Electrostatic Binding Free Energy Research Articles

Protein-Nucleic Acid Interactions for RNA Polymerase II Elongation Factors by Molecular Dynamics Simulations.

RNA polymerase II (Pol II) forms a complex with elongation factors to proceed to the elongation stage of the transcription process. In this work, we studied the elongation factor SPT5 and explored the protein-nucleic acid interactions for the isolated systems of KOW1 and KOW4 domains of SPT5 with DNA and RNA, respectively. We performed molecular dynamics (MD) simulations using three commonly used force fields that are CHARMM c36m, AMBER ff14sb, and ff19sb. Simulations showed strong protein-nucleic acid interactions and low electrostatic binding free energies for all force fields used. RNA was found to be highly dynamic with all force fields, while DNA had relatively more stable conformations with the AMBER force fields compared to that with CHARMM. Furthermore, we performed MD simulations of the complete elongation complex using CHARMM c36m and AMBER ff19sb force fields to compare the dynamics and interactions with the isolated systems. Similarly, strong KOW1 and DNA interactions were observed in the complete elongation complex simulations and DNA was further stabilized by a network of interactions involving SPT5-KOW1, SPT4, and rpb2 of Pol II. Overall, our study showed that the differences between CHARMM and AMBER force fields strongly affect the dynamics of the nucleic acids. CHARMM provides highly flexible DNA, while AMBER largely stabilizes the DNA structure. Although the presence of the entire interaction network stabilized the DNA and decreased the differences in the results from the two force fields, the discrepancies of the force fields for smaller systems may reflect their problems in generating accurate dynamics of nucleic acids.

Binding characteristics of staphylococcal protein A and streptococcal protein G for fragment crystallizable portion of human immunoglobulin G

In the wide array of physiological processes, protein–protein interactions and their binding are the most basal activities for achieving adequate biological metabolism. Among the studies on binding proteins, the examination of interactions between immunoglobulin G (IgG) and natural immunoglobulin-binding ligands, such as staphylococcal protein A (spA) and streptococcal protein G (spG), is essential in the development of pharmaceutical science, biotechnology, and affinity chromatography. The widespread utilization of IgG-spA/spG binding characteristics has allowed researchers to investigate these molecular interactions. However, the detailed binding strength of each ligand and the corresponding binding mechanisms have yet to be fully investigated. In this study, the authors analyzed the binding strengths of IgG–spA and IgG–spG complexes and identified the mechanisms enabling these bindings using molecular dynamics simulation, steered molecular dynamics, and advanced Poisson–Boltzmann Solver simulations. Based on the presented data, the binding strength of the spA ligand was found to significantly exceed that of the spG ligand. To find out which non-covalent interactions or amino acid sites have a dominant role in the tight binding of these ligands, further detailed analyses of electrostatic interactions, hydrophobic bonding, and binding free energies have been performed. In investigating their binding affinity, a relatively independent and different unbinding mechanism was found in each ligand. These distinctly different mechanisms were observed to be highly correlated to the protein secondary and tertiary structures of spA and spG ligands, as explicated from the perspective of hydrogen bonding.

Multidimensional Global Optimization and Robustness Analysis in the Context of Protein-Ligand Binding.

Accuracy of protein-ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein-ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based "kT-connectivity" approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.

Acylguanidine-BACE1 complex: Insights of intermolecular interactions and dynamics

Alzheimer disease (AD) is a harmful neurodegenerative disorder which arises mainly due to awful deposition of amyloid β (Aβ) peptide in the brain of AD patients. Aβ aggregates from the amyloid precursor protein (APP) by the sequential action of β-Secretase (Beta site APP Cleaving Enzyme, BACE1); hence, inhibition of BACE1 is the primary target for the treatment of AD. As per the experimental report, acylguanidine is a synthetic inhibitor of BACE1, it exhibits high binding affinity towards BACE1. In the present computational study, we aimed to understand the molecular binding mechanism of acylguanidine with BACE1 from the structure and conformation, intermolecular interactions, charge density and electrostatic properties, stability and binding free energy of acylguanidine molecule in the active site of BACE1. To investigate this, molecular docking, QM/MM based charge density analysis and MD simulation have been performed on acylguanidine with BACE1. Acylguanidine shows large binding affinity towards BACE1 and it gives strong hydrogen bonding and hydrophobic interactions with the active site amino acid residues of BACE1. In addition, QM/MM based charge density analysis of acylguanidine was carried out to understand its charge density distribution in the active site of BACE1. The conformational flexibility, charge density redistribution and the modification of electrostatic properties of acylguanidine in the active site have been compared to its corresponding gas phase structure. Further, the molecular dynamics simulation on acylguanidine-BACE1 was carried out, which gives the stability of acylguanidine in the active site of BACE1. The MM-GBSA free energy displays the binding affinity of the acylguanidine and further the decomposition energy reveals the validity of intermolecular interactions.

