- and holo PfTyrRS. Further, the presented attributes of the tyrosyl-adenylate conformational sub-states in situ along with their implications on the strength of intermolecular interactions would be a pertinent benchmark for molecular design studies. In addition, an analysis of the ligand hydration pattern foregrounds the structurally conserved water-mediated inter-molecular interactions. The quantitative assessment of the conformational landscape, based on the fluctuations of the distance between the ligand binding pockets, of apo-PfTyrRS and holo-PfTyrRS highlights the nature of diversity in conformational sampling for the two cases. Evidently, the holo-PfTyrRS adopts a rather compact conformation compared to the apo-PfTyrRS. An intriguing asymmetry in the dynamics of the two monomers is contextualized with the functional asymmetry of the symmetrically dimeric PfTyrRS. Importantly, the network of non-bonded contacts in the apo- and holo- simulated ensembles has been analyzed. The graph-theoretic analysis-based novel insights concerning the nature of information flow as a function of ligation state would prove valuable in understanding PfTyrRS functions. The results presented here contend that understanding allostery in PfTyrRS is essential to astutely design structure-based inhibitors.

MD Simulations of tRNA and Aminoacyl-tRNA Synthetases: Dynamics, Folding, Binding, and Allostery

While tRNA and aminoacyl-tRNA synthetases are classes of biomolecules that have been extensively studied for decades, the finer details of how they carry out their fundamental biological functions in protein synthesis remain a challenge. Recent molecular dynamics (MD) simulations are verifying experimental observations and providing new insight that cannot be addressed from experiments alone. Throughout the review, we briefly discuss important historical events to provide a context for how far the field has progressed over the past few decades. We then review the background of tRNA molecules, aminoacyl-tRNA synthetases, and current state of the art MD simulation techniques for those who may be unfamiliar with any of those fields. Recent MD simulations of tRNA dynamics and folding and of aminoacyl-tRNA synthetase dynamics and mechanistic characterizations are discussed. We highlight the recent successes and discuss how important questions can be addressed using current MD simulations techniques. We also outline several natural next steps for computational studies of AARS:tRNA complexes.

Molecular recognition mechanism of peptide chain bound to the tRNA(Lys3) anticodon loop in silico

The mechanism by which proteins recognize and bind the post-transcriptional modifications of RNAs is unknown, yet these interactions play important functions in biology. Atomistic molecular dynamics simulations were performed to examine the folding of the model peptide chain -RVTHHAFLGAHRTVG- and the complex formed by the folded peptide with the native anticodon stem and loop of the human tRNA(Lys3) (hASL(Lys3)) in order to explore the binding mechanism. By analyzing and comparing two folded conformations of this peptide obtained from the folding simulation, we found that the van der Waals (VDW) energy is necessary for the thermal stability of the peptide, and the charge-charge (ELE + EGB) energy is crucial for determining the three-dimensional folded structure of the peptide backbone. Subsequently, two conformations of the peptide were employed to investigate their binding behaviors to hASL(Lys3). The metastable folded peptide was found to bind to hASL(Lys3) much easier than the stable folded peptide in the binding simulations. An energetic analysis reveals that the VDW energy favors the binding, whereas the ELE + EGB energies disfavor the binding. Arginines on the peptide preferentially attract the phosphate backbone via the inter-chain ELE + EGB interaction, significantly contributing to the binding affinity. The hydrophobic phenylalanine interacts with the anticodon loop of hASL(Lys3) via the inter-chain VDW interaction, significantly contributing to the binding specificity.

