# Effect of Sodium and Chloride Binding on a Lecithin Bilayer. A Molecular Dynamics Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Ion-Lipid Binding Constants

#### 2.2. Finite-Size Effects

#### 2.3. Inter-Bilayer Forces

#### 2.4. Membrane Rigidity and Area Compressibility

## 3. Results and Discussion

## 4. Computational Details

#### 4.1. MD Simulations

#### 4.2. Force Field

#### 4.3. Analysis of Simulations

#### 4.3.1. Structural, Mechanical, Dynamic and Electrostatic Membrane Properties

#### 4.3.2. Thermodynamics of Ion-Membrane Binding

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Lösche, M.; Möhwald, H. Electrostatic interactions in phospholipid membranes. II. Influence of divalent ions on monolayer structure. J. Colloid Interface Sci.
**1989**, 131, 56–67. [Google Scholar] [CrossRef] - Clarke, R.J.; Lüpfert, C. Influence of anions and cations on the dipole potential of phosphatidylcholine vesicles: A basis for the Hofmeister effect. Biophys. J.
**1999**, 76, 2614–2624. [Google Scholar] [CrossRef] - Renoncourt, A.; Vlachy, N.; Bauduin, P.; Drechsler, M.; Touraud, D.; Verbavatz, J.M.; Dubois, M.; Kunz, W.; Ninham, B.W. Specific alkali cation effects in the transition from micelles to vesicles through salt addition. Langmuir
**2007**, 23, 2376–2381. [Google Scholar] [CrossRef] [PubMed] - Pabst, G.; Hodzic, A.; Štrancar, J.; Danner, S.; Rappolt, M.; Laggner, P. Rigidification of neutral lipid bilayers in the presence of salts. Biophys. J.
**2007**, 93, 2688–2696. [Google Scholar] [CrossRef] [PubMed] - Klasczyk, B.; Knecht, V.; Lipowsky, R.; Dimova, R. Interactions of alkali metal chlorides with phosphatidylcholine vesicles. Langmuir
**2010**, 26, 18951–18958. [Google Scholar] [CrossRef] [PubMed] - Ferber, U.M.; Kaggwa, G.; Jarvis, S.P. Direct imaging of salt effects on lipid bilayer ordering at sub-molecular resolution. Eur. Biophys. J.
**2011**, 40, 329–338. [Google Scholar] [CrossRef] [PubMed] - Zimmermann, R.; Küttner, D.; Renner, L.; Kaufmann, M.; Werner, C. Fluidity modulation of phospholipid bilayers by electrolyte ions: Insights from fluorescence microscopy and microslit electrokinetic experiments. J. Phys. Chem. A
**2012**, 116, 6519–6525. [Google Scholar] [CrossRef] [PubMed] - Rios, G.M.; Belleville, M.-P.; Paolucci-Jeanjean, D. Membrane engineering in biotechnology: Quo vamus? Trends Biotechnol.
**2007**, 25, 242–246. [Google Scholar] [CrossRef] [PubMed] - Saeui, C.T.; Mathew, M.P.; Liu, L.; Urias, E.; Yarema, K.J. Cell surface and membrane engineering: Emerging technologies and applications. J. Funct. Biomater.
**2015**, 6, 454–485. [Google Scholar] [CrossRef] [PubMed] - Satoh, K. Determination of binding constants of Ca
^{2+}, Na^{+}and Cl^{−}ions to liposomal membranes of dipalmitoylphosphatidylcholine at gel phase by particle electrophoresis. Biochim. Biophys. Acta**1995**, 1239, 239–248. [Google Scholar] [CrossRef] - Eisenberg, M.; Gresalfi, T.; Riccio, T.; McLaughlin, S. Adsorbtion of monovalent cations to bilayer membranes containing negative phospholipids. Biochemistry
**1979**, 18, 5213–5223. [Google Scholar] [CrossRef] [PubMed] - Evans, D.F.; Wennerstrom, H. The Colloidal Domain, 2nd ed.; VCH: Weinheim, Germany, 1999. [Google Scholar]
- Seimiya, T.; Ohki, S. Ionic structure of phospholipid membranes, and binding of calcium ions. Biochim. Biophys. Acta
