Vol. 43. No. 1 (1994) 23

ORIGINAL

Calcium Ion Adsorption on Phospholipid Bilayers

Theoretical Interpretation

Kyung Ok KWON1, Masahiko ABE1,2*, Keizo OGINO1, 2,

Myung Ja KIM3, and Hiroyuki OHSHIMA 2, 4

1 :Faculty of Science and Technology, Science University of Tokyo,

(2641, Yamazaki, Noda-shi , Chibaken, •§ 278)

2 : Institute of Colloid and Interface Science, Science University of

Tokyo (1-3, Kagrazaka, Shinjuku-ku , Tokyo, •§ 162)

3 : Department of Chemistry, Sookmyung Women's University

(Chungpa-dong Yongsan—ku, Seoul, Korea)

4 : Faculty of Pharmaceutical Sciences, Science University of Tokyo,

(1-3, Shinjuku-ku , Tokyo, •§ 162)

A theoretical approach to phase transition enthalpy change as a function of calcium ion concentra -

tion was studied in terms of calcium ion adsorption on a phospholipid surface. The phospholipids used

in this study were dipalmitoylphosphatidylcholine (DPPC), dipalmitoylphosphatidylethanolamine

(DPPE), and dipalmitoylphosphatidylglycerol (DPPG). The theory used here is based on the DLVO the -ory, taking into account electrostatic interaction caused by calcium ion adsorption on the membrane sur -

face. Calcium ion effects on DPPC and DPPG phase behavior can be explained by Helmholtz free energy

change. Experimental enthalpy change is dependent on the electrical contribution in the free energy

equation. This contribution is related to the binding constant K and effective surface area a'. Binding pa -

rameters, binding constant K and effective surface area a' were K=100 M-1 and a'=60,000 m2/g for DPPG,

and K=40 M-1 and a'=750 m2/g for DPPC as optimal values. These values for DPPE could not be deter-

mined owing to the absence of enthalpy change.

Introduction

If we consider the many processes in bio -

logical membranes such as permeation, fu -

sion, and structural transformations, then

electrostatic interactions between phospho -

lipid membrane and divalent cations may

be deemed to be of great importance for

their mechanism. Therefore, a large num -

ber of studies on the interaction between di -

valent cations and phospholipids have been

reported1)•`9). It is quite well known that cal -

cium ions exert many interesting effects on

lipid bilayer membranes, such as phase

transition inducements, separation of the

lipid components, or the aggregation and

fusion of the membrane 5 )- 11 ).

Although a few investigations of calcium

ion binding onto phospholipid head groups

have been done 12)•`16) , they have not been

systematically elucidated by theoretical ap -

proaches. Among the theoretical approach -

es, a majority of the studies on ion bindings

onto phospholipid bilayers or biological

membranes have been carried out from an

electric layer diffusion perspective, combin -

ing the Langmuir adsorption isotherm and

the Gouy-Chapman-Stern theory 6), 17), 18 )

Furthermore, most experimental results

are obtained through electrophoretic

mobility measurements for liposomal sys -

tems6),17), 18).

In previous papers, we have reported on

theoretical approaches of the calcium ion

concentration effect on phospholipid mono -

layer conformation with surface tension

* To whom all correspondence should be ad -

dressed

23

24 J. Jpn. Oil Chem. Soc. (YUKAGAKU)

measurements19) and on phospholipid bilay -

ers changes with X-ray diffraction mea -surements20). We have also studied the ther -modynamic behavior of phospholipid aggre -

gates in the presence of calcium ions with differential scanning calorimetry 21) . The thermograms at subzero temperatures for

phopholipids/Ca2+/buffer solution (TES) systems, which depended on the calcium ion concentration, showed a unique behavior. It was found that the thermodynamic proper -ties at subzero temperatures are related to an interaction between phospholipid aggre -

gates and metal ions. In this paper, the thermal analysis for a

phase transition in the presence of calcium ions is performed by using a differential scanning calorimetry technique, and such a thermodynamical approach as free energy and enthalpy changes are discussed regard -ing the cation adsorption on phospholipid aggregates. The theoretical approach is ap -

plied based on the Derjaguin-Landau- Ver -wey-Overbeek (DLVO) theory.