Molecular Basis for Drug Resistance in HIV-1 Protease

HIV-1 protease is one of the major antiviral targets in the treatment of patients infected with HIV-1. The nine FDA approved HIV-1 protease inhibitors were developed with extensive use of structure-based drug design, thus the atomic details of how the inhibitors bind are well characterized. From this structural understanding the molecular basis for drug resistance in HIV-1 protease can be elucidated. Selected mutations in response to therapy and diversity between clades in HIV-1 protease have altered the shape of the active site, potentially altered the dynamics and even altered the sequence of the cleavage sites in the Gag polyprotein. All of these interdependent changes act in synergy to confer drug resistance while simultaneously maintaining the fitness of the virus. New strategies, such as incorporation of the substrate envelope constraint to design robust inhibitors that incorporate details of HIV-1 protease’s function and decrease the probability of drug resistance, are necessary to continue to effectively target this key protein in HIV-1 life cycle.

Modeling Protein-Ligand Binding by Mining Minima

We present the first application of the mining minima algorithm to protein-small molecule binding. This end-point approach use an empirical force field and implicit solvent models, treats the protein binding-site as fully flexible and estimates free energies as sums over local energy wells. The calculations are found to yield encouraging agreement with experiment for three sets of HIV-1protease inhibitors and a set of phosphodiesterase 10a inhibitors. The contributions of various aspects of the model to its accuracy are examined, and the Poisson-Boltzmann correction is found to be the most critical. Interestingly, the computed changes in configurational entropy upon binding fall roughly along the same entropy-energy correlation previously observed for smaller host-guest systems. Strengths and weaknesses of the method are discussed, as are the prospects for enhancing accuracy and speed.

Decomposing the energetic impact of drug resistant mutations in HIV-1 protease on binding DRV

Darunavir (DRV) is a high affinity (4.5×10(-12) M, ΔG = -15.2 kcal/mol) HIV-1 protease inhibitor. Two drug-resistant protease variants FLAP+ (L10I, G48V, I54V, V82A) and ACT (V82T, I84V) decrease the binding affinity with DRV by 1.0 kcal/mol and 1.6 kcal/mol respectively. In this study the absolute and relative binding free energies of DRV with wild-type protease, FLAP+ and ACT were calculated with MM-PB/GBSA and thermodynamic integration methods, respectively. Free energy decomposition elucidated that the mutations conferred resistance by distorting the active site of HIV-1 protease so that the residues that lost binding free energy were not limited to the sites of mutation. Specifically the bis-tetrahydrofuranylurethane moiety of DRV maintained interactions with the FLAP+ and ACT variants, whereas the 4 - amino phenyl group lost more binding free energy with the protease in the FLAP+ and ACT complexes than in the wild-type protease which could account for the majority of the loss in binding free energy. This suggested that replacement of the 4 - amino phenyl group might generate new inhibitors less susceptible to the drug resistant mutations.

Free-energy simulations and experiments reveal long-range electrostatic interactions and substrate-assisted specificity in an aminoacyl-tRNA synthetase

Specific recognition of their cognate amino acid substrates by the aminoacyl-tRNA synthetase enzymes is essential for the correct translation of the genetic code. For aspartyl-tRNA synthetase (AspRS), electrostatic interactions are expected to play an important role, since its three substrates (aspartate, ATP, tRNA) are all electrically charged. We used molecular-dynamics free-energy simulations and experiments to compare the binding of the substrate Asp and its electrically neutral analogue Asn to AspRS. The preference for Asp is found to be very strong, with good agreement between simulations and experiment. The simulations reveal long-range interactions that electrostatically couple the amino acid ligand, ATP, and its associated Mg2+ cations, a histidine side chain (His448) next to the amino acid ligand and a flexible loop that closes over the active site in response to amino acid binding. Closing this loop brings a negatively charged glutamate into the active site; this causes His448 to recruit a labile proton, which interacts favorably with Asp and accounts for most of the Asp/Asn discrimination. Cobinding of the second substrate, ATP, increases specificity for Asp further and makes the system robust towards removal of His448, which is mutated to a neutral amino acid in many organisms. Thus, AspRS specificity is assisted by a labile proton and a cosubstrate, and ATP acts as a mobile discriminator for specific Asp binding to AspRS. In asparaginyl-tRNA synthetase, a close homologue of AspRS, a few binding-pocket differences modify the charge balance so that asparagine binding predominates.

