1
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Aho N, Groenhof G, Buslaev P. Do All Paths Lead to Rome? How Reliable is Umbrella Sampling Along a Single Path? J Chem Theory Comput 2024. [PMID: 39039621 DOI: 10.1021/acs.jctc.4c00134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
Molecular dynamics (MD) simulations are widely applied to estimate absolute binding free energies of protein-ligand and protein-protein complexes. A routinely used method for binding free energy calculations with MD is umbrella sampling (US), which calculates the potential of mean force (PMF) along a single reaction coordinate. Surprisingly, in spite of its widespread use, few validation studies have focused on the convergence of the free energy computed along a single path for specific cases, not addressing the reproducibility of such calculations in general. In this work, we therefore investigate the reproducibility and convergence of US along a standard distance-based reaction coordinate for various protein-protein and protein-ligand complexes, following commonly used guidelines for the setup. We show that repeating the complete US workflow can lead to differences of 2-20 kcal/mol in computed binding free energies. We attribute those discrepancies to small differences in the binding pathways. While these differences are unavoidable in the established US protocol, the popularity of the latter could hint at a lack of awareness of such reproducibility problems. To test if the convergence of PMF profiles can be improved if multiple pathways are sampled simultaneously, we performed additional simulations with an adaptive-biasing method, here the accelerated weight histogram (AWH) approach. Indeed, the PMFs obtained from AHW simulations are consistent and reproducible for the systems tested. To the best of our knowledge, our work is the first to attempt a systematic assessment of the pitfalls in one the most widely used protocols for computing binding affinities. We anticipate therefore that our results will provide an incentive for a critical reassessment of the validity of PMFs computed with US, and make a strong case to further benchmark the performance of adaptive-biasing methods for computing binding affinities.
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Affiliation(s)
- Noora Aho
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
- Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
| | - Pavel Buslaev
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
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2
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Kanduč M, Schneck E, Netz RR. Understanding the "Berg limit": the 65° contact angle as the universal adhesion threshold of biomatter. Phys Chem Chem Phys 2024; 26:713-723. [PMID: 38100091 DOI: 10.1039/d3cp05084j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2024]
Abstract
Surface phenomena in aqueous environments such as long-range hydrophobic attraction, macromolecular adhesion, and even biofouling are predominantly influenced by a fundamental parameter-the water contact angle. The minimal contact angle required for these and related phenomena to occur has been repeatedly reported to be around 65° and is commonly referred to as the "Berg limit." However, the universality of this specific threshold across diverse contexts has remained puzzling. In this perspective article, we aim to rationalize the reoccurrence of this enigmatic contact angle. We show that the relevant scenarios can be effectively conceptualized as three-phase problems involving the surface of interest, water, and a generic oil-like material that is representative of the nonpolar constituents within interacting entities. Our analysis reveals that attraction and adhesion emerge when substrates display an underwater oleophilic character, corresponding to a "hydrophobicity under oil", which occurs for contact angles above approximately 65°. This streamlined view provides valuable insights into macromolecular interactions and holds implications for technological applications.
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Affiliation(s)
- Matej Kanduč
- Department of Theoretical Physics, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia.
| | - Emanuel Schneck
- Department of Physics, Technische Universität Darmstadt, Hochschulstrasse 8, Darmstadt 64289, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
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3
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Zhang X, Wu R, Liu Q, Zhou L. Interfacial water molecules contribute to antibody binding to the receptor-binding domain of SARS-CoV-2 spike protein. J Biomol Struct Dyn 2023; 41:14929-14938. [PMID: 37042961 DOI: 10.1080/07391102.2023.2199336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 02/18/2023] [Indexed: 04/13/2023]
Abstract
Antibodies that recognize the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), especially the neutralizing antibodies, carry great hope in the treatment and final elimination of COVID-19. Driven by a synchronized global effort, thousands of antibodies against the spike protein have been identified during the past two years, with the structural information available at atomistic detail for hundreds of these antibodies. We developed an improved molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method including explicitly treated interfacial water to calculate the binding free energy between representative antibodies and the receptor binding domain (RBD) domain of SARS-COV-2 spike proteins. We discovered that explicit treatment of water molecules located at the interface between RBD and antibody effectively improves the results for the WT and variants of concern (VOC) systems. Interfacial water molecules, together with surface and internal water molecules, behave drastically from bulk water and exert peculiar impacts on protein dynamics and energy, and thus warrant explicit treatment to complement implicit solvent models. Our results illustrate the importance of including interfacial water molecules to approach efficient and reliable prediction of binding free energy.Communicated by Ramaswamy H. Sarma.
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Affiliation(s)
- Xin Zhang
- Institute of Molecular Physiology, Shenzhen Bay Laboratory, Shenzhen, Guangdong, P.R. China
| | - Ruiping Wu
- Institute of Molecular Physiology, Shenzhen Bay Laboratory, Shenzhen, Guangdong, P.R. China
- Department of Chemistry, Southern University of Science and Technology, Shenzhen, Guangdong, P. R. China
| | - Qinglian Liu
- Department of Physiology and Biophysics, School of Medicine, Virginia Commonwealth University, Richmond, Virginia, USA
| | - Lei Zhou
- Institute of Molecular Physiology, Shenzhen Bay Laboratory, Shenzhen, Guangdong, P.R. China
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4
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Zhu S. Computational characterization of homologous ligands binding to a deep hydrophobic pocket in
Shigella flexneri
pilot protein MxiM. Proteins 2022; 90:2116-2123. [DOI: 10.1002/prot.26402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Revised: 07/10/2022] [Accepted: 07/19/2022] [Indexed: 11/07/2022]
Affiliation(s)
- Shun Zhu
- Department of Cellular and Genetic Medicine, School of Basic Medical Sciences Fudan University Shanghai People's Republic of China
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5
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Suating P, Ernst NE, Alagbe BD, Skinner HA, Mague JT, Ashbaugh HS, Gibb BC. On the Nature of Guest Complexation in Water: Triggered Wetting-Water-Mediated Binding. J Phys Chem B 2022; 126:3150-3160. [PMID: 35438501 PMCID: PMC9059121 DOI: 10.1021/acs.jpcb.2c00628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Revised: 03/18/2022] [Indexed: 11/30/2022]
Abstract
The complexity of macromolecular surfaces means that there are still many open questions regarding how specific areas are solvated and how this might affect the complexation of guests. Contributing to the identification and classification of the different possible mechanisms of complexation events in aqueous solution, and as part of the recent SAMPL8 exercise, we report here on the synthesis and conformational properties of TEEtOA 2, a cavitand with conformationally flexible ethyl groups at its portal. Using a combination of ITC and NMR spectroscopy, we report the binding affinities of a series of carboxylates to 2 and compare it to a related cavitand TEMOA 1. Additionally, we report MD simulations revealing how the wetting of the pocket of 2 is controlled by the conformation of its rim ethyl groups and, correspondingly, a novel triggered wetting, guest complexation mechanism, whereby the approaching guest opens up the pocket of the host, inducing its wetting and ultimately allows the formation of a hydrated host-guest complex (H·G·H2O). A general classification of complexation mechanisms is also suggested.
