1
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Usefzay O, Yari S, Amiri P, Hasanein P. Evaluation of protective effects of methylene blue on cisplatin-induced nephrotoxicity. Biomed Pharmacother 2022; 150:113023. [PMID: 35483196 DOI: 10.1016/j.biopha.2022.113023] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Revised: 04/19/2022] [Accepted: 04/20/2022] [Indexed: 11/18/2022] Open
Abstract
Cisplatin (CP) is used to treat various types of cancer. However, its usage is limited due to nephrotoxicity. This study aims to examine the applicability of methylene blue (MB) against CP-induced kidney injuries. In this study, twenty-eight male rats were divided into four groups. Following administration of a single dose of CP (5 mg/kg), animals received intraperitoneal injections (IP) of MB (4 mg/kg) for seven days. In the final phase of the experiment, serum was collected from rats, with blood urea nitrogen (BUN) and creatinine (Cr) levels measured. Hematoxylin-Eosin (H&E) and Masson's trichrome staining were performed to examine histological changes. Immuno-histological staining was used to evaluate caspase-3 protein expression. The results showed that the MB (4 mg/kg) + CP treated rats underwent a lesser weight loss compared to the CP group (p < 0.05 and p < 0.001, respectively). The kidney weight decreased significantly in the CP + MB group compared to the CP group (p < 0.05 and p < 001, respectively). BUN and Cr levels that were increased significantly in the serum of the CP group (p < 0.001) compared to the control group showed no significant increase in the MB + CP group compared to the control group (p = 0.842 and p = 0.989, respectively). There was a significant decrease in kidney tissue injuries in the CP + MB compared to the CP group (p < 0.001). The glomerular size was recovered in the CP + MB group compared to the CP (p < 0.05). The significant increase in the capsular space of the CP group compared to the control group (p < 0.001) was attenuated in the CP + MB. MB restored the histological alterations in the kidneys. Treatment with 4 mg/kg of MB reduced the expression levels of Caspase-3. In conclusion, this study provides evidence concerning the anti-apoptotic roles of MB in CP-induced kidney damage. In conclusion, MB has a positive impact on kidney function.
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Affiliation(s)
- Obaidullah Usefzay
- Department of Biology, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran
| | - Siamak Yari
- Department of Biology, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran.
| | - Parsa Amiri
- Neurophysiology Research Center, Hamadan University of Medical Sciences, Hamadan, Iran
| | - Parisa Hasanein
- Department of Biology, School of Basic Sciences, University of Zabol, Zabol, Iran
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2
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Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting. Biophys J 2019; 117:1116-1124. [PMID: 31466697 DOI: 10.1016/j.bpj.2019.08.007] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Revised: 08/01/2019] [Accepted: 08/05/2019] [Indexed: 01/22/2023] Open
Abstract
RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg2+, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg2+-DNA and Mg2+-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.
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Ying J, Xie D. An accelerated nonlocal Poisson-Boltzmann equation solver for electrostatics of biomolecule. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3129. [PMID: 30021243 DOI: 10.1002/cnm.3129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Revised: 06/26/2018] [Accepted: 07/05/2018] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Jinyong Ying
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
| | - Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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4
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Abstract
Matrix metalloproteinases (MMPs) are a family of zinc-containing enzymes required for homeostasis. These enzymes are an important class of drug targets as their over expression is associated with many disease states. Most of the inhibitors reported against this class of proteins have failed in clinical trials due to lack of specificity. In order to assist in drug design endeavors for MMP targets, a computationally tractable pathway is presented, comprising, (1) docking of small molecule inhibitors against the target MMPs, (2) derivation of quantum mechanical charges on the zinc ion in the active site and the amino acids coordinating with zinc including the inhibitor molecule, (3) molecular dynamics simulations on the docked ligand-MMP complexes, and (4) evaluation of binding affinities of the ligand-MMP complexes via an accurate scoring function for zinc containing metalloprotein-ligand complexes. The above pathway was applied to study the interaction of the inhibitor Batimastat with MMPs, which resulted in a high correlation between the predicted and experimental binding free energies, suggesting the potential applicability of the pathway.