Alchemical free energy calculations and multiple conformational substates

Thermodynamic integration (TI) was combined with (adaptive) umbrella sampling to improve the convergence of alchemical free energy simulations in which multiple conformational substates are present. The approach, which we refer to as non-Boltzmann TI (NBTI), was tested by computing the free energy differences between three five-atomic model systems, as well as the free energy difference of solvation between leucine and asparagine. In both cases regular TI failed to give converged results, whereas the NBTI results were free from hysteresis and had standard deviations well below +/-0.7 kcal/mole. We also present theoretical considerations that make it possible to compute free energy differences between simple molecules, such as the five-atomic model systems, by numerical integration of the partition functions at the respective end points.

Molecular basis of peptide recognition by the TCR: affinity differences calculated using large scale computing

Free energy calculations of the wild-type and the variant human T cell lymphotropic virus type 1 Tax peptide presented by the MHC to the TCR have been performed using large scale massively parallel molecular dynamics simulations. The computed free energy difference (-1.86 +/- 0.44 kcal/mol) using alchemical mutation-based thermodynamic integration agrees well with experimental data (-2.9 +/- 0.2 kcal/mol). Our simulations exploit state-of-the-art hardware and codes whose algorithms have been optimized for supercomputing platforms. This enables us to simulate larger, more realistic biological systems for longer durations without the imposition of artificial constraints.

Thermodynamics of protein folding: a microscopic view

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.

The missing link between thermodynamics and structure in F1-ATPase

F(1)F(o)-ATP synthase is the enzyme responsible for most of the ATP synthesis in living systems. The catalytic domain F(1) of the F(1)F(o) complex, F(1)-ATPase, has the ability to hydrolyze ATP. A fundamental problem in the development of a detailed mechanism for this enzyme is that it has not been possible to determine experimentally the relation between the ligand binding affinities measured in solution and the different conformations of the catalytic beta subunits (beta(TP), beta(DP), beta(E)) observed in the crystal structures of the mitochondrial enzyme, MF(1). Using free energy difference simulations for the hydrolysis reaction ATP+H(2)O --> ADP+P(i) in the beta(TP) and beta(DP) sites and unisite hydrolysis data, we are able to identify beta(TP) as the "tight" (K(D) = 10(-12) M, MF(1)) binding site for ATP and beta(DP) as the "loose" site. An energy decomposition analysis demonstrates how certain residues, some of which have been shown to be important in catalysis, modulate the free energy of the hydrolysis reaction in the beta(TP) and beta(DP) sites, even though their structures are very similar. Combined with the recently published simulations of the rotation cycle of F(1)-ATPase, the present results make possible a consistent description of the binding change mechanism of F(1)-ATPase at an atomic level of detail.

Binding free energy differences in a TCR-peptide-MHC complex induced by a peptide mutation: a simulation analysis

Recognition by the T-cell receptor (TCR) of immunogenic peptides presented by class I major histocompatibility complexes (MHCs) is the determining event in the specific cellular immune response against virus-infected cells or tumor cells. It is of great interest, therefore, to elucidate the molecular principles upon which the selectivity of a TCR is based. These principles can in turn be used to design therapeutic approaches, such as peptide-based immunotherapies of cancer. In this study, free energy simulation methods are used to analyze the binding free energy difference of a particular TCR (A6) for a wild-type peptide (Tax) and a mutant peptide (Tax P6A), both presented in HLA A2. The computed free energy difference is 2.9 kcal/mol, in good agreement with the experimental value. This makes possible the use of the simulation results for obtaining an understanding of the origin of the free energy difference which was not available from the experimental results. A free energy component analysis makes possible the decomposition of the free energy difference between the binding of the wild-type and mutant peptide into its components. Of particular interest is the fact that better solvation of the mutant peptide when bound to the MHC molecule is an important contribution to the greater affinity of the TCR for the latter. The results make possible identification of the residues of the TCR which are important for the selectivity. This provides an understanding of the molecular principles that govern the recognition. The possibility of using free energy simulations in designing peptide derivatives for cancer immunotherapy is briefly discussed.