**1973**, 298, 546–561. [Google Scholar] [CrossRef] - Knecht, V.; Klasczyk, B. Specific binding of chloride ions to lipid vesicles and implications at molecular scale. Biophys. J.
**2013**, 104, 818–824. [Google Scholar] [CrossRef] [PubMed] - Klasczyk, B.; Knecht, V. Validating affinities for ion-lipid association from simulation against experiment. J. Phys. Chem. A
**2011**, 115, 10587–10595. [Google Scholar] [CrossRef] [PubMed] - Garcia-Celma, J.J.; Hatahet, L.; Kunz, W.; Fendler, K. Specific anion and cation binding to lipid membranes investigated on a solid supported membrane. Langmuir
**2007**, 23, 10074–10080. [Google Scholar] [CrossRef] [PubMed] - Collins, K.D. Ions from the Hofmeister series and osmolytes: Effects on proteins in solution and in the crystallization process. Methods
**2004**, 34, 300–311. [Google Scholar] [CrossRef] [PubMed] - Leontidis, E.; Aroti, A. Liquid expanded monolayers of lipids as model systems to understand the anionic Hofmeister series. 2. Ion partitioning is mostly a matter of size. J. Phys. Chem. B
**2009**, 113, 1460–1467. [Google Scholar] [CrossRef] [PubMed] - Böckmann, R.A.; Hac, A.; Heimburg, T.; Grubmüller, H. Effect of sodium chloride on a lipid bilayer. Biophys. J.
**2003**, 85, 1647–1655. [Google Scholar] [CrossRef] - Böckmann, R.A.; Grubmüller, H. Multistep binding of divalent cations to phospholipid bilayers: A molecular dynamics study. Angew. Chem. Int. Ed.
**2004**, 43, 1021–1024. [Google Scholar] [CrossRef] [PubMed] - Lin, Y.-W.; Liao, L.-F. Probing interactions between uranyl ions and lipid membrane by molecular dynamics simulation. Comput. Theor. Chem.
**2011**, 976, 130–134. [Google Scholar] [CrossRef] - Valley, C.C.; Perlmutter, J.D.; Braun, A.R.; Sachs, J.N. NaCl interactions with phosphatidylcholine bilayers do not alter membrane structure but induce long-range ordering of ions and water. J. Membr. Biol.
**2011**, 244, 35–42. [Google Scholar] [CrossRef] [PubMed] - Jarerattanachat, V.; Karttunen, M.; Wong-ekkabut, J. Molecular dynamics study of oxidized lipid bilayers in NaCl solution. J. Phys. Chem. B
**2013**, 117, 8490–8501. [Google Scholar] [CrossRef] [PubMed] - Sachs, J.N.; Woolf, T.B. Understanding the Hofmeister effect in interactions between chaotropic anions and lipid bilayers: Molecular dynamics simulations. J. Am. Chem. Soc.
**2003**, 125, 8742–8743. [Google Scholar] [CrossRef] [PubMed] - Sachs, J.N.; Nanda, H.; Petrache, H.I.; Woolf, T.B. Changes in phosphatidylcholine headgroup tilt and water order induced by monovalent salts: Molecular dynamics simulations. Biophys. J.
**2004**, 86, 3772–3782. [Google Scholar] [CrossRef] [PubMed] - Vácha, R.; Siu, S.W.I.; Petrov, M.; Böckmann, R.A.; Barucha-Kraszewska, J.; Jurkiewicz, P.; Hof, M.; Berkowitz, M.L.; Jungwirth, P. Effect of alkali cations and halide anions on the DOPC lipid membrane. J. Phys. Chem. A
**2009**, 113, 7235–7243. [Google Scholar] [CrossRef] [PubMed] - Vácha, R.; Jurkiewicz, P.; Petrov, M.; Berkowitz, M.L.; Böckmann, R.A.; Barucha-Kraszewska, J.; Hof, M.; Jungwirth, P. Mechanism of interaction of monovalent ions with phosphatidyl lipid membranes. J. Phys. Chem. B
**2010**, 114, 9504–9509. [Google Scholar] [CrossRef] [PubMed] - Phillips, R.B.; Kondev, J.; Theriot, J. Physical Biology of the Cell; Garland Science: New York, NY, USA, 2009. [Google Scholar]
- Kagawa, R.; Hirano, Y.; Taiji, M.; Yasuoka, K.; Yasui, M. Dynamic interactions of cations, water and lipids and influence on membrane fluidity. J. Membr. Sci.
**2013**, 435, 130–136. [Google Scholar] [CrossRef] - Zhou, Y.; Raphael, R.M. Solution pH alters mechanical and electrical properties of phosphatidylcholine membranes: Relation between interfacial electrostatics, intramembrane potential, and bending elasticity. Biophys. J.
**2007**, 92, 2451–2462. [Google Scholar] [CrossRef] [PubMed] - Babu Boggara, M.; Faraone, A.; Krishnamoorti, R. Effect of pH and ibuprofen on the phospholipid bilayer bending modulus. J. Phys. Chem. B
**2010**, 114, 8061–8066. [Google Scholar] [CrossRef] - Mitkova, D.; Marukovich, N.; Ermakov, Y.A.; Vitkova, V. Bending rigidity of phosphatidylserine-containing lipid bilayers in acidic aqueous solutions. Colloids Surf. A Physicochem. Eng. Asp.
