Interactions of Monovalent and Divalent Cations with Cardiolipin

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

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Interactions of Monovalent and Divalent Cations with Cardiolipin Monolayers Renko Kensbock, Heiko Ahrens, and Christiane A. Helm* Institute of Physics, University of Greifswald, Felix-Hausdorff-Straße 6, D-17487 Greifswald, Germany

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S Supporting Information *

ABSTRACT: Cardiolipin is a mitochondrial phospholipid with four alkyl chains and two phosphate moieties. Tetramyristoyl cardiolipin (TMCL, (14:0)4CL) monolayers at the air−water interface are characterized by compression isotherms, which show a liquid expanded/liquid condensed phase transition. The phase transition surface pressure πc depends on the composition of the aqueous solution. In a calculation, this is attributed to the electrostatic double layer, which is induced by the head groups of the model membrane, and competitive ion binding. The intrinsic binding constant is large for protons (KH = 10 L/mol) and small for monovalent cations (KM (Na+, K+, Cs+) = 10−3 L/mol). The different intrinsic binding constants explain the non-monotonic behavior of πc on increasing the salt concentration: raising the monovalent salt concentration increases πc by charging the TMCL monolayer until 0.1 mol/L, then screening effects dominate and decrease πc by reducing the electrostatic repulsion between lipid head groups. When at fixed 0.15 mol/L NaCl concentration, the concentration of divalent cations is increased, πc decreases. The intrinsic binding constants of divalent cations follow the sequence Sr2+ < Mg2+ < Mn2+ ≈ Zn2+ ≈ Ca2+ (KD,Ca = 1.2 L/mol). The predictive power of the calculations was tested with different solutions.

■

INTRODUCTION

Once all the intrinsic binding constants between lipids and the different ions in the solution are known, it is possible to calculate the percentage of charged lipids and surface charge density with the double-layer model.8,15 However, when binding constants between cardiolipin molecules and charged species are measured, apparent binding constants are determined. An important property of an ionizable surface is its pKa value, which is the surface pH at which half of its charged sites are dissociated. As Olofsson et al.16 discussed, pKa values between 1 and about 7 have been reported for cardiolipin bilayers and aggregates.16−19 Similarly, handbooks quote different pKa values for many lipids.1,20 Competitive binding of the different ions to the lipid membrane and the composition and pH of a solution determine the surface charge density and thus the measured pKa value. Therefore, depending on the solution, different apparent binding constants were obtained. Experiments with phosphatidic acid (PA) model membranes have previously demonstrated the dominance of electrostatics in membrane systems and a monovalent and divalent salt dependence of the transition surface pressure of PA monolayers (transition temperature for PA bilayers).21−24 The apparent binding constant between Cu2+ and phosphatidyl serine (PS) was determined to depend on the PS concentration in the model

Natural lipids can carry a negative net charge, or are neutral. This depends on the head-group structure that interacts with the aqueous phase.1 Cardiolipin, an anionic lipid with four alkyl chains and two phosphate groups, is mostly found in the inner mitochondrial membrane.2−4 It is associated with proteins of the electron transport chain, apoptosis, as well as in cristae formation of mitochondria, among others.2−7 Information on the ionization properties of cardiolipin and of the binding constants of monovalent and divalent cations is essential for understanding the biological functions of these molecules. Large lipids, such as cardiolipins, are insoluble as single molecules. In nature, they form aggregates (i.e., micelles, vesicles) or lipid bilayers. Cardiolipin aggregates have a negative surface charge density that induces a heightened surface concentration of oppositely charged ions, thereby increasing the surface pH.8 In biological systems, the pH is tightly controlled: it varies in different organelles and is adjusted for a specific function.9 Surface potential and charge density of a tetramyristoyl cardiolipin (TMCL) monolayer are influenced by cations found in mitochondria, such as potassium, calcium, and magnesium cations. These cations are important for mitochondrial homeostasis and signaling.10−12 Other divalent cations do not occur freely in biological solutions, for instance, iron ions dissolved in a solution are found to be poisonous.13,14 © XXXX American Chemical Society

Received: October 29, 2018 Revised: February 4, 2019 Published: February 8, 2019 A

DOI: 10.1021/acs.langmuir.8b03637 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir membrane.25 Changes of the apparent binding constant by a factor of 17 000 were described. Knowing the intrinsic binding constants, one can calculate the surface charge density and the surface potential for an aqueous solution with any composition. Furthermore, electrostatic interaction of lipids are important for domain formation and domain boundaries within membranes, nanodisks, pH sensing by lipid membranes, and interactions between proteins and plasma membrane (see, for instance,26,27 or28 including the quoted references). We want to try a simple approach to determine the intrinsic binding constants. We want to investigate the thermodynamics of model membranes. Monomolecular layers (monolayers) at the air−water interface provide a geometrically well-defined system. We combine the measurements with calculations to determine the intrinsic pKa value as well as the intrinsic binding constants for monovalent and divalent cations (and the apparent value pKa,app). A prominent and reproducible feature of an isotherm is the phase transition from the liquid-expanded (LE) phase to the liquid-condensed (LC) phase. We use lipid monolayers that undergo two-dimensional phase transitions, the two-dimensional gaseous phase, liquid-expanded (LE phase, fluid phase), and liquid-condensed phase (LC phase, gel or solid phase).8,20,29,30 Saturated tetramyristoyl cardiolipin (TMCL) monolayers are well known to undergo two-dimensional phase transitions at room temperature.31−33 In the present study, we examine the interaction between monovalent and divalent cations and TMCL monolayers at the air−water interface. Motivated by our interest in biological systems, we use physicochemical methods to find the intrinsic binding constants relevant to our system. The intrinsic binding constant of protons and monovalent ions are found through variation of the monovalent ion concentration at constant pH. Changes in the monovalent salt concentration occur in biological systems, however, not to the extent that allows for an unambiguous determination of the intrinsic proton-binding constant. In a second step, we determine the intrinsic binding constant of divalent ions. We use a biological concentration of monovalent ions at constant pH and vary the concentration of the divalent ions up to high values not found in biology. The theoretical treatment of electrostatic double layers is well established and supported by experimental evidence.8,15,25 Within this framework, surface charge density, surface potential, and the effect of competitive binding are calculated. Furthermore, the surface pressure of the monolayer due to electrostatic interaction of the lipid head groups is found. It is derived from the energy gained by charging the monolayers. In other words, an electric double-layer model is introduced into the thermodynamic relations.8,15,34 We measure the isotherms and focus on the transition surface pressure between LE and LC phases as a function of the subphase composition. As a derived quantity, the transition surface pressure is found to be in good agreement with experimental observations. Even though cardiolipins constitute divalent anions with four acyl chains, we find it sufficient to model cardiolipin as a monovalent anion, diacyl lipid at half the cardiolipin area per molecule. Our model simplifies the molecular structure and describes a lipid monolayer as a charged homogeneous plane. We find a large binding constant for H+ and small binding constants and no ion specificity for monovalent cations (Na+, K+, Cs+). The dissociation constants for divalent cations follow the sequence Sr2+ < Mg2+ < Ca2+ ≈ Zn2+ ≈ Mn2+ (without making any assumptions concerning the different kinds

