Bioelectrochemistry: Ions, Surfaces, Membranes - American Chemical

5 Effect of Cation Concentrations and

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on August 28, 2015 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1980-0188.ch005

Temperature on the Rates of Aggregation of Acidic Phospholipid Vesicles: Application to Fusion S H L O M O NIR, JOE BENTZ, and A R C H I E R. PORTIS, JR.

1

Department of Experimental Pathology, Roswell Park Memorial Institute, 666 Elm Street, Buffalo, N Y 14263

Rates of aggregation of acidic phospholipid vesicles are calculated from potential curves obtained as a sum of van der Waals and electrostatic interactions. The effect of temperature on rates of aggregation and on the equilibrium distribution is analyzed. The applicability of activation energies is discussed critically. The effects of cation binding (Ca , Mg and Na ) to phosphatidylserine vesicles are analyzed, and the rates of vesicle aggregation are shown to be very sensitive to cation concentration. Experimental results from light scattering and release of trapped fluorescent molecules are presented. The possibility is raised that Ca or Mg can produce destabilization of PS vesicles followed by aggregation and fusion. High concentrations of Na inhibit the fusion process although Na alone (> .4M) produces fast aggregation. 2+

2+

2+

+

+

2+

+

p h e extension of the Smoluchowski ( I ) theory for rates of aggregation of colloidal particles by Fuchs (2) requires a detailed knowledge of the free energy potential curves (see review i n Verwey and Overbeek ( 3 ) ) . I n the case of charged particles, these potentials have been taken

r

1

Current address: U.S. Department of Agriculture, Urbana, IL 61801. 0-8412-0473-X/80/33-188-075$08.00/l © 1980 American Chemical Society In Bioelectrochemistry: Ions, Surfaces, Membranes; Blank, M.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980.


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BIOELECTROCHEMISTRY: IONS, SURFACES, M E M B R A N E S

as a sum of van der Waals ( V D W ) and electrostatic interactions. As reviewed ( 3 ) , this approach gives qualitative predictions regarding the stability of many colloidal systems, and it has been expected that the prediction of rates of aggregation should improve w i t h corresponding progress i n the estimate of the potential curves. Overbeek (4) pointed out that i n spite of improvements i n the estimate of potentials and the introduction of various hydrodynamic corrections, the theory could not explain the approximate independence of size i n the measured rates of aggregation of colloidal particles. According to the theory, the rate of aggregation of colloidal particles should be reduced significantly with an increase i n colloidal particle size. A t the same time, the direct-force measurements i n vacuum or i n air (5-12) showed that the long-range interactions between particles are explained well. In a previous work (13) on phospholipid vesicles, we proposed that large particles, i.e., of radii larger than 1,000 A , can form stable aggregates in which the distances of separation between particles correspond to secondary minima, i.e., a few nanometers. The aggregation i n secondary minima is a rapid process since it does not involve a high potential barrier. W e also proved that for sonicated vesicles of radii between 150 and 500 A , the first step in the aggregation process, i.e., the formation of dimers, must occur at the primary minimum. Thus, our study of sonicated phosphatidyl serine ( P S ) vesicles considered the process of aggregation to occur at the primary minimum. It qualitatively explained the existing data on vesicle aggregation for given concentrations of C a , M g , and N a i n solution, and provided some more predictions which were confirmed. One of the main elements of this treatment has been the detailed consideration of the neutralization of the negative charges of PS by C a , M g , and N a . In the present study, we elaborate on some aspects of the computations of rates of aggregation of phospholipid vesicles. W e further examine the sensitivity of rates of aggregation to cation concentrations and study the dependence of rates of aggregation on temperature. Our analysis w i l l show that i n many cases the rates of aggregation should vary appreciably with temperature. Thus the experimental examination of the variation of the rate of aggregation with temperature can provide another test for the theory. W e have another purpose i n studying the temperature dependence of the rate of aggregation. It may be expected that the close approach of vesicles is the first stage in their fusion. The process of membrane fusion is known to be sensitive to temperature (14,15,16). In order to elucidate the temperature dependence of the rate of fusion per se, we have first to determine the temperature dependence of the process of close approach. W e provide here light-scattering measurements which were designed to test our predictions for the aggregation of sonicated 2+

2+

+

2+

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In Bioelectrochemistry: Ions, Surfaces, Membranes; Blank, M.; Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

5.

77

Acidic Phospholipid Vesicles

NIR E T A L .

PS vesicles. I n addition, we present the results of fluorescent probe leakage experiments which together with the aggregation experiments enable us to draw some conclusions on the mechanism of fusion of PS vesicles.


Expressions for the Kate of Aggregation of Vesicles W e assume that the initial phase of the aggregation process consists of forming pairs of vesicles or dimers and w i l l focus on the dimerization reaction. Light-scattering experiments (17) can elucidate the kinetics of dimerization when carried over periods of time short enough to preclude a significant accumulation of larger aggregates. The dimerization reaction is given stoichiometrically as, hi 2 C i ^± C

2

with reaction rate equation -^-=2fc {C } -2fc {C } 1

1

2

2

(1)

2

where C i and C are the monomeric and dimeric species, {Ci} and {C } are their respective molar concentrations, and fci and k are the reaction rate constants. According to Smoluchowski ( I ) , fci is given by 2

2

2

fc «4fcTN /(3i ) 1

A

?