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.

Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase

Specific amino acid binding by aminoacyl-tRNA synthetases (aaRS) is necessary for correct translation of the genetic code. Engineering a modified specificity into aminoacyl-tRNA synthetases has been proposed as a means to incorporate artificial amino acid residues into proteins in vivo. In a previous paper, the binding to aspartyl-tRNA synthetase of the substrate Asp and the analogue Asn were compared by molecular dynamics free energy simulations. Molecular dynamics combined with Poisson-Boltzmann free energy calculations represent a less expensive approach, suitable for examining multiple active site mutations in an engineering effort. Here, Poisson-Boltzmann free energy calculations for aspartyl-tRNA synthetase are first validated by their ability to reproduce selected molecular dynamics binding free energy differences, then used to examine the possibility of Asn binding to native and mutant aspartyl-tRNA synthetase. A component analysis of the Poisson-Boltzmann free energies is employed to identify specific interactions that determine the binding affinities. The combined use of molecular dynamics free energy simulations to study one binding process thoroughly, followed by molecular dynamics and Poisson-Boltzmann free energy calculations to study a series of related ligands or mutations is proposed as a paradigm for protein or ligand design. The binding of Asn in an alternate, "head-to-tail" orientation observed in the homologous asparagine synthetase is analyzed, and found to be more stable than the "Asp-like" orientation studied earlier. The new orientation is probably unsuitable for catalysis. A conserved active site lysine (Lys198 in Escherichia coli) that recognizes the Asp side-chain is changed to a leucine residue, found at the corresponding position in asparaginyl-tRNA synthetase. It is interesting that the binding of Asp is calculated to increase slightly (rather than to decrease), while that of Asn is calculated, as expected, to increase strongly, to the same level as Asp binding. Insight into the origin of these changes is provided by the component analyses. The double mutation (K198L,D233E) has a similar effect, while the triple mutation (K198L,Q199E,D233E) reduces Asp binding strongly. No binding measurements are available, but the three mutants are known to have no ability to adenylate Asn, despite the "Asp-like" binding affinities calculated here. In molecular dynamics simulations of all three mutants, the Asn ligand backbone shifts by 1-2 A compared to the experimental Asp:AspRS complex, and significant side-chain rearrangements occur around the pocket. These could reduce the ATP binding constant and/or the adenylation reaction rate, explaining the lack of catalytic activity in these complexes. Finally, Asn binding to AspRS with neutral K198 or charged H449 is considered, and shown to be less favorable than with the charged K198 and neutral H449 used in the analysis.

Modeling of the TCR-MHC-peptide complex

The methodology for generating a homology model of the T1 TCR-PbCS-K(d) class I major histocompatibility complex (MHC) class I complex is presented. The resulting model provides a qualitative explanation of the effect of over 50 different mutations in the region of the complementarity determining region (CDR) loops of the T cell receptor (TCR), the peptide and the MHC's alpha(1)/alpha(2) helices. The peptide is modified by an azido benzoic acid photoreactive group, which is part of the epitope recognized by the TCR. The construction of the model makes use of closely related homologs (the A6 TCR-Tax-HLA A2 complex, the 2C TCR, the 14.3.d TCR Vbeta chain, the 1934.4 TCR Valpha chain, and the H-2 K(b)-ovalbumine peptide), ab initio sampling of CDR loops conformations and experimental data to select from the set of possibilities. The model shows a complex arrangement of the CDR3alpha, CDR1beta, CDR2beta and CDR3beta loops that leads to the highly specific recognition of the photoreactive group. The protocol can be applied systematically to a series of related sequences, permitting the analysis at the structural level of the large TCR repertoire specific for a given peptide-MHC complex.