of ions Zn, Mn, Fe, etc.). Additionally, the predictive nature of our model is tested by using various aqueous solutions.

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MATERIALS AND METHODS

Materials. The TMCL sodium salt is from Avanti, Alabaster, AL. Chloroform is from Carl Roth, Karlsruhe, Germany. Sodium chloride, potassium chloride, cesium chloride, calcium chloride dihydrate, strontium chloride hexahydrate, manganese(II) chloride tetrahydrate, zinc(II) chloride, and iron(II) chloride tetrahydrate (all APS, ISO, Reag. Ph Eur grade) are from Merck, Darmstadt, Germany, and magnesium chloride hexahydrate is from Carl Roth, Karlsruhe, Germany. The pure water is provided from a Milli-Q Synthesis system with a conductance of 0.054 μS. Pockels−Langmuir Trough and Isotherms. Compression surface pressure isotherms (π−A isotherms) are recorded on a Teflon trough (Riegler & Kirstein, Potsdam, Germany). A Wilhelmy plate surface pressure sensor with a filter paper as a plate (accuracy of 0.1 mN/m) was used. The trough area is 3.5 × 30 cm2. The compression speed is 0.07 ± 0.03 nm2/(molecule min). TMCL is dissolved in chloroform solution. The solution is spread with a 100 μL syringe (Model 1710, Hamilton, Bonaduz, Switzerland) and the chloroform is allowed to dissipate for 10 min. For the subphase preparation, the weighted salts were dissolved in pure water. The trough temperature is kept constant at 25.0 ± 0.1 °C with a thermostat (DC-30 ThermoHaake, Haake Technik, Karlsruhe, Germany). The subphase pH is 5.8 ± 0.2. Part of the freshly prepared solution was poured into the Pockels−Langmuir trough and part into a beaker to measure the pH with a SevenCompact S220 pH/ion meter and an InLab Pure Pro-ISM pH electrode (pure water samples), or InLab Routine Pro-ISM pH electrode (nonpure water samples), all from Mettler-Toledo, Greifensee, Switzerland. It took 30 min to obtain a typical compression isotherm. During this period, the pH changes at most by 0.2 due to the low diffusion constants of the ions and the molecules involved.35 Always, the first compression isotherm is shown. It was measured after temperature equilibration was achieved. The number N of TMCL molecules on a Pockels−Langmuir trough with an area Atrough was calculated from the limiting area per molecule in an all-trans-state A0 known from X-ray diffraction (A0 = 0.8 nm2)33 at high surface pressure (usually 40 mN/m, at high salt concentrations of at least 30 mN/m) according to N = Atrough/A0.

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RESULTS AND DISCUSSION Theoretical Background: Electrostatics of Monovalent Ions. For the description of the TMCL monolayer, we choose an electrostatic model in the Gouy−Chapman−Stern theory.8,15,36 The charge density near the surface induces a surface concentration (number density), ci,s, of a charged species of charge e·zi, as given by a Boltzmann distribution, or Nernst equation ci ,s = ci exp( −e·ziψs/kBT )

(1)

which differs from the bulk concentration ci due to the presence of a surface potential ψs at the given thermal energy kBT, at temperature T, and with Boltzmann constant kB. With this expression, the electrostatic surface charge density is given, with the absolute permittivity ε defined as product of the dielectric constant of vacuum ε0 and the relative dielectric constant εr, by Grahame’s equation8,15 σel =

ij ji −e·ziψs zy y zz − 1zzzz 2εkBT ∑ cijjjjexpjjj z z j z i k k kBT { {

(2)

In the case of a simple solution with only protons and monovalent counter-ions, the equation simplifies to B


Article

Langmuir σel =

ij eψ yz 8εkBT sinhjjj s zzz j 2kBT z k {

KM =

[H+]∞

(2a)

This equation assumes that the proton concentration [H+]∞ in the solution is identical to the concentration of monovalent anions. To account for the charging and binding effects of the lipid phosphate groups, we employ an effective degree of dissociation αeff, which is a sum of the charge multiplicity zi of each negatively charged lipid species ci relative to all charged groups carrying the maximum lipid charge possible (=zmaxctot). This gives the chemical surface charge density near the air−water interface σchem = −e·zmaxαeff /A

e·zmax αeff A e [HL−] + [ML−] + 2[L2 −] =− A /2 2[L tot]

σchem = −

e [L2 −] A /2 [L tot] e 1 =− A /2 1 + (K [H+] + K [M+] )2 exp − 2eψs H M ∞ ∞ kT

(3)

≈−

( ) B

HL− + H+ ⇔ LH 2 at the simplified surface

(4a)

(7)