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Affiliation(s)
- Paolo Suating
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Nicholas E. Ernst
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Busayo D. Alagbe
- Department
of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Hannah A. Skinner
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Joel T. Mague
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Henry S. Ashbaugh
- Department
of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Bruce C. Gibb
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
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6
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Abstract
The intrinsic nature of macrocyclic molecules to preferentially absorb a specific solute has been opening up supramolecular chemistry. Nevertheless, the determinant factor with molecular perspectives in promoting host-guest complexations remains inconclusive, due to the lack of rigorous thermodynamic examination on the guest solubility inside the host. Here, we quantify the solute-solvent energetic and entropic contributions between the end states and on the docking route during inclusion of noble gases in cucurbit[5]uril, cucurbit[6]uril, and α-cyclodextrin, using molecular dynamics simulations in combination with the potential distribution theorem. Results show that in all of the pairs examined both the solute-solvent energy and entropy favor the inclusion, while the former is rather dominant. The frequency of interior drying, which pertains to the entropic contribution, differs between the hosts and is controlled by the existence of lid water at portal and the flexibility of host framework. Moreover, the hosts exhibit various types of absorption manners, involving non-, single-, and double-free-energy barriers.
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Affiliation(s)
- Yifeng Yao
- Department of Chemistry, Zhejiang University, Hangzhou, 310028, P. R. China
| | - Xuan Zhang
- Department of Chemistry, Zhejiang University, Hangzhou, 310028, P. R. China
| | - Kenji Mochizuki
- Department of Chemistry, Zhejiang University, Hangzhou, 310028, P. R. China
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7
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Ashbaugh HS, Gibb BC, Suating P. Cavitand Complexes in Aqueous Solution: Collaborative Experimental and Computational Studies of the Wetting, Assembly, and Function of Nanoscopic Bowls in Water. J Phys Chem B 2021; 125:3253-3268. [PMID: 33651614 PMCID: PMC8040017 DOI: 10.1021/acs.jpcb.0c11017] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Revised: 02/02/2021] [Indexed: 12/17/2022]
Abstract
Water is the dominant liquid on Earth. Despite this, the main focus of supramolecular chemistry research has been on binding and assembly events in organic solvents. This arose because it is more straightforward to synthesize organic-media-soluble hosts and because of the relative simplicity of organic solvents compared to water. Nature, however, relies on water as a solvent, and spurred by this fact, supramolecular chemists have recently been making forays into the aqueous domain to understand water-mediated non-covalent interactions. These studies can benefit from the substantial understanding of the hydrophobic effect and electrostatic interactions developed by physical chemists. Nearly 20 years ago, the Gibb group first synthesized a class of water-soluble host molecules, the deep-cavity cavitands, that possess non-polar pockets that readily bind non-polar moieties in aqueous solution and are capable of assembling into a wide range of complexes with distinct stoichiometries. As such, these amphipathic host species are ideal platforms for studying the role of negatively curved features on guest complexation and the structural requirements for guided assembly processes driven by the hydrophobic effect. Here we review the collaborative experimental and computational investigations between Gibb and Ashbaugh over the past 10 years exploring questions including the following: How does water wet/solvate the non-polar surfaces of non-polar pockets? How does this wetting control the binding of non-polar guests? How does wetting affect the binding of anionic species? How does the nature and size of a guest size impact the assembly of cavitand hosts into multimeric capsular complexes? What are the conformational motifs of guests packed within the confines of capsular complexes? How might the electrostatic environment engendered by hosts impact the properties and reactivity of internalized guests?
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Affiliation(s)
- Henry S. Ashbaugh
- Department
of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Bruce C. Gibb
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Paolo Suating
- Department
of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
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8
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Päslack C, Schäfer LV, Heyden M. Protein flexibility reduces solvent-mediated friction barriers of ligand binding to a hydrophobic surface patch. Phys Chem Chem Phys 2021; 23:5665-5672. [PMID: 33656505 DOI: 10.1039/d1cp00181g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Solvent fluctuations have been explored in detail for idealized and rigid hydrophobic model systems, but so far it has remained unclear how internal protein motions and their coupling to the surrounding solvent affect the dynamics of ligand binding to biomolecular surfaces. Here, molecular dynamics simulations were used to elucidate the solvent-mediated binding of a model ligand to the hydrophobic surface patch of ubiquitin. The ligand's friction profiles reveal pronounced long-time correlations and enhanced friction in the vicinity of the protein, similar to idealized hydrophobic surfaces. Interestingly, these effects are shaped by internal protein motions. Protein flexibility modulates water density fluctuations near the hydrophobic surface patch and smooths out the friction profile of ligand binding.
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Affiliation(s)
- Christopher Päslack
- Theoretical Chemistry, Faculty of Chemistry and Biochemistry, Ruhr University Bochum, D-44780 Bochum, Germany.
| | - Lars V Schäfer
- Theoretical Chemistry, Faculty of Chemistry and Biochemistry, Ruhr University Bochum, D-44780 Bochum, Germany.
| | - Matthias Heyden
- School of Molecular Sciences, Arizona State University, Tempe, AZ 85287-1604, USA.
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9
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Zhang Z, Ricci CG, Fan C, Cheng LT, Li B, McCammon JA. Coupling Monte Carlo, Variational Implicit Solvation, and Binary Level-Set for Simulations of Biomolecular Binding. J Chem Theory Comput 2021; 17:2465-2478. [PMID: 33650860 DOI: 10.1021/acs.jctc.0c01109] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
We develop a hybrid approach that combines the Monte Carlo (MC) method, a variational implicit-solvent model (VISM), and a binary level-set method for the simulation of biomolecular binding in an aqueous solvent. The solvation free energy for the biomolecular complex is estimated by minimizing the VISM free-energy functional of all possible solute-solvent interfaces that are used as dielectric boundaries. This functional consists of the solute volumetric, solute-solvent interfacial, solute-solvent van der Waals interaction, and electrostatic free energy. A technique of shifting the dielectric boundary is used to accurately predict the electrostatic part of the solvation free energy. Minimizing such a functional in each MC move is made possible by our new and fast binary level-set method. This method is based on the approximation of surface area by the convolution of an indicator function with a compactly supported kernel and is implemented by simple flips of numerical grid cells locally around the solute-solvent interface. We apply our approach to the p53-MDM2 system for which the two molecules are approximated by rigid bodies. Our efficient approach captures some of the poses before the final bound state. All-atom molecular dynamics simulations with most of such poses quickly reach the final bound state. Our work is a new step toward realistic simulations of biomolecular interactions. With further improvement of coarse graining and MC sampling, and combined with other models, our hybrid approach can be used to study the free-energy landscape and kinetic pathways of ligand binding to proteins.
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Affiliation(s)
- Zirui Zhang
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Clarisse G Ricci
- Department of Chemistry and Biochemistry and Department of Pharmacology, University of California, San Diego, La Jolla, California 92093-0365, United States
| | - Chao Fan
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Bo Li
- Department of Mathematics and Quantitative Biology Ph.D. Program, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry and Department of Pharmacology, University of California, San Diego, La Jolla, California 92093-0365, United States
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10
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Tang D, Dwyer T, Bukannan H, Blackmon O, Delpo C, Barnett JW, Gibb BC, Ashbaugh HS. Pressure Induced Wetting and Dewetting of the Nonpolar Pocket of Deep-Cavity Cavitands in Water. J Phys Chem B 2020; 124:4781-4792. [PMID: 32403924 DOI: 10.1021/acs.jpcb.0c02568] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Hydrophobic interactions drive the binding of nonpolar ligands to the oily pockets of proteins and supramolecular species in aqueous solution. As such, the wetting of host pockets is expected to play a critical role in determining the thermodynamics of guest binding. Here we use molecular simulations to examine the impact of pressure on the wetting and dewetting of the nonpolar pockets of a series of deep-cavity cavitands in water. The portals to the cavitand pockets are functionalized with both nonpolar (methyl) and polar (hydroxyl) groups oriented pointing either upward or inward toward the pocket. We find wetting of the pocket is favored by the hydroxyl groups and dewetting is favored by the methyl groups. The distribution of waters in the pocket is found to exhibit a two-state-like equilibrium between wet and dry states with a free energy barrier between the two states. Moreover, we demonstrate that the pocket hydration of the cavitands can be collapsed onto a unified adsorption isotherm by assuming the effective pressures within each cavitand pocket differ by a shift pressure that depends on the chemical identity and number of functional groups placed about the portal. These observations support the development of a two-state capillary evaporation model that accurately describes the equilibrium between states and naturally gives rise to the effective shift pressures observed from simulation. This work demonstrates that the hydration of host pockets can be tuned following simple design rules that in turn are expected to impact the thermodynamics of guest complexation.
