Poisson-Boltzmann analysis of the lambda repressor-operator interaction

Sensitivities to parameterization in the size-modified Poisson-Boltzmann equation

Experimental results have demonstrated that the numbers of counterions surrounding nucleic acids differ from those predicted by the nonlinear Poisson-Boltzmann equation, NLPBE. Some studies have fit these data against the ion size in the size-modified Poisson-Boltzmann equation, SMPBE, but the present study demonstrates that other parameters, such as the Stern layer thickness and the molecular surface definition, can change the number of bound ions by amounts comparable to varying the ion size. These parameters will therefore have to be fit simultaneously against experimental data. In addition, the data presented here demonstrate that the derivative, SK, of the electrostatic binding free energy, ΔGel, with respect to the logarithm of the salt concentration is sensitive to these parameters, and experimental measurements of SK could be used to parameterize the model. However, although better values for the Stern layer thickness and ion size and better molecular surface definitions could improve the model's predictions of the numbers of ions around biomolecules and SK, ΔGel itself is more sensitive to parameters, such as the interior dielectric constant, which in turn do not significantly affect the distributions of ions around biomolecules. Therefore, improved estimates of the ion size and Stern layer thickness to use in the SMPBE will not necessarily improve the model's predictions of ΔGel.

Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes

The predictions of the derivative of the electrostatic binding free energy of a biomolecular complex, ΔG(el), with respect to the logarithm of the 1:1 salt concentration, d(ΔG(el))/d(ln[NaCl]), SK, by the Poisson-Boltzmann equation, PBE, are very similar to those of the simpler Debye-Hückel equation, DHE, because the terms in the PBE's predictions of SK that depend on the details of the dielectric interface are small compared to the contributions from long-range electrostatic interactions. These facts allow one to obtain predictions of SK using a simplified charge model along with the DHE that are highly correlated with both the PBE and experimental binding data. The DHE-based model developed here, which was derived from the generalized Born model, explains the lack of correlation between SK and ΔG(el) in the presence of a dielectric discontinuity, which conflicts with the popular use of this supposed correlation to parse experimental binding free energies into electrostatic and nonelectrostatic components. Moreover, the DHE model also provides a clear justification for the correlations between SK and various empirical quantities, like the number of ion pairs, the ligand charge on the interface, the Coulomb binding free energy, and the product of the charges on the complex's components, but these correlations are weak, questioning their usefulness.

Facilitated DNA search by multidomain transcription factors: cross talk via a flexible linker

More than 70% of eukaryotic proteins are composed of multiple domains. However, most studies of the search for DNA focus on individual protein domains and do not consider potential cross talk within a multidomain transcription factor. In this study, the molecular features of the DNA search mechanism were explored for two multidomain transcription factors: human Pax6 and Oct-1. Using a simple computational model, we compared a DNA search of multidomain proteins with a search of isolated domains. Furthermore, we studied how manipulating the binding affinity of a single domain to DNA can affect the overall DNA search of the multidomain protein. Tethering the two domains via a flexible linker increases their affinity to the DNA, resulting in a higher propensity for sliding along the DNA, which is more significant for the domain with the weaker DNA-binding affinity. In this case, the domain that binds DNA more tightly anchors the multidomain protein to the DNA and, via the linker, increases the local concentration of the weak DNA-binding domain (DBD). The tethered domains directly exchange between two parallel DNA molecules via a bridged intermediate, where intersegmental transfer is promoted by the weaker DBD. We found that, in general, the relative affinity of the two domains can significantly affect the cross talk between them and thus their overall capability to search DNA efficiently. The results we obtained by examining various multidomain DNA-binding proteins support the necessity of discrepancies between the DNA-binding affinities of the constituent domains.

Electrostatic similarity of proteins: application of three dimensional spherical harmonic decomposition

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson-Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features.

How RNA unfolds and refolds

Understanding how RNA folds and what causes it to unfold has become more important as knowledge of the diverse functions of RNA has increased. Here we review the contributions of single-molecule experiments to providing answers to questions such as: How much energy is required to unfold a secondary or tertiary structure? How fast is the process? How do helicases unwind double helices? Are the unwinding activities of RNA-dependent RNA polymerases and of ribosomes different from other helicases? We discuss the use of optical tweezers to monitor the unfolding activities of helicases, polymerases, and ribosomes, and to apply force to unfold RNAs directly. We also review the applications of fluorescence and fluorescence resonance energy transfer to measure RNA dynamics.

Evaluation of electrostatic interactions

Described here are several computational procedures for the analysis of electrostatic interactions in molecular complexes, all based on a continuum model of solvation. The first section describes how to compute the residual potential, a measure of how electrostatically complementary a ligand is for its receptor. The second procedure describes electrostatic component analysis, a method by which the electrostatic contribution to the binding free energy can be broken up into terms directly attributable to individual chemical groups. Finally, electrostatic affinity optimization is described. This procedure is particularly useful in determining what portions of a ligand are the most suboptimal, and thus provide the greatest opportunity for the design of improvements.

Identification of DNA-binding protein target sequences by physical effective energy functions: free energy analysis of lambda repressor-DNA complexes

Background

Specific binding of proteins to DNA is one of the most common ways gene expression is controlled. Although general rules for the DNA-protein recognition can be derived, the ambiguous and complex nature of this mechanism precludes a simple recognition code, therefore the prediction of DNA target sequences is not straightforward. DNA-protein interactions can be studied using computational methods which can complement the current experimental methods and offer some advantages. In the present work we use physical effective potentials to evaluate the DNA-protein binding affinities for the λ repressor-DNA complex for which structural and thermodynamic experimental data are available.