We denote the proton concentration at the surface as [H+]s, the concentration or surface density of negative (dissociated) binding sites as [HL−], and the density of neutral (undissociated) states as [LH2]. [HL−] is related to the surface charge density σ via σ = e[LH−], with e as the elementary charge. The surface reaction with the intrinsic binding constant KH for the above reaction is defined by

where [M+]∞ corresponds to the bulk molar concentration of a salt consisting of monovalent ions. Note that [HL−] and [ML−] both depend on the surface concentration of [H+]s and [M+]s and thus on the surface potential ψs. For the calculations, the complete formula was used instead of the approximation shown in the first line of eq 7. The complete formula would make the equations extremely long and confusing; therefore, all equations presented in this paper are based on this approximation. To understand what the equations mean, we did some model calculations. Different cardiolipin species have been calculated with the equations for [Ltot], KH, and KM (eqs 4a−4c, 5, and 6). Additionally, the negative surface potential was assumed to be constant (ψs = −112 mV), as literature suggests.1,20,30 It increases the concentration of protons and monovalent cations at the surface by about a factor of 100; i.e., pHs and pMs are increased by 1.9 with respect to the bulk values pH and pM. Thus, for a constant bulk NaCl concentration of 0.1 mol/L, the surface concentration of Na+ is constant and amounts to almost 10 mol/L. For the calculations shown in Figure 1, a small binding constant of sodium cations (KM (Na+) = 0.65 L/mol) and a large one for protons (KH (H+) = 100 L/mol, i.e., pKa,eff = 2) were chosen; the binding constants are suggested by the literature.16 At low surface pHs, the lipid binds mainly protons. On increase of pHs, the lipids dissociate. However, the surface concentration of Na+ ([Na+]s = 10 mol/L) exceeds the assumed binding constant (KM (Na+) = 0.65 L/mol). Therefore, Na+ binds to the negatively charged lipids. At pHs > 4, we see mostly neutral M2L (85%) and few charged species (cf. Figure 1), e.g., ML− (13%), indicating the dominance of sodium binding. Note that Figure 1 shows the calculations as a function of the surface pHs (0 ≤ pHs ≤ 14). However, in lipid monolayers or bilayers, there is no source of electric energy to provide a constant electrical potential. Therefore, we have to expand the model calculations. We use the fact that different equations exist to describe the surface charge density, first the electrostatic Grahame equation (cf. eq 2) and additionally an equation based on the mass action law (cf. eq 7), σ = σel = σchem. We obtain

[H 2L] [H 2L] = (simplified) eψ − + [HL−][H+]s [HL ][H ]∞ exp − k Ts

( ) B

(4b)

here, [H+]s and [H+]∞ denote the proton concentrations at the surface and in the bulk, respectively. The increase of [H+]s with respect to [H+]∞ as described in eq 1 is due to the negative value of ψs. An important property of an ionizable surface is its pKa value, which is the surface pH at which half of its charged sites are dissociated (αeff = 0.5 or [H2L] = [HL−]). In this case, the eψ

( )

above equation reads 1/KH = [H+]∞ exp − k Ts . For the value B

of the surface pKa, one obtains pKa = −log10[H+]s = log10(KH). Besides the association or binding constant KH, the binding constant Ka = 1/KH is sometimes quoted.1,8,20 However, eqs 4a and 4b are too simple for cardiolipins. It is know that cardiolipin can carry up to two charges.16−18,37 Therefore, different charged species occur simultaneously. In a simplified approach, we define the total lipid concentration at the surface [L tot] = [L2 −] + [HL−] + [ML−] + [H 2L] + [HML] + [MHL] + [M 2L]

(4c)

where M denotes a monovalent cation. Considering the molecular structure of TMCL, the two phosphate groups are separated by a glycerol group consisting of three C atoms. Therefore, the phosphate groups influence each other very little.16 In a simplified approach, we assume that the same proton-binding constant KH describes different binding processes KH =

(6)

where we assume that [HML] = [MHL]. In the equations for [Ltot], KH, and KM, we can rewrite σchem for cardiolipin, with two similar proton association constants, as

A denotes the area per lipid molecule. If TMCL would be a very simple lipid that could dissociate just one proton and would not bind any other ion, we would write

KH =

[M 2L] [HML] [ML−] = = [ML−][M+]s [HL−][M+]s [L2 −][M+]s

[H 2L] [HML] [HL−] = = [HL−][H+]s [ML−][H+]s [L2 −][H+]s

(5)

Similarly, for binding of monovalent cations like sodium or cesium, the intrinsic binding constant is C


Article

Langmuir

ij eψ yz 8εkBT sinhjjj s zzz [H+]∞ + [M+]∞ j 2kBT z k { e 1 =− + A /2 1 + (K [H ] + K [M+] )2 exp − 2eψs H ∞ M ∞ kT

phase of cardiolipin (1 and 0.8 nm2, respectively). For the lower molecular area, the absolute values of the surface potential, |ψs|, and the surface charge density, |σ|, are larger for all salt concentrations. However, the effective degree of dissociation decreases strongly on decrease of the molecular area. At saturation, more lipids are charged in the LE phase than in the LC phase (the effective degree of dissociation is αeff = 0.94 and 0.70 for A = 1 and 0.8 nm2, respectively). In the next step, binding of divalent is included. The total lipid concentration becomes

σ=

( ) B

(8)

The surface charge density results as a subtle balance of electrostatic and chemical effects. With eq 8 and the intrinsic binding constants KH and KM, the surface potential ψs can be calculated at given area per molecule, A, and temperature, T. An example is shown in Figure 2. The intrinsic binding constants KM = 10−3 L/mol and KH = 10 L/mol are fixed parameters. ψs is obtained by numerically solving the nonlinear eq 8, as well as σ. For salt concentrations csalt < 0.1 mmol/L, the surface potential ψs and the surface charge density σ are large and remain mostly unaffected by the 1:1 electrolyte in the subphase. At very low salt concentrations, the electrostatic force has the largest amplitude and the longest range;8 therefore, the surface concentrations of protons and monovalent cations are much larger than bulk concentration. Note that in pure water, the surface potential is about −240 mV. The proton concentration at the surface is increased by a factor (cf. eq 1) exp(−eψs/kBT) = exp(−1.602 × 10−19 C × (−240) mV/1.38 × 10−23 × 298 J) = 11 500. This leads to a surface pH of 1.7 and pronounced binding of protons (cf. Figure 1). At higher salt concentration, electrostatic screening sets in. This causes a decrease in the absolute value of ψs and thus a decrease in the surface concentration of protons. Consequently, fewer binding sites of lipids are occupied, and the surface charge density |σ| increases until NaCl concentrations are above 0.1 mol/L, when |σ| saturates (hatched area in Figure 2). Note that due to the low intrinsic binding constant (KM = 10−3 L/mol) of Na+, sodium binding is almost of no importance. The calculations were performed at two molecular areas, one representative of the fluid (LE) and the other of the solid (LC) σ= =

