GLOSSARY

Top Abstract Glossary Introduction Materials & Methods Results Discussion Appendix A Appendix B References

A(i)				area of the ith phase (i = h, d, and n) (m2)
AL				area per one lipid (m2)
B				= (80 r RT Ce)1/2 (see Eq. 1)
C				capacitance/area (CV1m2)
Ce				bulk univalent electrolyte concentration (kmol · m3)
Cp				bulk peptide concentration (kmol · m3)
F				Faraday number (C · kmol1)
f(i)				fraction of acidic lipid in the ith phase (i = h, d, n)
G				free energy of phase (kJ)
g				free energy per unit area of a given phase (kJ · m2)
Kp				intrinsic binding constant of the peptide (m3 · kmol1)
NA				Avogadro's number (kmol1)
R				gas constant (kJ · kmol1 · K1)
T				temperature (K)
z				peptide valence
Z				average or effective surface charge per acidic lipid (in units of an elementary charge)

Greek letters

r				dielectric constant of the aqueous solution
0				dielectric permittivity of free space (F · m1)
				reciprocal of Debye screening length (m1)
µ				electrochemical potential (J · mol1)
				surface pressure (J · m2)
				surface charge density (C · m2)
				degree of occupancy of binding sites
				surface potential (V)

Subscripts

(h)				homogeneous (nonseparated) membrane consisting of 1 mole of lipids
(d)				domain phase
(n)				nondomain phase of the separated membrane
e				electrostatic term
m				mixing term

	INTRODUCTION

Top Abstract Glossary Introduction Materials & Methods Results Discussion Appendix A Appendix B References

Stimulation of the calcium/phospholipid second messenger system activates protein kinase C (PKC), as reviewed by Berridge (1993) and Clapham (1995). The major PKC substrate in many cell types is the myristoylated alanine-rich C kinase substrate (MARCKS) protein (reviewed by Aderem, 1992; Blackshear, 1993). The cellular function of MARCKS is not known, but there is good evidence that it binds membranes, calmodulin, and actin in a phosphorylation-dependent manner. It appears to be involved in phagocytosis, exocytosis, and membrane trafficking. Several recent studies have focused on the mechanism by which MARCKS binds to membranes, which requires both hydrophobic insertion of the myristate into the bilayer and electrostatic interaction of a cluster of basic residues in its "effector" region with acidic lipids (George and Blackshear, 1992; Taniguchi and Manenti, 1993; Kim et al., 1994a,b; Swierczynski and Blackshear, 1995, 1996; Seykora et al., 1996). Phosphorylation of MARCKS by PKC introduces negative charges into the cluster of basic residues, weakening the electrostatic interaction and producing translocation from membrane to cytoplasm in many cell types. This has been termed the "myristoyl electrostatic switch" mechanism (McLaughlin and Aderem, 1995; Bhatnagar and Gordon, 1997). Although there is general agreement that both hydrophobic and electrostatic interactions are required to anchor MARCKS to membranes, we know little about the factors that produce a nonuniform lateral distribution of this protein in biological membranes. For example, MARCKS has a punctate distribution in the membranes of macrophages (Rosen et al., 1990), and recent work indicates that these domains formed by MARCKS are localized to nascent phagosomes (Allen and Aderem, 1995). MARCKS also has a nonuniform distribution in the plasma membrane of fibroblasts (Myat et al., 1997). Many factors can contribute to the formation of domains in biological membranes, e.g., interactions with cytoskeletal proteins. To understand the physical factors that contribute to the spontaneous self-assembly of proteins into lateral domains, studies on model systems are useful.

The MARCKS(151-175) peptide (KKKKKRFSFKKSFKLSGFSFKKNKK), which corresponds to the effector region of bovine MARCKS, forms lateral domains when it binds to phospholipid vesicles formed from a mixture of the acidic lipid phosphatidylserine (PS) and the zwitterionic, electrically neutral lipid phosphatidylcholine (PC); these domains are enriched in PS (Yang and Glaser, 1995). The multivalent acidic lipid phosphatidylinositol 4,5-bisphosphate (PIP₂) is also concentrated in the domains if it is present in the vesicles, but phospholipase C, the enzyme that hydrolyzes PIP₂, is not (Glaser et al., 1996). This lateral separation of enzyme and substrate decreases the rate of PLC-catalyzed hydrolysis of PIP₂. Upon phosphorylation of MARCKS(151-175) by PKC, the peptide (and the intact MARCKS protein) desorbs from the membrane (Kim et al., 1994a,b), and PIP₂ is hydrolyzed rapidly by PLC (Glaser et al., 1996).

We would like to understand the molecular mechanism by which MARCKS(151-175) forms domains enriched in acidic lipids when it adsorbs to phospholipid vesicles. Unfortunately, three factors make analysis of domains difficult, even in a model system that comprises only phospholipid vesicles and MARCKS(151-175) peptide. First, this peptide is amphipathic (it contains 5 Phe hydrophobic groups and 13 basic residues) and could self-aggregate either in solution or when adsorbed to a vesicle; thus peptide-peptide interactions could contribute to domain formation. Second, the peptide penetrates the polar headgroup region of the membrane when it binds (Qin and Cafiso, 1996; Glaser et al., 1996), because of the five Phe residues; Wimley and White (1996) have shown that a Phe residue can contribute 1 kcal/mol to the binding energy of a peptide when it partitions into the interface. It has been argued that membrane penetration contributes to the domain formation observed with another amphipathic molecule, polymyxin (Hartmann et al., 1978; Sackmann, 1978). Third, MARCKS(151-175) binds to membranes in an extended form and may be represented as a rod ~100 Å long (Qin and Cafiso, 1996). Onsager's (1949) elegant analysis shows that entropic effects can cause long rods to separate into ordered (concentrated) and disordered (dilute) phases in three dimensions; this effect may contribute to domain formation when long peptides adsorb to the two-dimensional surface of a membrane. These three factors may contribute to domain formation with the MARCKS effector region peptide, and we postulate that a fourth factor, electrostatics, also contributes significantly to the formation of lateral domains when basic peptides bind to membranes.