Results

The binding free energy of two molecules can be expressed as the sum of an intermolecular energy (evaluated using a molecular mechanics forcefield), a solvation free energy term and an entropic term. Different solvation models are used including distance dependent dielectric constants, solvent accessible surface tension models and the Generalized Born model. The effect of conformational sampling by Molecular Dynamics simulations on the computed binding energy is assessed; results show that this effect is in general negative and the reproducibility of the experimental values decreases with the increase of simulation time considered. The free energy of binding for non-specific complexes, estimated using the best energetic model, agrees with earlier theoretical suggestions. As a results of these analyses, we propose a protocol for the prediction of DNA-binding target sequences. The possibility of searching regulatory elements within the bacteriophage λ genome using this protocol is explored. Our analysis shows good prediction capabilities, even in absence of any thermodynamic data and information on the naturally recognized sequence.

Conclusion

This study supports the conclusion that physics-based methods can offer a completely complementary methodology to sequence-based methods for the identification of DNA-binding protein target sequences.

GBr6NL: a generalized Born method for accurately reproducing solvation energy of the nonlinear Poisson-Boltzmann equation

The nonlinear Poisson-Boltzmann (NLPB) equation can provide accurate modeling of electrostatic effects for nucleic acids and highly charged proteins. Generalized Born methods have been developed to mimic the linearized Poisson-Boltzmann (LPB) equation at substantially reduced cost. The computer time for solving the NLPB equation is approximately fivefold longer than for the LPB equation, thus presenting an even greater obstacle. Here we present the first generalized Born method, GBr(6)NL, for mimicking the NLPB equation. GBr(6)NL is adapted from GBr(6), a generalized Born method recently developed to reproduce the solvation energy of the LPB equation [Tjong and Zhou, J. Phys. Chem. B 111, 3055 (2007)]. Salt effects predicted by GBr(6)NL on 55 proteins overall deviate from NLPB counterparts by 0.5 kcal/mol from ionic strengths from 10 to 1000 mM, which is approximately 10% of the average magnitudes of the salt effects. GBr(6)NL predictions for the salts effects on the electrostatic interaction energies of two protein:RNA complexes are very promising.

Do electrostatic interactions destabilize protein-nucleic acid binding?

The negatively charged phosphates of nucleic acids are often paired with positively charged residues upon binding proteins. It was thus counter-intuitive when previous Poisson-Boltzmann (PB) calculations gave positive energies from electrostatic interactions, meaning that they destabilize protein-nucleic acid binding. Our own PB calculations on protein-protein binding have shown that the sign and the magnitude of the electrostatic component are sensitive to the specification of the dielectric boundary in PB calculations. A popular choice for the boundary between the solute low dielectric and the solvent high dielectric is the molecular surface; an alternative is the van der Waals (vdW) surface. In line with results for protein-protein binding, in this article, we found that PB calculations with the molecular surface gave positive electrostatic interaction energies for two protein-RNA complexes, but the signs are reversed when the vdW surface was used. Therefore, whether destabilizing or stabilizing effects are predicted depends on the choice of the dielectric boundary. The two calculation protocols, however, yielded similar salt effects on the binding affinity. Effects of charge mutations differentiated the two calculation protocols; PB calculations with the vdW surface had smaller deviations overall from experimental data.

Poisson-Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies

The salt dependence of the binding free energy of five protein-protein hetero-dimers and two homo-dimers/tetramers was calculated from numerical solutions to the Poisson-Boltzmann equation. Overall, the agreement with experimental values is very good. In all cases except one involving the highly charged lactoglobulin homo-dimer, increasing the salt concentration is found both experimentally and theoretically to decrease the binding affinity. To clarify the source of salt effects, the salt-dependent free energy of binding is partitioned into screening terms and to self-energy terms that involve the interaction of the charge distribution of a monomer with its own ion atmosphere. In six of the seven complexes studied, screening makes the largest contribution but self-energy effects can also be significant. The calculated salt effects are found to be insensitive to force-field parameters and to the internal dielectric constant assigned to the monomers. Nonlinearities due to high charge densities, which are extremely important in the binding of proteins to negatively charged membrane surfaces and to nucleic acids, make much smaller contributions to the protein-protein complexes studied here, with the exception of highly charged lactoglobulin dimers. Our results indicate that the Poisson-Boltzmann equation captures much of the physical basis of the nonspecific salt dependence of protein-protein complexation.

Interactions of cationic ligands and proteins with small nucleic acids: analytic treatment of the large coulombic end effect on binding free energy as a function of salt concentration

For nonspecific binding of oligopeptides and other cationic ligands, including proteins, to nucleic acid oligomers, we develop a model capable of quantifying and predicting the salt concentration dependence of the binding free energy (deltaG(o)obs) by way of an analytic treatment of the Coulombic end effect (CEE). Ligands, nucleic acids, and their complexes (species j of valence Zj) are modeled as finite lattices with absolute value(Zj) charged residues; the CEE is quantified by its characteristic length Ne (specified in charged residues) and its consequences for the free energy and ion association of the oligomer. Expressions are developed for the individual site binding constants Ki as a function of position (site number i) of a bound ligand on a nucleic acid and for the observed binding constant Kobs as an ensemble average of Ki. Analysis of deltaG(o)obs = -RT ln Kobs and Sa Kobs identical with (partial differential ln Kobs)/(partial differential ln a(+/-)) for binding of the oligopeptide KWK6 (ZL = +8) to single-stranded (ss) dT(pdT)(absolute value(ZD) oligomers (dT-mers) where ZD = {-6, -10, -11, -14, -15} in the range 0.1-0.25 M Na+ yields Ne = 9.0 +/- 0.8 residues at each end, demonstrating that both KWK6 and the above dT-mers are sufficiently short so that the CEE extends over the entire molecule. The dependences of Kobs and of Sa Kobs on absolute value(ZD) for a given ZL are determined by the difference between 2Ne and the net number of charged residues Q in the complex (Q identical with absolute value(ZD) - ZL). For Q < 2Ne, characteristic of complexes of KWK6 with this set of dT-mers, the distribution of binding free energies deltaG(o)obs = -RT ln Ki for sites along the DNA oligomer is parabolic, and Kobs and Sa Kobs are strongly dependent on absolute value(ZD). For Q > or = 2Ne, the distribution of binding free energies deltaG(o)obs is trapezoidal, and the dependence of Kobs and Sa Kobs on absolute value(ZD) is weaker. Application of the model to nonspecific binding of human DNA polymerase beta to ssDNA demonstrates the significance of the CEE in determining Kobs and Sa Kobs of binding of a cationic site on a protein to a DNA oligomer.