**2014**, 460, 71–78. [Google Scholar] [CrossRef] - Winterhalter, M.; Helfrich, W. Effect of surface charge on the curvature elasticity membranes. J. Phys. Chem.
**1988**, 92, 6865–6867. [Google Scholar] [CrossRef] - Winterhalter, M.; Helfrich, W. Bending elasticity of electrical charged bilayers: Coupled monolayers, neutral surfaces, and balancing stresses. J. Phys. Chem.
**1992**, 96, 327–330. [Google Scholar] [CrossRef] - Berkowitz, M.L.; Raghavan, K. Interaction forces between membrane surfaces. Role of electrostatic concepts. In Biomembrane Electrochemistry; Blank, M., Vodyanoy, I., Eds.; American Chemical Society: Washington, DC, USA, 1994; Volume 235, pp. 3–25. [Google Scholar]
- Pandit, S.A.; Bostick, D.; Berkowitz, M.L. Molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer with NaCl. Biophys. J.
**2003**, 84, 3743–3750. [Google Scholar] [CrossRef] - De Jong, D.H.; Schäfer, L.; de Vries, A.H.; Marrink, S.J.; Berendsen, H.J.C.; Grubmüller, H. Determining equilibrium constants for dimerization reactions from molecular dynamics simulations. J. Comput. Chem.
**2011**, 32, 1919–1928. [Google Scholar] [CrossRef] [PubMed] - Smirnova, Y.G.; Aeffner, S.; Risselada, H.J.; Marrink, S.J.; Müller, M.; Knecht, V. Interbilayer repulsion forces between tension-free lipid bilayers from simulation. Soft Matter
**2013**, 9, 10705–10718. [Google Scholar] [CrossRef] - Landau, L.D.; Lifshitz, E.M. Theory of Elasticity, 3rd ed.; Elsevier: Oxford, UK, 1986. [Google Scholar]
- Helfrich, W. Out-of-plane fluctuations of lipid bilayers. Z. Naturforsch.
**1975**, 30, 841–842. [Google Scholar] - Bermúdez, H.; Hammer, D.A.; Discher, D.E. Effect of bilayer thickness on membrane bending rigidity. Langmuir
**2004**, 20, 540–543. [Google Scholar] [CrossRef] [PubMed] - Szleifer, I.; Kramer, D.; Ben-Shaul, A.; Roux, D.; Gelbart, W.M. Curvature elasticity of pure and mixed surfactant films. Phys. Rev. Lett.
**1988**, 60, 1966–1969. [Google Scholar] [CrossRef] - Zhang, W.; Róg, T.; Gurtovenko, A.A.; Vattulainen, I.; Karttunen, M. Atomic-scale structure and electrostatics of anionic palmitoyloleoylphosphatidylglycerol lipid bilayers with Na
^{+}counterions. Biophys. J.**2007**, 92, 1114–1124. [Google Scholar] - Von Deuster, C.I.E.; Knecht, V. Competing interactions for antimicrobial selectivity based on charge complementarity. Biochim. Biophys. Acta
**2011**, 1808, 2867–2876. [Google Scholar] [CrossRef] [PubMed] - Knecht, V.; Klasczyk, B.; Dimova, R. Macro-versus microscopic view on the electrokinetics of a water-membrane interface. Langmuir
**2013**, 29, 7939–7948. [Google Scholar] [CrossRef] [PubMed] - Reif, M.M.; Hünenberger, P.H. Origin of asymmetric solvation effects for ions in water and organic solvents investigated using molecular dynamics simulations: The Swain acity-basity scale revisited. J. Phys. Chem. B
**2016**, 120, 8485–8517. [Google Scholar] [CrossRef] [PubMed] - Lindahl, E.; Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J.
**2000**, 79, 426–433. [Google Scholar] [CrossRef] - Evans, E.; Rawicz, W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett.
**1990**, 64, 2094–2097. [Google Scholar] [CrossRef] - Nagle, J.F.; Tristram-Nagle, S. Structure of lipid bilayers. Biochim. Biophys. Acta
**2000**, 1469, 159–195. [Google Scholar] [CrossRef] - Tabony, J.; Perly, B. Quasielastic neutron scattering measurements of fast local translational diffusion of lipid molecules in phospholipid bilayers. Biochim. Biophys. Acta
**1991**, 1063, 67–72. [Google Scholar] [CrossRef] - König, S.; Pfeiffer, W.; Bayerl, T.; Richter, D.; Sackmann, E. Molecular dynamics of lipid bilayers studied by incoherent quasi-elastic neutron scattering. J. Phys. II Fr.
**1992**, 2, 1589–1615. [Google Scholar] [CrossRef] - Jeon, J.-H.; Martinez-Seara Monne, H.; Javanainen, M.; Metzler, R. Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins. Phys. Rev. Lett.
