Protein Dipoles Langevin Dipoles Research Articles

Semimicroscopic investigation of active site pK a values in peptidylarginine deiminase 4

Peptidylarginine deiminase 4 (PAD4), also known as protein arginine deiminase 4, performs a post-translational deimination that converts arginine to citrulline. The dysregulation of PAD4 has been implicated in a number of diseases, including rheumatoid arthritis (RA) and cancer. This makes PAD4 an important therapeutic target. To develop small-molecule inhibitors as potential treatments, it is advantageous if the catalytic mechanism is well understood. The protonation states of the active site residues, which have long been under controversy, have a direct impact on the catalytic mechanism. Two competing mechanisms are under investigation in the current literature. The first is a reverse protonation mechanism that depends on the active site histidine and cysteine existing as an ion pair. The second is a substrate-assisted mechanism that depends on the active site histidine and cysteine being neutral. This study uses the semimicroscopic protein dipoles Langevin dipoles (PDLD/S) linear response approximation method in the MOLARIS software package to calculate the change in solvation energy of moving the residue from water to the protein interior, and then using that information to assess the protonation states of the active site residues of PAD4. Results from these calculations suggest that in the enzyme–substrate complex of PAD4, the cysteine and histidine are protonated and deprotonated, respectively, and are therefore both neutral, analogous to the proposed protonation states of the active site residues in the Michaelis complex in the substrate-assisted mechanism.

Impact of Proximal and Distal Pocket Site-Directed Mutations on the Ferric/Ferrous Heme Redox Potential of Yeast Cytochrome-c-Peroxidase.

Cytochrome-c-peroxidase (CCP) contains a five-coordinate heme active site. The reduction potential for the ferric to ferrous couple in CCP is anomalously low and pH dependent (Eo = ~-180 mV vs. S.H.E. at pH 7). The contribution of the protein environment to the tuning of the redox potential of this couple is evaluated using site directed mutants of several amino acid residues in the environment of the heme. These include proximal pocket mutation to residues Asp-235, Trp-191, Phe-202 and His-175, distal pocket mutation to residues Trp-51, His-52, and Arg-48; and a heme edge mutation to Ala-147. Where unknown, the structural changes resulting from the amino acid substitution have been studied by X-ray crystallography. In most cases, ostensibly polar or charged residues are replaced by large hydrophobic groups or alternatively by Ala or Gly. These latter have been shown to generate large, solvent filled cavities. Reduction potentials are measured as a function of pH by spectroelectrochemistry. Starting with the X-ray derived structures of CCP and the mutants, or with predicted structures generated by Molecular Dynamics (MD), predictions of redox potential changes are modeled using the Protein Dipoles Langevin Dipoles (PDLD) method. These calculations serve to model an electrostatic assessment of the redox potential change with simplified assumptions about heme iron chemistry, with the balance of the experimentally observed shifts in redox potential being thence attributed to changes in the ligand set and heme coordination chemistry, and/or other changes in the structure not directly evident in the X-ray structures (e.g. ionization states, specific roles played by solvent species, or conformationally flexible portions of the protein). Agreement between theory and experiment is good for all mutant proteins with the exception of the mutation Arg 48 to Ala, and His 52 to Ala. In the former case, the influence of phosphate buffer is adduced to account for the discrepancy, and measurements made in a bis-tris propane/2-(N-morpholino)ethanesulfonic acid buffer system agree well with theory. For the latter case, an unknown structural element relevant to His-52, and/or solvent influence in the mutant akin to anion binding in the distal pocket (though lacking proof that it is) manifests in this mutant. The use of exogenous (sixth) ligands in dissecting the contributions to control of redox potential are also explored as a pathway for model building.

Probing the general base catalysis in the first step of BamHI action by computer simulations.

