Macroscopic models for studies of electrostatic interactions in proteins: limitations and applicability.

The validity of macroscopic models for calculations of electrostatic energies in proteins is examined. The Tanford-Kirkwood (TK) model is extended to include the self energy of the ionized groups. It is shown that ionized groups cannot exist inside nonpolar regions of proteins and argued that the experimental finding of ions inside proteins proves that the corresponding local environment is polar. The modified TK model (MTK model), which adjusts charge-charge interactions by the corresponding solvent accessibilities, is found to be inconsistent with the TK model, on which it is based. The MTK model corresponds to a polar interior whereas the TK model assumes a nonpolar interior. It is shown that models that assume a high dielectric constant for proteins give reasonable results for interactions between charged groups at equilibrium. It is then explained why, in contradiction to common belief, protein interiors are polar around charged groups. It is argued that in focusing on charge-charge interactions one overlooks the key contribution of the protein dipoles in determining the self energy of charges in the interior of proteins.     

Designing substrate specificity by protein engineering of electrostatic interactions.

Protein engineering of electrostatic interactions between charged substrates and complementary charged amino acids, at two different sites in the substrate binding cleft of the protease subtilisin BPN', increases kcat/Km toward complementary charged substrates (up to 1900 times) and decreases kcat/Km toward similarly charged substrates. From kinetic analysis of 16 mutants of subtilisin and the wild type, the average free energies for enzyme-substrate ion-pair interactions at the two different sites are calculated to be -1.8 +/- 0.5 and -2.3 +/- 0.6 kcal/mol (1 cal = 4.18 J) [at 25 degrees C in 0.1 M Tris X HCl (pH 8.6)]. The combined electrostatic effects are roughly additive. These studies demonstrate the feasibility for rational design of charged ligand binding sites in proteins by tailoring of electrostatic interactions.     

alpha-Helix dipole model and electrostatic stabilization of 4-alpha-helical proteins.

A simple dipole model is developed for estimation of the electrostatic interaction energy between alpha-helices in proteins. This model is used to estimate the electrostatic stabilization in a recurrent protein tertiary structural motif, an array of four closely packed alpha-helices. It is found that, for the proteins examined (cytochrome c', hemerythrin, myohemerythrin, cytochrome b562, and a T4 phage lysozyme domain), their common antiparallel arrangement of adjacent helices confers a stabilization of 5--7 kcal/mol (1 cal = 4.18 J). In contrast, a similarly packed array of parallel helices is relatively destabilized by 20 kcal/mol. These results show that helix-dipole interactions are important in the stabilization of this structural motif. These effects are discussed both in the context of folding pathways for 4-alpha-helical proteins and the stabilization of the higher aggregates.     

Evaluation of synthetic linear motor-molecule actuation energetics

By applying atomic force microscope (AFM)-based force spectroscopy together with computational modeling in the form of molecular force-field simulations, we have determined quantitatively the actuation energetics of a synthetic motor-molecule. This multidisciplinary approach was performed on specifically designed, bistable, redox-controllable [2]rotaxanes to probe the steric and electrostatic interactions that dictate their mechanical switching at the single-molecule level. The fusion of experimental force spectroscopy and theoretical computational modeling has revealed that the repulsive electrostatic interaction, which is responsible for the molecular actuation, is as high as 65 kcal.mol(-1), a result that is supported by ab initio calculations.     

A Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins

Characterization of the unfolded state is essential for understanding the protein folding problem. In the unfolded state, a protein molecule samples vastly different conformations. Here I present a simple theoretical method for treating residual charge-charge interactions in the unfolded state. The method is based on modeling an unfolded protein as a Gaussian chain. After sampling over all conformations, the electrostatic interaction energy between two charged residues (separated by l peptide bonds) is given by W = 332(6/pi)(1/2)[1 - pi(1/2)xexp(x(2))erfc(x)]/epsilond, where d = bl(1/2) + s and x = kappad/6(1/2). In unfolded barnase, the residual interactions lead to downward pK(a) shifts of approximately 0.33 unit, in agreement with experiment. pK(a) shifts in the unfolded state significantly affect pH dependence of protein folding stability, and the predicted effects agree very well with experimental results on barnase and four other proteins. For T4 lysozyme, the charge reversal mutation K147E is found to stabilize the unfolded state even more than the folded state (1.39 vs. 0.46 kcal/mol), leading to the experimentally observed result that the mutation is net destabilizing for the folding. The Gaussian-chain model provides a quantitative characterization of the unfolded state and may prove valuable for elucidating the energetic contributions to the stability of thermophilic proteins and the energy landscape of protein folding.     

