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Galassi VV, Wilke N. On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes. MEMBRANES 2021; 11:478. [PMID: 34203412 PMCID: PMC8306103 DOI: 10.3390/membranes11070478] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 06/18/2021] [Accepted: 06/22/2021] [Indexed: 12/24/2022]
Abstract
Cell membrane structure is proposed as a lipid matrix with embedded proteins, and thus, their emerging mechanical and electrostatic properties are commanded by lipid behavior and their interconnection with the included and absorbed proteins, cytoskeleton, extracellular matrix and ionic media. Structures formed by lipids are soft, dynamic and viscoelastic, and their properties depend on the lipid composition and on the general conditions, such as temperature, pH, ionic strength and electrostatic potentials. The dielectric constant of the apolar region of the lipid bilayer contrasts with that of the polar region, which also differs from the aqueous milieu, and these changes happen in the nanometer scale. Besides, an important percentage of the lipids are anionic, and the rest are dipoles or higher multipoles, and the polar regions are highly hydrated, with these water molecules forming an active part of the membrane. Therefore, electric fields (both, internal and external) affects membrane thickness, density, tension and curvature, and conversely, mechanical deformations modify membrane electrostatics. As a consequence, interfacial electrostatics appears as a highly important parameter, affecting the membrane properties in general and mechanical features in particular. In this review we focus on the electromechanical behavior of lipid and cell membranes, the physicochemical origin and the biological implications, with emphasis in signal propagation in nerve cells.
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Affiliation(s)
- Vanesa Viviana Galassi
- Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, Mendoza M5500, Argentina;
- Instituto Interdisciplinario de Ciencias Básicas (ICB), Universidad Nacional de Cuyo, CONICET, Mendoza M5500, Argentina
| | - Natalia Wilke
- Departamento de Química Biológica Ranwel Caputto, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Córdoba X5000HUA, Argentina
- Centro de Investigaciones en Química Biológica de Córdoba (CIQUIBIC), Universidad Nacional de Córdoba, CONICET, Córdoba X5000HUA, Argentina
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Sathappa M, Alder NN. The ionization properties of cardiolipin and its variants in model bilayers. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:1362-72. [PMID: 26965987 DOI: 10.1016/j.bbamem.2016.03.007] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2015] [Revised: 02/25/2016] [Accepted: 03/03/2016] [Indexed: 01/01/2023]
Abstract
The anionic phospholipid cardiolipin has an unusual dimeric structure with a two-phosphate headgroup and four acyl chains. Cardiolipin is present in energy-transducing membranes that maintain electrochemical gradients, including most bacterial plasma membranes and the mitochondrial inner membrane, where it mediates respiratory complex assembly and activation, among many other roles. Dysfunctional biogenesis of cardiolipin is implicated in the pathogenesis of several diseases including Barth syndrome. Because cardiolipin is a dominant anionic lipid in energy-conserving membranes, its headgroup is a major contributor to surface charge density and the bilayer electrostatic profile. However, the proton dissociation behavior of its headgroup remains controversial. In one model, the pKa values of the phosphates differ by several units and the headgroup exists as a monoanion at physiological pH. In another model, both phosphates ionize as strong acids with low pKa values and the headgroup exists in dianionic form at physiological pH. Using independent electrokinetic and spectroscopic approaches, coupled with analysis using Gouy-Chapman-Stern formalism, we have analyzed the ionization properties of cardiolipin within biologically relevant lipid bilayer model systems. We show that both phosphates of the cardiolipin headgroup show strong ionization behavior with low pKa values. Moreover, cardiolipin variants lacking structural features proposed to be required to maintain disparate pKa values--namely the secondary hydroxyl on the central glycerol or a full complement of four acyl chains--were shown to have ionization behavior identical to intact cardiolipin. Hence, these results indicate that within the physiological pH range, the cardiolipin headgroup is fully ionized as a dianion. We discuss the implications of these results with respect to the role of cardiolipin in defining membrane surface potential, activating respiratory complexes, and modulating membrane curvature.
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Affiliation(s)
- Murugappan Sathappa
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, United States
| | - Nathan N Alder
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, United States.
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Pierrat P, Lebeau L. Characterization of Titratable Amphiphiles in Lipid Membranes by Fluorescence Spectroscopy. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:12362-12371. [PMID: 26507074 DOI: 10.1021/acs.langmuir.5b03258] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Understanding the ionization behavior of lipid membranes is a key parameter for successful development of lipid-based drug delivery systems. Accurate determination of the ionization state of a titratable species incorporated in a lipid bilayer however requires special care. Herein we investigated the behavior of titratable lipids in liposomes by fluorescence spectroscopy and determined which extrinsic parameters-i.e., besides those directly related to their molecular structure-determine their ionization state. Two fluorescent dyes, TNS and R18, have been used to investigate basic and acidic titratable lipids, respectively. Our results suggest that the titration behavior of the ionizable lipid in the membrane is more sensitive to the composition of the membrane and to its physical state than to the presence of solutes in the aqueous phase. Essentially overlooked in earlier studies on ionizable lipid assemblies, the concentration of the titratable lipid in the membrane was found to have a major effect on the ionization state of the lipid polar head. This may result in a shift in the apparent pKa value which may be as large as two pKa units and cannot be satisfactorily predicted.