**2012**, 109. [Google Scholar] [CrossRef] - Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A.E.; Berendsen, H.J.C. GROMACS: Fast, flexible, and free. J. Comput. Chem.
**2005**, 26, 1701–1718. [Google Scholar] [CrossRef] [PubMed] - Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput.
**2008**, 4, 435–447. [Google Scholar] [CrossRef] [PubMed] - Berendsen, H.J.C.; Postma, J.P.M.; van Gunsteren, W.F.; di Nola, A.; Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys.
**1984**, 81, 3684–3690. [Google Scholar] [CrossRef] - Parrinello, M.; Rahman, A. Crystal structure and pair potentials: A molecular-dynamics study. Phys. Rev. Lett.
**1980**, 45, 1196–1199. [Google Scholar] [CrossRef] - Hess, B.; Bekker, H.; Berendsen, H.J.C.; Fraaije, J.G.E.M. LINCS: A linear constraint solver for molecular simulations. J. Comput. Chem.
**1997**, 18, 1463–1472. [Google Scholar] [CrossRef] - Hockney, R.W. The potential calculation and some applications. Methods Comput. Phys.
**1970**, 9, 135–211. [Google Scholar] - Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An Nlog(N) method for Ewald sums in large systems. J. Chem. Phys.
**1993**, 98, 10089–10092. [Google Scholar] [CrossRef] - Berger, O.; Edholm, O.; Jähnig, F. Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys. J.
**1997**, 72, 2002–2013. [Google Scholar] [CrossRef] - Van Gunsteren, W.F.; Billeter, S.R.; Eising, A.A.; Hünenberger, P.H.; Krüger, P.; Mark, A.E.; Scott, W.R.P.; Tironi, I.G. Biomolecular Simulation: The GROMOS96 Manual and User Guide; Verlag der Fachvereine: Zürich, Switzerland, 1996. [Google Scholar]
- Berendsen, H.J.C.; Postma, J.P.M.; van Gunsteren, W.F.; Hermans, J. Interaction models for water in relation to protein hydration. In Intermolecular Forces; Pullman, B., Ed.; Reidel: Dordrecht, The Netherlands, 1981; pp. 331–342. [Google Scholar]
- Hess, B.; van der Vegt, N.F.A. Cation specific binding with protein surface charges. Proc. Natl. Acad. Sci. USA
**2009**, 106, 13296–13300. [Google Scholar] [CrossRef] [PubMed] - Weerasinghe, S.; Smith, P.E. A Kirkwood-Buff derived force field for sodium chloride in water. J. Chem. Phys.
**2003**, 119, 11342–11349. [Google Scholar] [CrossRef] - Vorobjev, Y.N.; Hermans, J. A critical analysis of methods of calculation of a potential in simulated polar liquids : Strong arguments in favor of “Molecule-based” summation and of vacuum boundary conditions in Ewald summations. J. Phys. Chem. B
**1999**, 103, 10234–10242. [Google Scholar] [CrossRef] - Kastenholz, M.A.; Hünenberger, P.H. Computation of methodology-independent ionic solvation free energies from molecular simulations: I. The electrostatic potential in molecular liquids. J. Chem. Phys.
**2006**, 124. [Google Scholar] [CrossRef] [PubMed] - Waheed, Q.; Edholm, O. Undulation contributions to the area compressibility in lipid bilayer simulations. Biophys. J.
**2009**, 97, 2754–2760. [Google Scholar] [CrossRef] [PubMed] - Frigo, M.; Johnson, S.G. The design and implementation of FFTW3. Proc. IEEE
**2005**, 93, 216–231. [Google Scholar] [CrossRef] - Allen, M.P.; Tildesley, D.J. Computer Simulation of Liquids; Oxford University Press: New York, NY, USA, 1987. [Google Scholar]
- Reif, M.M.; Hünenberger, P.H. Computation of methodology-independent single-ion solvation properties from molecular simulations. IV. Optimized Lennard–Jones parameter sets for the alkali and halide ions in water. J. Chem. Phys.
**2011**, 134. [Google Scholar] [CrossRef] [PubMed] - Szklarczyk, O.M.; Bachmann, S.J.; van Gunsteren, W.F. A polarizable empirical force field for molecular dynamics simulation of liquid hydrocarbons. J. Comput. Chem.
**2014**, 35, 789–801. [Google Scholar] [CrossRef] [PubMed] - Anslyn, E.V.; Dougherty, D.A. Modern Physical Organic Chemistry; University Science Books: Philadelphia, PA, USA, 2006. [Google Scholar]