Experimental

Materials. Phospholipids, dipalmitoyl -

phosphatidylcholine (DPPC, 99.6 %), di -

palmitoylphosphatidylethanolamine ( DP PE ,

99.8 %), and dipalmitoylphosphatidylglyc -

erol (DPPG, 99.8 %) were supplied from

Nippon Oil and Fat Co., Ltd., Amagasaki,

Hyogo, Japan, and used without further pu -

rification. The purities of phospholipids

were ascertained by one-dimensional thin

layer chromatography in chloroform /

methanol/water (65/25/4 by volume). Calci -

um chloride was heated at 500•Ž for 2 h to

eliminate trace organic materials. All the

other reagents were of analytical grades

and used as received.

Differential Scanning Calorimetry (DSC )

measurement. Many samples of the phos -

pholipids-TES buffer solution (100 mM

NaCl, 2 mM N-tris(hydroxymethyl)methyl

-2- aminoethanesulfonic acid, pH 7.4 , con -

taining 0 to 40 mM calcium ion, were pre -

pared by using a microsyringe to add cer -

tain amounts of water to the dehydrated

compounds. All samples were heated to 80 •Ž

to ensure homogeneous mixing, and then

were cooled to -20•Ž and maintained at that

temperature for about 24 h, after which the

DSC measurements were started 22) The

DSC measurements were carried out with a

DSC 8240 type machine (Rigaku Co. Ltd .,

Tokyo, Japan) by placing the sample in a

high-pressure crucible. The samples were

heated from -40•Ž to above the T, transition

temperature at a heating rate of 1 K/min.

Sensitivities employed for DSC measure -

ment are described in the figure captions.

Theory

Helmholtz free energy, F, will be applied

to evaluate the enthalpy change based on the

phase transition of phospholipid bilayers in

the presence of calcium ions. The phospho -

lipid bilayer surfaces have a positive charge

as a result of calcium ion adsorption 19 ).

The increment of the free energy of the bi -

layer surface by adsorption of calcium ions

are as follows :

(1 )

where Fo is the Helmholtz free energy with -out calcium ion adsorption, Os the electrical

potential at the membrane surface in the ex -cess solution, 0 the membrane surface charge density, N the number of the calci -um ion, La corresponds to the constant term of gs the chemical potential of absorbed cal -cium ions [given later by equation (5)J, T the absolute temperature, and S the entropy of membrane surface. Equation (1) consists of four contributions. The first, F0 has been

described above ; the second,∫σσψsdσ,

is the

electric component, the third, μ0SN, and

fourth, TS, are the chemical contributions

for in the vicinity of Membrane surface.

If one assumes that the membrane sur -

face per unit area has Nmax sites for calci -

um ion binding, then entropy can be shown

as follows :

(2 )

24

Vol. 43. No. 1 (1994) 25

where, Nmax=1/

A,using the surface area oc-

cupied by a phospholipid (A), and k is the Boltzmann constant and Stirling formula is used. The charge density of the membrane sur-

face, a, is

(3 )

where uo is the surface charge density with-

out calcium ion adsorption, and e is the ele-

mentary charge. The surface charge density

without calcium ion adsorption for DPPC

and DPPE are zero, and that of DPPG is

σo=- eNmax= -e/ A.

Substituting equation (2) into equation

(1), Helmholtz free energy, F, can be ex-pressed as follows :

(4 )

Differentiating equation (4) with respect to N, we find the electrochemical potential us of bound cations

(5 )The electrochemical potential uB of cations

in the solution is given by

(6 )where μ0B is independent of calcium ion

concentration. [Ca2+] and no are the num-bers of CCa2+] ions and water molecules, re-spectively. (Since the electrical potential is

put zero in the excess solution, the electric part of the electrochemical potential uB is zero.)

The chemical equilibrium between the membrane and the bulk demands

(7 )Using equation (5)-(7), the N and bind-

ing constant K are introduced as follows :

(8 )

(9 )

Using equations (3)-(9), the surface charge density of the DPPG membrane can be obtained.

(10 )

The surface charge densities of DPPC and

DPPE are

(11 )

Equation (10) and (11) are identical to the Stern equation.

Absorption of N cations onto the bilayer surface leads to a decrease in the free ener-

gy in the bulk solution phase by NuB. The total free energy increase of the bilayer sur-face and the surrounding solution F is thus

given by(12 )

From equations (1), (2) and (3)-412), we have

(13 )

In the cases of DPPC and DPPE, the

equation can be as follows :

(14 )

Since the surface charge density of DPPG

has a negative charge, the equation becomes

(15 )

The electrostatic contributions to F, i.e., the second and third terms on the right hand side of equations (14) and (15) can be combined to give

second and third terms= -Jσ

0Sσ(ψ1)dψ's .

