# Interaction between Dipolar Lipid Headgroups and Charged Nanoparticles Mediated by Water Dipoles and Ions

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## Abstract

**:**

## 1. Introduction

## 2. Interaction between Lipid Headgroups and Charged Nanoparticle

#### 2.1. Space Dependence of Relative Permittivity within the Modified Langevin-Poisson-Boltzmann (MLPB) Model

^{2}= 1.33

^{2}, where n is the optical refractive index of water. The space dependency of permittivity within the MLPB model has the form [26,30]:

_{0}

_{w}is the constant number density of water molecules, p

_{0}is the magnitude of the water external dipole moment [31], E(x) is the magnitude of the electric field strength, ɛ

_{0}is the permittivity of the free space, β= 1/kT, kT is the thermal energy and $\mathcal{L}$(u) = (coth(u) −1/u) is the Langevin function, while $\gamma ={\scriptstyle \frac{3}{2}}\hspace{0.17em}\left({\scriptstyle \frac{2+{n}^{2}}{3}}\right)$ [31]. In the limit of E(x) →0, Equation (1) for ɛ

_{r}(x) gives the well-known Onsager expression: ɛ

_{r,b}≅ n

^{2}+ (2 + n

^{2}/3)

^{2}n

_{0}

_{w}p

_{0}

^{2}β/2ɛ

_{0}. At room temperature (298K), the above equation predicts ɛ

_{r}= 78.5 for the bulk solution. The parameters, p

_{0}and n

_{0}

_{w/}N

_{A}, are 3.1 Debye and 55 mol/L, respectively.

#### 2.2. Osmotic Pressure between Two Planar Charged Surfaces

_{1}, at x = 0 and surface charge density, σ

_{2}, at x = H (see Figure 2). The space dependency of permittivity, ɛ

_{r}(x), is taken into account by Equation (1). The corresponding Poisson equation, i.e., the MLPB equation, in a planar geometry can, thus, be written as: [26,30]:

_{0}is the unit charge, n

_{0}is the bulk number density of salt anions and cations and ɛ

_{r}(x) is defined by Equation (1). The boundary conditions are (see, for example, [30]):

_{inner}−P

_{bulk}in the form (see Appendix):

_{0}E(x)β, we can expand the third and fourth term in Equation (6) into a Taylor series to get:

## 3. Interaction between Dipolar Zwitterionic Lipid Headgroups and Charged Nanoparticle

_{1}at x = 0, while the positive surface charge of the nanoparticle (Figure 1) is approximated by the planar charged surface at x = H with the surface charged density, σ

_{2}. The corresponding Poisson equation in a planar geometry can be then written in the form [26]:

_{Zw}(x) is the macroscopic (net) volume charge density of positive charges of dipolar (zwitterionic) headgroups [26]:

## 4. Experimental Results

#### 4.1. Synthesis of Nanoparticles

_{2}O

_{3}) were synthesized through a controlled chemical co-precipitation method. An aqueous solution of iron (II) sulfate heptahydrate (FeSO

_{4}·7H

_{2}O) and iron (III) sulphate hydrate (Fe

_{2}(SO

_{4})

_{3}· H

_{2}O) was prepared at acidic conditions (purchased from Alfa Aesar). The co-precipitation method has been used as a two step process. In the first step, iron hydroxides were precipitated in an alkaline medium during the reaction between the aqueous solution of metal salts and an aqueous solution of ammonium hydroxide. The corresponding metal hydroxides were precipitated during the reaction between the alkaline precipitating reagent and the mixture of metal salts and, subsequently, oxidized in air to form γ − Fe

_{2}O

_{3}in the second step of the process. The temperature for this process was set constant at 25 ºC for 1 h. After the reaction, nanoparticles were washed with diluted ammonia solution at pH 10 several times and 5 mg/mL of a solution of citric acid (purchased from Sigma-Aldrich) during stirring to prepare stable aqueous suspension. Particles were additionally coated with SiO