[L tot] = [L2 −] + [HL−] + [ML−] + [H 2L] + [HML] + [HML] + [M 2L] + [DL]

(9)

where the intrinsic divalent binding constant is given by KD =

[DL] [DL] = 2eψ 2− 2+ [L2 −][D2 +]s [L ][D ]∞ exp( − k Ts ) B

(10)

which assumes a 1:1 complex of one divalent cation binding to one divalent anionic cardiolipin molecule. Due to the stronger electrostatic attraction, the surface concentration of divalent cations is more increased than the surface concentration of monovalent cations (note the changed Boltzmann factor). The 2:1 complexes are sufficient to describe the binding of one divalent cation to two negatively charged diacyl lipids;38,39 by comparison, the 1:1 complexes of divalent cations with cardiolipin are reasonable to assume. For the surface charge density σel calculated from the Grahame equation (eq 2), we describe the case of mixed 1:1 and 2:1 electrolytes, i.e., monovalent anions and both monovalent and divalent cations (for instance, a solution containing NaCl and CaCl2 is described by this equation).8 To include the divalent cations and allow for competitive binding, the equations for the surface charge density become

ij eψ yz i i eψ yy 8εkBT sinhjjj s zzz [H+]∞ + [M+]∞ + [D2 +]∞ jjjj2 + expjjj− s zzzzzzz j 2kBT z k kT {{ k k { −2e/A 2eψ

( ) + K [D

1 + (KH[H+]∞ + KM[M+]∞ )2 exp − k Ts B

Two more considerations are important before the end of this part: (i) the assumption of an effective pK value and (ii) impurities. Two similar pKa values for cardiolipin have been described in the literature.16,37 We assume that both phosphate groups of TMCL have the same binding constant. This assumption leads to an effective pKa value (or pKa,eff) for both phosphate groups. This assumption simplified the model calculations considerably. Whether it is justified, comparison with the experiments will show. Impurities are included to account for the dissociation of cardiolipins (the volume of the subphase is 40 mL; usually 8 μL solution containing 0.5 mmol/L TMCL was deposited on the surface), which leads to “pure water” to contain 0.2 μmol/L Na ions. This NaCl concentration is an order of magnitude lower than the proton concentration at pH 5.8 and has very little influence on the surface potential and the surface charge. Furthermore, we learned from Gerald Brezesinski, who performed X-ray fluorescence measurements, that Millipore water contains about 0.1 μmol/L divalent ions.40,41 For the

2+

D

2eψ

( )

]∞ exp − k Ts B

(11)

calculations, we assumed the solution to contain 0.1 μmol/L MgCl2. The small effects of MgCl2 on the surface potential, and on the available binding sites, were taken into account. Additionally, at high ion concentrations, we included the impurities listed in the data sheets of the supplier.42 In this case, the equations for surface charge densities (eqs 2 and 7) were further extended to include the contribution of the impurities to electrostatic screening and to allow for the binding of the impurities. Electrostatic Contribution to Surface Pressure. The electrostatic energy of a cardiolipin monolayer is34,36 Gel = Gd + Gc

(12)

It has two contributions. First, the charging contribution was derived both by Derjaguin in 1940 and by Verwey and Overbeek in 194836 Gc1 = A D

∫0

σ

ψ (σ ′)dσ ′

(12a) DOI: 10.1021/acs.langmuir.8b03637 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir Each ion desorption or adsorption leads to a reduction in Δμ, the chemical potential. This “chemical” part of the free energy is exactly compensated by the increase in chemical energy. Gc2 = −Aσψs

(12b)

Thus, one obtains Gd = A

∫0

σ

ψ (σ ′)dσ ′ − Aσψs = −A

∫0

ψs

σ(ψ ′)dψ ′

In case of monovalent ions only, one obtains ÅÄÅ ÑÉÑ ij eψ yz Å Ñ Gel = −AεκD(2kBT /e)2 ÅÅÅÅcoshjjj− s zzz − 1ÑÑÑÑ j 2kBT z ÅÅ ÑÑ k { ÅÇ ÑÖ

(12c)

Figure 1. Cardiolipin species (left y-axis) and effective degree of dissociation (right y-axis) calculated for a cardiolipin monolayer as a function of pHs, the pH at the surface. The Na+ surface concentration is constant ([M]s = 10 mol/L) due to the fixed surface potential (ψs = −112 mV, estimated from literature values1,20). The binding constants are pKa,eff = 2 (corresponds to KH = 100 L/mol) and KM (Na+) = 0.65 L/mol at T = 25 °C. The surface potential ψs induces a shift between bulk and surface pH (denoted pHs) and between bulk and surface pM (denoted pMs): pH − pHs = pM − pMs = |eψs/(kBT)|/ln(10) = 1.9.8 Therefore, this situation corresponds to a subphase with a NaCl concentration of [M] = 0.1 mol/L.