Probing the salt bridge in the dihydrofolate reductase-methotrexate complex by using the coordinate-coupled free-energy perturbation method.

The importance of the ionic interaction due to the formation of the salt bridge between the Asp-27 and the pteridine ring in Escherichia coli dihydrofolate reductase-methotrexate complex has been studied by using the free-energy perturbation method. The calculation suggests that the ion-pair contribution to the binding energy is insignificant, as the enzyme surroundings do not stabilize the salt bridge to the extent of the desolvation of the charged groups. The activation barrier for the proton exchange between the pteridine ring and the Asp-27 is calculated to be 20.1 kcal/mol (1 cal = 4.184 J) by using the coordinate-coupled perturbation method, implying that this may be a channel to the proton exchange from the pteridine ring to the solvent. The Gibbs-energy difference of binding between the Asn-27 and Ser-27 is calculated to be 3.2 kcal/mol and is mainly due to the electrostatic interactions.     

Binding of buried structural water increases the flexibility of proteins.

Water deeply buried in proteins is considered to be an integral part of the folded structure. Such structural water molecules make strong H bonds with polar groups of the surrounding protein and therefore are believed to tighten the protein matrix. Surprisingly, our computational analysis of the binding of a buried water molecule to bovine pancreatic trypsin inhibitor shows that the protein actually becomes more flexible, as revealed by an increase in the vibrational entropy. We find that this effect must be common in proteins, because the large entropic cost of immobilizing a single water molecule [-TDeltaS = 20.6 kcal/mol (1 kcal = 4.18 kJ) for the lost translational and rotational degrees of freedom] can only be partly compensated by water-protein interactions, even when they are nearly perfect, as in the case of bovine pancreatic trypsin inhibitor (DeltaE = -19.8 kcal/mol), leaving no room for a further decrease in entropy from protein tightening. This study illustrates the importance of considering changes in protein flexibility (which in this case favor binding by 3.5 kcal/mol) for the prediction of ligand binding affinities.     

Why do A.T base pairs inhibit Z-DNA formation?

We have carried out free energy perturbation calculations on DNA double-stranded hexanucleotides. The sequence d(CGCGCG)2 has been "mutated" into d(CGTGCG).d(CGCACG) with the oligonucleotide in the A, B, and Z structural forms, both in vacuo and in aqueous solution. In addition, model free energy calculations have been carried out in which the electrostatic charges of the H-bonding groups of the bases in the major and minor grooves of the DNA are reduced to zero as a way of assessing the relative solvation effects of these groups in the different structural forms of DNA. Finally, energy component analyses have been carried out to assess the relative roles of different intranucleotide interactions on the B----Z equilibrium as a function of base sequence. In vacuo, the free energy for changing a G.C to an A.T base pair is largest in the Z conformation; in the A and B conformations, the free energy cost is approximately 2 kcal/mol lower (1 cal = 4.184 J). The results are similar when the simulations are run in explicit solvent: the change costs 3 kcal/mol more in the Z conformation than in the B form. These results are consistent with experimental data, where it is clear that A.T sequences are significantly more "Z-phobic" than G.C sequences. The calculations indicate that both intranucleotide and solvation interactions contribute to this Z-phobicity.     