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Affiliation(s)
- Philippe Pierrat
- Laboratoire de Conception et Application de Molécules Bioactives, Faculté de Pharmacie, UMR7199 CNRS - Université de Strasbourg , 74 route du Rhin - BP 60024, 67401 Illkirch, France
| | - Luc Lebeau
- Laboratoire de Conception et Application de Molécules Bioactives, Faculté de Pharmacie, UMR7199 CNRS - Université de Strasbourg , 74 route du Rhin - BP 60024, 67401 Illkirch, France
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Caruso B, Villarreal M, Reinaudi L, Wilke N. Inter-Domain Interactions in Charged Lipid Monolayers. J Phys Chem B 2014; 118:519-29. [DOI: 10.1021/jp408053a] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Benjamín Caruso
- Centro de Investigaciones en Química Biológica de Córdoba
(CIQUIBIC), Dpto. de Química Biológica, and ‡Instituto de Investigaciones
en Físico-Química de Córdoba (INFIQC), Dpto.
de Matemática y Física, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Pabellón Argentina, Ciudad Universitaria, X5000HUA Córdoba, Argentina
| | - Marcos Villarreal
- Centro de Investigaciones en Química Biológica de Córdoba
(CIQUIBIC), Dpto. de Química Biológica, and ‡Instituto de Investigaciones
en Físico-Química de Córdoba (INFIQC), Dpto.
de Matemática y Física, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Pabellón Argentina, Ciudad Universitaria, X5000HUA Córdoba, Argentina
| | - Luis Reinaudi
- Centro de Investigaciones en Química Biológica de Córdoba
(CIQUIBIC), Dpto. de Química Biológica, and ‡Instituto de Investigaciones
en Físico-Química de Córdoba (INFIQC), Dpto.
de Matemática y Física, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Pabellón Argentina, Ciudad Universitaria, X5000HUA Córdoba, Argentina
| | - Natalia Wilke
- Centro de Investigaciones en Química Biológica de Córdoba
(CIQUIBIC), Dpto. de Química Biológica, and ‡Instituto de Investigaciones
en Físico-Química de Córdoba (INFIQC), Dpto.
de Matemática y Física, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Pabellón Argentina, Ciudad Universitaria, X5000HUA Córdoba, Argentina
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Caldés C, Vilanova B, Adrover M, Donoso J, Muñoz F. The hydrophobic substituent in aminophospholipids affects the formation kinetics of their Schiff bases. Bioorg Med Chem Lett 2013; 23:2202-6. [PMID: 23462644 DOI: 10.1016/j.bmcl.2013.01.100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2012] [Revised: 01/22/2013] [Accepted: 01/22/2013] [Indexed: 11/16/2022]
Abstract
Schiff bases (SBs) are the initial products of non-enzymatic glycation reactions, which are associated to some diabetes-related diseases. In this work, we used physiological pH and temperature conditions to study the formation kinetics of the SBs of 1,2-dihexanoyl-sn-glycero-3-phosphoethanolamine (DPHE) and 1,2-dihexanoyl-sn-glycero-3-phospho-l-serine (DHPS) with various glycating compounds and with pyridoxal 5'-phosphate (an effective glycation inhibitor). Based on the obtained results, the hydrophobic environment simultaneously decreases the nucleophilic character of the amino group (k1) and increases its pKa, thereby increasing the formation rate of SB (kobs). Therefore, the presence of hydrophobic chains in aminophospholipids facilitates the formation and stabilization of SBs, and also, in a biological environment, their glycation. Additionally, the results confirm the inhibitory action of B6 vitamers on aminophospholipid glycation.