(12d)

here, 1/κD denotes the Debye length. It measures the range of the electrostatic interaction into the solution (normal to the surface plane) and depends on the ion concentration only8,15 κD =

∑ cizi2e 2/(εkBT ) i

(12e)

In case of a mixture of salts, one needs to solve the integral numerically. The second contribution is of entropic nature, describing the mixture of charged and neutralized head groups Gd = kBT [(1 − αeff )ln(1 − αeff ) + αeff ln αeff ]

(12f)

Figure 3 shows the electrostatic energy calculated with the same set of parameters as in Figure 2. As expected, the electrostatic energy is negative, i.e., energy is gained by charging the monolayer. Up to 0.001 mol/L of monovalent salt Gel changes little, followed by a further decrease, when the charging of the monolayer starts (cf. Figure 2). |Gel| reaches a maximum value at ≈0.1 mol/L when the surface charge density reaches its saturation value, whereas |ψs| is still rather large. At even higher salt concentrations, the absolute value of |Gel| decreases due to the decrease in surface potential (increased charge screening), whereas the surface charge density remains at its maximum value. On decrease of the molecular area, |Gel| is always smaller. Furthermore, the maximum shifts slightly to larger salt concentrations. The electrostatic contribution to the surface pressure of the phase transition is obtained according to πel = −

δGel δA

Figure 2. Model describing a tetramyristoyl cardiolipin (TMCL) monolayer surface potential ψs and surface charge density σ as functions of monovalent salt concentration, at 25 °C, pH = 5.8 (in the bulk), and pKa,eff = 1 (corresponds to KH = 10 L/mol) and KM = 10−3 L/mol. The molecular area of TMCL molecules is indicated. The typical values of 0.8 and 1 nm2 were selected for the LC and LE phase, respectively. With increase of csalt, the surface potential ψs (straight lines) shows a decrease in absolute value, whereas the surface charge density σ (dashed lines) increases in absolute value. The hatched area indicates the regime in which σ has reached the saturation value.

(13)

Influence of Monovalent Cations on Phase Transition Pressure. Figure 4 shows the TMCL pressure−area diagrams at different ionic strengths. NaCl is the monovalent salt. Each TMCL isotherm has a shape, as known from phospholipid monolayers.29,43 Upon monolayer compression, the lipidexpanded (LE) phase is observed, which is marked by a surface pressure increase, whereas the molecular area decreases. Further compressing the monolayer, the isotherm flattens. This sudden change in the slope marks the onset of the LE/LC phase transition. The phase transition surface pressure πc is positioned at the sudden change of slope.29,44 The corresponding lipid molecular area is Ac. The following plateau, at smaller areas per molecule than Ac, is the LE/LC phase coexistence regime. At the end of the plateau, the monolayer is in the LC phase and the surface pressure rises steeply. The NaCl concentration in the subphase was increased and the compression isotherms were measured (cf. Figure 4). A non-

with δGel and δA as the change in electrostatic energy and molecular area, respectively.34 Calculating the surface pressure for different molecular areas, one finds a similar maximum in the surface pressure as a function of the salt concentration as shown in Figure 3.22 However, experimentally, the best accessible surface pressure is the surface pressure at the onset of the LE/LC phase transition. Due to the plateau in the LE/LC coexistence regime in the π−A-isotherms, we can take the area per molecule at the beginning (Ac = A(πc)) and the end of the phase transition (A0 = 0.8 nm2 according to X-ray diffraction measurements33) to calculate the corresponding transition surface pressure from the electrostatic energy of the monolayer via πc,el = −

ΔGel with ΔGel = Gel(Ac) − Gel(A 0) and ΔA ΔA

= Ac − A 0

(14) E


Article

Langmuir

Figure 5. Phase transition pressure πc of TMCL monolayers as a function of monovalent salt concentration. Different monovalent salts are used (always pH = 5.8 and 25 °C). πc is calculated according to eq 14 (black line). Besides pH and temperature, the fixed parameters of the calculations according to eq 14 are Agel = 0.8 nm2 and Ac = 1.0 nm2. KM and KH were adjusted to describe the data. The model shown is based on KH = 10 L/mol (corresponds to pKa,eff = 1) and KM = 0.001 L/mol. When more than one monolayer was prepared, error bars are shown.

Figure 3. Model describing the electrostatic energy Gel of a TMCL monolayer as a function of monovalent salt concentration, at 25 °C, pH = 5.8, KH = 10 L/mol, and KM = 10−3 L/mol. Also shown is the inverse Debye length κD (dashed line). Molecular area of the TMCL gel and fluid phase is assumed to be 0.8 nm2 (black) and 1.0 nm2 (blue), respectively.

understand the maximum, πc = πc,0 + πc,el is calculated with eq 14. πc,0 denotes the phase transition pressure of uncharged cardiolipins. Fixed parameters are pH = 5.8, T = 25 °C, πc,0 = 0 mN/m, Ac = 1 nm2, and A0 = 0.8 nm2. Two parameters need to be determined: the intrinsic binding constant for protons (KH) and the intrinsic binding constant for monovalent cations (KM). The binding constant for protons KH is estimated to be 10 L/ mol, leading to pKa,eff = 1, an assumption that is supported by the literature on cardiolipins.19,37 The binding constant of cations, KM (for Na+, K+ or Cs+), is adjusted to describe the data and found to be 10−3 L/mol, which is much smaller than KH (10 L/ mol). We find the experimentally observed non-monotonic behavior of πc to depend on csalt, with a characteristic maximum at 0.1 mol/L. Motivated by the two binding sites of a TMCL molecule, we considered working with two different binding constants for protons, KH,1 and KH,2. The result of taking an “effective” pKa,eff value is wrong in the sense that it overestimates the rise in the transition surface pressure. Working with two pK values would broaden the maximum in Figure 5 (phase transition pressure as a function of the concentration of 1:1 electrolyte), especially if one accounts for a one-unit shift between two pKa values. However, it would make the calculations much more extensive without giving an unambiguous result. To understand the maximum of πc, the surface charge and the surface potential of the monolayer as functions of csalt were considered (cf. Figure 2). Both surface potential and surface charge were calculated with the same parameters as were obtained from the fits to the experimental πc values. With increase of csalt up to 0.1 mol/L, the surface charge increases. Thus, the electrostatic repulsion between the head groups increases, as is evidenced by the increase of the electrostatic energy |Gel(Ac) − Gel(A0)| (cf. Figure 3). Therefore, a higher surface pressure is necessary to induce the LC phase. If csalt exceeds 0.1 mol/L, the surface charge is constant, whereas the absolute value of the surface potential decreases. This leads to a decrease of |Gel(Ac) − Gel(A0)| and πc. We found two very different binding constants for protons and other monovalent ions like Na+. The binding constant for protons is high, whereas that for Na+ is very low. This is an asymmetric situation. When the proton concentration at the surface is high, many protons bind to the membrane and the absolute value of the surface charge density is low. But when the