BamHI is a type II restriction endonuclease that catalyzes the scission of the phoshodiester bond in the GAGTCC cognate sequence in the presence of two divalent metal ions. The first step of the reaction is the preparation of water for nucleophilic attack by Glu-113, which has been proposed to abstract the proton from the attacking water molecule. Alternatively, the 3'-phosphate group to the susceptible phosphodiester bond has been suggested to play a role as the general base. The two hypotheses have been tested by computer simulations using the semiempirical protein dipoles Langevin dipoles (PDLD/S) method. Deprotonation of water by Glu-113 has been found to be less favorable by 5.7 kcal/mol than metal-catalyzed deprotonation with a concomitant proton transfer to bulk solvent. The preparation of the nucleophile by the 3'-phosphate group is less favorable by 12.3 kcal/mol. These results suggest that both the general base and the substrate-assisted mechanisms in the first step of BamHI action are less likely than the metal-catalyzed reaction. The metal ions in the active site of BamHI make the largest contributions to the reduction of the free energy of hydroxide ion formation. On the basis of these findings we propose that the first step of endonuclease catalysis does not require a general base; rather, the essential attacking nucleophile in BamHI catalytic action is stabilized by the metal ions.

Examining methods for calculations of binding free energies: LRA, LIE, PDLD‐LRA, and PDLD/S‐LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 4;5:215–228) and the Linear Interaction Energy (LIE) method (Åqvist et. al., Prot Eng 5;7:385–391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 4;5:215–228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the “non-polar” ligand, ℓ`, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant β (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant β, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, ΔGbind,ℓ`. Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate ΔGbind,ℓ` by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total ΔGbind,ℓ`. The sum of these contributions is scaled by a factor θ and it is argued that obtaining a quantitative balance between these contributions should result in θ = 1. By doing so we should have a reliable estimate of the value of the LIE β and a way to understand its origin. The present approach gives θ values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE θ between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation, and hydrophobic contributions). The practical difference is that the LIE method approximates the non-electrostatic term by the average of the van der Waals interaction, while our LRA method evaluates this term by the PDLD method. This point is illustrated by the fact that our LRA approach gives results of similar quality to those obtained by the LIE approach. Finally it is found that results of similar quality are obtained by the PDLD/S method and the LRA method. This is significant since the PDLD/S method is much faster than the LRA and LIE methods. However, more studies of the relative accuracy on other systems are needed in order to establish their relative merits. Proteins 2000;39:393–407. © 2000 Wiley-Liss, Inc.

Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist et. al., Prot Eng 1994;7:385-391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total DeltaG(bind,l;). The sum of these contributions is scaled by a factor straight theta and it is argued that obtaining a quantitative balance between these contributions should result in straight theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta and a way to understand its origin. The present approach gives straight theta values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE straight theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation,

Computer Simulation Studies of the Catalytic Mechanism of Human Aldose Reductase

Aldose reductase, an NADPH dependent oxidoreductase, has received considerable attention due to its possible link to diabetic and galactosemic complications. It is known that the catalytic reaction involves a hydride shift from NADPH and a proton transfer from a suitable proton donor to the carbonyl group of the substrate. However, the details of the process are still unclear. The present work explores the catalytic mechanism of the enzyme by using the semi-microscopic protein dipoles Langevin dipoles (PDLD/S) and the empirical valence bond (EVB) methods. The pKa values of His-110 and Tyr-48 are evaluated to determine which of these two residues donates the proton in the reaction. It is found that the free energy of protonation of His-110 in its protein site is ∼9 kcal/mol and hence the pKa of this residue is abnormally low. Consequently, His-110 is not protonated in the active site of aldose reductase. On the other hand, it is found that the pKa of Tyr-48 is lowered to ∼8.5 in the active site due to the stabilization by the unique local environment of the phenol group. We conclude that Tyr-48 acts as the proton donor in the reduction of aldehydes by aldose reductase, while the neutral His-110 has a role in substrate binding during the catalysis. To obtain a quantitative picture of the energetics of different feasible catalytic mechanisms in the protein we follow the EVB philosophy and calibrate the potential surface of the catalytic reaction in a solvent cage by using the relevant energetics from experiments. It is found that a mechanism where a proton transfer precedes the hydride transfer is unfavorable in the solvent cage, relative to the alternative mechanism where the hydride transfer precedes protonation. Furthermore, our study of the reaction in the actual protein environment indicates that an initial proton transfer step would require prohibitively high energy. Thus, the most probable catalytic mechanism commences with the hydride shift, followed by a proton transfer from Tyr-48. The calculations show that in water the activation barrier for the hydride shift is ∼20 kcal/mol, which is far above the barrier of the subsequent proton transfer. The protein environment stabilizes the transition state of the hydride shift by ∼3 kcal/mol and destabilizes the intermediate state by ∼8 kcal/mol relative to the corresponding states in the water cage. This finding is consistent with the physiological role of the enzyme in detoxification where it catalyzes the reduction of a wide range of carbonyl-containing substrates without particular specificity. It is argued that it may be difficult for an enzyme to both satisfy this demand and catalyze the reaction beyond the simple role of bringing the proton and hydride donor groups to the proximity of the substrate.