Intrinsic backbone preferences are fully present in blocked amino acids

The preferences of amino acid residues for ,psi backbone angles vary strikingly among the amino acids, as shown by the backbone angle found from the (3)J(H(alpha),H(N)) coupling constant for short peptides in water. New data for the (3)J(H(alpha),H(N)) values of blocked amino acids (dipeptides) are given here. Dipeptides exhibit the full range of coupling constants shown by longer peptides such as GGXGG and dipeptides present the simplest system for analyzing backbone preferences. The dipeptide coupling constants are surprisingly close to values computed from the coil library (conformations of residues not in helices and not in sheets). Published coupling constants for GGXGG peptides agree closely with dipeptide values for all nonpolar residues and for some polar residues but not for X = D, N, T, and Y, which are probably affected by polar side chain-backbone interactions in GGXGG peptides. Thus, intrinsic backbone preferences are already determined at the dipeptide level and remain almost unchanged in GGXGG peptides and are strikingly similar in the coil library of conformations from protein structures. The simplest explanation for the backbone preferences is that backbone conformations are strongly affected by electrostatic dipole-dipole interactions in the peptide backbone and by screening of these interactions with water, which depends on nearby side chains. Strong backbone electrostatic interactions occur in dipeptides. This is shown by calculations both of backbone electrostatic energy for different conformers of the alanine dipeptide in the gas phase and by electrostatic solvation free energies of amino acid dipeptides.     

Electrostatic field around cytochrome c: theory and energy transfer experiment.

Energy transfer in the "rapid diffusion" limit from electronically excited terbium(III) chelates in three different charge states to horse heart ferricytochrome c was measured as a function of ionic strength. Theoretical rate constants calculated by numerical integration of the Forster integral (containing the Poisson-Boltzmann-generated protein electrostatic potential) were compared with the experimental data to evaluate the accuracy of protein electrostatic field calculations at the protein/solvent interface. Two dielectric formalisms were used: a simple coulombic/Debye-Hückel procedure and a finite difference method [Warwicker, J. & Watson, H. C. (1982) J. Mol. Biol. 157, 671-679] that accounts for the low-dielectric protein interior and the irregular protein/solvent boundary. Good agreement with experiment was obtained and the ionic-strength dependence of the reaction was successfully reproduced. The sensitivity of theoretical rate constants to the choices of effective donor sphere size and the energy transfer distance criterion was analyzed. Electrostatic potential and rate-constant calculations were carried out on sets of structures collected along two molecular dynamics trajectories of cytochrome c. Protein conformational fluctuations were shown to produce large variations in the calculated energy transfer rate constant. We conclude that protein fluctuations and the resulting transient structures can play significant roles in biological or catalytic activities that are not apparent from examination of a static structure. For calculating protein electrostatics, large-scale low-frequency conformational fluctuations, such as charged side-chain reorientation, are established to be as important as the computational method for incorporating dielectric boundary effects.     

Protein contents in biological membranes can explain abnormal solvation of charged and polar residues

Transmembrane helices are generally believed to insert into membranes based on their hydrophobicity. Nevertheless, there are important exceptions where polar residues have great functional importance, for instance the S4 helix of voltage-gated ion channels. It has been shown experimentally that insertion can be accomplished by hydrophobic counterbalance, predicting an arginine insertion cost of only 2.5 kcal/mol, compared with 14.9 kcal/mol in cyclohexane. Previous simulations of pure bilayers have produced values close to the pure hydrocarbon, which has lead to spirited discussion about the experimental conditions. Here, we have performed computer simulations of models better mimicking biological membranes by explicitly including protein helices at mass fractions from 15% to 55%, as well as an actual translocon. This has a striking effect on the solvation free energy of arginine. With some polar residues present, the solvation cost comes close to experimental observation at approximately 30% mass fraction, and negligible at 40%. In the presence of a translocon in the membrane, the cost of inserting arginine next to the lateral gate can be as low as 3–5 kcal/mol. The effect is mainly due to the extra helices making it easier to retain hydration water. These results offer a possible explanation for the discrepancy between the in vivo hydrophobicity scale and computer simulations and highlight the importance of the high protein contents in membranes. Although many membrane proteins are stable in pure bilayers, such simplified models might not be sufficiently accurate for insertion of polar or charged residues in biological membranes.     