Direct Observation of Salt Effects on Molecular Interactions through Explicit-Solvent Molecular Dynamics Simulations: Differential Effects on Electrostatic and Hydrophobic Interactions and Comparisons to Poisson−Boltzmann Theory

Proteins and other biomolecules function in cellular environments that contain significant concentrations of dissolved salts and even simple salts such as NaCl can significantly affect both the kinetics and thermodynamics of macromolecular interactions. As one approach to directly observing the effects of salt on molecular associations, explicit-solvent molecular dynamics (MD) simulations have been used here to model the association of pairs of the amino acid analogues acetate and methylammonium in aqueous NaCl solutions of concentrations 0, 0.1, 0.3, 0.5, 1, and 2 M. By performing simulations of 500 ns duration for each salt concentration properly converged estimates of the free energy of interaction of the two molecules have been obtained for all intermolecular separation distances and geometries. The resulting free energy surfaces are shown to give significant new insights into the way salt modulates interactions between molecules containing both charged and hydrophobic groups and are shown to provide valuable new benchmarks for testing the description of salt effects provided by the simpler but faster Poisson-Boltzmann method. In addition, the complex many-dimensional free energy surfaces are shown to be decomposable into a number of one-dimensional effective energy functions. This decomposition (a) allows an unambiguous view of the qualitative differences between the salt dependence of electrostatic and hydrophobic interactions, (b) gives a clear rationalization for why salt exerts different effects on protein-protein association and dissociation rates, and (c) produces simplified energy functions that can be readily used in much faster Brownian dynamics simulations.

Structure of the central hub of bacteriophage Mu baseplate determined by X-ray crystallography of gp44

Bacteriophage Mu is a double-stranded DNA phage that consists of an icosahedral head, a contractile tail with baseplate and six tail fibers, similar to the well-studied T-even phages. The baseplate of bacteriophage Mu, which recognizes and attaches to a host cell during infection, consists of at least eight different proteins. The baseplate protein, gp44, is essential for bacteriophage Mu assembly and the generation of viable phages. To investigate the role of gp44 in baseplate assembly and infection, the crystal structure of gp44 was determined at 2.1A resolution by the multiple isomorphous replacement method. The overall structure of the gp44 trimer is similar to that of the T4 phage gp27 trimer, which forms the central hub of the T4 baseplate, although these proteins share very little primary sequence homology. Based on these data, we confirm that gp44 exists as a trimer exhibiting a hub-like structure with an inner diameter of 25A through which DNA can presumably pass during infection. The molecular surface of the gp44 trimer that abuts the host cell membrane is positively charged, and it is likely that Mu phage interacts with the membrane through electrostatic interactions mediated by gp44.

Predicting interactions of winged-helix transcription factors with DNA

Determining protein-DNA interactions is important for understanding gene regulation, DNA repair and chromatin structure. Unfortunately, the structures of DNA-bound complexes are often difficult to obtain experimentally, so the development of computational methods that provide good models of these complexes would be valuable. Here, we present a rigid-body docking approach using the computer program DOT. DOT performs a complete, six-dimensional search of all orientations for two rigid molecules and calculates the interaction energy as the sum of electrostatic and van der Waals terms. DOT was applied to three winged-helix transcription factors that share similar DNA-binding structural motifs but bind DNA in different ways. Docking with linear B-form DNA models accomplished several objectives; it (1) distinguished the different ways the transcription factors bind DNA, (2) identified each protein's DNA-binding site and the DNA orientation at the site and (3) gave at least one solution among the three best-ranked that shows the protein side chain-DNA base interactions responsible for recognition. Furthermore, the ensemble of top-ranked, docked linear B-DNA fragments indicated the DNA bending induced upon protein binding. Docking linear B-DNA to structures of the transcription factor FadR suggests that the allosteric, conformational change induced upon effector binding results in loss of the ability to bend DNA as well as loss of sequence-specific interactions with DNA. The electrostatic energy term calculated by DOT is comparable to the electrostatic binding energy calculated by Poisson-Boltzmann methods. Our results show rigid-body docking that includes a rigorous treatment of the electrostatic interaction energy can be effective in predicting protein-DNA interactions.

Molecular Basis of Box C/D RNA-Protein Interactions

We have determined and refined a crystal structure of the initial assembly complex of archaeal box C/D sRNPs comprising the Archaeoglobus fulgidus (AF) L7Ae protein and a box C/D RNA. The box C/D RNA forms a classical kink-turn (K-turn) structure and the resulting protein-RNA complex serves as a distinct platform for recruitment of the fibrillarin-Nop5p complex. The cocrystal structure confirms previously proposed secondary structure of the box C/D RNA that includes a protruded U, a UU mismatch, and two sheared tandem GA base pairs. Detailed structural comparisons of the AF L7Ae-box C/D RNA complex with previously determined crystal structures of L7Ae homologs in complex with functionally distinct K-turn RNAs revealed a set of remarkably conserved principles in protein-RNA interactions. These analyses provide a structural basis for interpreting the functional roles of the box C/D sequences in directing specific assembly of box C/D sRNPs.