Figure 4. TMCL monolayer measured on different NaCl subphases. Depending on the NaCl concentration, the phase transition surface pressure πc increases up to 0.1 mol/L and then decreases. Black indicates a pure water subphase. Up to eight different monolayers were prepared for each NaCl concentration. Additional isotherms are shown in the Supporting Information. Thus, the standard deviation of πc was determined.

monotonic behavior of πc is found. The transition surface pressure πc peaks at about 0.1 mol/L. More isotherms measured at salt concentrations above 0.1 mol/L document the decrease of the surface transition pressure πc with the increase of c(NaCl). Furthermore, isotherms were repeated with different monolayers (cf. Figure S1 in the Supporting Information). This maximum points to changes in the electrostatics, especially of the lipid head-group cation interaction. Similar observations were made for KCl and CsCl subphases (cf. Supporting Information Figure S2 for CsCl and Figure S3 for KCl). No cation specificity is detectable. Note that the gaseous/LE transition occurs at roughly the same molecular area, 1.8−2 nm2. At this large molecular density, both surface charge density and surface potential are small (cf. Figure 2). Therefore, it is concluded and also observed that the isotherms change little at large molecular areas. Furthermore, for normalization, we assumed that the molecular area at high surface pressure (40 mN/m) is 0.8 nm2.33 If there are different gel phases with tilted alkyl chains, then normalization has an error of less than 10%. X-ray diffraction measurements could clarify this point. In Figure 5, the dependence of πc on the concentration of monovalent salts is shown. The salts used are NaCl, KCl, and CsCl (cf. Figures 4 and S1−S3 in the Supporting Information; Figure S1 also shows error bars of πc). Independent of the kind of monovalent ion, πc shows a maximum at csalt = 0.1 mol/L. To F


Article

Langmuir Na+ concentration is high and the proton concentration low, few ions bind to the surface and the absolute value of the surface charge density is high. One could achieve a high proton concentration at the surface by lowering the pH. We chose another approach: the high degree of dissociation of the lipids was achieved by increasing the NaCl concentration. Na+ hardly binds; therefore, the high NaCl concentration almost does not change the degree of dissociation of the lipids. But the high NaCl concentration lowers the absolute value of the surface potential. Therefore, the surface concentration of the protons is lowered. That is why fewer protons become bound to the lipids. Influence of Divalent Cations on Phase Transition Pressure. To determine the binding constant of divalent ions, pronounced changes of πc are necessary. Therefore, we start close to the largest value of πc found, at 0.15 mol/L NaCl in the subphase. According to the calculations, at these conditions, the value of the surface potential is still large, whereas the degree of dissociation reaches its maximum value. We chose c(NaCl) = 0.15 mol/L and kept it constant (which coincides with the biological concentration of monovalent cations). We increased the concentration of divalent ions. In Figure 6, isotherms are

Figure 7. Phase transition pressure πc of TMCL monolayers as a function of the concentration of different divalent salts. Calculated πc is indicated by straight lines with different binding constants for divalent cations. The fixed parameters are 25 °C, pH = 5.8, KH = 10 L/mol, KM = 0.001 L/mol, Agel = 0.8 nm2 and Afluid = 1.0 nm2, and c(NaCl) = 0.15 mol/L. The binding constant of divalent ions was fitted.

These observations point to the dominance of charge screening and binding effects of divalent cations. In numbers, we found KD,Zn ≈ KD,Mn ≈ KD,Ca = 1.2 ± 0.6 L/mol, KD,Mg = 0.15 ± 0.05 L/ mol, and KD,Sr = 0.035 ± 0.015 L/mol. The binding constants are summarized in Table 1. Table 1. Binding Constants as Determined from the Isotherms at 25 °C and from Chloride Salts binding constants KH (L/mol) and KM (L/mol) for monovalent cations KH for H+ 10 ± 5

Figure 6. TMCL monolayer measured on subphases containing different CaCl2 concentrations. The transition surface pressure πc decreases with increasing CaCl2 concentration. Black indicates a 0.15 mol/L NaCl subphase without any CaCl2. All isotherms were with fixed 0.15 mol/L NaCl in the solution (pH = 5.8, 25 °C).

KM for Na+

KM for K+

KM for Cs+

0.001 0.001 0.001 binding constants KD (L/mol) for divalent ions

KD,Sr from SrCl2

KD,Mg from MgCl2

KD,Ca from CaCl2

KD,Zn from ZnCl2

KD,Mn from MnCl2

0.035 ± 0.015

0.15 ± 0.05

1.2 ± 0.6

1.2 ± 0.6

1.2 ± 0.6

Up to now, all subphases contained c(NaCl) = 0.15 mol/L and varying concentrations of divalent cations. To verify the obtained intrinsic binding constants and to test our model, we also tried different combinations of MgCl2 and NaCl. Figure 8 shows a series of isotherms measured when c(MgCl2) is varied and c(NaCl) = 0. The isotherms are very similar; πc does not change. This experimental result is expected from the deduced binding constants for protons and Mg2+ (cf. Table 1): Al low MgCl2 concentration mostly protons are bound (cf. Figure 2). With increase of the Mg2+ concentration, most protons bound to the lipids are replaced by Mg2+. Thus, the degree of dissociation αeff remains low and so does the surface transition pressure πc. Calculations show a very weak maximum in surface pressure (0.2 mN/m) at 0.05 mol/L MgCl2. These observations demonstrate the subtle interplay between surface charge density and surface potential: the surface charge density increases slightly up to 0.05 mol/L MgCl2 and then reaches maximum and the surface potential and the transition surface pressure decrease with further increase of c(MgCl2). To induce an observable increase in the degree of dissociation αeff, we have to limit the amount of lipids bound to Mg2+. Thus, we reduced c(MgCl2) to 0.001 mol/L and varied c(NaCl) (cf. Figure 8). By increasing the c(NaCl), the calculations predict an increase of the degree of dissociation and thus an increase in the surface pressure at c(NaCl) ≥ 0.15 mol/L. This is indeed observed and consistent with the binding constants for Na+ and Mg2+ determined earlier in the paper. Summarizing, the electrostatic interactions of the system were modeled with a mean-field theory: Grahame’s equation and a