On the thermodynamic stability of a charged arginine side chain in a transmembrane helix

Biological membranes consist of bilayer arrangements of lipids forming a hydrophobic core that presents a physical barrier to all polar and charged molecules. This long-held notion has recently been challenged by biological translocon-based experiments that report small apparent free energies to insert charged side chains near the center of a transmembrane (TM) helix. We have carried out fully atomistic simulations to provide the free-energy profile for moving a TM helix containing a protonated Arg side chain across a lipid bilayer. Our results reveal the fundamental thermodynamics governing the stability of charged side chains in membranes and the microscopic interactions involved. Despite local membrane deformations, where large amounts of water and lipid head groups are pulled into the bilayer to interact with Arg, the free-energy barrier is 17 kcal/mol. We provide a rationale for the differences in our microscopic free energies and cell biological experiments using free-energy calculations that indicate that a protonated Arg at the central residue of a TM helix of the Leader peptidase might reside close to the interface and not at the membrane center. Our findings have implications for the gating mechanisms of voltage-gated ion channels, suggesting that movements of protonated Arg residues through the membrane will be prohibited.     

Effect of charge,hydrophobicity, and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex

The molecular structure of the yeast nuclear pore complex (NPC) and the translocation of model particles have been studied with a molecular theory that accounts for the geometry of the pore and the sequence and anchoring position of the unfolded domains of the nucleoporin proteins (the FG-Nups), which control selective transport through the pore. The theory explicitly models the electrostatic, hydrophobic, steric, conformational, and acid-base properties of the FG-Nups. The electrostatic potential within the pore, which arises from the specific charge distribution of the FG-Nups, is predicted to be negative close to pore walls and positive along the pore axis. The positive electrostatic potential facilitates the translocation of negatively charged particles, and the free energy barrier for translocation decreases for increasing particle hydrophobicity. These results agree with the experimental observation that transport receptors that form complexes with hydrophilic/neutral or positively charged proteins to transport them through the NPC are both hydrophobic and strongly negatively charged. The molecular theory shows that the effects of electrostatic and hydrophobic interactions on the translocating potential are cooperative and nonequivalent due to the interaction-dependent reorganization of the FG-Nups in the presence of the translocating particle. The combination of electrostatic and hydrophobic interactions can give rise to complex translocation potentials displaying a combination of wells and barriers, in contrast to the simple barrier potential observed for a hydrophilic/neutral translocating particle. This work demonstrates the importance of explicitly considering the amino acid sequence and hydrophobic, electrostatic, and steric interactions in understanding the translocation through the NPC.     

A free-energy perturbation study of the binding of methotrexate to mutants of dihydrofolate reductase.

The importance of hydrophobic residues to the binding of methotrexate in the active site of dihydrofolate reductase (EC 1.5.1.3) was examined by a free-energy perturbation method. The replacement of a strictly conserved residue, Phe-31, by tyrosine or valine costs 1.8 and 5.1 kcal/mol, respectively, to the binding of the drug (1 cal = 4.184 J). In the case of the Phe31----Tyr mutation, the loss of the binding energy is due to the desolvation of the phenolic group; in the case of Phe31----Val mutation, it is mainly due to the loss of the interaction with the drug. The replacement of Leu-54 by glycine decreases the binding energy by 4.0 kcal/mol. A calculation on the mutation of Phe-31 to serine shows that the alteration could reduce the binding energy of methotrexate by 9.7 kcal/mol. The calculations clearly show that the hydrophobic interactions are as important as the hydrophilic ones in the binding of methotrexate.     

Calculation of protein-ligand binding free energy by using a polarizable potential