Structure-based prediction of DNA-binding sites on proteins Using the empirical preference of electrostatic potential and the shape of molecular surfaces

Protein-DNA interactions play an essential role in the genetic activities of life. Many structures of protein-DNA complexes are already known, but the common rules on how and where proteins bind to DNA have not emerged. Many attempts have been made to predict protein-DNA interactions using structural information, but the success rate is still about 80%. We analyzed 63 protein-DNA complexes by focusing our attention on the shape of the molecular surface of the protein and DNA, along with the electrostatic potential on the surface, and constructed a new statistical evaluation function to make predictions of DNA interaction sites on protein molecular surfaces. The shape of the molecular surface was described by a combination of local and global average curvature, which are intended to describe the small convex and concave and the large-scale concave curvatures of the protein surface preferentially appearing at DNA-binding sites. Using these structural features, along with the electrostatic potential obtained by solving the Poisson-Boltzmann equation numerically, we have developed prediction schemes with 86% and 96% accuracy for DNA-binding and non-DNA-binding proteins, respectively.

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.

Energetic and structural considerations for the mechanism of protein sliding along DNA in the nonspecific BamHI-DNA complex

The molecular mechanism by which DNA-binding proteins find their specific binding sites is still unclear. To gain insights into structural and energetic elements of this mechanism, we used the crystal structure of the nonspecific BamHI-DNA complex as a template to study the dominant electrostatic interaction in the nonspecific association of protein with DNA, and the possible sliding pathways that could be sustained by such an interaction. Based on calculations using the nonlinear Poisson-Boltzmann method and Brownian dynamics, a model is proposed for the initial nonspecific binding of BamHI to B-form DNA that differs from that seen in the crystal structure of the nonspecific complex. The model is electrostatically favorable, and the salt dependence as well as other thermodynamic parameters calculated for this model are in good agreement with experimental results. Several residues in BamHI are identified for their important contribution to the energy in the nonspecific binding model, and specific mutagenesis experiments are proposed to test the model on this basis. We show that a favorable sliding pathway of the protein along DNA is helical.

Association of protein-DNA recognition complexes: electrostatic and nonelectrostatic effects

In this study the electrostatic and nonelectrostatic contributions to the binding free energy of a number of different protein-DNA recognition complexes are investigated. To determine the electrostatic effects in the protein-DNA association the Poisson-Boltzmann approach was applied. Overall the salt-dependent electrostatic free energy opposed binding in all protein-DNA complexes except one, and the salt-independent electrostatic contribution favored binding in more than half of the complexes. Further the salt-dependent electrostatic free energy increased with higher ionic concentrations and therefore complex association is stronger opposed at higher ionic concentrations. The hydrophobic effect in the protein-DNA complexes was determined from the buried accessible surface area and the surface tension. A majority of the complexes showed more polar than nonpolar buried accessible surface area. Interestingly the buried DNA-accessible surface area was preferentially hydrophilic, only in one complex a slightly more hydrophobic buried accessible surface area was observed. A quite sophisticated balance between several different free energy components seems to be responsible for determining the free energy of binding in protein-DNA systems.

Brownian dynamics simulations of the recognition of the scorpion toxin maurotoxin with the voltage-gated potassium ion channels

The recognition of the scorpion toxin maurotoxin (MTX) by the voltage-gated potassium (Kv1) channels, Kv1.1, Kv1.2, and Kv1.3, has been studied by means of Brownian dynamics (BD) simulations. All of the 35 available structures of MTX in the Protein Data Bank (http://www.rcsb.org/pdb) determined by nuclear magnetic resonance were considered during the simulations, which indicated that the conformation of MTX significantly affected both the recognition and the binding between MTX and the Kv1 channels. Comparing the top five highest-frequency structures of MTX binding to the Kv1 channels, we found that the Kv1.2 channel, with the highest docking frequencies and the lowest electrostatic interaction energies, was the most favorable for MTX binding, whereas Kv1.1 was intermediate, and Kv1.3 was the least favorable one. Among the 35 structures of MTX, the 10th structure docked into the binding site of the Kv1.2 channel with the highest probability and the most favorable electrostatic interactions. From the MTX-Kv1.2 binding model, we identified the critical residues for the recognition of these two proteins through triplet contact analyses. MTX locates around the extracellular mouth of the Kv1 channels, making contacts with its beta-sheets. Lys23, a conserved amino acid in the scorpion toxins, protrudes into the pore of the Kv1.2 channel and forms two hydrogen bonds with the conserved residues Gly401(D) and Tyr400(C) and one hydrophobic contact with Gly401(C) of the Kv1.2 channel. The critical triplet contacts for recognition between MTX and the Kv1.2 channel are Lys23(MTX)-Asp402(C)(Kv1), Lys27(MTX)-Asp378(D)(Kv1), and Lys30(MTX)-Asp402(A)(Kv1). In addition, six hydrogen-bonding interactions are formed between residues Lys23, Lys27, Lys30, and Tyr32 of MTX and residues Gly401, Tyr400, Asp402, Asp378, and Thr406 of Kv1.2. Many of them are formed by side chains of residues of MTX and backbone atoms of the Kv1.2 channel. Five hydrophobic contacts exist between residues Pro20, Lys23, Lys30 and Tyr32 of MTX and residues Asp402, Val404, Gly401, and Arg377 of the Kv1.2 channel. The simulation results are in agreement with the previous molecular biology experiments and explain the binding phenomena between MTX and Kv1 channels at the molecular level. The consistency between the results of the BD simulations and the experimental data indicated that our three-dimensional model of the MTX-Kv1.2 channel complex is reasonable and can be used in additional biological studies, such as rational design of novel therapeutic agents blocking the voltage-gated channels and in mutagenesis studies in both the toxins and the Kv1 channels. In particular, both the BD simulations and the molecular mechanics refinements indicate that residue Asp378 of the Kv1.2 channel is critical for its recognition and binding functionality toward MTX. This phenomenon has not been appreciated in the previous mutagenesis experiments, indicating this might be a new clue for additional functional study of Kv1 channels.