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Affiliation(s)
- Catalina Caldés
- Institut Universitari d'Investigació en Ciències de la Salut (IUNICS), Departament de Química, Universitat de les Illes Balears, Cra. Valldemossa km 7.5, Ed. Mateu Orfila i Rotger, E-07122 Palma de Mallorca, Spain
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Wolf-Goldberg T, Barbul A, Ben-Dov N, Korenstein R. Low electric fields induce ligand-independent activation of EGF receptor and ERK via electrochemical elevation of H(+) and ROS concentrations. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2013; 1833:1396-408. [PMID: 23481041 DOI: 10.1016/j.bbamcr.2013.02.011] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2012] [Revised: 02/11/2013] [Accepted: 02/13/2013] [Indexed: 11/17/2022]
Abstract
Physiological electric fields are involved in many biological processes and known to elicit their effects during long exposures ranging from a few hours to days. Following exposure to electric fields of physiological amplitude, epidermal growth factor receptor (EGFR) was demonstrated to be redistributed and upregulated with further intracellular signaling such as the MAPK signaling cascade. In our study we demonstrated EGFR activation and signaling induced by short train of pulsed low electric field (LEF) (10V/cm, pulse-width 180μs, 500Hz, 2min) in serum-free medium, following 24-hour starvation, and in the absence of exogenous EGF ligand, suggesting a ligand-independent pathway for EGFR activation. This ligandless activation was further confirmed by using neutralizing antibodies (LA1) that block the EGFR ligand-binding site. EGFR activation was found to be EGFR kinase dependent, yet with no dimerization following exposure to LEF. ERK activation was found to be mainly a result of EGFR downstream signaling though it partially occurred via EGFR-independent way. We demonstrate that reactive oxygen species and especially decrease in pH generated during exposure to LEF are involved in EGFR ligandless activation. We propose a possible mechanism for the LEF-induced EGFR ligand-independent activation and show activation of other receptor tyrosine kinases following exposure to LEF.
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Affiliation(s)
- Tami Wolf-Goldberg
- Department of Physiology and Pharmacology, Tel-Aviv University, Tel-Aviv, Israel
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Henriques VB, Germano R, Lamy MT, Tamashiro MN. Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2011; 27:13130-13143. [PMID: 21848301 DOI: 10.1021/la202302x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.
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Affiliation(s)
- V B Henriques
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil.
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Kovalchuk VI, Zholkovskiy EK, Bondarenko MP, Starov VM, Vollhardt D. Concentration polarization effect at the deposition of charged Langmuir monolayers. Adv Colloid Interface Sci 2011; 168:114-23. [PMID: 21620351 DOI: 10.1016/j.cis.2011.05.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2011] [Revised: 05/04/2011] [Accepted: 05/04/2011] [Indexed: 11/17/2022]
Abstract
The review summarizes the results of the recent studies of the electrokinetic relaxation process within the meniscus region during the deposition of charged Langmuir monolayers. Such electrokinetic relaxation is the consequence of the initial misbalance of partial ion fluxes within a small region near the contact line, where the diffuse parts of electric double layers, formed at the monolayer and the substrate surface, overlap. The concentration polarization within the solution near the three-phase contact line should lead to long-term relaxations of the meniscus after beginning and stopping the deposition process, to changes of the ionic composition within the deposited films, to change of the interaction of the monolayer with the substrate, and to dependence of the maximum deposition rate on the subphase composition.
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Alakoskela JM, Parry MJ, Kinnunen PKJ. The intermediate state of DMPG is stabilized by enhanced positive spontaneous curvature. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:4892-4900. [PMID: 20205407 DOI: 10.1021/la100411p] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
1,2-Dimyristoyl-sn-glycero-3-phospho-rac-glycerol (DMPG) at low salt concentrations has a complex endotherm with at least four components and extending over the span of 20 degrees. During this ongoing melting, the solution becomes viscous and scatters light poorly. This multipeak endotherm was suggested to result from the effects of curvature on the relative free energies of gel and fluid DMPG bilayers, further relating to the formation of an intermediate sponge phase between the lamellar gel and fluid phases. Although later studies appear to exclude a connected bilayer network, the relation of the endotherm peaks to curvature remains an appealing hypothesis. This was tested by including in the system both water-soluble small molecules (dimethyl sulfoxide, ethanol, and urea) as well as amphiphiles (myristoyl-lyso-PG, cholesterol, cholesterol-3-sulfate, and dimyristoylglycerol) known to alter the spontaneous curvature of bilayers. All compounds increasing the monolayer positive spontaneous curvature (ethanol, urea, myristoyl-lyso-PG, cholesterol-3-sulfate) increased the temperature span of the intermediate state and elevated the temperature of its dissolution, while all compounds increasing the negative spontaneous curvature (dimethyl sulfoxide, cholesterol, dimyristoylglycerol) had the opposite effect, implying that the intermediate state contains a structure with positive curvature. The results support the view that the intermediate state consists of vesicles with a large number of holes. The viscosity increase could be related to vesicle expansion needed to accommodate the numerous holes.
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Affiliation(s)
- Juha-Matti Alakoskela
- Helsinki Biophysics and Biomembrane Group, Institute of Biomedicine, Division of Biochemistry, P.O. Box 63, 00014 University of Helsinki, Finland.