The binding of charged ligands benzamidine and diazamidine to trypsin was investigated by using a polarizable potential energy function and explicit-water molecular dynamics simulations. The binding free energies were computed from the difference between the free energies of decoupling the ligand from water and protein environments. Both the absolute and the relative free energies from the perturbation simulations agree with experimental measurements to within 0.5 kcal.mol(-1). Comparison of free-energy components sampled from different thermodynamic paths indicates that electrostatics is the main driving force behind benzamidine recognition of trypsin. The contribution of electronic polarization to binding appears to be crucial. By computing the free-energy contribution caused by the polarization between the ligand and its surroundings, we found that polarization has the opposite effect in dissimilar environments. Although polarization favors ligand solvation in water, it weakens the protein-ligand attraction by screening the electrostatic interaction between trypsin and benzamidine. We also examined the relative binding free energies of a benzamidine analog diazamidine to trypsin. The changes in free energy on benzamidine-diazamidine substitution were tens of kilocalories in both water and trypsin environments; however, the change in the total binding free energy is <2 kcal.mol(-1) because of cancellation, consistent with the experimental results. Overall, our results suggest that the use of a polarizable force field, given adequate sampling, is capable of achieving chemical accuracy in molecular simulations of protein-ligand recognition.     

Factors influencing redox potentials of electron transfer proteins.

The redox potentials of electron transfer proteins vary over a wide range, even when the type of redox center is the same. Rees [Proc. Natl. Acad. Sci. USA (1985) 82, 3082-3085] proposed that this variation of redox potential partly reflects the different net charges of the proteins, and he presented a linear correlation between these two properties for 36 proteins. A review of the factors that influence protein redox potentials makes it clear that this linear correlation is fortuitous. The key factors influencing redox potentials are the contributions to the Gibbs energy difference between the two redox states, resulting from bonding interactions at the redox center, electrostatic interactions between the redox-center charge and polar groups within the protein and solvent, and redox-state conformational changes. The relative importance of these terms is likely to vary from protein to protein.     

The proficiency of a thermophilic chorismate mutase enzyme is solely through an entropic advantage in the enzyme reaction

A study of the Thermus thermophilus chorismate mutase (TtCM) is described by using quantum mechanics (self-consistent-charge density-functional tight binding)/molecular mechanics, umbrella sampling, and the weighted histogram analysis method. The computed free energies of activation for the reactions in water and TtCM are comparable to the experimental values. The free energies for formation of near attack conformer have been determined to be 8.06 and 0.05 kcal/mol in water and TtCM, respectively. The near attack conformer stabilization contributes approximately 90% to the proficiency of the enzymatic reaction compared with the reaction in water. The transition state (TS) structures and partial atom charges are much the same in the enzymatic and water reactions. The difference in the electrostatic interactions of Arg-89 with O13 in the enzyme-substrate complex and enzyme-TS complex provides the latter with but 0.55 kcal/mol of 1.92 kcal/mol total TS stabilization. Differences in electrostatic interactions between components at the active site in the enzyme-substrate complex and enzyme-TS complex are barely significant, such that TS stabilization is of minor importance and the enzymatic catalysis is through an entropic advantage.     

In-silico modelling and identification of a possible inhibitor of H1N1 virus

ObjectiveTo find the neuraminidase H1N1 inhibition potential of 4-hydroxypanduratin A and its derivatives along with associated binding mechanism through virtual screening and molecular docking.MethodsInitially, the structural templates for neuraminidase proteins were identified from structural database using homology search and performed homology and ab initio modeling to predict native 3D structure using Modeller 9.10 and I-TASSER server, respectively. The reliability of the three-dimensional models was validated using Ramachandran plot. The molecular docking was performed using Autodcok 4.2 and molecular interactions were analyzed through PyMol, Chimera and LigPlot.ResultsThe neuraminidase protein sequences of ADH29478, ADD85918, AEM62864 (2009) and AFO38701 (2011) from India were modeled and validated. 4-hydroxypanduratin A and its 88 derivatives were docked in to active binding pockets of neuraminidase. The guanidine group of residues Arg152 and Trp179 of ADH29478 (Chennai) and AFO38701 (Gwalior) neuraminidase models present in the hydrophilic domain (-OH and =O groups) was found to have molecular interactions with high binding affinities of −7.40 kcal/mol and −8.66 kcal/mol, respectively to 1-(2,4-dihydroxyphenyl)-3,3-diphenylpropan-1-one (CID: 19875815) than other FDA approved drugs such as oseltamivir, zana-mivir, and peramivir.Conclusions1-(2,4-dihydroxyphenyl)-3,3-diphenylpropan-1-one will be a breakthrough for further drug development against swine flu.