Letter pubs.acs.org/JPCL
Mechanism of Divalent-Ion-Induced Charge Inversion of Bacterial Membranes Binquan Luan,*,† Kai Loon Chen,‡ and Ruhong Zhou*,† †
Computational Biological Center, IBM Thomas J. Watson Research, Yorktown Heights, New York 10598, United States Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
‡
S Supporting Information *
ABSTRACT: The surface charge inversion (CI), critical for functions of many biological nanomachinery, is a counterintuitive phenomenon in which the net charge of a strongly charged surface bound with many counterions changes its sign. Many phenomena of CI cannot be explained in the framework of mean-field theories, such as linear Debye− Hückel and nonlinear Poisson−Boltzmann, and is so far best described by the strongly correlated liquid (SCL) theory for multivalent (Z ≥ 3) ions. However, the potential CI by divalent ions, which are more relevant in the biological environment, is much less studied and remains mostly illusive. In this study, we examine the divalent-ion-induced CI of a negatively charged bacterium’s cell membrane and reveal its underlying mechanism, using all-atom molecular dynamics simulations and free energy perturbation theory. Our simulation results are compared with theoretical predications from SCL, and noticeable discrepancies with SCL theory, originating from the fluidity of membrane lipids whose negatively charged PO−4 groups aggregate around adsorbed Ca2+, are found. Our simulation data suggest that the CI of the bacterial membrane results from the strong binding of Ca2+ to the membrane’s phosphate groups via an induced-fit mechanism, forming positively charged Ca2+-centered clusters that replace originally negatively charged lipids.
P
the 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane in a Ca2+ electrolyte was indicated in the experiment on attaching multiwalled carbon nanotubes to the membrane.10 However, the underlying mechanism of the membrane’s CI is so far still elusive. Theoretically, charge screening by monovalent ions (the Couloumb coupling constant Γ ≤ 1) can be well understood by Poisson−Boltzmann (PB) theory. For multivalent (≥3) ions, due to their strong coupling and strong adsorption to a charged surface (Γ ≫ 1), the strongly correlated liquid (SCL) theory11 applies. CI by divalent ions is on the borderline and thus is not well understood theoretically.12,13 For the Escherichia coli membrane in a CaCl2 electrolyte, Γ = 1.5 (see below). Therefore, we resort to the all-atom molecular dynamics (MD) method to investigate the possible CI of the E. coli membrane by mono- or divalent ions revealed in experiments.9,10 We found that the CI observed directly from our simulations can be only qualitatively understood by SCL theory because the adsorbed Ca2+ are not packed orderly on the membrane due to the Ca2+-binding-induced nonuniform distribution of negatively charged phosphate (PO−4 ) groups on the membrane surface as well as the weak coupling compared with multivalent (Z ≥ 3) ions.
roteins, DNA, and many other biological molecules are often charged under physiological conditions, and their electrostatic interactions are, normally, only partially screened by surrounding ions, such as Na+, K+, Ca2+, and Cl−. The unscreened electrostatic interaction can, for example, guide the protein self-assembly and protein−DNA recognition in a biological cell. With stronger screenings (such as by multivalent ions), like-charge molecules can attract each other,1 such as DNA−DNA interaction inside of the cell nucleus and viral capsids. Interestingly, a highly charged biomolecule (e.g., DNA) can even be overscreened, resulting in charge inversion (CI).2 The cell membrane of a bacterium is negatively charged under the physiological conditions of a human body and thus is the target of positively charged antimicrobial polymers (AMPs).3 It is conceivable that understanding the charge screening on a membrane surface can help to optimize the efficiency of AMPs. For the membrane formed by anionic 1,2-dimyristoyl-snglycero-3-phosphatidic acid (DMPA) lipids, CI with added La3+ was previously observed experimentally.4 Additionally, trivalention-induced CI of a membrane containing charged lipids was demonstrated by measuring the conductance of a protein channel embedded in the membrane.5 It is commonly thought that CI occurs only if the valencey of counterions is Z ≥ 3.6−8 A previous experiment9 has, however, shown that Ca2+ can significantly enhance the binding between DNA and the 1,2dipalmitoylphosphatidylcholine (DPPC) membrane (slightly negatively charged at pH = 7), indicating the possibility of forming a cationic lipid−calcium system. More recently, CI of © XXXX American Chemical Society
Received: May 17, 2016 Accepted: June 13, 2016
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DOI: 10.1021/acs.jpclett.6b01065 J. Phys. Chem. Lett. 2016, 7, 2434−2438
Letter
The Journal of Physical Chemistry Letters
driving force was balanced by the hydrodynamic friction, that is, QE = ξv (where ξ is the friction coefficient and Q is the net charge after screening). Consequently, one obtains
We carried out MD simulations on the charge screening of the E. coli membrane by mono- and divalent ions using the program NAMD2.9.14 Figure 1a illustrates the simulated
μ = Q /ξ