X-ray structures of small ligand-FKBP complexes provide an estimate for hydrophobic interaction energies

A new crystal form of native FK506 binding protein (FKBP) has been obtained which has proved useful in ligand binding studies. Three different small molecule ligand complexes and the native enzyme have been determined at higher resolution than 2.0 A. Dissociation constants of the related small molecule ligands vary from 20 mM for dimethylsulphoxide to 200 microM for tetrahydrothiophene 1-oxide. Comparison of the four available crystal structures shows that the protein structures are identical to within experimental error, but there are differences in the water structure in the active site. Analysis of the calculated buried surface areas of these related ligands provides an estimated van der Waals contribution to the binding energy of -0.5 kJ/A(2) for non-polar interactions between ligand and protein.

Protein-protein recognition: an experimental and computational study of the R89K mutation in Raf and its effect on Ras binding

Binding of the protein Raf to the active form of Ras promotes activation of the MAP kinase signaling pathway, triggering cell growth and differentiation. Raf/Arg89 in the center of the binding interface plays an important role determining Ras-Raf binding affinity. We have investigated experimentally and computationally the Raf-R89K mutation, which abolishes signaling in vivo. The binding to [gamma-35S]GTP-Ras of a fusion protein between the Raf-binding domain (RBD) of Raf and GST was reduced at least 175-fold by the mutation, corresponding to a standard binding free energy decrease of at least 3.0 kcal/mol. To compute this free energy and obtain insights into the microscopic interactions favoring binding, we performed alchemical simulations of the RBD, both complexed to Ras and free in solution, in which residue 89 is gradually mutated from Arg into Lys. The simulations give a standard binding free energy decrease of 2.9+/-1.9 kcal/mol, in agreement with experiment. The use of numerous runs with three different force fields allows insights into the sources of uncertainty in the free energy and its components. The binding decreases partly because of a 7 kcal/mol higher cost to desolvate Lys upon binding, compared to Arg, due to better solvent interactions with the more concentrated Lys charge in the unbound state. This effect is expected to be general, contributing to the lower propensity of Lys to participate in protein-protein interfaces. Large contributions to the free energy change also arise from electrostatic interactions with groups up to 8 A away, namely residues 37-41 in the conserved effector domain of Ras (including 4 kcal/mol from Ser39 which loses a bifurcated hydrogen bond to Arg89), the conserved Lys84 and Lys87 of Raf, and 2-3 specific water molecules. This analysis will provide insights into the large experimental database of Ras-Raf mutations.

An example of a protein ligand found by database mining: description of the docking method and its verification by a 2.3 A X-ray structure of a thrombin-ligand complex

A computer program (SANDOCK) has been developed for the automated docking of small ligands to a target protein. It uses a guided matching algorithm to fit ligand atoms into the protein binding pocket. The protein is described by a modified Lee-Richard's dotted surface with each dot coded by chemical property and accessibility. Orientations of the ligand in the active site are generated such that a chemical and a shape complementary between the ligand and the active site cavity have to be fulfilled. The generated fits are evaluated with scoring functions which account for van der Waals, hydrophobic and hydrogen bonding interactions. This newly developed docking program can efficiently screen very large databases in a reasonable time and has been used to successfully identify novel ligands. The X-ray structure of a thrombin-ligand complex predicted by SANDOCK is described. The ligand binds to thrombin with a Kd of 65 microM and has an rmsd of 0.7 A for all ligand atoms from the predicted binding mode by SANDOCK.