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Affiliation(s)
- Du Tang
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Tobias Dwyer
- Department of Chemical Engineering, University of Arkansas, Fayetteville, Alaska 72701, United States
| | - Hussain Bukannan
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Odella Blackmon
- Department of Chemistry, William Carey University, Hattiesburg, Mississippi 39401, United States
| | - Courtney Delpo
- Department of Chemistry, Ursinus College, Collegeville, Pennsylvania 19426, United States
| | - J Wesley Barnett
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Bruce C Gibb
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States
| | - Henry S Ashbaugh
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
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11
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Borisov DV, Veselovsky AV. [Ligand-receptor binding kinetics in drug design]. BIOMEDITSINSKAIA KHIMIIA 2020; 66:42-53. [PMID: 32116225 DOI: 10.18097/pbmc20206601042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Traditionally, the thermodynamic values of affinity are considered as the main criterion for the development of new drugs. Usually, these values for drugs are measured <i>in vitro</i> at steady concentrations of the receptor and ligand, which are differed from <i>in vivo</i> environment. Recent studies have shown that the kinetics of the process of drug binding to its receptor make significant contribution in the drug effectiveness. This has increased attention in characterizing and predicting the rate constants of association and dissociation of the receptor ligand at the stage of preclinical studies of drug candidates. A drug with a long residence time can determine ligand-receptor selectivity (kinetic selectivity), maintain pharmacological activity of the drug at its low concentration in vivo. The paper discusses the theoretical basis of protein-ligand binding, molecular determinants that control the kinetics of the drug-receptor binding. Understanding the molecular features underlying the kinetics of receptor-ligand binding will contribute to the rational design of drugs with desired properties.
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Affiliation(s)
- D V Borisov
- Institute of Biomedical Chemistry, Moscow, Russia
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12
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Escalante DE, Aksan A. Role of Water Hydrogen Bonding on Transport of Small Molecules inside Hydrophobic Channels. J Phys Chem B 2019; 123:6673-6685. [PMID: 31310534 DOI: 10.1021/acs.jpcb.9b03060] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We conducted a systematic analysis of water networking inside smooth hyperboloid hydrophobic structures (cylindrical, barrel, and hourglass shapes) to elucidate the role of water hydrogen bonding on the transport of small hydrophobic molecules (ligands). Through a series of molecular dynamics simulations, we established that a hydrogen-bonded network forming along the centerline resulted in a water exclusion zone adjacent to the walls. The size of the exclusion zone is a function of the geometry and the nonbonded interaction strength, defining the effective hydrophobicity of the structure. Exclusion of water molecules from this zone results in lower apparent viscosity, leading to acceleration of ligand transport up to 7 times faster than that measured in the bulk. Transport of ligands into and out of the hydrophobic structures was shown to be controlled by a single water molecule that capped the narrow regions in the structure. This mechanism provides physical insights into the behavior and role of water in the bottleneck regions of hydrophobic enzyme channels. These findings were then used in a sister publication [ Escalante , D. E. , Comput. Struct. Biotechnol. J. 2019 17 757 760 ] to develop a model that can accurately predict the transport of ligands along nanochannels of broad-substrate specificity enzymes.
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Affiliation(s)
- Diego E Escalante
- Department of Mechanical Engineering , University of Minnesota , Minneapolis , Minnesota 55455 , United States
| | - Alptekin Aksan
- Department of Mechanical Engineering , University of Minnesota , Minneapolis , Minnesota 55455 , United States.,BioTechnology Institute , University of Minnesota , St. Paul , Minnesota 55108 , United States
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13
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Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics. Proc Natl Acad Sci U S A 2019; 116:14989-14994. [PMID: 31270236 DOI: 10.1073/pnas.1902719116] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ("dry" and "wet") hydration states. The resulting dry-wet transition rates are then used in a spatially dependent multistate continuous-time Markov chain Brownian dynamics simulation and the related Fokker-Planck equation calculations of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semiquantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of nonequilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding vs. unbinding. Our study thus provides a significant step forward toward efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.
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14
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Weiß RG, Chudoba R, Setny P, Dzubiella J. Affinity, kinetics, and pathways of anisotropic ligands binding to hydrophobic model pockets. J Chem Phys 2018; 149:094902. [DOI: 10.1063/1.5025118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Affiliation(s)
- R. Gregor Weiß
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
- Laboratory of Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Richard Chudoba
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
- Research Group Simulations of Energy Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Straße 3, D-79104 Freiburg, Germany
| | - Piotr Setny
- Centre of New Technologies, University of Warsaw, Stefana Banacha 2c, 00-927 Warsaw, Poland
| | - Joachim Dzubiella
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
- Research Group Simulations of Energy Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Straße 3, D-79104 Freiburg, Germany
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15
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Schuetz DA, Richter L, Amaral M, Grandits M, Grädler U, Musil D, Buchstaller HP, Eggenweiler HM, Frech M, Ecker GF. Ligand Desolvation Steers On-Rate and Impacts Drug Residence Time of Heat Shock Protein 90 (Hsp90) Inhibitors. J Med Chem 2018; 61:4397-4411. [DOI: 10.1021/acs.jmedchem.8b00080] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Doris A. Schuetz
- Department of Pharmaceutical Chemistry, University of Vienna, UZA 2, Althanstrasse 14, 1090 Vienna, Austria
| | - Lars Richter
- Department of Pharmaceutical Chemistry, University of Vienna, UZA 2, Althanstrasse 14, 1090 Vienna, Austria
| | - Marta Amaral
- Discovery Technologies, Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Melanie Grandits
- Department of Pharmaceutical Chemistry, University of Vienna, UZA 2, Althanstrasse 14, 1090 Vienna, Austria
| | - Ulrich Grädler
- Discovery Technologies, Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Djordje Musil
- Discovery Technologies, Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | | | | | - Matthias Frech
- Discovery Technologies, Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Gerhard F. Ecker
- Department of Pharmaceutical Chemistry, University of Vienna, UZA 2, Althanstrasse 14, 1090 Vienna, Austria
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16
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Ricci CG, Li B, Cheng LT, Dzubiella J, McCammon JA. Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly. Front Mol Biosci 2018; 5:13. [PMID: 29484300 PMCID: PMC5816062 DOI: 10.3389/fmolb.2018.00013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Accepted: 01/26/2018] [Indexed: 01/12/2023] Open
Abstract
Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture “dewetting” effects and heterogeneous hydration by relying on a pre-established (i.e., guessed) solvation interface. Here we focus on the Variational Implicit Solvent Method, an implicit solvent method that adds water “plasticity” back to the picture by formulating the solvation free energy as a functional of all possible solvation interfaces. We survey VISM's applications to the problem of molecular recognition and report some of the most recent efforts to tailor VISM for more challenging scenarios, with the ultimate goal of including thermal fluctuations into the framework. The advances reported herein pave the way to make VISM a uniquely successful approach to characterize complex solvation properties in the recognition and binding of large-scale biomolecular complexes.
