Charge inversion on membranes induced by multivalent-counterion fluctuations

Abstract

Based on the two state model, we study the condensation of counterions on oppositely charged membranes in the presence of monovalent salts. Using the Gaussian approximation, we evaluate the contribution of two-dimensional charge fluctuation to the free energy, from which the number of condensed counterions is determined self-consistently. It is shown that charge inversion can occur upon the addition of divalent ions of millimolar range, or of trivalent ions of micromolar range. The driving force for the overcharging mechanism is the charge correlation induced by thermal fluctuation, in which the multivalency of the counterions plays a crucial role.(Some figures in this article are in colour only in the electronic version)Counterions in watery solution dominantly distribute near an oppositely charged surface of macroions, forming a diffuse electric double layer. The structure of a double layer of counterions, which has been usually described by the mean-field Poisson-Boltzmann theory, is of great importance in interaction and phase behaviours of macroions [1,2]. When the macroions are subject to an external electric field, they instantaneously reach a stationary velocity due to the viscous friction from the ambient solution. This is called electrophoresis, and it provides an efficient way to probe the double layer structure and thus to measure the surface potential of charged colloidal systems [3,4]. The counterions strongly bound to the macroion play an important role in this transport property by renormalizing the electrokinetic charges of the surface [5]. According to the Poisson-Boltzmann theory, the macroion charge is only partially compensated (neutralized) by the counterions so that the sign of the net charge is retained even in the presence of the strongly associated counterions.It has been however observed that the counterions can further condense on the surface beyond compensation of the macroion charge, leading to reversal of the drift direction in electrophoretic experiments [6]. This phenomenon is called charge inversion, and has been

How Nature Modulates Inherent Fluctuations for Biological Self-Organization – The Case of Membrane Fusion

“…Using the analysis as above, we find charge over-condensation of trivalent cations at the concentration as small as µM range (Figure 3), which is in accord with a recent theoretical result [12] and with fusion experiments using La 3+ and Tb 3+ [8]. The discontinuity in change of the effective surface charge density shown in Figure 3 is the outcome of a first-order phase transition between the condensed trivalent ion and free ions [11]. This strong effect of multi-valency can be explained as follows.…”

“…And then the membranes merge together due to a certain instability process [7]. In order to study what happens after adhesion, we set out a mesoscopic theory [4,11] that highlights coupling of two aspects of thermal fluctuation in membranes. One is fluctuating distribution of mobile membrane-bound charges inclusive of the counter-ions condensed on membrane surface, noted above.…”

Biomolecular electrostatics and solvation: a computational perspective

“…In other words, ions interact with each other only through their average densities rather than through the steric, Coulombic, and solvent-mediated correlations that occur in real electrolyte systems. As a consequence, the PB model cannot capture a number of phenomena (Chen & Weeks, 2006; Savelyev & Papoian, 2007; Tan & Chen, 2005), including charge inversion (Besteman et al , 2004, 2005; Goel et al , 2008; Kim & Sung, 2005; Luan & Aksimentiev, 2010; Martin-Molina et al , 2009; Nguyen et al , 2000; Qiao & Aluru, 2004; Taheri-Araghi & Ha, 2005; Wen & Tang, 2004) and like-charge attraction (Angelini et al , 2003; Kim et al , 2008; Mukherjee, 2004; Netz & Naji, 2004; Pietronave et al , 2008; Podgornik & Dobnikar, 2001; Qiu et al , 2010; Todd et al , 2008; Zelko et al , 2010) that can be important for highly charged systems. Such systems include solutes such as DNA, charged biomembrane interfaces, and solutions with even moderate concentrations of di- or multi-valent ions.…”

Scaling Laws and Ionic Current Inversion in Polyelectrolyte-Grafted Nanochannels

“…Charge inversion (CI) was discussed in the Introduction and is a phenomenon where the electrostatic potential in the vicinity of a charged wall has an electrostatic potential whose sign is opposite to that of the bare charge of the wall. The primary cause of such inversion is the presence of multivalent counterions − (and the resulting ionic correlation effects) or the presence of finite-sized co-ions and counterions . Such multivalent-counterion-driven CI was witnessed in conical nanopores in the experiments of He et al; the presence of multivalent counterions like Ca 2+ and Co 3+ caused local CI, thereby changing the effective charge of the nanopore from negative to positive.…”

“…This is the second key finding of this paper. Please note that this inversion is different from charge inversion (CI) and the inversion of streaming current typically employed to quantify this CI. , In CI, which is typically caused by the presence of multivalent counterions − or finite sized monovalent co-ions and counterions, the electrostatic potential in the vicinity of the charged wall shows a sign opposite to that of the bare charge; this inversion is quantified by measuring the corresponding inversion of the streaming current triggered by the downstream advection of mobile electrolyte ions within the electric double layer (or EDL) in the presence of a background pressure-driven transport. − Quantifying ionic current is central to a number of applications of nanochannels with and without PE grafting; some of these applications are sensing and detecting biomolecules, devising nanofluidic diodes and rectifiers, and so on. For all of these applications, it is paramount to know the base state current.…”