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Ruixuan H, Majee A, Dobnikar J, Podgornik R. Electrostatic interactions between charge regulated spherical macroions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:115. [PMID: 38019363 DOI: 10.1140/epje/s10189-023-00373-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/20/2023] [Indexed: 11/30/2023]
Abstract
We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.
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Affiliation(s)
- Hu Ruixuan
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Arghya Majee
- Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany
| | - Jure Dobnikar
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China
- Songshan Lake Materials Laboratory, Guangdong, 523808, Dongguan, China
| | - Rudolf Podgornik
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, 325011, Zhejiang, China.
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
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Celora GL, Blossey R, Münch A, Wagner B. Counterion-controlled phase equilibria in a charge-regulated polymer solution. J Chem Phys 2023; 159:184902. [PMID: 37942872 DOI: 10.1063/5.0169610] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 10/17/2023] [Indexed: 11/10/2023] Open
Abstract
We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni-modal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: Re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions.
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Affiliation(s)
- Giulia L Celora
- Department of Mathematics, University College London, 25 Gordon Street, London WC1H 0AY, United Kingdom
| | - Ralf Blossey
- Univ. Lille, CNRS, UMR 8576 - UGSF - Unité de Glycobiologie Structurale et Fonctionnelle, F-59000 Lille, France
| | - Andreas Münch
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Barbara Wagner
- Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany
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3
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Levin Y, Bakhshandeh A. A new method for reactive constant pH simulations. J Chem Phys 2023; 159:111101. [PMID: 37721322 DOI: 10.1063/5.0166840] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 08/29/2023] [Indexed: 09/19/2023] Open
Abstract
We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions-such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, and proteins. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation-which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that the Donnan potential dramatically affects the pH of a suspension. Counterintuitively, we find that in suspensions with a large volume fraction of nanoparticles and low ionic strength, the number of deprotonated groups can be 100% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane-both systems being at exactly the same pH.
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Affiliation(s)
- Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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Khunpetch P, Majee A, Ruixuan H, Podgornik R. Curvature effects in interfacial acidity of amphiphilic vesicles. Phys Rev E 2023; 108:024402. [PMID: 37723726 DOI: 10.1103/physreve.108.024402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge-regulated moieties. Basing our approach on the linear Debye-Hückel approximation, as well as on the nonlinear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-Guggenheim adsorption isotherm model of the charge-regulation process, we analyze and review the dependence of the local pH on the position, as well as bulk electrolyte concentration, bulk pH, and curvature of the amphiphilic single membrane vesicle. With appropriately chosen adsorption parameters of the charge-regulation model, we find a good agreement with the available experimental data.
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Affiliation(s)
- Petch Khunpetch
- Department of Physics, Faculty of Science, Ramkhamhaeng University, Bang Kapi, 10240 Bangkok, Thailand
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
| | - Arghya Majee
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Hu Ruixuan
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
| | - Rudolf Podgornik
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190 Beijing, China
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, 325000 Zhejiang, China
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Obstbaum T, Sivan U. Thermodynamics of Charge Regulation near Surface Neutrality. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:8477-8483. [PMID: 35759684 DOI: 10.1021/acs.langmuir.2c01352] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The interaction between two adjacent charged surfaces immersed in aqueous solution is known to be affected by charge regulation─the modulation of surface charge as two charged surfaces approach each other. This phenomenon is particularly important near surface neutrality where the stability of objects such as colloids or biomolecules is jeopardized. Focusing on this ubiquitous case, we elucidate the underlying thermodynamics and show that charge regulation is governed in this case by surface entropy. We derive explicit expressions for charge regulation and formulate a new universal limiting law for the free energy of ion adsorption to the surfaces. The latter turns out to be proportional to kBT, and independent of the association energy of ions to surface groups. These new results are applied to the analysis of unipolar as well as amphoteric surfaces such as oxides near their point of zero charge or proteins near their isoelectric point.
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Affiliation(s)
- Tal Obstbaum
- Department of Physics and the Russell Berrie Nanotechnology Institute, Technion - Israel Institute of Technology, Haifa 3200003, Israel
| | - Uri Sivan
- Department of Physics and the Russell Berrie Nanotechnology Institute, Technion - Israel Institute of Technology, Haifa 3200003, Israel
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Khunpetch P, Majee A, Podgornik R. Curvature effects in charge-regulated lipid bilayers. SOFT MATTER 2022; 18:2597-2610. [PMID: 35294512 DOI: 10.1039/d1sm01665b] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigated go beyond the paradigm of electrostatic renormalization of the mechano-elastic properties of membranes.