Electrostatic contributions to protein-protein binding affinities: application to Rap/Raf interaction.

The challenge of evaluating absolute binding free energies of protein-protein complexes is addressed using the scaled Protein Dipoles Langevin Dipoles (PDLD/S) model in combination with the Linear Response Approximation (LRA). This is done by taking the complex between Rap1A (Rap) and the p21ras binding domain of c-Raf (Raf-RBD) (Nassar et al., Nature 375:554-560, 1995) as a model system. Several formulations and different thermodynamic cycles are explored taking advantage of the LRA method and considering the protein reorganization during complex formation. The performance of different approximations is examined by comparing the calculated and observed absolute binding energies for the native complex and some of its mutants. The evaluation of the contributions of individual residues to the binding free energy, which is referred to here as group contributions is also examined. Special attention is paid to the role of the "dielectric constant," epsilon(in) which is in fact a scaling factor that represents the contributions that are treated implicitly. It is found that explicit consideration of protein relaxation is crucial for obtaining reasonable results with small values of epsilon(in), but it is also found that such a treatment of protein-protein interactions is very challenging and does not always give stable results. This indicates that more advanced explicit calculations should be based on experimentally determined structures of both the complex and the isolated proteins. Nevertheless, it is demonstrated that the qualitative trend of the effect of mutations can be reproduced by considering the effect of protein reorganization implicitly, using epsilon(in) approximately 25 for ionized residues and epsilon(in) approximately 4 for polar residues. Thus, it is concluded that an explicit treatment of solvent relaxation (which is common to current continuum models) does not provide sufficient compensation for turning off the charges of ionized residues on the interaction surface of the Raf-RBD/Rap complex. Representing the missing contribution by large epsilon(in) can, of course, reproduce the observed effect of ionized residues, but now the contribution of uncharged residues will be largely underestimated. Regardless of these conceptual problems, it is established that a very simple nonrelaxed approach, where the relaxation of both the protein and the solvent are considered implicitly, can provide an effective qualitative way for evaluating group contributions, using large and small values for epsilon(in) of ionized and neutral residues, respectively. As much as the actual system studied is concerned we find that more residues than generally assumed play a role in Raf-RBD/Rap interaction. This includes residues that are not located at the protein-protein interaction surface. These residues contribute to the binding energy through direct charge-charge interaction without leading to drastic structural changes. The overall contribution of the surface residues is quite significant since Raf and Rap are positively and negatively charged, respectively, and their charges are distributed along the interaction site between the two proteins.