**Figure 1.**Profiles of water (${\rho}_{\mathrm{OW}}(z)$) and ion (${\rho}_{I}(z)$; $I\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}$ Na${}^{+}$ or Cl${}^{-}$) number densities normal to the membrane, along with integrated ion density profiles giving the cumulative number of ions (${N}_{I}(z)$; $I\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}$ Na${}^{+}$ or Cl${}^{-}$), for simulation S${}_{\mathrm{NaCl}}$(o,wc), i.e., a simulation based on the unmodified force field (Table 7). The dashed vertical lines indicate z-values where the water oxygen number density evaluates to half of its bulk value, i.e., the location of the shear plane ${z}_{\mathrm{s}}$ (Section 4.3.2). The corresponding apparent binding constants are reported in Table 2. Note that in this illustration, the lipid bilayer is centered.

**Figure 4.**Symmetrized electrostatic potential $\varphi (z)$ along the bilayer normal (Equation (16)), for simulations S${}_{\mathrm{wat}}$(wc), S${}_{\mathrm{NaCl}}$(o,wc), S${}_{\mathrm{NaCl}}$(m1,wc) and S${}_{\mathrm{NaCl}}$(m2,wc), shown as black, red, green and blue curves, respectively. The underlying atom-based charge density ${\rho}_{\mathrm{a}}(z)$ involves (

**a**) all atoms, (

**b**) ions or (

**c**) only lipid (dashed lines; labeled “POPC”) or water (solid lines; labeled “water”) atoms. The anchoring of the curves was done as described in Section 4.3.1. The simulation acronyms are explained in Table 7. Note that in this illustration, the lipid bilayer is centered.

**Figure 5.**Spectral intensity of membrane undulations $\langle {u}^{2}(q)\rangle $ as a function of the wavenumber q for simulations L${}_{\mathrm{wat}}$(wc), L${}_{\mathrm{NaCl}}$(o,wc), L${}_{\mathrm{NaCl}}$(m1,wc) and L${}_{\mathrm{NaCl}}$(m2,wc), shown as black, red, green and blue circles, respectively. $\langle {u}^{2}(q)\rangle $ was obtained from a Fourier transform of the discretized undulation $\overline{\tilde{z}}({x}_{i},{y}_{j})$ (Section 4.3.1). The data refer to the results from the analysis employing twelve grid cells per dimension. Solid lines indicate a fit according to Equation (18), carried out in the low-wavenumber regime. The simulation acronyms are explained in Table 7.

**Figure 6.**Deuterium order parameter $-{S}_{i}$ (Equation (11)) of the CH${}_{n}$ groups i of the oleoyl (

**a**) and palmitoyl (

**b**) chains for simulations S${}_{\mathrm{wat}}$(wc), S${}_{\mathrm{NaCl}}$(o,wc), S${}_{\mathrm{NaCl}}$(m1,wc) and S${}_{\mathrm{NaCl}}$(m2,wc), shown as black, red, green and blue circles, respectively. The first (carboxylate) and last CH${}_{n}$ groups are omitted from the analysis. The simulation acronyms are explained in Table 7.

**Table 1.**Area per lipid ${a}_{\mathrm{L}}$ (Equation (9)), area compressibility ${\kappa}_{\mathrm{A}}$ (Equation (17)), bilayer thickness ${D}_{\mathrm{HH}}$ (Section 4.3.1) and water layer thickness ${d}_{\mathrm{w}}$ (Equation (10)) for systems containing membrane patches of 64 lipids per leaflet. The simulation acronyms are explained in Table 7. The area compressibility is only reported for simulations involving the Parrinello–Rahman barostat.

Simulation | ${\mathit{a}}_{\mathbf{L}}$ | ${\mathit{\kappa}}_{\mathbf{A}}$ | ${\mathit{D}}_{\mathbf{HH}}$ | ${\mathit{d}}_{\mathbf{w}}$ |
---|---|---|---|---|

(nm${}^{2}$) | (kJ·mol${}^{-1}\xb7$nm${}^{-2}$) | (nm) | (nm) | |

S${}_{\mathrm{wat}}$(wc) | $0.607\pm 0.002{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | - | 3.98 | 4.13 |

S${}_{\mathrm{wat}}$(pr) | $0.608\pm 0.002{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $202\pm 81{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 4.19 | 3.91 |

S${}_{\mathrm{NaCl}}$(o,wc) | $0.542\pm 0.002{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | - | 4.31 | 4.71 |

S${}_{\mathrm{NaCl}}$(o,pr) | $0.542\pm 0.001{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $376\pm 84{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 4.20 | 4.82 |

S${}_{\mathrm{NaCl}}$(m1,wc) | $0.629\pm 0.001{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | - | 3.86 | 3.90 |

S${}_{\mathrm{NaCl}}$(m1,pr) | $0.623\pm 0.002{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $222\pm 24{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 4.03 | 3.81 |

S${}_{\mathrm{NaCl}}$(m2,wc) | $0.617\pm 0.002{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | - | 3.95 | 3.97 |

S${}_{\mathrm{NaCl}}$(m2,pr) | $0.626\pm 0.001{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $263\pm 5{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 3.75 | 4.05 |