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Affiliation(s)
- Petch Khunpetch
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
| | - Arghya Majee
- Max Planck Institute for Intelligent Systems, Stuttgart, Germany
- IV. Institute for Theoretical Physics, University of Stuttgart, Stuttgart, Germany.
| | - Rudolf Podgornik
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, China
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang, China
- Department of Theoretical Physics, Jožef Stefan Institute, Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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7
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Bakhshandeh A, Frydel D, Levin Y. Reactive Monte Carlo simulations for charge regulation of colloidal particles. J Chem Phys 2022; 156:014108. [PMID: 34998334 DOI: 10.1063/5.0077956] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 7820275 Santiago, Chile
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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Zheng B, Avni Y, Andelman D, Podgornik R. Phase Separation of Polyelectrolytes: The Effect of Charge Regulation. J Phys Chem B 2021; 125:7863-7870. [PMID: 34232047 PMCID: PMC8389888 DOI: 10.1021/acs.jpcb.1c01986] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Complex
coacervation, known as the liquid–liquid phase separation
of solutions with oppositely charged polyelectrolytes, has attracted
substantial interest in recent years. We study the effect of the charge
regulation (CR) mechanism on the complex coacervation by including
short-range interactions between the charged sites on the polymer
chains as well as an association–dissociation energy parameter
in the CR mechanism. We investigate the phase diagrams of two CR models:
(i) the hopping CR model (HCR) and (ii) the asymmetric CR model (ACR).
It is shown that during the phase separation that the polymers in
the condensed phase are more charged than those in the dilute phase,
in accordance with Le Chatelier’s principle. In addition, secondary CR effects also influence the change in the volume
fraction of the two phases. The latter can cause the charge difference
between the two phases to change nonmonotonically as a function of
the CR parameters.
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Affiliation(s)
- Bin Zheng
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - Yael Avni
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.,Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China.,CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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Abstract
The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation-dissipation theorem, there is an additional friction force associated with such fluctuations. However, the impact of these fluctuations on the diffusion and dynamics of proteins in the cytoplasm is unclear. Here, we provide an order-of-magnitude estimate of this effect by treating electric field fluctuations within a generalized Langevin equation model with a time-dependent friction memory kernel. We find that electric friction is generally negligible compared to solvent friction. However, a significant slowdown of protein diffusion and dynamics is expected for biomolecules with high net charges such as intrinsically disordered proteins and RNA. The results show that direct contacts between biomolecules in a cell are not necessarily required to alter their dynamics.
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Affiliation(s)
- Dmitrii E Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, United States
| | - Hagen Hofmann
- Department of Chemical and Structural Biology, Weizmann Institute of Science, 76100 Rehovot, Israel
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Gomez DA, Frydel D, Levin Y. Lattice-gas model of a charge regulated planar surface. J Chem Phys 2021; 154:074706. [PMID: 33607887 DOI: 10.1063/5.0039029] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.
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Affiliation(s)
- Daniel Alejandro Gomez
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquin, Santiago, Chile
| | - Derek Frydel
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquin, Santiago, Chile
| | - Yan Levin
- Institute of Physics, The Federal University of Rio Grande do Sul, Porto Alegre 91501-970, Brazil
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Fink L, Allolio C, Feitelson J, Tamburu C, Harries D, Raviv U. Bridges of Calcium Bicarbonate Tightly Couple Dipolar Lipid Membranes. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:10715-10724. [PMID: 32787004 PMCID: PMC7586406 DOI: 10.1021/acs.langmuir.0c01511] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Revised: 08/02/2020] [Indexed: 06/11/2023]
Abstract
The interaction between lipid membranes and ions is associated with a range of key physiological processes. Most earlier studies have focused on the interaction of lipids with cations, while the specific effects of the anions have been largely overlooked. Owing to dissolved atmospheric carbon dioxide, bicarbonate is an important ubiquitous anion in aqueous media. In this paper, we report on the effect of bicarbonate anions on the interactions between dipolar lipid membranes in the presence of previously adsorbed calcium cations. Using a combination of solution X-ray scattering, osmotic stress, and molecular dynamics simulations, we followed the interactions between 1,2-didodecanoyl-sn-glycero-3-phosphocholine (DLPC) lipid membranes that were dialyzed against CaCl2 solutions in the presence and absence of bicarbonate anions. Calcium cations adsorbed onto DLPC membranes, charge them, and lead to their swelling. In the presence of bicarbonate anions, however, the calcium cations can tightly couple one dipolar DLPC membrane to the other and form a highly condensed and dehydrated lamellar phase with a repeat distance of 3.45 ± 0.02 nm. Similar tight condensation and dehydration has only been observed between charged membranes in the presence of multivalent counterions. Bridging between bilayers by calcium bicarbonate complexes induced this arrangement. Furthermore, in this condensed phase, lipid molecules and adsorbed ions were arranged in a two-dimensional oblique lattice.
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Affiliation(s)
- Lea Fink
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Christoph Allolio
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
- The
Fritz Haber Center, The Hebrew University
of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Jehuda Feitelson
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Carmen Tamburu
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Daniel Harries
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
- The
Fritz Haber Center, The Hebrew University
of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Uri Raviv
- Institute
of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
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