_{2}cover and functionalized with different groups. In order to stabilize the aqueous suspension of the magnetic nanoparticles, the particles were coated with a silica layer prepared by hydrolysis and polycondensation of tetraethyl orthosilicate (TEOS, purchased from Alfa Aesar) using alkaline medium. TEOS was added to the mixture by dropwise addition for 1 h and, after that, rigorously stirred for 3 h at room temperature. Using silica cover helps to prevent agglomeration, as well as provides an easily modifiable surface for creating different charges or groups on the surface of the nanoparticles. As shown in recent publications the cover is also biocompatible regarding cell viability studies [49]. Additional amino [ ${\text{NH}}_{3}^{+}$] groups were added to their surface to create a positive charge using grafting with 3-(2-aminoethylamino) propylmethyldimethoxysilane (APMS, 97 %), purchased from Alfa Aesar. The similarly charged particles reduce the rate of aggregation, due to strong electrostatic repulsions, thereby ensuring increased stability. The nanoparticles were characterized for size and morphology using Transmission Electron Microscopy (TEM) model JEM 2100 at 200 kV from JEOL. The size of the synthesized γ −Fe

_{2}O

_{3}nanoparticles was found to be 10±2 nm, observed by TEM analysis, as shown in Figure 7.

_{3})

_{6}·9H

_{2}O and Co(NO

_{3})

_{2}·6H

_{2}O in aqueous solutions. The pH was maintained between 9.5–11 using 10 % NaOH solution, and the temperature was set between 70–95 ºC for 4–5 h under vigorous magnetic agitation. The resulting mixture was then centrifuged for fifteen minutes at 3,000 rpm. The supernatant was then decanted and centrifuged rapidly, until a thick black precipitate was obtained. The precipitate was then washed thoroughly with water and acetone for purification and dried overnight at 100 ºC in hot air oven. The dried samples were then dispersed in double distilled water. The cobalt ferrite NPs were coated with citric acid to impart a negative charge to their surface. The size of CoFe

_{2}O

_{4}NPs was found to be in the range of 10–15 nm by TEM, and the zeta potential value was estimated to be ±34 mV using DLS.

#### 4.2. Preparation of Liposome—Nanoparticle Conjugates

#### 4.3. Fluorescence Anisotropy Measurements: Anisotropy and Fluidity

_{||}and I

_{⊥}represent the parallel and perpendicular fluorescence emission intensities, respectively.

_{HV}) and horizontally polarized light (I

_{HH})) were determined for each sample separately. The lipid-order parameter, S, was calculated from the anisotropy value using the following analytical expression [53]:

_{0}is the fluorescence anisotropy of DPH in the absence of any rotational motion of the probe. The theoretical value of r

_{0}of DPH is 0.4, while the experimental values of r

_{0}lie between 0.362 and 0.394 [53].

#### 4.4. Influence of Nanoparticle-Membrane Interactions on Membrane Fluidity

## 5. Conclusions

## Acknowledgments

## Appendix

#### A. Derivation of Osmotic Pressure by Integration of the MLPB Equation

^{2}ϕ/dx

^{2}and dϕ = ϕ′ dx. By subtracting the corresponding bulk values from the local pressure, we obtain the expression for the osmotic pressure difference, Π = P

_{inner}−P

_{bulk}:

## Conflict of Interest

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**Figure 1.**Schematic figure of dipolar zwitterionic lipid bilayer membrane in contact with the positively and negatively charged nanoparticles.

**Figure 2.**Schematic figure of the model of a negatively charged surface characterized by surface charge density, σ

_{1}, at x = 0 and a positively charged surface with surface charge density, σ

_{2}, at x = H.