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Affiliation(s)
- Clarisse Gravina Ricci
- Department of Pharmacology and Department of Chemistry and Biochemistry, National Biomedical Computation Resource, University of California, San Diego, La Jolla, CA, United States
| | - Bo Li
- Department of Mathematics, University of California, San Diego, La Jolla, CA, United States.,Quantitative Biology Graduate Program, University of California, San Diego, La Jolla, CA, United States
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, CA, United States
| | - Joachim Dzubiella
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany.,Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Berlin, Germany
| | - J Andrew McCammon
- Department of Pharmacology and Department of Chemistry and Biochemistry, National Biomedical Computation Resource, University of California, San Diego, La Jolla, CA, United States
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17
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Affiliation(s)
- Qing Shao
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Carol K. Hall
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
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18
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Ricci CG, Li B, Cheng LT, Dzubiella J, McCammon JA. "Martinizing" the Variational Implicit Solvent Method (VISM): Solvation Free Energy for Coarse-Grained Proteins. J Phys Chem B 2017; 121:6538-6548. [PMID: 28613904 PMCID: PMC5740479 DOI: 10.1021/acs.jpcb.7b04113] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Solvation is a fundamental driving force in many biological processes including biomolecular recognition and self-assembly, not to mention protein folding, dynamics, and function. The variational implicit solvent method (VISM) is a theoretical tool currently developed and optimized to estimate solvation free energies for systems of very complex topology, such as biomolecules. VISM's theoretical framework makes it unique because it couples hydrophobic, van der Waals, and electrostatic interactions as a functional of the solvation interface. By minimizing this functional, VISM produces the solvation interface as an output of the theory. In this work, we push VISM to larger scale applications by combining it with coarse-grained solute Hamiltonians adapted from the MARTINI framework, a well-established mesoscale force field for modeling large-scale biomolecule assemblies. We show how MARTINI-VISM (MVISM) compares with atomistic VISM (AVISM) for a small set of proteins differing in size, shape, and charge distribution. We also demonstrate MVISM's suitability to study the solvation properties of an interesting encounter complex, barnase-barstar. The promising results suggest that coarse-graining the protein with the MARTINI force field is indeed a valuable step to broaden VISM's and MARTINI's applications in the near future.
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Affiliation(s)
- Clarisse G Ricci
- Department of Pharmacology and Department of Chemistry & Biochemistry, Howard Hughes Medical Institute, National Biomedical Computation Resource, University of California at San Diego , La Jolla, California 92093, United States
| | - Bo Li
- Department of Mathematics and Quantitative Biology Graduate Program, University of California at San Diego , La Jolla, California 92093, United States
| | - Li-Tien Cheng
- Department of Mathematics and Quantitative Biology Graduate Program, University of California at San Diego , La Jolla, California 92093, United States
| | - Joachim Dzubiella
- Institut für Physik, Humboldt-Universität zu Berlin, D-12849, Berlin, Germany, and Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin , D-14109, Berlin, Germany
| | - J Andrew McCammon
- Department of Pharmacology and Department of Chemistry & Biochemistry, Howard Hughes Medical Institute, National Biomedical Computation Resource, University of California at San Diego , La Jolla, California 92093, United States
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19
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Weiß RG, Setny P, Dzubiella J. Principles for Tuning Hydrophobic Ligand–Receptor Binding Kinetics. J Chem Theory Comput 2017; 13:3012-3019. [DOI: 10.1021/acs.jctc.7b00216] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- R. Gregor Weiß
- Institut
für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
- Institut
für Weiche Materie and Funktionale Materialen, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, D-14109 Berlin, Germany
| | - Piotr Setny
- Centre
of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Joachim Dzubiella
- Institut
für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
- Institut
für Weiche Materie and Funktionale Materialen, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, D-14109 Berlin, Germany
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20
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Djikaev Y, Ruckenstein E. Recent developments in the theoretical, simulational, and experimental studies of the role of water hydrogen bonding in hydrophobic phenomena. Adv Colloid Interface Sci 2016; 235:23-45. [PMID: 27312562 DOI: 10.1016/j.cis.2016.05.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Revised: 04/27/2016] [Accepted: 05/10/2016] [Indexed: 10/21/2022]
Abstract
Hydrophobic effects (hydrophobic hydration and hydrophobic interaction) constitute an important element of a wide variety of phenomena relevant to biological, physical, chemical, environmental, engineering, and pharmaceutical sciences, such as the immiscibility of oil and water, self-assembly of amphiphiles leading to micelle and membrane formation, folding and stability and unfolding of the native structure of a biologically active protein, gating of ion channels, wetting, froth floatation, and adhesion. On the other hand, the hydrogen bonding ability of water plays a major (if not crucial) role in hydrophobic phenomena. We present a review of most important and relatively recent experimental, simulational, and theoretical research on hydrophobic phenomena in various systems. With a particular interest we survey investigations clarifying the role of water hydrogen bonding therein, because it has been the main object of our own recent research. We have developed a probabilistic hydrogen bond (PHB) model that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of its distance to a hydrophobe, hydrophobe radius, and temperature. Knowing that function, one can explicitly identify a water hydrogen bond contribution to the external potential whereto a water molecule is subjected near a hydrophobe. Combining the PHB model with the classical density functional theory (DFT), one can examine the contribution of water hydrogen bonding to the temperature and lengthscale effects on the hydration of particles and on their solvent-mediated interactions over the entire low-to-high temperature and small-to-large lengthscale ranges. We applied the combined DFT/PHB model to study a variety of hydrophobic phenomena such as (liquid) water in contact with a hydrophobic plate, solvation of spherical solutes of various radii in associated and non-associated liquids at various temperatures, the solvent-mediated interaction of spherical solutes and its temperature dependence, interaction of C60 fullerenes in water, temperature effect on the evaporation lengthscale of water confined between two hydrophobes, temperature dependence of the effective width of the solute-solvent transition layer and average density therein. These applications demonstrated that the DFT/PHB model can serve as a valuable tool in studying hydrophobic phenomena because it constitutes a balanced combination of simplicity, accuracy, and detail. The predictions of the combined DFT/PHB approach for the solvent density profiles and thermodynamic aspects of hydrophobic phenomena are generally in good agreement with experiments and simulations. For example, it predicts the small-to-large crossover lengthscale of its mechanism to be approximately in the range from 1nm to 4nm, and decreasing with increasing temperature. It also suggests that, in terms of the average fluid density in the solute-solvent transition layer, the transition layer for small hydrophobes (of radii ≲2 nm) becomes enriched with rather than depleted of fluid when both the solvent-solute affinity and hb-energy alteration ratio become large enough. The boundary values of these parameters, needed for the depletion-to-enrichment crossover, are predicted to decrease with increasing temperature.
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Zhou S, Sun H, Cheng LT, Dzubiella J, Li B, McCammon JA. Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations. J Chem Phys 2016; 145:054114. [PMID: 27497546 PMCID: PMC4975753 DOI: 10.1063/1.4959971] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2016] [Accepted: 07/05/2016] [Indexed: 12/29/2022] Open
Abstract
Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the "normal velocity" that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.
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Affiliation(s)
- Shenggao Zhou
- Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Jiangsu, Suzhou 215006, China
| | - Hui Sun
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, USA
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, USA
| | - Joachim Dzubiella
- Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany and Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Bo Li
- Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, La Jolla, California 92093-0112, USA
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, USA
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22
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Sun H, Zhou S, Moore DK, Cheng LT, Li B. Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules. JOURNAL OF SCIENTIFIC COMPUTING 2016; 67:705-723. [PMID: 27365866 PMCID: PMC4922513 DOI: 10.1007/s10915-015-0099-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Revised: 09/02/2015] [Accepted: 09/05/2015] [Indexed: 06/06/2023]
Abstract
We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.