shown. A decrease in πc with increasing CaCl2 concentration was observed. The isotherms shown are representative for all other investigated divalent salts (MgCl2, SrCl2, MnCl2, FeCl2, ZnCl2; see Figures S4−S8 in the Supporting Information). The decrease in πc is attributed to the binding of divalent ions, which reduces the electrostatic repulsion between the lipid head groups. The decrease is specific to each divalent cation. All isotherms show a LE/LC phase transition with a nonzero transition slope in the plateau (coexistence) regime. Increasing the divalent salt concentration decreases the surface transition pressure πc and increases the transition area per molecule, Ac, at the onset of the phase transition. The reduction in transition pressure πc at fixed divalent concentration (provided it exceeds 10−4 mol/L) is lowest for SrCl2, increases for MgCl2, and is highest for CaCl2, ZnCl2, and MnCl2. FeCl2 was inconclusive at high salt concentrations due to the solidification of the monolayer and the lack of LE/LC phase transition. We performed the calculations for the divalent salts in the same manner as for the monovalent salts: we calculate σ and ψs to determine Gel and eventually πc. For a constant area difference of ΔA = 0.2 nm2 between LE and LC phase, limiting area A0 = Agel = 0.8 nm2, pH = 5.8, T = 25 °C, and binding constants KM and KH as stated before, we obtain the results shown in Figure 7. The calculated πc is in good agreement with the experiment. G


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Langmuir

Figure 8. TMCL monolayer on subphases containing different concentrations of MgCl2 and NaCl. Left: MgCl2 concentration was varied without NaCl in the solution. Right: c(MgCl2) = 10−3 mol/L and c(NaCl) was varied. Calculated πc in the respective insets are indicated by straight lines with intrinsic binding constants KH = 10 L/mol, KM = 10−3 L/mol, and KD,Mg = 0.15 L/mol for protons, Na+, and Mg2+, respectively. The fixed parameters are 25 °C, pH = 5.8, Agel = 0.8 nm2, and Ac = 1.0 nm2. Note the different scales of the y-axis in the insets.

effects were observed, which pointed to the prevalence of electrostatic interactions in the system. A small intrinsic binding constant for K+, Na+, and Cs+ was determined (10−3 L/mol). The maximum was caused by the asymmetry in the system: the intrinsic binding constant for protons was four orders of magnitude larger (10 L/mol). Note that not only the concentration of cations is important for influencing the surface charge density but also which cations are used. The different cations are not interchangeable. As protons bind strongly, a high proton concentration at the surface reduces the degree of dissociation. Because Na ions almost do not bind, a high sodium concentration does not affect the surface charge density. However, a high Na ion concentration may influence the surface charge density indirectly. Namely, with increase of Na ion concentration, the absolute value of the surface potential is reduced, which affects the surface concentration of other cations (e.g., protons). In the presented work, we used this effect. By increasing the sodium ion/chloride concentration, we lowered the surface potential (the absolute value of the surface potential, to be exact). By decreasing the magnitude of the surface potential, we varied the surface concentration of the protons. The lower the surface concentrations of the protons, the fewer protons are bound and the higher the degree of dissociation. With increase of the degree of dissociation, πc is increased. Subphases containing magnesium, calcium, strontium, manganese, iron, or zinc salts with a fixed physiological monovalent salt concentration of 0.15 mol/L were used to determine the respective πc. The addition of divalent salts leads to decrease in πc. These findings indicate increased screening and binding effects. Strongest binding effects were observed for calcium, manganese, and zinc salts. To test our model and the predictive power of our approach, subphases with different combinations of monovalent and divalent cations were also used. We think that the model with its known intrinsic binding constants can be applied to supported lipid membranes and vesicles, as well as describe the electrostatic contributions to domain formation, interactions between proteins and membranes. If the model assumption of large extended surfaces is no longer valid, as for nanodisks or for domain boundaries, or if molecular conformations are to be determined, more exact calculations need to be performed. We used a simple approach, calculations, and a Pockels− Langmuir trough to determine the intrinsic binding constants of the system. More exact determinations of the intrinsic and apparent binding constants could be achieved with more elaborate experiments, like titration calorimetry of vesicles46 or vibrational sum frequency.25

simple law of mass action. Both incorporate a Boltzmann distribution derived in thermodynamic equilibrium from the electrochemical potential consisting of an electrostatic term and an entropic contribution.8,20,30,36 TMCL was modeled at half its molecular area and half its charge, with an average intrinsic proton-binding constant of the phosphate group KH = 10 L/mol leading to an intrinsic pKa,eff = 1. The model transition surface pressures πc and the binding constants of the monovalent and divalent ions to charged cardiolipin were obtained. The agreement with the experiment was satisfactory: the nonmonotonic behavior induced by the monovalent salt was recovered. For the divalent salt added to a 0.15 mol/L fixed monovalent salt, subphase of magnesium, calcium, and strontium reproduced the specific behavior, allowing the determination of the respective intrinsic binding constants, assuming a lipid/divalent cation binding of 1:1. The intrinsic proton-binding constant KH = 10 L/mol (corresponds to pKa,eff = 1) and the intrinsic monovalent cation binding constant KM = 10−3 L/mol were deduced. For divalent cations, the intrinsic binding constants KD,Ca = 1.2 ± 0.6 L/mol, KD,Mg = 0.15 ± 0.05 L/mol, and KD,Sr = 0.035 ± 0.015 L/mol were determined for calcium, magnesium, and strontium, respectively. Furthermore, the binding constants of calcium and zinc are the same KD,Ca ≈ KD,Zn = 1.2 ± 0.6 L/mol. For the binding constants of divalent cations, we obtained KD,Ca ≈ KD,Zn ≈ KD,Mn > KB,Mg > KB,Sr.