Brownian dynamics simulations of the recognition of the scorpion toxin P05 with the small-conductance calcium-activated potassium channels

The recognition of the scorpion toxin P05 and the small-conductance, calcium-activated potassium (SK) channels, rsk1, rsk2, and rsk3, has been studied by means of the Brownian dynamics (BD) method. All of the 25 available structures of P05 in the RCSB Protein Data Bank determined by NMR were considered during the simulation, which indicated that the conformation of P05 affects both the recognition and binding between the two proteins significantly. Comparing the top four high-frequency structures of P05 binding to the SK channels, we found that the rsk2 channel, with high frequencies and lowest electrostatic interaction energies (E (int)(ES)), is the most favorable for P05 binding, while rsk3 is intermediate, and rsk1 is the least favorable. Among the 25 structures of P05, the 13th structure docks into the binding site of the rsk2 channel with the highest probability and most favorable electrostatic interactions. From the P05-rsk2 channel binding model, we identified the residues critical for the recognition of these two proteins through triplet contact analyses. P05 locates around the extracellular mouth of the SK channels and contacts the SK channels using its alpha-helix rather than beta-sheets. The critical triplet contacts for recognition between P05 and the rsk2 channel are Arg6 (P05)-Asp364 (SK), Arg7 (P05)-Asn368 (SK), and Arg13 (P05)-Asp341 (SK). The structure of the P05-rsk2 complex with the most favorable electrostatic interaction energy was further refined by molecular mechanics, showing that six hydrogen bonding interactions exist between P05 and the rsk2 channel: one hydrogen bond is formed between Arg6 (P05) and Asp364(D) (rsk2); Arg7 (P05) forms three hydrogen bonds with Asp341(B) (rsk2)) and Asp364(C) (rsk2); two hydrogen bonds are formed by Arg13 (P05) with Asp341(A) (rsk2) and Asp364(B) (rsk2). The simulation results are in good agreement with the previous molecular biological experiments and can explain the binding phenomena between P05 and SK channels at the level of molecular structure. The consistency between the results of the BD simulations and the experimental data indicated that our 3D model of the P05-rsk2 channel complex is reasonable and can be employed in further biological studies, such as rational design of the novel therapeutic agents blocking the small-conductance, calcium-activated and apamin-sensitive potassium channels, and for mutagenesis studies in both toxins and SK channels. In particular, both the BD simulations and the molecular mechanics refinements indicate that residue Asp364 of the rsk2 channel is critical for its recognition and binding functionality towards P05. This phenomenon has not been appreciated in the previous mutagenesis experiments, indicating that this might be a new clue for further functional study of SK channels.

Free-energy component analysis of 40 protein-DNA complexes: a consensus view on the thermodynamics of binding at the molecular level

Noncovalent association of proteins to specific target sites on DNA--a process central to gene expression and regulation--has thus far proven to be idiosyncratic and elusive to generalizations on the nature of the driving forces. The spate of structural information on protein--DNA complexes sets the stage for theoretical investigations on the molecular thermodynamics of binding aimed at identifying forces responsible for specific macromolecular recognition. Computation of absolute binding free energies for systems of this complexity transiting from structural information is a stupendous task. Adopting some recent progresses in treating atomic level interactions in proteins and nucleic acids including solvent and salt effects, we have put together an energy component methodology cast in a phenomenological mode and amenable to systematic improvements and developed a computational first atlas of the free energy contributors to binding in approximately 40 protein-DNA complexes representing a variety of structural motifs and functions. Illustrating vividly the compensatory nature of the free energy components contributing to the energetics of recognition for attaining optimal binding, our results highlight unambiguously the roles played by packing, electrostatics including hydrogen bonds, ion and water release (cavitation) in protein-DNA binding. Cavitation and van der Waals contributions without exception favor complexation. The electrostatics is marginally unfavorable in a consensus view. Basic residues on the protein contribute favorably to binding despite the desolvation expense. The electrostatics arising from the acidic and neutral residues proves unfavorable to binding. An enveloping mode of binding to short stretches of DNA makes for a strong unfavorable net electrostatics but a highly favorable van der Waals and cavitation contribution. Thus, noncovalent protein-DNA association is a system-specific fine balancing act of these diverse competing forces. With the advances in computational methods as applied to macromolecular recognition, the challenge now seems to be to correlate the differential (initial vs. final) energetics to substituent effects in drug design and to move from affinity to specificity.

One nanosecond molecular dynamics simulation of the N-terminal domain of the lambda repressor protein

We have carried out molecular dynamics simulation of the N-terminal domain of the lambda repressor protein in a surrounding environment including explicit waters and ions. We observe two apparent dynamics substates in the nanosecond protein simulation, the transition occurring around 500 ps. The existence of these two apparent substates results from a high flexibility of the arm in each monomer, a relative flexibility of both arms with respect to each other, and a relative displacement of the recognition helices from 30 to 40 A of interhelical distance. Many amino acid residues, including those involved in DNA recognition, undergo a simultaneous transition in their side-chain conformations, consistent with the relationship between side-chain conformation and secondary structural elements, as observed in protein crystal structures. This result suggests plausible conformational changes experienced by the protein upon DNA binding. On the whole, the non-consensus monomer appears to be more flexible than its consensus counterpart.