An accelerated nonlocal Poisson‐Boltzmann equation solver for electrostatics of biomolecule

The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly used dielectric continuum model, the Poisson-Boltzmann equation (PBE), for computing electrostatics of biomolecules. In this paper, an accelerated NMPBE solver is constructed by finite element and finite difference hybrid techniques. It is then programmed as a software package for computing electrostatic solvation and binding free energies for a protein in a symmetric 1:1 ionic solvent. Numerical results validate the new solver and its numerical stability. They also demonstrate that the new solver has much better performance than the corresponding finite element solver in terms of computer CPU time. Furthermore, they show that the binding free energies produced by NMPBE can match chemical experiment data better than those by PBE.

Grid-Based Surface Generalized Born Model for Calculation of Electrostatic Binding Free Energies

Fast and accurate calculation of solvation free energies is central to many applications, such as rational drug design. In this study, we present a grid-based molecular surface implementation of "R6" flavor of the generalized Born (GB) implicit solvent model, named GBNSR6. The speed, accuracy relative to numerical Poisson-Boltzmann treatment, and sensitivity to grid surface parameters are tested on a set of 15 small protein-ligand complexes and a set of biomolecules in the range of 268 to 25099 atoms. Our results demonstrate that the proposed model provides a relatively successful compromise between the speed and accuracy of computing polar components of the solvation free energies (ΔGpol) and binding free energies (ΔΔGpol). The model tolerates a relatively coarse grid size h = 0.5 Å, where the grid artifact error in computing ΔΔGpol remains in the range of kBT ∼ 0.6 kcal/mol. The estimated ΔΔGpols are well correlated (r2 = 0.97) with the numerical Poisson-Boltzmann reference, while showing virtually no systematic bias and RMSE = 1.43 kcal/mol. The grid-based GBNSR6 model is available in Amber (AmberTools) package of molecular simulation programs.

Accurate, robust, and reliable calculations of Poisson-Boltzmann binding energies.

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, ΔGel, and binding free energy, ΔΔGel, is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with solvent excluded surfaces for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of ΔGel obtained at the grid spacing of 1.0 Å compared to ΔGel at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.

Accurate estimation of electrostatic binding energy with Poisson-Boltzmann equation solver DelPhi program

Poisson–Boltzmann (PB) model is a widely used implicit solvent approximation in biophysical modeling because of its ability to provide accurate and reliable PB electrostatic salvation free energies ([Formula: see text] as well as electrostatic binding free energy ([Formula: see text] estimations. However, a recent study has warned that the 0.5[Formula: see text]Å grid spacing which is normally adopted can produce unacceptable errors in [Formula: see text] estimation with the solvent excluded surface (SES) (Harris RC, Boschitsch AH and Fenley MO, Influence of grid spacing in Poisson–Boltzmann equation binding energy estimation, J Chem Theory Comput 19: 3677–3685, 2013). In this work, we investigate the grid dependence of the widely used PB solver DelPhi v6.2 with molecular surface (MS) for estimating both electrostatic solvation free energies and electrostatic binding free energies. Our results indicate that, for the molecular complex and components the absolute errors of [Formula: see text] are smaller than that of [Formula: see text], and grid spacing of 0.8[Formula: see text]Å with DelPhi program ensures the accuracy and reliability of [Formula: see text]; however, the accuracy of [Formula: see text] largely relies on the order of magnitude of [Formula: see text] itself rather than that of [Formula: see text] or [Formula: see text]. Our findings suggest that grid spacing of 0.5[Formula: see text]Å is enough to produce accurate [Formula: see text] for molecules whose [Formula: see text] are large, but finer grids are needed when [Formula: see text] is very small.

A nonlocal modified Poisson–Boltzmann equation and finite element solver for computing electrostatics of biomolecules

The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson–Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson–Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation.

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

Interplay between Electrostatics and Cation-PI Interactions Governs the Specific Membrane Binding of Phosphatidylinositol-Specific Phospholipase-C