This integral can be calculated as follows. Assuming that the electric potential 0 in the solution obeys the Poisson-Boltzmann equa-tion (in SI units),

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26 J. Jpn. Oil Chem. Soc. (YUKAGAKU )

(17 )

where the x-axis is taken in the normal di -rection to the interface in such a way that the plane x=0 coincides with the plane of the lipid head groups and a half space (x>0) is the solution phase.

The boundary conditions for 0 (x) are

(18 )

Here no electric field within the lipid monolayer is assumed. Integrating equation

(17) once and using equation (18), we ob -tain

(19)

where K=2(n1+3n2)e2/

εrε0kT

1/2

is the Debye -

Mickel parameter, ys=e 0 s/kT is the scaled

surface potential, Er is the relative permittiv -ity of the solution, E0 is the permittivity of

vacuum and is defined by

Here, n1 is monovalent ion concentration, n2 is divalent ion concentration19).

Introducing the equations (10) and (11) into equation (19), respectively, the function of dimensionless surface potential gives the following transcendental equation for y s . Those for DPPC and DPPE are shown in equation (20) and that of DPPG is shown in equation (21)

(20 )

(21 )

The relation between a and ys (or (s) holds at any stage in the changing process. By us -ing this fact, the integral given by equation

(16) can be calculated as follows :

(22)

Using the dimensionless surface potential

of ys, the Helmholtz free energy is calculat -

ed.

Results and Discussion

Fig.-1 shows the thermogram for phos -

pholipids (DPPC, DPPE and DPPG) as a

function of calcium ion concentration.

As can be seen from Fig.-1, the thermo -

gram for the DPPE system are almost in -

dependent of calcium ion concentration ; the

thermogram for DPPC system shows a lit -

tle dependence on calcium ion concentra -

tion. Namely, the pretransition which is a

small peak in the vicinity of 40•Ž, shifts to a

higher temperature with increasing calcium

ion concentrations. Casal and Mantsch 23)

have suggested that the pretransition of DP -

PC involves mainly a change in the packing

arrangement, the introduction of a very

small number of gauche conformers. The

enthalpy change at transition temperature Tc

decreases with increasing calcium ion con -

centrations. On the other hand, the thermo -

grams for DPPG systems are considerably

different from other systems. Namely, new

peaks are observed due to the existence of

calcium ions. This implies that DPPG

membrane is deprived of the hydrated water

and binding with calcium ions results in

changes in the rigidity of the membrane.

Enthalpy change in Fig.-1 for phospho -

lipids as a function of calcium ion concen -

tration was thermodynamically evaluated.

In the presence of calcium ions, the sur -

face potential of the phospholipid bilayers

are considered as positive for calcium ion

adsorption. The surface potential ( 0 s) are

calculated by the scaled surface potential

(ys) obtained from the equations (19, 20 ) .

26

Vol. 43. No. 1 (1994) 27

Fig.-2 shows the calculated surface po-

tential for the DPPC phospholipid bilayer,

ψs, as a function of calcium ion concentra -

tion with different binding constants, 1, 10, 20, 30, and 40 M-1- . Based on experimental conditions, area per lipid molecule of DPPC

(A), absolute temperature, relative permit -tivity of the solution and monovalent ion concentration are used as A=0.505 nm2, T=315.15 K, er=72.26, and n1=0.1 M (NaCl concentration) respectively. The surface po -tential of DPPC is zero in pure water, and increases positively with increasing calcium ion concentrations. This is due to calcium ion adsorption onto the phospholipid bilayer

surface in calcium chloride solution. The surface potentials of DPPE were cal -

culated using A=0.464 nm2, T=334.15 K, Er

=66 .06 based on the experimental condi -tions, and shown in Fig.-3. The binding constants used in this calculation were 0.5, 1, 1.5, and 2 M-1. As the concentration of calcium ions increased, the surface poten -tials of DPPE increased. As shown in Fig. -1, the enthalpy change by phase transition decreased with increasing calcium ion con -centrations in the DPPC system. However , an enthalpy change in the DPPE system was independent of calcium ion concentra -tion. The smaller binding constant for the DPPE system than for that of the DPPC system was, therefore, applied in the calcu - lation process. Although both DPPC and DPPE have a zwitterionic head group, DPPE (—PO4-, -NH3) seems to have a more

positive surface charge and smaller surface

Fig . - 1 DSC thermograms of phospholipids (DPPC, DPPE and DPPG ) in buffer solution (100 mM NaC1, 2 mM TES, pH 7.4) as a function of temperature and Ca2+ concentration.

Fig . - 2 The predicted value of surface potential

change for DPPC as a function of bind -

ing constant and calcium ion concentra -

tion.