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Dahlberg M, Marini A, Mennucci B, Maliniak A. Quantum Chemical Modeling of the Cardiolipin Headgroup. J Phys Chem A 2010; 114:4375-87. [DOI: 10.1021/jp9110019] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Martin Dahlberg
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden, and Department of Chemistry, University of Pisa, Via Risorgimento 35, 56126 Pisa, Italy
| | - Alberto Marini
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden, and Department of Chemistry, University of Pisa, Via Risorgimento 35, 56126 Pisa, Italy
| | - Benedetta Mennucci
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden, and Department of Chemistry, University of Pisa, Via Risorgimento 35, 56126 Pisa, Italy
| | - Arnold Maliniak
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden, and Department of Chemistry, University of Pisa, Via Risorgimento 35, 56126 Pisa, Italy
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Manuel M, Martins J. Partitioning of 1-pyrenesulfonate into zwitterionic and mixed zwitterionic/anionic fluid phospholipid bilayers. Chem Phys Lipids 2008; 154:79-86. [DOI: 10.1016/j.chemphyslip.2008.04.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2007] [Revised: 04/23/2008] [Accepted: 04/25/2008] [Indexed: 11/28/2022]
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Dukhin SS, Zimmermann R, Werner C. Electrokinetic fingerprinting of grafted polyelectrolyte layers--a theoretical approach. Adv Colloid Interface Sci 2006; 122:93-105. [PMID: 16901456 DOI: 10.1016/j.cis.2006.06.009] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Electrokinetic fingerprinting (EF) was introduced by Marlow and Rowell [Marlow BJ, Rowel RL. Langmuir 1990;6:1088] for the comprehensive characterization of charged particle surfaces. Afterwards, EF was applied by many groups for the characterization of "hard" (i.e. non-swelling) surfaces. However, the advantages of EF could not yet utilized for the characterization of grafted polyelectrolyte layers (PL) since the theoretical background was not yet elaborated. A theory for the characterization of PL at complete dissociation of the functional groups was developed by Ohshima [Adv Colloid Interface Sci 1995;62:189] and later extended by Dukhin et al. [Dukhin S, Zimmermann R, Werner C. J Colloid Interface Sci 2005;286:761] for any degree of dissociation. Further progress in the characterization of soft surfaces may be achieved by combining EF and surface conductivity (SC) measurements. Both theory and experiment demonstrate that integrated measurements of SC and apparent zeta potential zeta(a) in broad ranges of pH and ionic strength provide information about Donnan potential Psi(D), surface charge, pK and surface potential Psi(0), while the interpretation is more uncertain, when only zeta(a) is measured. This advanced method of PL characterization is established for PL grafted on flat surfaces. When PL are formed on spherical particles, the SC may be measured by means of conductometry and/or dielectric spectroscopy. However, the current theories can only be applied within a rather narrow range of the practically relevant conditions. To overcome this limitation, an unified approach to the theory of electrophoresis for spherical particles with grafted PL was elaborated taking into account the existence of two different electrokinetic models for soft surfaces. While one model is focused on hydrodynamic permeability of soft surface and disregards surface current, another model considers the surface current and disregards electrokinetic water transport within the soft surface layer. Unification became possible through generalization of the capillary osmosis theory over soft surfaces.
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Dukhin S, Zimmermann R, Werner C. A concept for the generalization of the standard electrokinetic model. Colloids Surf A Physicochem Eng Asp 2001. [DOI: 10.1016/s0927-7757(01)00833-0] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Egorova EM. Some applications of the Dukhin theory in studies of lipid membranes. Colloids Surf A Physicochem Eng Asp 2001. [DOI: 10.1016/s0927-7757(01)00732-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Kovalchuk VI, Zholkovskiy EK, Bondarenko NP, Vollhardt D. Dissociation of Fatty Acid and Counterion Binding at the Langmuir Monolayer Deposition: Theoretical Considerations. J Phys Chem B 2001. [DOI: 10.1021/jp0112020] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- V. I. Kovalchuk
- Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam/Golm, Germany, and Institute of Biocolloid Chemistry, Kiev, Ukraine
| | - E. K. Zholkovskiy
- Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam/Golm, Germany, and Institute of Biocolloid Chemistry, Kiev, Ukraine
| | - N. P. Bondarenko
- Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam/Golm, Germany, and Institute of Biocolloid Chemistry, Kiev, Ukraine
| | - D. Vollhardt
- Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam/Golm, Germany, and Institute of Biocolloid Chemistry, Kiev, Ukraine
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16
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Egorova E. Dissociation constants of lipid ionizable groups II. Changes in surface pK at low ionic strengths. Colloids Surf A Physicochem Eng Asp 1998. [DOI: 10.1016/s0927-7757(96)03959-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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