Bacillus thuringiensis phosphatidylinositol-specific phospholipase C (BtPI-PLC) is an amphitropic enzyme which cleaves GPI-anchored proteins off the outer surface of eukaryotic plasma membranes. Amphitropic proteins bind specifically and transiently to the surface of cell membranes, and their functions are regulated upon binding. It is commonly acknowledged that non-specific electrostatic forces are responsible for their long-range interactions with membranes. Using continuum electrostatics calculations we show how, despite having an overall negative charge (−7e), the charge distribution of BtPI-PLC leads to favorable electrostatic interactions with anionic membranes. However, the resulting electrostatic binding free energy, which is essential for membrane binding, is quite low. Mutation of a single, key basic residue to alanine diminishes this long range electrostatic contribution making it difficult for BtPI-PLC to associate with membranes. Once close to the membrane surface, short range non-specific hydrophobic interactions and specific cation-pi interactions with the N(Me)3 groups of phosphatidylcholine (PC) lipids of the membrane likely come into play for BtPI-PLC binding to the membrane surface. 500ns-long all-atom molecular dynamics simulations of BtPI-PLC docked to mixed bilayers with varying ratio of zwitterionic lipids indeed confirm this. Finally, we see that the interplay between long range electrostatics and short range, PC specific cation-pi interactions governs the specificity of BtPI-PLC for PC rich membrane. Moreover, our results show that BtPI-PLC can achieve favorable electrostatics interactions with lipid bilayers without having surface-exposed basic clusters suggesting that such clusters are not always necessary for the regulation of amphitropic enzyme binding.

Combined kinetic studies and computational analysis on kojic acid analogous as tyrosinase inhibitors.

Tyrosinase is a key enzyme in melanin synthesis and widely distributed in plants and animals tissues. In mammals, this enzyme is related to pigment production, involved in wound healing, primary immune response and it can also contribute to catecholamines synthesis in the brain. Consequently, tyrosinase enzyme represents an attractive and selective target in the field of the medicine, cosmetics and bio-insecticides. In this paper, experimental kinetics and computational analysis were used to study the inhibition of tyrosinase by analogs of Kojic acid. The main interactions occurring between inhibitors-tyrosinase complexes and the influence of divalent cation (Cu2+) in enzymatic inhibition were investigated by using molecular docking, molecular dynamic simulations and electrostatic binding free energy by using the Linear Interaction Energy (LIE) method. The results showed that the electrostatic binding free energy are correlated with values of constant inhibition (r2 = 0.97).Thus, the model obtained here could contribute to future studies of this important system and, therefore, eventually facilitate development of tyrosinase inhibitors.

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.

Influence of Grid Spacing in Poisson–Boltzmann Equation Binding Energy Estimation

Grid-based solvers of the Poisson-Boltzmann, PB, equation are routinely used to estimate electrostatic binding, ΔΔGel, and solvation, ΔGel, free energies. The accuracies of such estimates are subject to grid discretization errors from the finite difference approximation to the PB equation. Here, we show that the grid discretization errors in ΔΔGel are more significant than those in ΔGel, and can be divided into two parts: (i) errors associated with the relative positioning of the grid and (ii) systematic errors associated with grid spacing. The systematic error in particular is significant for methods, such as the molecular mechanics PB surface area, MM-PBSA, approach that predict electrostatic binding free energies by averaging over an ensemble of molecular conformations. Although averaging over multiple conformations can control for the error associated with grid placement, it will not eliminate the systematic error, which can only be controlled by reducing grid spacing. The present study indicates that the widely-used grid spacing of 0.5 Å produces unacceptable errors in ΔΔGel, even though its predictions of ΔGel are adequate for the cases considered here. Although both grid discretization errors generally increase with grid spacing, the relative sizes of these errors differ according to the solute-solvent dielectric boundary definition. The grid discretization errors are generally smaller on the Gaussian surface used in the present study than on either the solvent-excluded or van der Waals surfaces, which both contain more surface discontinuities (e.g., sharp edges and cusps). Additionally, all three molecular surfaces converge to very different estimates of ΔΔGel.

Influences of Mutations on the Electrostatic Binding Free Energies of Chloride Ions in Escherichia coli ClC

Mutations in ClC channel proteins may cause serious functional changes and even diseases. The function of ClC proteins mainly manifests as Cl(-) transport, which is related to the binding free energies of chloride ions. Therefore, the influence of a mutation on ClC function can be studied by investigating the mutational effect on the binding free energies of chloride ions. The present study provides quantitative and systematic investigations on the influences of residue mutations on the electrostatic binding free energies in Escherichia coli ClC (EcClC) proteins, using all-atom molecular dynamics simulations. It was found that the change of the electrostatic binding free energy decreases linearly with the increase of the residue-chloride ion distance for a mutation. This work reveals how changes in the charge of a mutated residue and in the distance between the mutated residue and the binding site govern the variations in the electrostatic binding free energies and therefore influence the transport of chloride ions and conduction in EcClC. This work would facilitate our understanding of the mutational effects on transport of chloride ions and functions of ClC proteins and provide a guideline to estimate which residue mutations will have great influences on ClC functions.