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Affiliation(s)
- Hui Sun
- Department of Mathematics, University of California, San Diego, CA 92093
| | - Shenggao Zhou
- School of Mathematical Sciences and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, Jiangsu 215006, China
| | - David K. Moore
- Department of Physics, University of California, San Diego, CA 92093
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, CA 92093
| | - Bo Li
- Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, CA 92093
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23
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Weiß RG, Setny P, Dzubiella J. Solvent Fluctuations Induce Non-Markovian Kinetics in Hydrophobic Pocket-Ligand Binding. J Phys Chem B 2016; 120:8127-36. [DOI: 10.1021/acs.jpcb.6b01219] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- R. Gregor Weiß
- Institut
für Physik, Humboldt-Universität zu Berlin, Newtonstrasse
15, D-12489 Berlin, Germany
- Institut
für Weiche Materie and Funktionale Materialen, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, D-14109 Berlin, Germany
| | - Piotr Setny
- Centre
of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Joachim Dzubiella
- Institut
für Physik, Humboldt-Universität zu Berlin, Newtonstrasse
15, D-12489 Berlin, Germany
- Institut
für Weiche Materie and Funktionale Materialen, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, D-14109 Berlin, Germany
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24
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Ou SC, Cui D, Patel S. Molecular modeling of ions at interfaces: exploring similarities to hydrophobic solvation through the lens of induced aqueous interfacial fluctuations. Phys Chem Chem Phys 2016; 18:30357-30365. [DOI: 10.1039/c6cp04112d] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ion specific effects are ubiquitous in chemistry and biology.
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Affiliation(s)
- Shu-Ching Ou
- Sealy Center for Structural Biology and Molecular Biophysics
- University of Texas Medical Branch
- 301 University Boulevard
- Galveston
- USA
| | - Di Cui
- Department of Chemistry
- Temple University
- Philadelphia
- USA
| | - Sandeep Patel
- Department of Chemistry and Biochemistry
- University of Delaware
- Newark
- USA
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25
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Sun H, Wen J, Zhao Y, Li B, McCammon JA. A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics. J Chem Phys 2015; 143:243110. [PMID: 26723595 DOI: 10.1063/1.4932336] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.
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Affiliation(s)
- Hui Sun
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - Jiayi Wen
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - Yanxiang Zhao
- Department of Mathematics, the George Washington University, Monroe Hall, 2115 G St. NW, Washington, DC 20052, USA
| | - Bo Li
- Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, Mail Code 0112. La Jolla, California 92093-0112, USA
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, and Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, USA
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26
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Zhou S, Cheng LT, Sun H, Che J, Dzubiella J, Li B, McCammon JA. LS-VISM: A software package for analysis of biomolecular solvation. J Comput Chem 2015; 36:1047-59. [PMID: 25766844 PMCID: PMC4412808 DOI: 10.1002/jcc.23890] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Accepted: 02/08/2015] [Indexed: 12/30/2022]
Abstract
We introduce a software package for the analysis of biomolecular solvation. The package collects computer codes that implement numerical methods for a variational implicit-solvent model (VISM). The input of the package includes the atomic data of biomolecules under consideration and the macroscopic parameters such as solute-solvent surface tension, bulk solvent density and ionic concentrations, and the dielectric coefficients. The output includes estimated solvation free energies and optimal macroscopic solute-solvent interfaces that are obtained by minimizing the VISM solvation free-energy functional among all possible solute-solvent interfaces enclosing the solute atoms. We review the VISM with various descriptions of electrostatics. We also review our numerical methods that consist mainly of the level-set method for relaxing the VISM free-energy functional and a compact coupling interface method for the dielectric Poisson-Boltzmann equation. Such numerical methods and algorithms constitute the central modules of the software package. We detail the structure of the package, format of input and output files, workflow of the codes, and the postprocessing of output data. Our demo application to a host-guest system illustrates how to use the package to perform solvation analysis for biomolecules, including ligand-receptor binding systems. The package is simple and flexible with respect to minimum adjustable parameters and a wide range of applications. Future extensions of the package use can include the efficient identification of ligand binding pockets on protein surfaces.
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Affiliation(s)
- Shenggao Zhou
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Hui Sun
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Jianwei Che
- Parallel Computing Labs, 3525 Del Mar Heights Road, No. 288, San Diego, CA 92130
| | - Joachim Dzubiella
- Soft Matter and Functional Materials, Helmholtz-Center Berlin, 14109 Berlin, Germany, and Physics Department, Humboldt-University of Berlin, 12489 Berlin, Germany
| | - Bo Li
- Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J. Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, United States
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27
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Sim AYL, Verma C. How does a hydrocarbon staple affect peptide hydrophobicity? J Comput Chem 2015; 36:773-84. [DOI: 10.1002/jcc.23859] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Revised: 01/06/2015] [Accepted: 01/19/2015] [Indexed: 11/09/2022]
Affiliation(s)
- Adelene Y. L. Sim
- Bioinformatics Institute (A*STAR); 30 Biopolis Street #07-01 Matrix 138671 Singapore
| | - Chandra Verma
- Bioinformatics Institute (A*STAR); 30 Biopolis Street #07-01 Matrix 138671 Singapore
- School of Biological Sciences, Nanyang Technological University; 60 Nanyang Drive 637551 Singapore
- Department of Biological Sciences; National University of Singapore; 14 Science Drive 4 Singapore 117543
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28
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LI BO, SUN HUI, ZHOU SHENGGAO. STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS. SIAM JOURNAL ON APPLIED MATHEMATICS 2015; 75:907-928. [PMID: 26877555 PMCID: PMC4752181 DOI: 10.1137/140972093] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.
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Affiliation(s)
- BO LI
- Department of Mathematics and NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
| | - HUI SUN
- Department of Mathematics and NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
| | - SHENGGAO ZHOU
- Department of Mathematics and NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
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29
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Klebe G. The Use of Thermodynamic and Kinetic Data in Drug Discovery: Decisive Insight or Increasing the Puzzlement? ChemMedChem 2014; 10:229-31. [DOI: 10.1002/cmdc.201402521] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 11/07/2022]
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30
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Varma S, Botlani M, Leighty RE. Discerning intersecting fusion-activation pathways in the Nipah virus using machine learning. Proteins 2014; 82:3241-54. [DOI: 10.1002/prot.24541] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2014] [Revised: 02/10/2014] [Accepted: 02/14/2014] [Indexed: 12/19/2022]
Affiliation(s)
- Sameer Varma
- Department of Cell Biology; Microbiology and Molecular Biology, University of South Florida; Tampa Florida 33620
| | - Mohsen Botlani
- Department of Cell Biology; Microbiology and Molecular Biology, University of South Florida; Tampa Florida 33620
| | - Ralph E. Leighty
- Department of Cell Biology; Microbiology and Molecular Biology, University of South Florida; Tampa Florida 33620
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31
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Ou SC, Patel S. Electrostatic contribution from solvent in modulating single-walled carbon nanotube association. J Chem Phys 2014; 141:114906. [PMID: 25240371 PMCID: PMC4187323 DOI: 10.1063/1.4892566] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2014] [Accepted: 07/28/2014] [Indexed: 11/14/2022] Open
Abstract
We perform all-atom molecular dynamics simulations to compute the potential of mean force (PMF) between two (10,10) single-walled carbon nanotubes solvated in pure nonpolarizable SPC/E and polarizable TIP4P-FQ water, at various temperatures. In general, the reversible work required to bring two nanotubes from a dissociated state (free energy reference) to contact state (free energy minimum) is more favorable and less temperature-dependent in TIP4P-FQ than in SPC/E water models. In contrast, molecular properties and behavior of water such as the spatially-resolved water number density (intertube, intratube, or outer regions), for TIP4P-FQ are more sensitive to temperature than SPC/E. Decomposition of the solvent-induced PMF into different spatial regions suggests that TIP4P-FQ has stronger temperature dependence; the opposing destabilizing/stabilizing contributions from intertube water and more distal water balance each other and suppress the temperature dependence of total association free energy. Further investigation of hydrogen bonding network in intertube water reveals that TIP4P-FQ retains fewer hydrogen bonds than SPC/E, which correlates with the lower water number density in this region. This reduction of hydrogen bonds affects the intertube water dipoles. As the intertube volume decreases, TIP4P-FQ dipole moment approaches the gas phase value; the distribution of dipole magnitude also becomes narrower due to less average polarization/perturbation from other water molecules. Our results imply that the reduction of water under confinement may seem trivial, but underlying effects to structure and free energetics are non-negligible.