Nuclear receptor-DNA binding specificity: A COMBINE and Free-Wilson QSAR analysis

Specific binding of transcription factors to DNA is crucial for gene regulation. We derived models for the binding specificity of transcription factors of the nuclear receptor family to DNA using two QSAR methods: a Free-Wilson-like method and COMparative BINding Energy (COMBINE) analysis. The analysis is based on experimental data for the interaction of 20 mutant glucocorticoid receptor DNA-binding domains with 16 different response elements in a total of 320 complexes (Zilliacus, J.; Wright, A. P.; Carlstedt-Duke, J.; Nilsson, L.; Gustafsson, J. A. Proteins 1995, 21, 57-67). The predictive abilities of the models obtained by the two methods are similar. The COMBINE analysis indicates that the most important properties for determining binding specificity for this dataset are the changes upon binding of the solvation free energies of the bases that are mutated in the dataset and the electrostatic interactions of the mutated nucleotides with certain charged amino acids. Further important descriptors are the changes of solvation free energy and surface area of the side chain of the mutated residue. It is clear, however, that there are additional features important for the specificity of binding that are not included in the models, such as differences in interfacial hydration of the complexes.

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr-Lys-Pro-Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson-Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed.

Electrostatic potentials of DNA. Comparative analysis of promoter and nonpromoter nucleotide sequences

Distribution of electrostatic potential of DNA fragments was evaluated. A method for calculation of electrostatic potential distribution based on Coulomb's law is proposed for long DNA fragments (approximately 1000 nucleotide pairs). For short DNA sequences, this technique provides a good correlation with the results obtained using Poisson-Boltzmann equation thus justifying its application in comparative studies for long DNA fragments. Calculation was performed for several DNA fragments from E. coli and bacteriophage T7 genomes containing promoter and nonpromoter regions. The results obtained indicate that coding regions are characterized by more homogeneous distribution of electrostatic potential whereas local inhomogeneity of DNA electrostatic profile is typical for promoter regions. The possible role of electrostatic interactions in RNA polymerase-promoter recognition is discussed.

Electrostatic potential of B-DNA: effect of interionic correlations

Modified Poisson-Boltzmann (MPB) equations have been numerically solved to study ionic distributions and mean electrostatic potentials around a macromolecule of arbitrarily complex shape and charge distribution. Results for DNA are compared with those obtained by classical Poisson-Boltzmann (PB) calculations. The comparisons were made for 1:1 and 2:1 electrolytes at ionic strengths up to 1 M. It is found that ion-image charge interactions and interionic correlations, which are neglected by the PB equation, have relatively weak effects on the electrostatic potential at charged groups of the DNA. The PB equation predicts errors in the long-range electrostatic part of the free energy that are only approximately 1.5 kJ/mol per nucleotide even in the case of an asymmetrical electrolyte. In contrast, the spatial correlations between ions drastically affect the electrostatic potential at significant separations from the macromolecule leading to a clearly predicted effect of charge overneutralization.

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.

Electrostatic contributions to heat capacity changes of DNA-ligand binding

Significant heat capacity changes (DeltaCp) often accompany protein unfolding, protein binding, and specific DNA-ligand binding reactions. Such changes are widely used to analyze contributions arising from hydrophobic and polar hydration. Current models relate the magnitude of DeltaCp to the solvent accessible surface area (ASA) of the molecule. However, for many binding systems-particularly those involving non-peptide ligands-these models predict a DeltaCp that is significantly different from the experimentally measured value. Electrostatic interactions provide a potential source of heat capacity changes and do not scale with ASA. Using finite-difference Poisson-Boltzmann methods (FDPB), we have determined the contribution of electrostatics to the DeltaCp associated with binding for DNA binding reactions involving the ligands DAPI, netropsin, lexitropsin, and the lambda repressor binding domain.

Electrostatic contributions to the stability of halophilic proteins

Examination of the first crystal structures of proteins from a halophilic organism suggests that an abundance of acidic residues distributed over the protein surface is a key determinant of adaptation to high-salt conditions. Although one extant theory suggests that acidic residues are favored because of their superior water-binding capacity, it is clear that extensive repulsive electrostatic interactions will also be present in such proteins at physiological pH. To investigate the magnitude and importance of such electrostatic interactions, we conducted a theoretical analysis of their contributions to the salt and pH-dependence of stability of two halophilic proteins. Our approach centers on use of the Poisson-Boltzmann equation of classical electrostatics, applied at an atomic level of detail to crystal structures of the proteins. We first show that in using the method, it is important to account for the fact that the dielectric constant of water decreases at high salt concentrations, in order to reproduce experimental changes in pKa values of small acids and bases. We then conduct a comparison of salt and pH effects on the stability of 2Fe-2S ferredoxins from the halophile Haloarcula marismortui and the non-halophile anabaena. In both proteins, substantial upward shifts in pKa accompany protein folding, though shifts are considerably larger, on average, in the halophile. Upward shifts for basic residues occur because of favorable salt-bridge interactions, whilst upward shifts for acidic residues result from unfavorable electrostatic interactions with other acidic groups. Our calculations suggest that at pH 7 the stability of the halophilic protein is decreased by 18.2 kcal/mol on lowering the salt concentration from 5 M to 100 mM, a result that is in line with the fact that halophilic proteins generally unfold at low salt concentrations. For comparison, the non-halophilic ferredoxin is calculated to be destabilized by only 5.1 kcal/mol over the same range. Analysis of the pH stability curve suggests that lowering the pH should increase the intrinsic stability of the halophilic protein at low salt concentrations, although in practice this is not observed because of aggregation effects. We report the results of a similar analysis carried out on the tetrameric malate dehydrogenase from H. marismortui. In this case, we investigated the salt and pH dependence of the various monomer-monomer interactions present in the tetramer. All monomer-monomer interactions are found to make substantial contributions to the salt-dependence of stability of the tetramer. Excellent agreement is obtained between our calculated results for the stability of the tetramer and experimental results. In particular, the finding that at 4 M NaCl, the tetramer is stable only between pH 4.8 and 10 is accurately reproduced. Taken together, our results suggest that repulsive electrostatic interactions between acidic residues are a major factor in the destabilization of halophilic proteins in low-salt conditions, and that these interactions remain destabilizing even at high salt concentrations. As a consequence, the role of acidic residues in halophilic proteins may be more to prevent aggregation than to make a positive contribution to intrinsic protein stability.