Origin of the Catalytic Power of Acetylcholinesterase: Computer Simulation Studies

The energetics of the acylation step of AChE (acetylcholinesterase) is explored by using molecular simulation approaches. These include the evaluation of activation free energies by using the empirical valence bond (EVB) potential surface and an all-atom free energy perturbation (FEP) approach, as well as estimates of the catalytic effect of the enzyme by using the semimicroscopic version of the Protein Dipoles Langevin Dipoles (PDLD/S) method. The determination of the effect of the enzyme is based on the use of reliable experimental information in evaluating the energetics of the reference reaction in water and then on using robust simulations for the evaluation of the effect of moving the reacting system from a solvent cage to the protein active site. This procedure reduces the error range of the overall analysis since the energetics in water is not evaluated by a first principle approach. The use of two simulation methods and different initial conditions provide a way for assessing the error range of the calculations and the validity of the corresponding conclusions. Both the EVB and PDLD/S approaches show that the enzyme reduces the activation barrier of the acylation step by 10−15 kcal/mol relative to the corresponding reference reaction in water. This corresponds to a (107−1011)-fold rate acceleration, which is in good agreement with the corresponding experimental estimate. The origin of the catalytic power of the enzyme appears to be associated with electrostatic stabilization of the transition state. This electrostatic effect can be classified as a combination of reduction of the energy of the charged intermediate and reduction in the reorganization energy. The contributions of different protein residues to the stabilization of the transition state are estimated. It is demonstrated that, in contrast to some proposals, AChE and other enzymes do not work by providing a hydrophobic environment but rather a polar environment. This work concludes that the most important catalytic effects are associated with nearby residues rather than distant ionized residues. It is also concluded that the enzyme has evolved first to optimize the speed of the actual bond breaking/bond making chemical processes and only then to fine-tune the rate by optimizing the barrier for the diffusion step. Since the optimization of the chemical step involves more than 10 kcal/mol and the optimization of the diffusion step involves at most 1 or 2 kcal/mol, it appears that the possible acceleration of the diffusion step is a second-order effect. These conclusions are consistent with the available experimental studies.

Consistent Calculations of pKa's of Ionizable Residues in Proteins: Semi-microscopic and Microscopic Approaches

One of the most direct benchmarks for electrostatic models of macromolecules is provided by the pKa's of ionizable groups in proteins. Obtaining accurate results for such a benchmark presents a major challenge. Microscopic models involve very large opposing contributions and suffer from convergence problems. Continuum models that consider the protein permanent dipoles as a part of the dielectric constant cannot reproduce the correct self-energy. Continuum models that treat the local environment in a semi-microscopic way do not take into account consistently the protein relaxation during the charging process. This work describes calculations of pKa's in protein in an accurate yet consistent way, using the semi-microscopic version of the protein dipoles Langevin dipoles (PDLD) model, which treats the protein relaxation in the microscopic framework of the linear response approximation. This approach allows one to take into account the protein structural reorganization during formation of charges, thus reduci...

Calculation of the Redox Potentials of Iron-Sulfur Proteins: The 2-/3- Couple of [Fe4S4Cys4] Clusters in Peptococcus aerogenes Ferredoxin, Azotobacter vinelandii Ferredoxin I, and Chromatium vinosum High-Potential Iron Protein

Calculations of the redox potentials of the 2-/3-couples of [Fe4S*4Cys4] clusters in the iron-sulfur proteins Peptococcus aerogenes ferredoxin (PaFd), Azotobacter vinelandii ferredoxin I (AvFdI) and Chromatium vinosum high potential iron protein (CvHiPIP) based on the Protein Dipoles Langevin Dipoles (PDLD) method are reported. The structures of these proteins have been determined by X-ray crystallography; in the case of PaFd the structure has recently been revised due to a change in the sequence close to Cluster II. The large differences between the potentials of the [Fe4S*4Cys4] clusters of PaFd and AvFdI and the potential of the [Fe4S*4Cys4] cluster of CvHiPIP are successfully modeled and originate principally in differences in the configuration of main-chain amide groups near the clusters. The small difference between the potentials of PaFd and AvFdI is also satisfactorily modeled in the case of Cluster I of PaFd. Solvent dipoles close to the cluster in PaFd are an important contributor to its higher potential. The two X-ray structures of PaFd yield similar results for Cluster I of PaFd. In contrast, the results for Cluster II differ substantially; for reasons not yet clear, the recently revised structure leads to results in worse agreement with experiment.

Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs

AbstractDifferent microscopic and semimicroscopic approaches for calculations of electrostatic energies in macromolecules are examined. This includes the Protein Dipoles Langevin Dipoles (PDLD) method, the semimicroscopic PDLD (PDLD/S) method, and a free energy perturbation (FEP) method. The incorporation of these approaches in the POLARIS and ENZYMIX modules of the MOLARIS package is described in detail. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions, as well as the effects of the ionic strength and external pH. Determination of the hydrophobic energy involves an approach that considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. Ionic strength effects are studied by modeling the ionic environment around the given system using a grid of residual charges and evaluating the relevant interaction using Coulomb's law with the dielectric constant of water. The performance of the FEP calculations is significantly enhanced by using special boundary conditions and evaluating the long‐range electrostatic contributions using the Local Reaction Field (LRF) model. A diverse set of electrostatic effects are examined, including the solvation energies of charges in proteins and solutions, energetics of ion pairs in proteins and solutions, interaction between surface charges in proteins, and effect of ionic strength on such interactions, as well as electrostatic contributions to binding and catalysis in solvated proteins. Encouraging results are obtained by the microscopic and semimicroscopic approaches and the problems associated with some macroscopic models are illustrated. The PDLD and PDLD/S methods appear to be much faster than the FEP approach and still give reasonable results. In particular, the speed and simplicity of the PDLD/S method make it an effective strategy for calculations of electrostatic free energies in interactive docking studies. Nevertheless, comparing the results of the three approaches can provide a useful estimate of the accuracy of the calculated energies. © 1993 John Wiley & Sons, Inc.

Effect of the Asn52 → Ile mutation on the redox potential of yeast cytochrome c: Theory and experiment

Theoretical methods for correlation of sequence changes and redox potential of electron transport proteins are examined using the Asn52 → Ile mutation in cytochrome c as a test case. The first approach uses the protein dipoles Langevin dipoles (PDLD) method and the high resolution X-ray structures of the native and the mutant proteins. This approach is found to give reliable results where all the solvent molecules are represented by Langevin dipoles and also when some bound water molecules are represented explicitly. A free energy perturbation method is also found to give reasonable results but at the expense of much more computer time. Finally, an approach that generates mutant structures from the native structure by molecular dynamics simulation and then uses these configurations in PDLD calculations is found to give a reasonable estimate of the effect of the mutation on the corresponding redox potential. The encouraging results obtained here and in a preliminary test case of the Phe82 → Ser mutation indicates that the present strategies can provide a useful tool for structure-redox and sequence-redox correlation in proteins.

Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.

Energetics of ion permeation through membrane channels. Solvation of Na+ by gramicidin A

Calculations of the solvation energetics for a Na+ ion inside the Gramicidin A channel and in water are presented. The protein dipoles Langevin dipoles (PDLD) method is used to obtain an electrostatic free energy profile for ion permeation through the channel. To gauge the quality of the PDLD results the solvation free energy of a Na+ ion in water and in the center of the channel is also calculated using free energy perturbation (FEP) simulations. The effect of the polarisability of the surrounding lipid membrane is taken into account by representing the membrane by a large grid of polarisable point dipoles. The two methods give similar solvation energies in the interior of the channel and these are less than 5 kcal/mol above the solvation free energy for Na+ in water, in good agreement with experimental data on the activation barriers for ion permeation. It appears that the problems associated with previous calculations of energy profiles in membrane channels can be overcome by a consistent treatment of all the relevant electrostatic contributions. In particular, we find that the induced dipoles of the membrane and the protein contributes with approximately 10 kcal/mol to the solvation energy inside the channel and can therefore not be discarded in a realistic description of ion solvation in the Gramicidin channel.