Fig . - 3 The predicted value of surface potential

change for DPPE as a function of bind -

ing constant and calcium ion concentra -

tion.

27

28 J. Jpn. Oil Chem. Soc. (YUKAGAKU)

area than DPPC [ -PO4-, -N (CH3) 3]. Therefore, the surface potential of DPPC was larger than that of DPPE since the binding constant of calcium ions onto the

phospholipid bilayer was larger for DPPC than for DPPE.

The two cases of the changes of surface

potentials for DPPG (K=100 and 50 M-1 ) are plotted as a function of calcium ion con -centration in Fig.-4. Data for the calcula -tion process are A = 0.431 nm2, T = 314.15 K and Er = 72.6. In the absence of calcium ad-sorption, the bilayer surface is negatively charged, showing a large negative surface

potential. As the CaCl2 concentration is in -creased, calcium ions are adsorbed so that the surface potential becomes less negative , reducing the electric component of F. The surface potential of DPPG reached to zero at 10 mM calcium ion concentration for K=100 M-1 and at 20 mM for K=50 M - 1 . From this surface potential curve, we can determine the bindng constant of K. The calculated surface potential for K = 100 M - 1 , showing a zero potential at 10 mM calcium concentration, agrees with the experimental curve. The reason will be described by in -terpreting Fig.-6 as mentioned later. The enthalpy change, obtained by the DSC ther -mogram, with different calcium ion concen -trations in the presence of 100 mM NaCl

was evaluated. The enthalpy change is iden -

tified with Helmholtz free energy change . The enthalpy change A H is related to the free energy change ( AG = AF ) in

It was observed that A H shows a strong dependence on the CaCl2 concentration. This dependence should arise mostly from the electric part of P H, since the calcium ad -sorption causes this change in H. We iden -tify the CaCl2 -concentrationdependence of

PH approximately as that of the energy component of F. The induced enthalpy change by calcium ion adsorption was ex -

perimentally obtained by the following equation, A ( A H)= A H - PH (0), where A H and AH(0) are enthalpies in the presence of and in the absence of calcium ions, respec -tively. We identify A ( A H ) as A F = F - F

([CaC12]=0). Important factors for A ( AH ) analysis are the binding constant and the ef -fective surface area, a'. If an accurate bilay -

er surface area and the number of phospho -lipid particles are known, it would be possi -ble to obtain the accurate effective bilayer surface area. Unfortunately, such informa -tion as the number of phospholipid particles is not available. Therefore, the experimental enthalpy data was simulated to determine the binding constant K and effective surface area a'. Fig.-5 depicts the curve simula -tion results with experimental enthalpy change of DPPC (open circle). The solid lines are theoretically calculated by the elec -

trostatic term ∫0σψsdσ-σ ψs

in equation

(14) which can be interpreted as the en -thalpy term. In calculation, the fourth term of equation (14), corresponding to the en -tropy term, has been omitted. The theoreti -cal value of pH calculated with K = 40 M - 1 and a'=750 m2/g is in agreement with the experimental data. A similar procedure was applied and simulated for the DPPG sys -tem. Fig.-6 shows calculated free energies using different effective surface areas drawn by solid lines and experimental values by open circles. As can be seen from Fig . -6 , the values K=100 1VI-' and a'= 60,000 m2/g fit well with experimental results. As the CaCl2

Fig . - 4 The predicted value of surface potential

change for DPPG as a function of bind -

ing constant and calcium ion concentra -

tion .

28

Vol. 43. No. 1 (1994) 29

concentration is increased, calcium ions are

adsorbed so that the surface potential be -

comes less negative reducing the electric

component of F (in other words, •¢ F be -

comes larger). When the surface potential is

zero (Fig. - 4 ) , F becomes also zero and O F

reaches its maximum. While further in -

crease of CaCl2 concentration, the surface

potential changes its sign, becoming posi -

tive and the electric part of F begins to in -

crease again ( PF decreased). It is noted

that the theoretical values show a deviation

from the experimental data in the region of

high calcium concentration. In high concen -

tration of calcium ions, it is expected that a

shielding effect caused by the adsorption of

counter ions takes place, which is not count -

ed in our calculation. One more can explain

that theoretical values can only be con -

tributed to the electrical component of the

Helmholtz free energy. Therefore, the chem -

ical component, which is not considered in

our calculation, is more appreciable of high

concentrations of metal ions. However, the

calculated values of the binding constant K

were very reasonable compared with other

K values calculated by different meth -

ods 4), 24), 25) Comparing with DPPC, the

large effective surface area is obtained. It

might be speculated that ions may also

change the vesicles into other forms of lipid

assembly, such as tubular microstructure

or flattening microstructure. Since the lipo -

some concentration on the. surface, the for -

mer is unlikely. Considering the phase tran -

sition temperature shift to a higher side for

DPPG bound with calcium represented the

rigidity of the phospholipid membrane, flat -

tening could occur as a result of osmotic

stress25). Therefore, it might be considered

that the flattening leads the large effective

surface area for DPPG .