The pH-induced release of iron from transferrin investigated with a continuum electrostatic model

A reduction in pH induces the release of iron from transferrin in a process that involves a conformational change in the protein from a closed to an open form. Experimental evidence suggests that there must be changes in the protonation states of certain, as yet not clearly identified, residues in the protein accompanying this conformational change. Such changes in protonation states of residues and the consequent changes in electrostatic interactions are assumed to play a large part in the mechanism of release of iron from transferrin. Using the x-ray crystal structures of human ferri- and apo-lactoferrin, we calculated the pKa values of the titratable residues in both the closed (iron-loaded) and open (iron-free) conformations with a continuum electrostatic model. With the knowledge of a residue's pKa value, its most probable protonation state at any specified pH may be determined. The preliminary results presented here are in good agreement with the experimental observation that the binding of ferric iron and the synergistic anion bicarbonate/carbonate results in the release of approximately three H+ ions. It is suggested that the release of these three H+ ions may be accounted for, in most part, by the deprotonation of the bicarbonate and residues Tyr-92, Lys-243, Lys-282, and Lys-285 together with the protonation of residues Asp-217 and Lys-277.

Analysis of the stability of looped-out and stacked-in conformations of an adenine bulge in DNA using a continuum model for solvent and ions

A combination of conformational search, energy minimization, and energetic evaluation using a continuum solvent treatment has been employed to study the stability of various conformations of the DNA fragment d(CGCAGAA)/d(TTCGCG) containing a single adenine bulge. The extra-helical (looped-out) bulge conformation derived from a published x-ray structure and intra-helical (stacked bulge base) model structures partially based on nuclear magnetic resonance (NMR) data were used as start structures for the conformational search. Solvent-dependent contributions to the stability of the conformations were calculated from the solvent exposed molecular surface area and by using the finite difference Poisson-Boltzmann approach. Three classes (I-III) of bulge conformations with calculated low energies can be distinguished. The lowest-energy conformations were found in class I, corresponding to structures with the bulge base stacked between flanking helices, and class II, composed of structures forming a triplet of the bulge base and a flanking base pair. All extra-helical bulge structures, forming class III, were found to be less stable compared with the lowest energy structures of class I and II. The results are consistent with NMR data on an adenine bulge in the same sequence context indicating an intra-helical or triplet bulge conformation in solution. Although the total energies and total electrostatic energies of the low-energy conformations show only relatively modest variations, the energetic contributions to the stability were found to vary significantly among the classes of bulge structures. All intra-helical bulge structures are stabilized by a more favorable Coulomb charge-charge interaction but destabilized by a larger electrostatic reaction field contribution compared with all extra-helical and most triplet bulge structures. Van der Waals packing interactions and nonpolar surface-area-dependent contributions appear to favor triplet class II structures and to a lesser degree also the intra-helical stacked bulge conformations. The large conformational variation found for class III conformers might add a favorable entropic contribution to the stability of the extra-helical bulge form.

Electrostatic and non-electrostatic contributions to the binding free energies of anthracycline antibiotics to DNA

The knowledge about molecular factors driving simple ligand-DNA interactions is still limited. The aim of the present study was to investigate the electrostatic and non-electrostatic contributions to the binding free energies of anthracycline compounds with DNA. Theoretical calculations based on continuum methods (Poisson-Boltzmann and solvent accessible surface area) were performed to estimate the binding free energies of five selected anthracycline ligands (daunomycin, adriamycin, 9-deoxyadriamycin, hydroxyrubicin, and adriamycinone) to DNA. The free energy calculations also took into account the conformational change that DNA undergoes upon ligand binding. This conformational change appeared to be very important for estimating absolute free energies of binding. Our studies revealed that the absolute values of all computed contributions to the binding free energy were quite large compared to the total free energy of binding. However, the sum of these large positive and negative values produced a small negative value of the free energy around -10 kcal/mol. This value is in good agreement with experimental data. Experimental values for relative binding free energies were also reproduced for charged ligands by our calculations. Together, it was found that the driving force for ligand-DNA complex formation is the non-polar interaction between the ligand and DNA even if the ligand is positively charged.

The transcription activation domains of Fos and Jun induce DNA bending through electrostatic interactions

Transcription factor-induced DNA bending is essential for the assembly of active transcription complexes at many promoters. However, most eukaryotic transcription regulatory proteins have modular DNA-binding and activation domains, which appeared to exclude DNA bending as a mechanism of transcription activation by these proteins. We show that the transcription activation domains of Fos and Jun induce DNA bending. In chimeric proteins, the transcription activation domains induce DNA bending independent of the DNA-binding domains. DNA bending by the chimeric proteins is directed diametrically away from the transcription activation domains. Therefore, the opposite directions of DNA bending by Fos and Jun are caused, in part, by the opposite locations of the transcription activation domains relative to the DNA-binding domains in these proteins. DNA bending is reduced in the presence of multivalent cations, indicating that electrostatic interactions contribute to DNA bending by Fos and Jun. Consequently, regions outside the minimal DNA-binding domain can influence DNA structure, and may thereby contribute to the architectural reorganization of the promoter region required for gene activation.