A Stochastic Technique that Computes Electrostatic Solvation and Binding Free Energies in the Generalized Born Model with Exact Born Radii

A stochastic generalized Born (GB) solver is presented whose predictions converge to those given by exact GB radii to arbitrary precision. By solving for the Born radii stochastically, the exact Born radii can be computed without the need for multiple expensive deterministic calculations. In addition, although the proposed method strictly works only on a van der Waals surface, it can be modified to closely match the predictions of the linearized Poisson-Boltzmann equation on a solvent-excluded (SE) surface by determining prior to the calculation which spheres are not solvent exposed in the SE surface and inflating these spheres by the probe radius. Additionally, because the predictions of this method can be made arbitrarily close to those given by exact Born radii, this method can be used to evaluate the ability of the Born approximation to reproduce the electrostatic binding free energy given by the Poisson-Boltzmann equation independently of the approximations usually made to derive the Born radii. This study presents the results of such an investigation for a broad range of biomolecular complexes.

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.

Computational analysis of aspartic protease plasmepsin II complexed with EH58 inhibitor: a QM/MM MD study

Plasmepsin (PM) II is one of four enzymes in the food vacuole of Plasmodium falciparum. It has become an attractive target for combating malaria through research regarding its importance in the P. falciparum metabolism and life cycle, making it the target of choice for structure-based drug design. This paper reports the results of hybrid quantum mechanics / molecular mechanics (QM/MM) molecular dynamics (MD) simulations employed to study the details of the interactions established between PM II and N-(3-{(2-benzo[1, 3]dioxol-5-yl-ethyl)[3-(1-methyl-3-oxo-1,3-dihydro-isoindol-2-yl) propionyl]-amino}-1-benzyl-2-(hydroxyl-propyl)-4-benzyloxy-3,5dimethoxy-benzamide (EH58), a well-known potent inhibitor for this enzyme. Electrostatic binding free energy and energy terms decomposition have been computed for PM II complexed with the EH58 inhibitor. The results reveal that there is a strong interaction between Asp34, Val78, Ser79, Tyr192 and Asp214 residues and the EH58 inhibitor. In addition, we have computed the potential of the mean force (PMF) profile in order to assign the protonation state of the two catalytic aspartates in PM II-EH58 complex. The results indicate that the protonation of Asp214 favors a stable active site structure, which is consistent with our electrostatic binding free energy calculation and with previous published works.

Calculations of the binding affinities of protein-protein complexes with the fast multipole method

In this paper, we used a coarse-grained model at the residue level to calculate the binding free energies of three protein-protein complexes. General formulations to calculate the electrostatic binding free energy and the van der Waals free energy are presented by solving linearized Poisson-Boltzmann equations using the boundary element method in combination with the fast multipole method. The residue level model with the fast multipole method allows us to efficiently investigate how the mutations on the active site of the protein-protein interface affect the changes in binding affinities of protein complexes. Good correlations between the calculated results and the experimental ones indicate that our model can capture the dominant contributions to the protein-protein interactions. At the same time, additional effects on protein binding due to atomic details are also discussed in the context of the limitations of such a coarse-grained model.

Revisiting the Association of Cationic Groove-Binding Drugs to DNA Using a Poisson-Boltzmann Approach

Proper modeling of nonspecific salt-mediated electrostatic interactions is essential to understanding the binding of charged ligands to nucleic acids. Because the linear Poisson-Boltzmann equation (PBE) and the more approximate generalized Born approach are applied routinely to nucleic acids and their interactions with charged ligands, the reliability of these methods is examined vis-à-vis an efficient nonlinear PBE method. For moderate salt concentrations, the negative derivative, SKpred, of the electrostatic binding free energy, ΔGel, with respect to the logarithm of the 1:1 salt concentration, [M+], for 33 cationic minor groove drugs binding to AT-rich DNA sequences is shown to be consistently negative and virtually constant over the salt range considered (0.1–0.4 M NaCl). The magnitude of SKpred is approximately equal to the charge on the drug, as predicted by counterion condensation theory (CCT) and observed in thermodynamic binding studies. The linear PBE is shown to overestimate the magnitude of SKpred, whereas the nonlinear PBE closely matches the experimental results. The PBE predictions of SKpred were not correlated with ΔGel in the presence of a dielectric discontinuity, as would be expected from the CCT. Because this correlation does not hold, parameterizing the PBE predictions of ΔGel against the reported experimental data is not possible. Moreover, the common practice of extracting the electrostatic and nonelectrostatic contributions to the binding of charged ligands to biopolyelectrolytes based on the simple relation between experimental SK values and the electrostatic binding free energy that is based on CCT is called into question by the results presented here. Although the rigid-docking nonlinear PB calculations provide reliable predictions of SKpred, at least for the charged ligand-nucleic acid complexes studied here, accurate estimates of ΔGel will require further development in theoretical and experimental approaches.