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Affiliation(s)
- Shu-Ching Ou
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, USA
| | - Sandeep Patel
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, USA
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32
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Abstract
The stability of liquids under solvophobic confinement can tip in favor of the vapor phase, nucleating a liquid-to-vapor phase transition that induces attractive forces between confining surfaces. In the case of water adjacent to hydrophobic surfaces, experimental and theoretical evidence support confinement-mediated evaporation stabilization of biomolecular and colloidal assemblies. The macroscopic thermodynamic theory of cavitation under confinement establishes the connection between the size of the confining surfaces, interfacial free energies, and bulk solvent pressure with the critical evaporation separation and interfacial forces. While molecular simulations have confirmed the broad theoretical trends, a quantitative comparison based on independent measurements of the interfacial free energies and liquid-vapor coexistence properties has, to the best of our knowledge, not yet been performed. To overcome the challenges of simulating a large number of systems to validate scaling predictions for a three-dimensional fluid, we simulate both the forces and liquid-vapor coexistence properties of a two-dimensional Lennard-Jones fluid confined between solvophobic plates over a range of plate sizes and reservoir pressures. Our simulations quantitatively agree with theoretical predictions for solvent-mediated forces and critical evaporation separations once the length dependence of the solvation free energy of an individual confining plate is taken into account. The effective solid-liquid line tension length dependence results from molecular scale correlations for solvating microscopic plates and asymptotically decays to the macroscopic value for plates longer than 150 solvent diameters. The success of the macroscopic thermodynamic theory at describing two-dimensional liquids suggests application to surfactant monolayers to experimentally confirm confinement-mediated cavitation.
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Affiliation(s)
- Henry S Ashbaugh
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, USA.
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33
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Wanjari PP, Gibb BC, Ashbaugh HS. Simulation optimization of spherical non-polar guest recognition by deep-cavity cavitands. J Chem Phys 2014; 139:234502. [PMID: 24359375 DOI: 10.1063/1.4844215] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Biomimetic deep-cavity cavitand hosts possess unique recognition and encapsulation properties that make them capable of selectively binding a range of non-polar guests within their hydrophobic pocket. Adamantane based derivatives which snuggly fit within the pocket of octa-acid deep cavity cavitands exhibit some of the strongest host binding. Here we explore the roles of guest size and attractiveness on optimizing guest binding to form 1:1 complexes with octa-acid cavitands in water. Specifically we simulate the water-mediated interactions of the cavitand with adamantane and a range of simple Lennard-Jones guests of varying diameter and attractive well-depth. Initial simulations performed with methane indicate hydrated methanes preferentially reside within the host pocket, although these guests frequently trade places with water and other methanes in bulk solution. The interaction strength of hydrophobic guests increases with increasing size from sizes slightly smaller than methane to Lennard-Jones guests comparable in size to adamantane. Over this guest size range the preferential guest binding location migrates from the bottom of the host pocket upwards. For guests larger than adamantane, however, binding becomes less favorable as the minimum in the potential-of-mean force shifts to the cavitand face around the portal. For a fixed guest diameter, the Lennard-Jones well-depth is found to systematically shift the guest-host potential-of-mean force to lower free energies, however, the optimal guest size is found to be insensitive to increasing well-depth. Ultimately our simulations show that adamantane lies within the optimal range of guest sizes with significant attractive interactions to match the most tightly bound Lennard-Jones guests studied.
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Affiliation(s)
- Piyush P Wanjari
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, USA
| | - Bruce C Gibb
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
| | - Henry S Ashbaugh
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, USA
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34
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Müller A, Garai S, Schäffer C, Merca A, Bögge H, Al-Karawi AJM, Prasad TK. Water repellency in hydrophobic nanocapsules--molecular view on dewetting. Chemistry 2014; 20:6659-64. [PMID: 24782303 DOI: 10.1002/chem.201402216] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2014] [Indexed: 11/11/2022]
Abstract
The hydrophobic effect plays a major role in a variety of important phenomena in chemistry, materials science and biology, for instance in protein folding and protein-ligand interactions. Studies--performed within cavities of the unique metal oxide based porous capsules of the type {(pentagon)12(linker)30}≡{(W)W5}12{Mo2(ligand)}30 with different acetate/water ligand ratios--have provided unprecedented results revealing segregation/repellency of the encapsulated "water" from the internal hydrophobic ligand walls of the capsules, while the disordered water molecules, interacting strongly with each other via hydrogen bonding, form in all investigated cases the same type of spherical shell. The present results can be (formally) compared--but only regarding the repellency effect--with the amazing "action" of the (super)hydrophobic Lotus (Nelumbo) leaves, which are self-cleaning based on water repellency resulting in the formation of water droplets picking up dirt. The present results were obtained by constructing deliberately suitable hydrophobic interiors within the mentioned capsules.
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Affiliation(s)
- Achim Müller
- Fakultät für Chemie, Universität Bielefeld, Postfach 100131, 33501 Bielefeld (Germany), Fax: (+49) 521-106-6003.
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35
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Zhou S, Cheng LT, Dzubiella J, Li B, McCammon JA. Variational Implicit Solvation with Poisson-Boltzmann Theory. J Chem Theory Comput 2014; 10:1454-1467. [PMID: 24803864 PMCID: PMC3985794 DOI: 10.1021/ct401058w] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Indexed: 12/26/2022]
Abstract
We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host-guest system. We finally discuss several issues for further improvement of VISM.
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Affiliation(s)
- Shenggao Zhou
- Department
of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Li-Tien Cheng
- Department
of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - Joachim Dzubiella
- Soft
Matter and Functional Materials, Helmholtz-Center Berlin, 14109 Berlin,
Germany, and Physics Department, Humboldt-University
of Berlin, 12489 Berlin, Germany
| | - Bo Li
- Department
of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093-0112, United States
| | - J. Andrew McCammon
- Department
of Chemistry and Biochemistry, Department of Pharmacology, Center
for Theoretical Biological Physics, and Howard Hughes Medical Institute, University of California, San Diego, La Jolla, California 92093-0365, United States
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36
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Müller A, Gouzerh P. Capsules with Highly Active Pores and Interiors: Versatile Platforms at the Nanoscale. Chemistry 2014; 20:4862-73. [DOI: 10.1002/chem.201305010] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
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37
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Cao Y, Li L. Improved protein–ligand binding affinity prediction by using a curvature-dependent surface-area model. Bioinformatics 2014; 30:1674-80. [DOI: 10.1093/bioinformatics/btu104] [Citation(s) in RCA: 78] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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38
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Guo Z, Li B, Dzubiella J, Cheng LT, McCammon JA, Che J. Heterogeneous Hydration of p53/MDM2 Complex. J Chem Theory Comput 2014; 10:1302-1313. [PMID: 24803860 PMCID: PMC3958133 DOI: 10.1021/ct400967m] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2013] [Indexed: 12/23/2022]
Abstract
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Water-mediated
interactions play critical roles in biomolecular
recognition processes. Explicit solvent molecular dynamics (MD) simulations
and the variational implicit-solvent model (VISM) are used to study
those hydration properties during binding for the biologically important
p53/MDM2 complex. Unlike simple model solutes, in such a realistic
and heterogeneous solute–solvent system with both geometrical
and chemical complexity, the local water distribution sensitively
depends on nearby amino acid properties and the geometric shape of
the protein. We show that the VISM can accurately describe the locations
of high and low density solvation shells identified by the MD simulations
and can explain them by a local coupling balance of solvent–solute
interaction potentials and curvature. In particular, capillary transitions
between local dry and wet hydration states in the binding pocket are
captured for interdomain distance between 4 to 6 Å, right at
the onset of binding. The underlying physical connection between geometry
and polarity is illustrated and quantified. Our study offers a microscopic
and physical insight into the heterogeneous hydration behavior of
the biologically highly relevant p53/MDM2 system and demonstrates
the fundamental importance of hydrophobic effects for biological binding
processes. We hope our study can help to establish new design rules
for drugs and medical substances.