Electrostatic effects in homeodomain-DNA interactions

We report here an investigation of the role of electrostatics in homeodomain-DNA interactions using techniques based around the use of the Poisson-Boltzmann equation. In the present case such a study is of particular interest, since in contrast to other proteins previously studied with this method, the homeodomain is a small, highly charged protein that forms extensive ion pairs upon binding DNA. We have investigated the salt dependence of the binding constant for specific association and for a variety of models for non-specific association. The results indicate that, in line with the models proposed by Manning and Record, the entropy of counterion release accounts for a significant fraction of the salt dependence of the binding free energy, though this is perhaps due to fortuitous cancellation of other contributing terms. The thermodynamic effects of a number of specific homeodomain mutants were also investigated, and partly rationalized in terms of favorable electrostatic interactions in the major goove of DNA. Investigation of the temperature-dependence of the free energy of association indicates that the electrostatic contributions become increasingly favorable as the temperature rises. For this particular system, however, there appears to be no significant electrostatic contribution to the delta(delta C(p)) of association. Finally, an analysis of the free energy of interaction when the homeodomain is moved ca one Debye length from the DNA suggests that pure electrostatic forces are able to steer the homeodomain into a partially correct orientation for binding to the DNA.

Helix-helix interactions in lipid bilayers

Using a continuum model, we calculated the electrostatic interaction free energy between two alpha-helices in three environments: the aqueous phase, a low dielectric alkane phase, and a simple representation of a lipid bilayer. As was found in previous work, helix-helix interactions in the aqueous phase are quite weak, because of solvent screening, and slightly repulsive, because of desolvation effects that accompany helix assembly. In contrast, the interactions can be quite strong in a hypothetical alkane phase because desolvation effects are essentially nonexistent and because helix-helix interactions are not well screened. In this type of environment, the antiparallel helix orientation is strongly favored over the parallel orientation. In previous work we found that the free energy penalty associated with burying helix termini in a bilayer is quite high, which is why the termini tend to protrude into the solvent. Under these conditions the electrostatic interaction is strongly screened by solvent; indeed, it is sufficient for the termini to protrude a few angstroms from the two surfaces of the bilayer for their interaction to diminish almost completely. The effect is consistent with the classical model of the helix dipole in which the dipole moment is represented by point charges located at either terminus. Our results suggest, in agreement with previous models, that there is no significant nonspecific driving force for helix aggregation and, hence, that membrane protein folding must be driven by specific interactions such as close packing and salt-bridge and hydrogen bond formation.

Thermodynamics of sequence-specific protein-DNA interactions

The molecular recognition processes in sequence-specific protein-DNA interactions are complex. The only feature common to all sequence-specific protein-DNA structures is a large interaction interface, which displays a high degree of complementarity in terms of shape, polarity and electrostatics. Many molecular mechanisms act in concert to form the specific interface. These include conformational changes in DNA and protein, dehydration of surfaces, reorganization of ion atmospheres, and changes in dynamics. Here we review the current understanding of how different mechanisms contribute to the thermodynamics of the binding equilibrium and the stabilizing effect of the different types of noncovalent interactions found in protein-DNA complexes. The relation to the thermodynamics of small molecule-DNA binding and protein folding is also briefly discussed.

Electrostatic interactions in hirudin-thrombin binding

Hirudin is a good anticoagulant owing to potent inhibition of the serine protease thrombin. An aspartate- and glutamate-rich portion of hirudin plays an important part in its tight binding to thrombin through a ladder of salt bridges, and these residues have previously been mutated to asparagine or glutamine. Detailed calculations of the electrostatic contribution to changes in binding from these mutations have been performed using the finite-difference Poisson-Boltzmann method which include charge--charge interactions, solvation interactions, the residual electrostatic interaction of mutant residues, pKa shifts, and ionic strength. Single mutant effects on binding energy were close to experimental values, except for the D55N mutant whose effect is overestimated, perhaps because of displacement of a bound chloride ion from the site where it binds. Multiple mutation values were generally overestimated. The effect of pKa shifts upon the binding is significant for one hirudin residue E58, but this appears to be due to a poor salt bridge with thrombin caused by crystal contacts. Electrostatic interaction between the acidic residues is unfavorable. However, analysis of experimental multiple mutation/single mutation data shows apparently negative interactions between these residues, from which it is concluded that structural changes can occur in the complex to relieve an unfavorable interaction when more than one acidic residue is mutated. In all cases, there is a loss in stability of the complex from mutations due to loss of favorable charge--charge interactions with thrombin, but this is largely compensated for by reduced unfavorable desolvation interactions, and by residual polar interactions in the Asn/Gln mutants.

Binding of small basic peptides to membranes containing acidic lipids: theoretical models and experimental results

We measured directly the binding of Lys3, Lys5, and Lys7 to vesicles containing acidic phospholipids. When the vesicles contain 33% acidic lipids and the aqueous solution contains 100 mM monovalent salt, the standard Gibbs free energy for the binding of these peptides is 3, 5, and 7 kcal/mol, respectively. The binding energies decrease as the mol% of acidic lipids in the membrane decreases and/or as the salt concentration increases. Several lines of evidence suggest that these hydrophilic peptides do not penetrate the polar headgroup region of the membrane and that the binding is mainly due to electrostatic interactions. To calculate the binding energies from classical electrostatics, we applied the nonlinear Poisson-Boltzmann equation to atomic models of the phospholipid bilayers and the basic peptides in aqueous solution. The electrostatic free energy of interaction, which arises from both a long-range coulombic attraction between the positively charged peptide and the negatively charged lipid bilayer, and a short-range Born or image charge repulsion, is a minimum when approximately 2.5 A (i.e., one layer of water) exists between the van der Waals surfaces of the peptide and the lipid bilayer. The calculated molar association constants, K, agree well with the measured values: K is typically about 10-fold smaller than the experimental value (i.e., a difference of about 1.5 kcal/mol in the free energy of binding). The predicted dependence of K (or the binding free energies) on the ionic strength of the solution, the mol% of acidic lipids in the membrane, and the number of basic residues in the peptide agree very well with the experimental measurements. These calculations are relevant to the membrane binding of a number of important proteins that contain clusters of basic residues.