**Table 2.**Apparent binding constants ${K}_{\mathrm{app}}$ (Equation (21)) for sodium and chloride ions, computed from ions binding to either leaflet (which is why two values are reported; Section 4.3.2), the corresponding numbers of bound ions ${\tilde{N}}_{\mathrm{b}}({\mathrm{Na}}^{+})$ and ${\tilde{N}}_{\mathrm{b}}({\mathrm{Cl}}^{-})$, respectively (Equations (19) and (20)), and mean salt concentration in the bulk ${\overline{c}}_{\mathrm{blk}}$ (Equation (22)). The underlying ion density profiles along the bilayer normal are displayed in Figure 1 (S${}_{\mathrm{NaCl}}$(o,wc)), Figure 2 (S${}_{\mathrm{NaCl}}$(m1,wc)) and Figure 3 (S${}_{\mathrm{NaCl}}$(m2,wc)). The simulation acronyms are explained in Table 7.

Simulation | ${\mathit{K}}_{\mathbf{app}}({\mathbf{Na}}^{+})$ | ${\mathit{K}}_{\mathbf{app}}({\mathbf{Cl}}^{-})$ | ${\tilde{\mathit{N}}}_{\mathbf{b}}({\mathbf{Na}}^{+})$ | ${\tilde{\mathit{N}}}_{\mathbf{b}}({\mathbf{Cl}}^{-})$ | ${\overline{\mathit{c}}}_{\mathbf{blk}}$ | ||||
---|---|---|---|---|---|---|---|---|---|

(M${}^{-1}$) | (M${}^{-1}$) | (M) | |||||||

S${}_{\mathrm{NaCl}}$(o,wc) | 0.71 | 1.02 | 0.009 | 0.012 | 12.43 | 16.47 | 0.20 | 0.27 | 0.34 |

S${}_{\mathrm{NaCl}}$(m1,wc) | 0.34 | 0.36 | 0.29 | 0.30 | 7.74 | 8.26 | 6.77 | 6.96 | 0.41 |

S${}_{\mathrm{NaCl}}$(m2,wc) | 0.50 | 0.28 | 0.39 | 0.21 | 10.66 | 6.53 | 8.69 | 4.97 | 0.40 |

**Table 3.**Average number of atoms j found in the first (${N}_{ij}^{(1)}$; Equation (13)) and second (${N}_{ij}^{(2)}$; Equation (14)) coordination shells of atom i, reported for simulations S${}_{\mathrm{NaCl}}$(o,wc), S${}_{\mathrm{NaCl}}$(m1,wc) and S${}_{\mathrm{NaCl}}$(m2,wc). Atoms i are Na${}^{+}$ or Cl${}^{-}$ ions, and atoms j are water oxygen atoms (OW), lipid tail carbon atoms (CH${}_{n}$), lipid ester carbonyl oxygen atoms (OC), or lipid ester phosphate oxygen atoms (OP). The simulation acronyms are explained in Table 7.

Simulation | S${}_{\mathbf{NaCl}}$(o,wc) | S${}_{\mathbf{NaCl}}$(m1,wc) | S${}_{\mathbf{NaCl}}$(m2,wc) | |
---|---|---|---|---|

i,j | ||||

Na${}^{+}$, OW | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | 3.36 ± 0.05 | 4.95 ± 0.09 | 4.97 ± 0.07 |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 8.8 ± 0.2 | 12.7 ± 0.4 | 12.7 ± 0.2 | |

Na${}^{+}$, OC | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | 1.62 ± 0.05 | 1.1$\times {10}^{-2}\pm 0.1\times {10}^{-2}$ | 1.3$\times {10}^{-2}\pm 0.1\times {10}^{-2}$ |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 0.35 ± 0.07 | 0.652 ± 0.006 | 0.745 ± 0.002 | |

Na${}^{+}$, OP | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | 8.0$\times {10}^{-2}\pm 0.9\times {10}^{-2}$ | $1.03\times {10}^{-3}\pm 0.04\times {10}^{-3}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ | $9.8\times {10}^{-4}\pm 0.5\times {10}^{-4}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 2.25 ± 0.05 | 0.97 ± 0.01 | 0.93 ± 0.06 | |

Na${}^{+}$, CH${}_{n}$ | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | 2.76 ± 0.07 | $3.2\pm 0.4{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ | $2.8\pm 0.4{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 2.6 ± 0.2 | 3.8 ± 0.8 | 4.4 ± 0.7 | |

Cl${}^{-}$, OW | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | 7.227 ± 0.007 | 6.1 ± 0.2 | 6.3 ± 0.1 |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 21.81 ± 0.05 | 18.4 ± 0.7 | 18.2 ± 0.4 | |

Cl${}^{-}$, CH${}_{n}$ | ${N}_{ij}^{(1)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $1.0\times {10}^{-3}\pm 0.4\times {10}^{-3}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ | $2.0\pm 0.3{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ | $2.0\pm 0.2{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