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CONCLUSIONS A biological membrane is primarily a lipid bilayer, a composite of two lipid monolayers, with joined hydrophobic parts.20,30,45 A lipid monolayer can undergo a phase transition from a disordered LE phase to an ordered LC phase. Experimentally, this is realized by compressing a tetramyristoyl cardiolipin (TMCL) monolayer in a Pockels−Langmuir trough. The surface pressure π is monitored with a Wilhelmy plate tensiometer as a function of the molecular area A. Lipids with saturated acyl chains show a LE−LC phase transition,29 whose onset is marked by a phase transition pressure πc. As model system, we used TMCL monolayers at 25 °C. We use calculations based on classical double-layer theory8,15 and thermodynamics to determine the electrostatic-induced shift in the phase transition pressure πc. We obtained meaningful results if we chose the solutions so that we could see big changes in πc if we changed just one parameter systematically. When the concentration of monovalent ions in the subphase was varied, πc exhibited a non-monotonic behavior: a maximum in πc is found for a salt concentration of 0.1 mol/L. This finding extends to subphases containing KCl, NaCl, and CsCl. No ion-specific H


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Langmuir

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(14) Ross, A. C.; Caballero, B.; Cousins, R. J.; Tucker, K. L.; Ziegler, T. R. Modern Nutrition in Health and Disease; Lippincott Williams & Wilkins, 2014. (15) Butt, H.-J.; Kappl, M. Surface and Interfacial Forces; Wiley-VCH, 2010. (16) Olofsson, G.; Sparr, E. Ionization constants pKa of cardiolipin. PLoS One 2013, 8, No. e73040. (17) Malyshka, D.; Pandiscia, L. A.; Schweitzer-Stenner, R. Cardiolipin containing liposomes are fully ionized at physiological pH. An FT-IR study of phosphate group ionization. Vib. Spectrosc. 2014, 75, 86−92. (18) Kooijman, E.; Swim, L.; Graber, Z.; Tyurina, Y.; Bayır, H.; Kagan, V. Magic angle spinning 31P NMR spectroscopy reveals two essentially identical ionization states for the cardiolipin phosphates in phospholipid liposomes. Biochim. Biophys. Acta, Biomembr. 2017, 1859, 61−68. (19) Sathappa, M.; Alder, N. N. The ionization properties of cardiolipin and its variants in model bilayers. Biochim. Biophys. Acta, Biomembr. 2016, 1858, 1362−1372. (20) Cevc, G.; Marsh, D. Phospholipid Bilayers: Physical Principles and Models; Wiley, 1987. (21) Träuble, H.; Eibl, H. Electrostatic effects on lipid phase transitions: membrane structure and ionic environment. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 214−219. (22) Helm, C. A.; Laxhuber, L.; Lö sche, M.; Mö hwald, H. Electrostatic interactions in phospholipid membranes I: Influence of monovalent ions. Colloid Polym. Sci. 1986, 264, 46−55. (23) Lösche, M.; Helm, C.; Mattes, H.; Möhwald, H. Formation of Langmuir-Blodgett films via electrostatic control of the lipid/water interface. Thin Solid Films 1985, 133, 51−64. (24) Zhang, T.; Brantley, S. L.; Verreault, D.; Dhankani, R.; Corcelli, S. A.; Allen, H. C. Effect of pH and Salt on Surface pKa of Phosphatidic Acid Monolayers. Langmuir 2018, 34, 530−539. (25) Cong, X.; Poynton, M. F.; Baxter, A. J.; Pullancheri, S.; Cremer, P. S. Unquenchable surface potential dramatically enhances Cu2+ binding to phosphatidylserine lipids. J. Am. Chem. Soc. 2015, 137, 7785−7792. (26) Fuhs, T.; Klausen, L. H.; Sønderskov, S. M.; Han, X.; Dong, M. Direct measurement of surface charge distribution in phase separating supported lipid bilayers. Nanoscale 2018, 10, 4538−4544. (27) Fanani, M. L.; Wilke, N. Regulation of phase boundaries and phase-segregated patterns in model membranes. Biochim. Biophys. Acta, Biomembr. 2018, 1972−1984. (28) Longo, M. L. Preface to Emergence of Complex Behavior in Biomembranes. Biochim. Biophys. Acta, Biomembr. 2018, 1860, 1955− 1956. (29) Kaganer, V. M.; Möhwald, H.; Dutta, P. Structure and phase transitions in Langmuir monolayers. Rev. Mod. Phys. 1999, 71, 779. (30) Heimburg, T. Thermal Biophysics of Membranes; John Wiley & Sons, 2008. (31) Hädicke, A.; Blume, A. Binding of the cationic peptide (KL)4K to lipid monolayers at the air−water interface: Effect of lipid headgroup charge, acyl chain length, and acyl chain saturation. J. Phys. Chem. B 2016, 120, 3880−3887. (32) Petit, P. X.; Dupaigne, P.; Pariselli, F.; Gonzalvez, F.; Etienne, F.; Rameau, C.; Bernard, S. Interaction of the alpha-helical H6 peptide from the pro-apoptotic protein tBid with cardiolipin. FEBS J. 2009, 276, 6338−6354. (33) Etienne, F.; Roche, Y.; Peretti, P.; Bernard, S. Cardiolipin packing ability studied by grazing incidence X-ray diffraction. Chem. Phys. Lipids 2008, 152, 13−23. (34) Payens, T. A. J. Ionized Monolayers, Philips Research Reports, 1955; pp 425−481. (35) Stumm, W.; Morgan, J. J. Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters; John Wiley & Sons, 2012; Vol. 126. (36) Hunter, R. J. Foundations of Colloid Science; Oxford University Press, 2001. (37) Few, A.; Gilby, A.; Seaman, G. An electrophoretic study of structural components of Micrococcus lysodeikticus. Biochim. Biophys. Acta 1960, 38, 130−136.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b03637. Isotherms with different CsCl and KCl concentrations in the subphase; series of isotherms on subphases containing NaCl in concentrations between 0.1 and 1 mol/L; series of isotherms was measured with 0.15 mol/L NaCl and varying concentrations of MgCl2, SrCl2, MnCl2, ZnCl2, and FeCl2; all measurements were performed at 25 °C and pH 5.8 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Christiane A. Helm: 0000-0001-5181-1688 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Discussions and talks within the RTG 1947 “BiOx” are appreciated. We also thank the Deutsche Forschungsgemeinschaft (DFG, RTG 1947 “BiOx”, project B1) for financial support.

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Interactions of Monovalent and Divalent Cations with Cardiolipin

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