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5
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Ringe S, Oberhofer H, Reuter K. Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions. J Chem Phys 2017; 146:134103. [DOI: 10.1063/1.4978850] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Affiliation(s)
- Stefan Ringe
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Harald Oberhofer
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
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Li A, Gao K. Accurate estimation of electrostatic binding energy with Poisson-Boltzmann equation solver DelPhi program. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2016. [DOI: 10.1142/s0219633616500711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Anbang Li
- College of Physics Science and Technology, Central China Normal University, Wuhan, P.R. China, 430079, P.R. China
| | - Kaifu Gao
- College of Physics Science and Technology, Central China Normal University, Wuhan, P.R. China, 430079, P.R. China
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Harris RC, Mackoy T, Fenley MO. Problems of robustness in Poisson-Boltzmann binding free energies. J Chem Theory Comput 2016; 11:705-12. [PMID: 26528091 PMCID: PMC4610304 DOI: 10.1021/ct5005017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Indexed: 11/29/2022]
Abstract
Although models based on the Poisson–Boltzmann (PB) equation have been fairly successful at predicting some experimental quantities, such as solvation free energies (ΔG), these models have not been consistently successful at predicting binding free energies (ΔΔG). Here we found that ranking a set of protein–protein complexes by the electrostatic component (ΔΔGel) of ΔΔG was more difficult than ranking the same molecules by the electrostatic component (ΔGel) of ΔG. This finding was unexpected because ΔΔGel can be calculated by combining estimates of ΔGel for the complex and its components with estimates of the ΔΔGel in vacuum. One might therefore expect that if a theory gave reliable estimates of ΔGel, then its estimates of ΔΔGel would be reliable. However, ΔΔGel for these complexes were orders of magnitude smaller than ΔGel, so although estimates of ΔGel obtained with different force fields and surface definitions were highly correlated, similar estimates of ΔΔGel were often not correlated.
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Affiliation(s)
- Robert C Harris
- Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555-0304, United States
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Iwahara J, Esadze A, Zandarashvili L. Physicochemical Properties of Ion Pairs of Biological Macromolecules. Biomolecules 2015; 5:2435-63. [PMID: 26437440 PMCID: PMC4693242 DOI: 10.3390/biom5042435] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Revised: 09/09/2015] [Accepted: 09/11/2015] [Indexed: 11/23/2022] Open
Abstract
Ion pairs (also known as salt bridges) of electrostatically interacting cationic and anionic moieties are important for proteins and nucleic acids to perform their function. Although numerous three-dimensional structures show ion pairs at functionally important sites of biological macromolecules and their complexes, the physicochemical properties of the ion pairs are not well understood. Crystal structures typically show a single state for each ion pair. However, recent studies have revealed the dynamic nature of the ion pairs of the biological macromolecules. Biomolecular ion pairs undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. This dynamic behavior is reasonable in light of the fundamental concepts that were established for small ions over the last century. In this review, we introduce the physicochemical concepts relevant to the ion pairs and provide an overview of the recent advancement in biophysical research on the ion pairs of biological macromolecules.
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Affiliation(s)
- Junji Iwahara
- Department of Biochemistry & Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX 77555, USA.
| | - Alexandre Esadze
- Department of Biochemistry & Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX 77555, USA
| | - Levani Zandarashvili
- Department of Biochemistry & Molecular Biology, Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX 77555, USA
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Ovanesyan Z, Medasani B, Fenley MO, Guerrero-García GI, de la Cruz MO, Marucho M. Excluded volume and ion-ion correlation effects on the ionic atmosphere around B-DNA: theory, simulations, and experiments. J Chem Phys 2014; 141:225103. [PMID: 25494770 PMCID: PMC4265039 DOI: 10.1063/1.4902407] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2014] [Accepted: 11/12/2014] [Indexed: 12/19/2022] Open
Abstract
The ionic atmosphere around a nucleic acid regulates its stability in aqueous salt solutions. One major source of complexity in biological activities involving nucleic acids arises from the strong influence of the surrounding ions and water molecules on their structural and thermodynamic properties. Here, we implement a classical density functional theory for cylindrical polyelectrolytes embedded in aqueous electrolytes containing explicit (neutral hard sphere) water molecules at experimental solvent concentrations. Our approach allows us to include ion correlations as well as solvent and ion excluded volume effects for studying the structural and thermodynamic properties of highly charged cylindrical polyelectrolytes. Several models of size and charge asymmetric mixtures of aqueous electrolytes at physiological concentrations are studied. Our results are in good agreement with Monte Carlo simulations. Our numerical calculations display significant differences in the ion density profiles for the different aqueous electrolyte models studied. However, similar results regarding the excess number of ions adsorbed to the B-DNA molecule are predicted by our theoretical approach for different aqueous electrolyte models. These findings suggest that ion counting experimental data should not be used alone to validate the performance of aqueous DNA-electrolyte models.