${N}_{ij}^{(2)}{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 3.7$\times {10}^{-2}\pm 0.3\times {10}^{-2}$ | 1.3 ± 0.5 | 1.3 ± 0.3 |

Simulation | ${\mathit{P}}_{\mathbf{MD}}$ | ${\mathit{P}}_{\mathbf{TH}}$ |
---|---|---|

(kJ·mol${}^{-1}\xb7$nm${}^{-3}$) | ||

S${}_{\mathrm{NaCl}}$(o,wc) | $8.55{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ (8.47)${\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 2.74 × ${10}^{-3}$ |

S${}_{\mathrm{NaCl}}$(m1,wc) | $-2.06{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ (−1.44)${\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 1.00 × ${10}^{-3}$ |

S${}_{\mathrm{NaCl}}$(m2,wc) | $-1.09{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ (−1.92)${\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | 1.04 × ${10}^{-3}$ |

**Table 5.**Bending stiffness ${k}_{\mathrm{c}}$ (Equation (18)) for simulations of large membrane patches in pure water or a NaCl solution described with the original or modified force-field versions. The average box-edge length along the (quadratic) membrane plane $\langle {L}_{\mathrm{x}}\rangle (=\langle {L}_{\mathrm{y}}\rangle )$ and the microscopic surface tension coefficient $\tilde{\gamma}$ (Equation (18)) are also provided. The coefficient B (Equation (8)) characterizing the extent of membrane interdigitation was calculated using ${k}_{\mathrm{c}}$ reported in this table along with the membrane thickness ${D}_{\mathrm{HH}}$ and area compressibility ${\kappa}_{\mathrm{A}}$ reported in Table 1 for the corresponding small systems S${}_{\mathrm{wat}}$(pr), S${}_{\mathrm{NaCl}}$(o,pr), S${}_{\mathrm{NaCl}}$(m1,pr) and S${}_{\mathrm{NaCl}}$(m2,pr). The simulation acronyms are explained in Table 7.

Simulation | ${\mathit{k}}_{\mathbf{c}}$ | $\langle {\mathit{L}}_{\mathbf{x}}\rangle $ | $\tilde{\mathit{\gamma}}$ | B |
---|---|---|---|---|

(${10}^{-20}$ J) | (nm) | (mN·m${}^{-1}$) | (${10}^{-3}$) | |

L${}_{\mathrm{wat}}$(wc) | $2.8\pm 0.7{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $12.47\pm 0.01{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | $17.3\pm 1.9{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $4.8\pm 2.2{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

L${}_{\mathrm{NaCl}}$(o,wc) | $1.7\pm 0.2{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $11.83\pm 0.01{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | $31.1\pm 3.5{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $1.5\pm 0.4{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

L${}_{\mathrm{NaCl}}$(m1,wc) | $3.3\pm 0.1{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $12.76\pm 0.01{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | $8.3\pm 0.1{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $5.5\pm 0.6{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

L${}_{\mathrm{NaCl}}$(m2,wc) | $1.7\pm 0.1{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $12.70\pm 0.01{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{b}}$ | $17.6\pm 0.5{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{a}}$ | $2.8\pm 0.2{\phantom{\rule{3.33333pt}{0ex}}}^{\mathrm{c}}$ |

**Table 6.**Long- (2–6 ns), medium- (100–500 ps) and short-timescale (2–10 ps) lipid center of mass diffusion coefficients (Equation (15)) for simulations S${}_{\mathrm{wat}}$(wc), S${}_{\mathrm{NaCl}}$(o,wc), S${}_{\mathrm{NaCl}}$(m1,wc) and S${}_{\mathrm{NaCl}}$(m2,wc). The time intervals refer to the regime used for a linear fit to the mean square displacement. The simulation acronyms are explained in Table 7.