Because the friction coefficient ξ of the entire membrane is not sensitive to the membrane surface charge, the CI of the membrane can be manifested in experiment as the change of the membrane’s moving direction in the electric field. Due to the binding and screening of counterions near the negatively charged membrane, the net charge Q changed during the simulation time. Here, we define Q as the sum of the entire charge of the membrane itself and charges of ions within the Debye length from the membrane. During the simulation of the membrane in the 0.1 M type-III electrolyte, several Ca2+ ions were observed to be adsorbed on the membrane surface during the first 20 ns. After that, the net charge Q changed from negative to positive (Figure 1b), that is, the CI. Accordingly, the membrane’s electrophoretic motion (tangential to the membrane surface) was affected. The center of mass (COM) of the membrane moved opposite the field direction initially, but after CI, the COM of the membrane moved along the field direction (Figure 1c). The COM velocity v became constant (see the constant slope in Figure 1c) after Q saturated, that is, no more adsorption of and steady distribution of nearby counterions. However, in the 0.1 M NaCl electrolyte, the net charge of the membrane remained negative (Figure 1b). Thus, no CI occurred, and the membrane kept moving opposite the field direction (Figure 1c). In the 0.1 M CaCl2 type-I electrolyte, similar CI was also observed (see Figure S1 in the Supporting Information). While no CI is expected for the membrane in the 0.1 M NaCl electrolyte, it is surprising to observe the CI of the membrane in the divalent electrolyte. We further investigated the ion distribution and dynamics near the bacterial membrane. In the 0.1 M NaCl electrolyte, Figure 2a shows that the concentration of counterions (Na+) near the membrane surface (d ≈ 2.1 nm) is much higher than the bulk one (d ≈ 5 nm) due to the screening effect. Meanwhile, co-ions (Cl−) of the membrane were depleted from the surface. Therefore, inside of the Debye layer (2.1 < d < 3.1 nm), the counterion concentration dominates the co-ion one, that is, no CI. Outside of the Debye layer, both concentrations approach the bulk value. However, in the 0.1 M CaCl2 electrolyte, the screening effect is quite different (Figure 2b). At the membrane surface, the concentration of Ca2+ is about two to three times larger than that of Na+, suggesting a much stronger binding of Ca2+ to the membrane and the formation of a Stern layer. Outside of the Stern layer, the concentration of Ca2+ drops and that of Cl− increases sharply. Consistent with the aforementioned CI, in the diffusive layer, the concentration of Cl− is much higher than that of Ca2+, that is, Cl− becomes the counterion after CI. Far away from the surface, bulk concentrations n of Ca2+ and Cl−, where nCl = 2nCa, are recovered. By analyzing simulation trajectories, we found that counterions (Na+ and Ca2+) can bind the lipid’s PO−4 . Figure 2c shows the probability of Na+’s residence time on a PO−4 . The fast decay of the probability indicates that the characteristic residence time is only about a few picoseconds, which is consistent with the previous study on the residence time of K+ on a PO−4 of DNA.17 Thus, Na+ can only transiently bind PO−4 . In contrast, for Ca2+, we did not observe a dissociation event once a Ca2+ was adsorbed on the membrane during the
Figure 1. MD simulation of electrophoretic motion of the bacterial membrane in various electrolytes. (a) Illustration of one simulated system with the 0.1 M CaCl2 electrolyte. Lipids in the membrane are in stick representation (negatively charged 1-palmitoyl-2-oleoyl-snglycero-3-phosphoglycerol (POPG) lipids are highlighted in cyan), and phosphorus atoms are represented as van der Waals spheres (tan); water is shown transparently; and Ca2+ and Cl− ions in water are colored orange and blue, respectively. The electric field is applied in the x direction. (b) Time-dependent net charges of the lipid membrane in the 0.1 M NaCl (type-II) and CaCl2 (type-III) electrolytes. (c) Time-dependent COMs of the membrane in these two electrolytes.
system. A patch of lipid bilayer, containing both neutral 1palmitoyl-2-oleoyl-sn-phosphatidylethanolamine (POPE) and negatively charged POPG (net charge: −1 e, where e is the proton’s charge) was solvated by water. To mimic the cell membrane of the bacterium E. coli, the number ratio between POPE lipids and POPG lipids was set roughly at 5.3:115 (inner membrane), resulting in a nonuniform surface charge density σ of −0.28 e/nm2. Specifically, the bilayer contained 128 POPE lipids and 24 POPG lipids. POPG lipids were evenly distributed inside of the bilayer. Three types of electrolytes were studied: (I) containing CaCl2 only (close to the experimental condition16); (II) containing NaCl only; (III) containing the CaCl2 bulk electrolyte and 24 Na+ ions that neutralize the membrane charge (close to the bioenvironment where Na+ ions are always present). For each type of electrolyte, four different molar concentrations c (=0.001, 0.01, 0.1, and 1 M) of ions were modeled. The molar concentration c is defined from the concentration of cations in the electrolyte but not including cations that neutralize the membrane charge. To study the electrophoretic motion of the modeled membrane, an electric field E (=1.5 mV/nm) was applied in the x direction (Figure 1a). Electrophoresis is routinely used in experiment to measure the net charge of a particle (e.g., a vesicle10). Here, we modeled electrophoresis of the charged membrane in various electrolytes (see the Supporting Information for methods), which can be characterized by the membrane’s electrophoretic mobility μ = v/E
(2)
(1)
In the steady state of each simulated system, the membrane along with adsorbed counterions moved at a nearly constant velocity v in the external electric field E. Thus, the electric 2435
DOI: 10.1021/acs.jpclett.6b01065 J. Phys. Chem. Lett. 2016, 7, 2434−2438
Letter
The Journal of Physical Chemistry Letters
Figure 3. Electrophoretic mobility of the membrane in the NaCl (red dots) and CaCl2 electrolytes at various concentrations. For the CaCl2 bulk electrolyte, the membrane charge was neutralized by either Ca2+ (blue squares) or Na+ (green diamonds). Dashed lines are guides to the eye. Figure 2. Analyses of ions near the charged membrane. (a) Distribution of Na+ (blue) and Cl− (orange) away from the membrane, in the 0.1 M NaCl electrolyte. (b) Distribution of Ca2+ (blue) and Cl− (orange) away from the membrane, in the 0.1 M CaCl2 electrolyte. (c) The probability of Na+’s residence time on a phosphate group. (d) Time-dependent distance between a Ca2+ ion and the phosphorus atom in its binding site. Two binding events (cyan and purple) are illustrated.
For the type-I and type-III electrolytes containing Ca2+, the linear behavior is also evident for low ion concentrations (