As shown above, it is possible to explain

the P H change caused by calcium ion ad -

sorption on the phospholipid surface usig

DLVO theory .

Conclusion

A theoretical approach to phase transition

enthalpy change as a function of calcium

ion concentration was studied in terms of

calcium ion adsorption on a phospholipid

surface. The enthalpy change as a function

of calcium ion concentration was evaluated

by using DLVO theory, taking into account

electrostatic interaction caused by calcium

ion adsorption on the membrane surfaces .

The calcium ion effect on DPPC and

DPPG phase behaviors can be explained by

Helmholtz free energy change, and the ex -

Solid lines represent theoretical curve with fac -tors; (1) K=1, a'=1,000 (2) K=20, a'=1,000, (3) K=40, a'=750 (4) K=30, a'=1,000 (m2/g). Experi -mental values are represented by open circles .Fig . - 5 Helmholtz free energy (AF) for DPPC

as a function of calcium ion concentra -tion .

Solid lines represent theoretical curve with fac -tors; (1) a'=50,000, (2) a'=60,000 (3) a'=70,000 ,

(4) a'=80,000 (m2/g). Experimental values are in -dicated by open circles .Fig . - 6 Helmholtz free energy (AF) for DPPG

phospholipid as a function of calcium ion concentration and K=100 M-1 .

29

30 J. Jpn. Oil Chem. Soc. (YUKAGAKU)

perimental enthalpy change are dependent on the electrical contribution in the free energy equation. Furthermore, the electrical contri -bution is related to the binding constant K and effective surface area a'. The binding constant and the effective surface area were simulated to the experimental values and found to be ; K=100 M-1 and a'=60,000 m2 / g for DPPG, and K=40 M-1 and a'=750 m2 / g for DPPG. In the case of DPPE, it was not

able to determine the binding constant and the effective surface area because of a lack

of enthalpy change .

(Received April 16, 1993 )

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(1992) .

リン脂質二分子膜へのカルシウム

イオ ンの吸着-理 論的解釈-

権 敬 玉1・ 阿部 正 彦1,2・ 荻 野 圭 三1,2・

金 明子3・ 大 島広 行 2,4

1: 東京理科大学理工学部工業化学科 (〒 278 野田市山崎 2641)

2: 東 京理科大学 界面科 学研究所 (〒 162 東京都新宿 区神楽 坂

1-3 )

3 : 淑明女子大学化学科 (140 大韓民 国ソウル龍 山区青坡洞 2 街)

4 : 東京理科大学薬学部製薬学科 (〒 162 東京 都新宿 区市 ヶ谷船

河原町 12)

相変化エ ンタル ピーのカル シウムイオ ン濃度依存性を

説 明す るための理論的アプ ローチが,リ ン脂質表面への

カルシウムイオ ンの吸着によ り検討 された。用いた リン

脂 質 は、 ジパ ル ミ トイル ホス フ ァチ ジル コ リン (DP -

PC), ジパ ル ミ トイルホス ファチ ジルエ タノールア ミン

(DPPE), ジパ ル ミ トイ ルホ ス フ ァチ ジル グ リセ リン

(DPPG) である。本研 究で用 いた理論 は DLVO 理 論

に基づ くものであ り, 膜表面へのカル シウムイオ ンの吸

着 に起 因す る静電気的相互作用 を説 明 しようとす るもの

である｡

DPPC と DPPG の相挙動に及 ぼす カルシウムイオ ン

の効果 は,ヘ ル ムホルツ 自由エネルギー変化で説明す る

ことができ,実 測 したエ ンタル ピー変化 は上式の電気的

寄与 に依存す ることが分か った。さ らに,そ の電気的寄

与 は結合定数Kと 有効表面積 α'に関係す ることが分か

り, DPPG と DPPC の最適値を求めた ところ, それぞ

れ K = 100 M-1, α'=60,000m2/g と K = 40M-1, α' = 750

m2/g であ った。 しか し, DPPE の場合 はエ ンタル ピー

変化 がないため最適値は得 られなか った｡

連絡者 : 阿部正彦

30