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Affiliation(s)
- Zuojun Guo
- Genomics Institute of the Novartis Research Foundation , 10675 John Jay Hopkins Drive, San Diego, California 92121, United States
| | - Bo Li
- Department of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego , 9500 Gilman Drive, La Jolla, California 92093-0112, United States
| | - Joachim Dzubiella
- Department of Physics, Humboldt University of Berlin , Newtonstr. 15, 12489 Berlin, Germany ; Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin , Hahn-Meitner Platz 1, 14109 Berlin, Germany
| | - Li-Tien Cheng
- Department of Mathematics, University of California, San Diego , 9500 Gilman Drive, La Jolla, California 92093-0112, United States
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, and Center for Theoretical Biological Physics, University of California , San Diego, 9500 Gilman Drive, La Jolla, California 92093-0365, United States
| | - Jianwei Che
- Genomics Institute of the Novartis Research Foundation , 10675 John Jay Hopkins Drive, San Diego, California 92121, United States
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39
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Molinero V. Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water. J Chem Phys 2013; 139:054511. [DOI: 10.1063/1.4816005] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Zhou S, Rogers KE, de Oliveira CAF, Baron R, Cheng LT, Dzubiella J, Li B, McCammon JA. Variational Implicit-Solvent Modeling of Host-Guest Binding: A Case Study on Cucurbit[7]uril|. J Chem Theory Comput 2013; 9:4195-4204. [PMID: 24039554 PMCID: PMC3770055 DOI: 10.1021/ct400232m] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Indexed: 01/18/2023]
Abstract
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The synthetic host
cucurbit[7]uril (CB[7]) binds aromatic guests
or metal complexes with ultrahigh affinity compared with that typically
displayed in protein–ligand binding. Due to its small size,
CB[7] serves as an ideal receptor–ligand system for developing
computational methods for molecular recognition. Here, we apply the
recently developed variational implicit-solvent model (VISM), numerically
evaluated by the level-set method, to study hydration effects in the
high-affinity binding of the B2 bicyclo[2.2.2]octane derivative to
CB[7]. For the unbound host, we find that the host cavity favors the
hydrated state over the dry state due to electrostatic effects. For
the guest binding, we find reasonable agreement to experimental binding
affinities. Dissection of the individual VISM free-energy contributions
shows that the major driving forces are water-mediated hydrophobic
interactions and the intrinsic (vacuum) host–guest van der
Waals interactions. These findings are in line with recent experiments
and molecular dynamics simulations with explicit solvent. It is expected
that the level-set VISM, with further refinement on the electrostatic
descriptions, can efficiently predict molecular binding and recognition
in a wide range of future applications.
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Affiliation(s)
- Shenggao Zhou
- Department of Mathematics and Center for Theoretical Biological Physics, University of California , San Diego, La Jolla, California 92093-0112, United States
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41
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Zhao Y, Kwan YY, Che J, Li B, McCammon JA. Phase-field approach to implicit solvation of biomolecules with Coulomb-field approximation. J Chem Phys 2013; 139:024111. [PMID: 23862933 DOI: 10.1063/1.4812839] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A phase-field variational implicit-solvent approach is developed for the solvation of charged molecules. The starting point of such an approach is the representation of a solute-solvent interface by a phase field that takes one value in the solute region and another in the solvent region, with a smooth transition from one to the other on a small transition layer. The minimization of an effective free-energy functional of all possible phase fields determines the equilibrium conformations and free energies of an underlying molecular system. All the surface energy, the solute-solvent van der Waals interaction, and the electrostatic interaction are coupled together self-consistently through a phase field. The surface energy results from the minimization of a double-well potential and the gradient of a field. The electrostatic interaction is described by the Coulomb-field approximation. Accurate and efficient methods are designed and implemented to numerically relax an underlying charged molecular system. Applications to single ions, a two-plate system, and a two-domain protein reveal that the new theory and methods can capture capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics simulations. Comparisons of the phase-field and the original sharp-interface variational approaches are discussed.
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Affiliation(s)
- Yanxiang Zhao
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, California 92093-0112, USA.
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42
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Pan AC, Borhani DW, Dror RO, Shaw DE. Molecular determinants of drug–receptor binding kinetics. Drug Discov Today 2013; 18:667-73. [DOI: 10.1016/j.drudis.2013.02.007] [Citation(s) in RCA: 265] [Impact Index Per Article: 24.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2012] [Revised: 02/01/2013] [Accepted: 02/15/2013] [Indexed: 12/01/2022]
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43
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Affiliation(s)
- Riccardo Baron
- Department of Medicinal Chemistry, College of Pharmacy, and The Henry Eyring Center for Theoretical Chemistry, The University of Utah, Salt Lake City, Utah 84112-5820;
| | - J. Andrew McCammon
- Howard Hughes Medical Institute, Department of Chemistry and Biochemistry, Department of Pharmacology, and Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, California 92093-0365;
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44
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Guo Z, Li B, Dzubiella J, Cheng LT, McCammon JA, Che J. Evaluation of Hydration Free Energy by Level-Set Variational Implicit-Solvent Model with Coulomb-Field Approximation. J Chem Theory Comput 2013; 9:1778-1787. [PMID: 23505345 PMCID: PMC3596957 DOI: 10.1021/ct301087w] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2012] [Indexed: 01/22/2023]
Abstract
![]()
In this article, we systematically apply a novel implicit-solvent
model, the variational implicit-solvent model (VISM) together with
the Coulomb-Field Approximation (CFA), to calculate the hydration
free energy of a large set of small organic molecules. Because these
molecules have been studied in detail by molecular dynamics simulations
and other implicit-solvent models, they provide a good benchmark for
evaluating the performance of VISM-CFA. With all-atom Amber force
field parameters, VISM-CFA is able to reproduce well not only the
experimental and MD simulated total hydration free energy but also
the polar and nonpolar contributions individually. The correlation
between VISM-CFA and experiments is R2 = 0.763 for the total hydration free energy, with a root-mean-square
deviation (RMSD) of 1.83 kcal/mol, and the correlation to results
from TIP3P explicit water MD simulations is R2 = 0.839 with a RMSD = 1.36 kcal/mol. In addition, we demonstrate
that VISM captures dewetting phenomena in the p53/MDM2 complex and
hydrophobic characteristics in the system. This work demonstrates
that the level-set VISM-CFA can be used to study the energetic behavior
of realistic molecular systems with complicated geometries in solvation,
protein–ligand binding, protein–protein association,
and protein folding processes.