Specific amino acid recognition by aspartyl-tRNA synthetase studied by free energy simulations

Specific amino acid binding by aminoacyl-tRNA synthetases is necessary for correct translation of the genetic code. To obtain insight into the origin of the specificity, the binding to aspartyl-tRNA synthetase (AspRS) of the negatively charged substrate aspartic acid and the neutral analogue asparagine are compared by use of molecular dynamics and free energy simulations. Simulations of the Asn-AspRS complex show that although Asn cannot bind in the same position as Asp, several possible positions exist 1.5 to 2 A away from the Asp site. The binding free energy of Asn in three of these positions was compared to that of Asp through alchemical free energy simulations, in which Asp is gradually mutated ito Asn in the complex with the enzyme. To correctly account for the electrostatic interactions in the system (including bulk solvent), a recently developed hybrid approach was used, in which the region of the mutation site is treated microscopically, whereas distant protein and solvent are treated by continuum electrostatics. Seven free energy simulations were performed in the protein and two in solution. The various Asn positions and orientations sampled at the Asn endpoints of the protein simulations yielded very similar free energy differences. The calculated Asp-->Asn free energy change is 79.8(+/-1.5) kcal/mol in solution and 95.1(+/-2.8) kcal/mol in the complex with the protein. Thus, the substrate Asp is predicted to bind much more strongly than Asn, with a binding free energy difference of 15.3 kcal/mol. This implies that erroneous binding of Asn by AspRS is highly improbable, and cannot account for any errors in the translation of the genetic code. Almost all of the protein contributions to the Asp versus Asn binding free energy difference arise from an arginine and a lysine residue that hydrogen bond to the substrate carboxylate group and an Asp and a Glu that hydrogen bond to these; all four amino acid residues are completely conserved in AspRSs. The protein effectively "solvates" the Asp side-chain more strongly than water does. The simulations are analyzed to determine the interactions that Asn is able to make in the binding pocket, and which sequence differences between AspRS and the highly homologous AsnRS are important for modifying the amino acid specificity. A double or triple mutation of AspRS that could make it specific for Asn is proposed, and supported by preliminary simulations of a mutant complex.

The nature of trypsin-pancreatic trypsin inhibitor binding: free energy calculation of Tyr39-->Phe39 mutation in trypsin

The main goal of this work is the detailed study of the binding interactions in the trypsin-pancreatic trypsin inhibitor (PTI) complex and, here, we present how meaningful the Tyr39-Ile19 interaction is to the stability of that particular complex using free energy methods. This knowledge should be very important in the design of new inhibitors for trypsin and enzymes homologous to it. In particular, it could help to decide whether it is possible to produce selective inhibitors for these enzymes by appropriate mutations of residues in the contact region of PTI.

Aminoacyl-tRNA synthetases

Detailed mechanisms for each step of the reaction catalyzed by both class I and class II aminoacyl-tRNA synthetases have been proposed on the basis of crystallographic data of aminoacyl-tRNA synthetases in complex with their different substrates. Despite the very different topologies of the two classes, there are striking and unanticipated chemical similarities between their active sites and proposed mechanisms.

Free energy simulations: the meaning of the individual contributions from a component analysis

A theoretical analysis is made of the decomposition into contributions from individual interactions of the free energy calculated by thermodynamic integration. It is demonstrated that such a decomposition, often referred to as "component analysis," is meaningful, even though it is a function of the integration path. Moreover, it is shown that the path dependence can be used to determine the relation of the contribution of a given interaction to the state of the system. To illustrate these conclusions, a simple transformation (Cl- to Br- in aqueous solution) is analyzed by use of the Reference Interaction Site Model-Hypernetted Chain Closure integral equation approach; it avoids the calculational difficulties of macromolecular simulation while retaining their conceptual complexity. The difference in the solvation free energy between chloride and bromide is calculated, and the contributions of the Lennard-Jones and electrostatic terms in the potential function are analyzed by the use of suitably chosen integration paths. The model is also used to examine the path dependence of individual contributions to the double free energy differences (delta delta G or delta delta A) that are often employed in free energy simulations of biological systems. The alchemical path, as contrasted with the experimental path, is shown to be appropriate for interpreting the effects of mutations on ligand binding and protein stability. The formulation is used to obtain a better understanding of the success of the Poisson-Boltzmann continuum approach for determining the solvation properties of polar and ionic systems.