**Figure 3.**Osmotic pressure between between a negatively and positively surface (see Figure 2) as a function of the distance between both surfaces (H), calculated within the modified Langevin-Poisson-Boltzmann (MLPB) model for two values of the bulk salt concentration, n

_{0}/N

_{A}= 0.1 mol/L (dashed line) and n

_{0}/N

_{A}= 0.01 mol/L (full line). Other model parameters are : σ

_{1}= −0.3 As/m

^{2}, σ

_{2}= 0.3 As/m

^{2}, T = 298K, concentration of water, n

_{0}

_{w}/N

_{A}= 55 mol/L, and dipole moment of water, p

_{0}= 3.1 Debye, where N

_{A}is the Avogadro number.

**Figure 4.**Negative charges of dipolar (zwitterionic) lipid headgroups are described by the surface charge density, σ

_{1}, at x = 0. The positive charges of the headgroups of dipolar lipids protrude in the electrolyte solution. Here, D, is the distance between the charges within the single dipolar lipid headgroup, and ω describes the orientation angle of the dipole within the single headgroup. The positive charge of the interacting nanoparticle is described by the surface charge density, σ

_{2}.

**Figure 5.**Average lipid dipolar headgroup orientation angle, < ω > (see, also, Figure 4), as a function of the distance (H) between the plane of the phosphate groups of dipolar (zwitterionic) headgroups and the surface of positively (

**left**panel) and negatively (

**right**panel) charged nanoparticle for the bulk concentration of salt, n

_{0}/N

_{A}= 0.1 mol/L, and two values of parameter, α: 0.5 (full line) and five (dashed line). The values of the model parameters are: the dipole moment of water, p

_{0}= 3.1 Debye, and concentration of water, n

_{0}

_{w/}N

_{A}= 55 mol/L.

**Figure 6.**Osmotic pressure between the plane of the phosphate groups of dipolar (zwitterionic) headgroups and the surface of positively (

**left**panel) and negatively (

**right**panel) charged nanoparticle, as a function of the distance (H) (see, also, Figures 4 and 5) calculated for α = 5 and the bulk concentration of salt, n

_{0/}N

_{A}= 0.01 mol/L, by using Equation (9). The values of other model parameters are the same as in Figure 5.

**Figure 7.**TEM image of superparamagnetic maghemite nanoparticles (γ −Fe

_{2}O

_{3}), covered with 20 nm thick silica.

**Figure 8.**Temperature-dependent fluorescence anisotropy measurement of zwitterionic SOPC bilayer membranes in the presence of negatively or positively charged nanoparticles (NPs). The control curve corresponds to the absence of the nanoparticles.

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**MDPI and ACS Style**

Velikonja, A.; Santhosh, P.B.; Gongadze, E.; Kulkarni, M.; Eleršič, K.; Perutkova, Š.; Kralj-Iglič, V.; Ulrih, N.P.; Iglič, A.
Interaction between Dipolar Lipid Headgroups and Charged Nanoparticles Mediated by Water Dipoles and Ions. *Int. J. Mol. Sci.* **2013**, *14*, 15312-15329.
https://doi.org/10.3390/ijms140815312

**AMA Style**

Velikonja A, Santhosh PB, Gongadze E, Kulkarni M, Eleršič K, Perutkova Š, Kralj-Iglič V, Ulrih NP, Iglič A.
Interaction between Dipolar Lipid Headgroups and Charged Nanoparticles Mediated by Water Dipoles and Ions. *International Journal of Molecular Sciences*. 2013; 14(8):15312-15329.
https://doi.org/10.3390/ijms140815312

**Chicago/Turabian Style**

Velikonja, Aljaž, Poornima Budime Santhosh, Ekaterina Gongadze, Mukta Kulkarni, Kristina Eleršič, Šarka Perutkova, Veronika Kralj-Iglič, Nataša Poklar Ulrih, and Aleš Iglič.
2013. "Interaction between Dipolar Lipid Headgroups and Charged Nanoparticles Mediated by Water Dipoles and Ions" *International Journal of Molecular Sciences* 14, no. 8: 15312-15329.
https://doi.org/10.3390/ijms140815312