Time Scale | 2–6 ns | 100–500 ps | 2–10 ps |
---|---|---|---|

Simulation | D (${10}^{-8}$ cm${}^{2}\xb7$s${}^{-1}$) | ||

S${}_{\mathrm{wat}}$(wc) | 7.8 ± 0.3 | 45.4 ± 0.7 | 386 ± 3 |

S${}_{\mathrm{NaCl}}$(o,wc) | 4.2 ± 0.2 | 31.0 ± 0.7 | 336 ± 3 |

S${}_{\mathrm{NaCl}}$(m1,wc) | 8.1 ± 0.3 | 46.1 ± 0.4 | 374 ± 3 |

S${}_{\mathrm{NaCl}}$(m2,wc) | 7.5 ± 0.3 | 43.4 ± 0.7 | 366 ± 3 |

**Table 7.**Overview of the performed simulations. The first column provides an acronym for the different simulations, consisting of a label for the simulated system (NACL, S${}_{\mathrm{wat}}$, S${}_{\mathrm{NaCl}}$, L${}_{\mathrm{wat}}$ or L${}_{\mathrm{NaCl}}$; Section 4.1) and an indication of the employed force field (o, m1, m2) and barostatting (wc, pr). ${N}_{\mathrm{wat}}$ and ${N}_{\mathrm{NaCl}}$ denote the number of water molecules and cation-anion ion pairs, respectively; ${N}_{\mathrm{L}}$ denotes the number of lipid molecules. The parameters ${s}_{{\mathrm{Cl}}^{-}}$, ${s}_{{\mathrm{Na}}^{+}}$ and ${s}_{\mathrm{NaCl}}$ specify the scaling factors applied to chloride ion-lipid (tail), sodium ion-lipid and sodium ion-chloride ion ${C}_{12}$ Lennard–Jones parameters. The total simulation time is reported, along with the length of the initial time period discarded for equilibration in parentheses. Barostatting was done with either the weak-coupling (wc) [55] or the Parrinello–Rahman (pr) [56] barostat. Except for simulation NACL, where barostatting was applied isotropically (iso.), a semi-isotropic (sem. iso.) scaling of box edges was applied.

Simulation | System | ${\mathit{N}}_{\mathbf{wat}}$ | ${\mathit{N}}_{\mathbf{NaCl}}$ | ${\mathit{N}}_{\mathbf{L}}$ | ${\mathit{s}}_{{\mathbf{Cl}}^{-}}$, ${\mathit{s}}_{{\mathbf{Na}}^{+}}$, ${\mathit{s}}_{\mathbf{NaCl}}$ | Simulation Time (ns) | Barostatting |
---|---|---|---|---|---|---|---|

NACL | NACL | 6715 | 121 | 0 | -, -, 1.33 | 10 (1) | wc, iso. |

S${}_{\mathrm{wat}}$(wc) | S${}_{\mathrm{wat}}$ | 5120 | 0 | 128 | 1.0, 1.0, 1.0 | 210 (90) | wc, sem. iso. |

S${}_{\mathrm{wat}}$(pr) | S${}_{\mathrm{wat}}$ | 5120 | 0 | 128 | 1.0, 1.0, 1.0 | 120 (30) | pr, sem. iso. |

L${}_{\mathrm{wat}}$(wc) | L${}_{\mathrm{wat}}$ | 20,480 | 0 | 512 | 1.0, 1.0, 1.0 | 210 (90) | wc, sem. iso. |

S${}_{\mathrm{NaCl}}$(o,wc) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 1.0, 1.0, 1.0 | 210 (90) | wc, sem. iso. |

S${}_{\mathrm{NaCl}}$(o,pr) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 1.0, 1.0, 1.0 | 120 (30) | pr, sem. iso. |

S${}_{\mathrm{NaCl}}$(m1,wc) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 0.057, 3.2, 1.33 | 210 (90) | wc, sem. iso. |

S${}_{\mathrm{NaCl}}$(m2,wc) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 0.057, 3.0, 1.33 | 210 (90) | wc, sem. iso. |

S${}_{\mathrm{NaCl}}$(m1,pr) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 0.057, 3.2, 1.33 | 120 (30) | pr, sem. iso. |

S${}_{\mathrm{NaCl}}$(m2,pr) | S${}_{\mathrm{NaCl}}$ | 5020 | 50 | 128 | 0.057, 3.0, 1.33 | 120 (30) | pr, sem. iso. |

L${}_{\mathrm{NaCl}}$(o,wc) | L${}_{\mathrm{NaCl}}$ | 20,080 | 200 | 512 | 1.0, 1.0, 1.0 | 210 (90) | wc, sem. iso. |

L${}_{\mathrm{NaCl}}$(m1,wc) | L${}_{\mathrm{NaCl}}$ | 20,080 | 200 | 512 | 0.057, 3.2, 1.33 | 210 (90) | wc, sem. iso. |

L${}_{\mathrm{NaCl}}$(m2,wc) | L${}_{\mathrm{NaCl}}$ | 20,080 | 200 | 512 | 0.057, 3.0, 1.33 | 210 (90) | wc, sem. iso. |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Reif, M.M.; Kallies, C.; Knecht, V.
Effect of Sodium and Chloride Binding on a Lecithin Bilayer. A Molecular Dynamics Study. *Membranes* **2017**, *7*, 5.
https://doi.org/10.3390/membranes7010005

**AMA Style**

Reif MM, Kallies C, Knecht V.
Effect of Sodium and Chloride Binding on a Lecithin Bilayer. A Molecular Dynamics Study. *Membranes*. 2017; 7(1):5.
https://doi.org/10.3390/membranes7010005

**Chicago/Turabian Style**

Reif, Maria M., Christopher Kallies, and Volker Knecht.
2017. "Effect of Sodium and Chloride Binding on a Lecithin Bilayer. A Molecular Dynamics Study" *Membranes* 7, no. 1: 5.
https://doi.org/10.3390/membranes7010005