(2)

in which k is Boltzmann's constant, T is the absolute temperature, N is Avogadro's number, and rj is the viscosity of the medium. F o r sufficiently short times, the second term i n Equation 1 can be neglected and an integration yields a half time, ti , for dimerization given by A

/2

^-l/2fciC!(0),

(3)

where C i ( 0 ) is the initial molar concentration of vesicles. Thus a measurement of these half times should show that they are inversely proportional to C i ( 0 ) . If such a relation is not obeyed, it means that effects of higher stages i n the aggregation process are superimposed. The neglect of the second term i n Equation 1 can yield other inverse linear relations such as £3/4 = l / 6 f c i C i ( 0 ) where we refer to a shorter time for which Ci(t) = 3 / 4 C i ( 0 ) . F o r any number q between zero and one, we could define the time t* by Ci(t*) = g C i ( O ) and the integration would yield


78

BIOELECTROCHEMISTRY: IONS, SURFACES, M E M B R A N E S

t* = (1/q — l)/2fciCi(0). F o r a given value of q the inverse linear relation between t* and the initial monomer concentration Ci(0) still holds. The neglect of higher-order aggregates becomes more justified as t* gets smaller or as q approaches 1. Clearly the best estimates of the rate constant k w i l l be obtained by taking measurements (e.g., light scattering) for a value of q near 1, but this requires greater machine sensitivity than would be the case for measuring t — when q = 1/2. Overbeek (18) has shown that taking higher-order aggregates into account, with certain approximations, also w i l l give an inverse linear relation between the initial number of particles (monomers) and the time over which the number of particles is halved. Therefore, from an inverse linear plot between initial concentrations and the time it takes to achieve a certain increase i n light scattering, we cannot necessarily deduce the half times for dimerization. Increases i n light scattering of less than 50% would be necessary to minimize the contribution of higher-order aggregates. According to the treatment of Fuchs (2), ki is given by x


1/2

fc = 4 f c r N / ( 3 ^ ) 1

(4)

A

where ir/

o

f °° dR

/Vt(R)\

The term 2a is the center-to-center distance between the vesicles i n the dimeric state and V (R) is the total free energy caused by intermolecular interactions—as a function of the center-to-center distance R. A convenient simplification is used frequently ( 3 ) , T

W & exp (V */kT) T

(6)

in which V * is the height of the maximum of the potential barrier. T h e introduction of hydrodynamic corrections may result i n an order-ofmagnitude reduction of the rate of aggregation (19-25). Following Spielman (22), the expression for W in Equation 5 becomes T

in which D (R) and D ( oo ) are the diffusion coefficients of the relative motions of spherical particles at a distance R and at infinity. F o r small separations, i.e., when d = R — 2a is small when compared w i t h R, there is a simplification (21,22), 12

12


5.


NIR E T A L .

£12(00) ^ D (R)

-

12

79 ( R )

2d

K

;

so that

F o r spherical particles, our calculations of the total free energy V are in most cases the same as in Ref. 13. Here we outline the approach and present a minimal number of equations needed for the analysis i n the subsequent section. The potential V is given as


T

T

V = V + V T

e

(10)

w

in which V is the electrostatic free energy, and V is the V D W free energy. In cases of slow aggregation, the most important term for determining the rate constant ifci is V , which is positive and forms the repulsive barrier i n a system of negatively charged PS vesicles. W e use the equation of Wiese and Healy (26), with the boundary conditions of fixed surface charges. e

w

e

4 ^ /_a^_\ CK \ a i + a J 2

+

^ - ^

2

2

1

i \

" ( l

/ 1 \ \1 — e x p ( — x d ) /

+

exp(-^))}

(

U

)

in which ^ is the surface charge density of vesicle i of radius c 1.5mM. A n increase i n the amount of N a above .1M (with 1.5mM C a ) would result i n a reduction i n the ratio C a / P S 2+

2+

+

2+

2+

2+

2+

+

2+

+

2+


2+

5.

NIR E T A L .


95

below -35. O n the other hand, the potential barrier for aggregation is lowered by an addition of N a , as is illustrated i n Tables I and V . I n contrast, when the amount of N a i n the medium is reduced to l O m M or less, the ratio of C a / P S w i l l exceed .35 even with . I m M C a (27,28). However, with such low N a concentrations, the calculated rates of aggregation are extremely slow even i n the presence of 2 m M C a (see Tables I and V ) . The experiments presented i n Figures 4 through 7 were designed to show the effect which the amount of divalent cation bound (to the vescile) has on the processes of vesicle aggregation, leakage, and fusion. The results i n Figure 4 A indicate a significant amount of release of C F from PS vesicles i n a solution of . 1 M N a + 1.5mM C a . The amount, or at least the rate, of C F released increases with 5 m M C a . The lightscattering results i n Figure 4B indicate a significant increase i n particle +

+

2+

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+


2+

+

2+

2+

Fluortsctnct

FtfAX

20 lOOmM NoCI No NaCl ~

15-

s

io-

5mM Co

lOOmM NoCI

Bioelectrochemistry: Ions, Surfaces, Membranes - American Chemical

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