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Affiliation(s)
- Zaven Ovanesyan
- Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, Texas 78249-5003, USA
| | - Bharat Medasani
- Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, Texas 78249-5003, USA
| | - Marcia O Fenley
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, USA
| | - Guillermo Iván Guerrero-García
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, San Luis Potosí, Mexico
| | - Mónica Olvera de la Cruz
- Department of Chemistry and Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Marcelo Marucho
- Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, Texas 78249-5003, USA
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10
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Fenley MO, Harris RC, Mackoy T, Boschitsch AH. Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid. J Comput Chem 2014; 36:235-43. [PMID: 25430617 DOI: 10.1002/jcc.23791] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Revised: 09/14/2014] [Accepted: 10/12/2014] [Indexed: 11/10/2022]
Abstract
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software.
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Affiliation(s)
- Marcia O Fenley
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida, 32306
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11
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Harris RC, Boschitsch AH, Fenley MO. Sensitivities to parameterization in the size-modified Poisson-Boltzmann equation. J Chem Phys 2014; 140:075102. [PMID: 24559370 DOI: 10.1063/1.4864460] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
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Affiliation(s)
- Robert C Harris
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306-3408, USA
| | | | - Marcia O Fenley
- Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306-3408, USA
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12
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Abstract
The electric polarizability of DNA, represented by the dielectric constant, is a key intrinsic property that modulates DNA interaction with effector proteins. Surprisingly, it has so far remained unknown owing to the lack of experimental tools able to access it. Here, we experimentally resolved it by detecting the ultraweak polarization forces of DNA inside single T7 bacteriophages particles using electrostatic force microscopy. In contrast to the common assumption of low-polarizable behavior like proteins (εr ∼ 2-4), we found that the DNA dielectric constant is ∼ 8, considerably higher than the value of ∼ 3 found for capsid proteins. State-of-the-art molecular dynamic simulations confirm the experimental findings, which result in sensibly decreased DNA interaction free energy than normally predicted by Poisson-Boltzmann methods. Our findings reveal a property at the basis of DNA structure and functions that is needed for realistic theoretical descriptions, and illustrate the synergetic power of scanning probe microscopy and theoretical computation techniques.
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Vankayala R, Kalluru P, Tsai HH, Chiang CS, Hwang KC. Effects of surface functionality of carbon nanomaterials on short-term cytotoxicity and embryonic development in zebrafish. J Mater Chem B 2014; 2:1038-1047. [DOI: 10.1039/c3tb21497d] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Cationic surface functionalities of nanomaterials, such as imidazolium and trimethylammonium ethyl methacrylate, induce strong cytotoxicity in vitro and in zebrafish.
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Affiliation(s)
- Raviraj Vankayala
- Department of Chemistry
- National Tsing Hua University
- Hsinchu 30013, Taiwan
| | - Poliraju Kalluru
- Department of Chemistry
- National Tsing Hua University
- Hsinchu 30013, Taiwan
| | - Hsin-Hui Tsai
- Department of Chemistry
- National Tsing Hua University
- Hsinchu 30013, Taiwan
| | - Chi-Shiun Chiang
- Department of Biomedical Engineering and Environmental Sciences
- National Tsing Hua University
- Hsinchu 30013, Taiwan
| | - Kuo Chu Hwang
- Department of Chemistry
- National Tsing Hua University
- Hsinchu 30013, Taiwan
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Harris RC, Boschitsch AH, Fenley MO. Influence of Grid Spacing in Poisson-Boltzmann Equation Binding Energy Estimation. J Chem Theory Comput 2013; 9:3677-3685. [PMID: 23997692 DOI: 10.1021/ct300765w] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Robert C Harris
- Department of Physics, Florida State University, Tallahasse, FL 32306
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Ning J, Chen W, Li J, Peng Z, Wang J, Ni Z. Structural and energetic insights into sequence-specific interaction in DNA–drug recognition: development of affinity predictor and analysis of binding selectivity. J Mol Model 2012; 19:1573-82. [DOI: 10.1007/s00894-012-1722-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2012] [Accepted: 12/03/2012] [Indexed: 11/28/2022]
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16
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Boschitsch AH, Fenley MO. A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids. J Chem Theory Comput 2011; 7:1524-1540. [PMID: 21984876 DOI: 10.1021/ct1006983] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities - obtained with both linear and nonlinear Poisson-Boltzmann equation - for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers.
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Harris RC, Bredenberg JH, Silalahi ARJ, Boschitsch AH, Fenley MO. Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes. Biophys Chem 2011; 156:79-87. [PMID: 21458909 DOI: 10.1016/j.bpc.2011.02.010] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2010] [Revised: 02/08/2011] [Accepted: 02/21/2011] [Indexed: 12/01/2022]
Abstract
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.
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Affiliation(s)
- Robert C Harris
- Department of Physics, Institute of Molecular Biophysics, Florida State University, Tallahasse, 32306, USA.
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