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Affiliation(s)
- Zuojun Guo
- Genomics Institute of the Novartis Research Foundation, 10675 John Jay Hopkins Drive, San Diego, California 92121, United States
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45
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Solvent fluctuations in hydrophobic cavity-ligand binding kinetics. Proc Natl Acad Sci U S A 2013; 110:1197-202. [PMID: 23297241 DOI: 10.1073/pnas.1221231110] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Water plays a crucial part in virtually all protein-ligand binding processes in and out of equilibrium. Here, we investigate the role of water in the binding kinetics of a ligand to a prototypical hydrophobic pocket by explicit-water molecular dynamics (MD) simulations and implicit diffusional approaches. The concave pocket in the unbound state exhibits wet/dry hydration oscillations whose magnitude and time scale are significantly amplified by the approaching ligand. In turn, the ligand's stochastic motion intimately couples to the slow hydration fluctuations, leading to a sixfold-enhanced friction in the vicinity of the pocket entrance. The increased friction considerably decelerates association in the otherwise barrierless system, indicating the importance of molecular-scale hydrodynamic effects in cavity-ligand binding arising due to capillary fluctuations. We derive and analyze the diffusivity profile and show that the mean first passage time distribution from the MD simulation can be accurately reproduced by a standard Brownian dynamics simulation if the appropriate position-dependent friction profile is included. However, long-time decays in the water-ligand (random) force autocorrelation demonstrate violation of the Markovian assumption, challenging standard diffusive approaches for rate prediction. Remarkably, the static friction profile derived from the force correlations strongly resembles the profile derived on the Markovian assumption apart from a simple shift in space, which can be rationalized by a time-space retardation in the ligand's downhill dynamics toward the pocket. The observed spatiotemporal hydrodynamic coupling may be of biological importance providing the time needed for conformational receptor-ligand adjustments, typical of the induced-fit paradigm.
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46
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Li B, Zhao Y. Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models. SIAM JOURNAL ON APPLIED MATHEMATICS 2013; 73:1-23. [PMID: 24058213 PMCID: PMC3778507 DOI: 10.1137/120883426] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.
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Affiliation(s)
- Bo Li
- Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
| | - Yanxiang Zhao
- Department of Mathematics, and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
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47
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Cheng LT, Li B, White M, Zhou S. Motion of a Cylindrical Dielectric Boundary. SIAM JOURNAL ON APPLIED MATHEMATICS 2013; 73:594-616. [PMID: 23885130 PMCID: PMC3718573 DOI: 10.1137/120867986] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The interplay between geometry and electrostatics contributes significantly to hydrophobic interactions of biomolecules in an aqueous solution. With an implicit solvent, such a system can be described macroscopically by the dielectric boundary that separates the high-dielectric solvent from low-dielectric solutes. This work concerns the motion of a model cylindrical dielectric boundary as the steepest descent of a free-energy functional that consists of both the surface and electrostatic energies. The effective dielectric boundary force is defined and an explicit formula of the force is obtained. It is found that such a force always points from the solvent region to solute region. In the case that the interior of a cylinder is of a lower dielectric, the motion of the dielectric boundary is initially driven dominantly by the surface force but is then driven inward quickly to the cylindrical axis by both the surface and electrostatic forces. In the case that the interior of a cylinder is of a higher dielectric, the competition between the geometrical and electrostatic contributions leads to the existence of equilibrium boundaries that are circular cylinders. Linear stability analysis is presented to show that such an equilibrium is only stable for a perturbation with a wavenumber larger than a critical value. Numerical simulations are reported for both of the cases, confirming the analysis on the role of each component of the driving force. Implications of the mathematical findings to the understanding of charged molecular systems are discussed.
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Affiliation(s)
- Li-Tien Cheng
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
| | - Bo Li
- Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
| | - Michael White
- Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, U.S.A
| | - Shenggao Zhou
- Department of Mathematics, Zhejiang University, No. 38 Zheda Road, Hangzhou, 310027, P. R. China, and Department of Mathematics and the NSF Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, USA
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48
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Biedermann F, Uzunova VD, Scherman OA, Nau WM, De Simone A. Release of High-Energy Water as an Essential Driving Force for the High-Affinity Binding of Cucurbit[n]urils. J Am Chem Soc 2012; 134:15318-23. [DOI: 10.1021/ja303309e] [Citation(s) in RCA: 401] [Impact Index Per Article: 33.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Frank Biedermann
- Melville Laboratory for Polymer
Synthesis and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, U.K
| | - Vanya D. Uzunova
- School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen,
Germany
| | - Oren A. Scherman
- Melville Laboratory for Polymer
Synthesis and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, U.K
| | - Werner M. Nau
- School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen,
Germany
| | - Alfonso De Simone
- Division of Molecular
Biosciences, Imperial College London, South
Kensington, SW7 2AZ,
U.K
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49
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Jamadagni SN, Godawat R, Garde S. Hydrophobicity of proteins and interfaces: insights from density fluctuations. Annu Rev Chem Biomol Eng 2012; 2:147-71. [PMID: 22432614 DOI: 10.1146/annurev-chembioeng-061010-114156] [Citation(s) in RCA: 170] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Macroscopic characterizations of hydrophobicity (e.g., contact angle measurements) do not extend to the surfaces of proteins and nanoparticles. Molecular measures of hydrophobicity of such surfaces need to account for the behavior of hydration water. Theory and state-of-the-art simulations suggest that water density fluctuations provide such a measure; fluctuations are enhanced near hydrophobic surfaces and quenched with increasing surface hydrophilicity. Fluctuations affect conformational equilibria and dynamics of molecules at interfaces. Enhanced fluctuations are reflected in enhanced cavity formation, more favorable binding of hydrophobic solutes, increased compressibility of hydration water, and enhanced water-water correlations at hydrophobic surfaces. These density fluctuation-based measures can be used to develop practical methods to map the hydrophobicity/philicity of heterogeneous surfaces including those of proteins. They highlight that the hydrophobicity of a group is context dependent and is significantly affected by its environment (e.g., chemistry and topography) and especially by confinement. The ability to include information about hydration water in mapping hydrophobicity is expected to significantly impact our understanding of protein-protein interactions as well as improve drug design and discovery methods and bioseparation processes.
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Affiliation(s)
- Sumanth N Jamadagni
- The Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
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50
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Jin Z, Kim J, Wu J. Shape effect on nanoparticle solvation: a comparison of morphometric thermodynamics and microscopic theories. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2012; 28:6997-7006. [PMID: 22500946 DOI: 10.1021/la2051178] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Conventional wisdom for controlling the nanoparticle size and shape during synthesis is that particle growth favors the direction of a facet with the highest surface energy. However, the particle solvation free energy, which dictates the particle stability and growth, depends not only on the surface area and surface free energy but also on other geometric measures such as the solvent excluded volume and the surface curvature and their affiliated thermodynamic properties. In this work, we study the geometrical effects on the solvation free energies of nonspherical nanoparticles using morphometric thermodynamics and density functional theories. For idealized systems that account for only molecular excluded-volume interactions, morphometric thermodynamics yields a reliable solvation free energy when the particle size is significantly larger than the solvent correlation length. However, noticeable deviations can be identified in comparison to the microscopic theories for predicting the solvation free energies of small nanoparticles. This conclusion also holds for predicting the potential of mean force underlying the colloidal "key-and-lock" interactions. Complementary to the microscopic theories, morphometric thermodynamics requires negligible computational cost, therefore making it very appealing for a broad range of practical applications.
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Affiliation(s)
- Zhehui Jin
- Department of Chemical and Environmental Engineering, University of California-Riverside, Riverside, California 92521, United States
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