To investigate this possibility, we studied pentalysine (Lys₅, or KKKKK), a basic peptide that corresponds to the first five residues of bovine MARCKS(151-175). There are three advantages to using this peptide: first, it does not self-aggregate in solution, so attractive interactions between the peptides adsorbed to membranes are almost certainly negligible; second, NMR, surface potential, and surface pressure measurements show that Lys₅ does not penetrate the membrane when it binds (Roux et al., 1988; Kim et al., 1991; Ben Tal et al., 1996); third, because it is relatively small (dimensions ~4 Å × 14 Å × 21 Å), the long rod effects described by Onsager (1949) do not contribute to domain formation. We show here, using fluorescence digital imaging microscopy, that when Lys₅ binds to PC/PS phospholipid vesicles, it forms domains enriched in the acidic lipid PS (and PIP₂ if the vesicles also contain PIP₂). We obtained similar results with another basic ligand, spermine.

We present a simple theoretical model that can account qualitatively for several aspects of this domain formation. Although there have been many theoretical studies of domain formation in membranes (for reviews see, e.g., Vaz, 1994; Mouritsen and Jorgensen, 1994; Thompson et al., 1995; Raudino, 1995; Sackmann, 1995), to the best of our knowledge this is the first proposal that a change in the electrostatic free energy can produce lateral domains.

Träuble (1977) discussed how domains will form if they decrease the free energy of the system. As illustrated in Fig. 1 A, the acidic lipids (filled circles) in a fluid membrane are not in domains but appear to be distributed randomly in the plane of the membrane in the absence of basic peptides. Two factors oppose the formation of domains enriched in acidic lipids (Fig. 1 B): first, electrostatic work must be done to bring negatively charged lipids together; second, the decrease in the entropy of mixing is unfavorable. When a basic peptide (e.g., pentalysine) binds to a PC/PS vesicle (Fig. 1 C), it stabilizes domains enriched in PS (Fig. 1 D). Our explanation for this observation hinges on the assumption that pentalysine is attracted electrostatically to the domain phase and thus is preferentially bound to this phase (lower right-hand portion of Fig. 1 D). Less pentalysine is bound to a unit area of either the nondomain phase (upper left-hand portion of Fig. 1 D) or a nonseparated membrane (Fig. 1 C).

View larger version (53K): [in this window] [in a new window]   FIGURE 1   Schema for domain formation. The open circles represent zwitterionic lipids (e.g., PC), and the stippled circles represent acidic phospholipids (e.g., PS). The fractions of acidic lipids in the homogeneous membrane, domain, and nondomain phase are designated f(h), f(d), and f(n), respectively. In the absence of basic peptides, acidic lipids do not form domains (A); we assume that they are distributed randomly in the plane of the membrane. Acidic lipids will not spontaneously form domains (B) because the change in the Gibbs free energy due to both entropy of mixing and electrostatics is unfavorable. When pentalysine is added to the membrane (C), it stabilizes domains (D) because it binds much more strongly to regions of the membrane that contain high fractions of acidic lipids.

When pentalysine binds to a membrane containing acidic lipids, it reduces the net charge density and the electrostatic free energy stored in the diffuse double layer. Specifically, the negatively charged lipids in the membrane (e.g., PS) and the counterions (e.g., K⁺) in the aqueous diffuse double layer adjacent to the surface may be considered as a parallel plate capacitor, at least when the surface potential, , is small (McLaughlin, 1989). The Debye length, 1/, the average distance between the surface and the counterions (~10 Å in a 0.1 M monovalent salt solution) corresponds to the distance between the plates of this capacitor. Electrical energy equal to 1/2C² is stored in a unit area of the diffuse double layer, just as it is stored in a conventional parallel plate capacitor; here C = _0r is the capacitance/area of the diffuse double layer, ₀ is the permittivity of free space, and _r is the dielectric constant of the aqueous phase. Thus reducing the charge density and surface potential of the membrane reduces the free energy of the system. The increased binding of pentalysine to the membranes due to the formation of domains must reduce the electrostatic free energy sufficiently to overcome the increase in free energy due to an entropy of mixing term, which represents the tendency of PS to diffuse out of the domain, where its mole fraction is high (e.g., Träuble, 1977). In this report we present a quantitative, albeit highly oversimplified model of how electrostatics could drive domain formation, and then compare the predictions of the model with the experimental results.

	THEORETICAL MODEL

Outline of the model

We consider a membrane formed from a mixture of two lipids: a zwitterionic (electrically neutral) lipid such as PC and a monovalent acidic (negatively charged) lipid such as PS. The lipids have the same cross-sectional area and are distributed randomly in the initial homogeneous membrane. Upon the addition of peptide, the membrane separates into two macroscopic phases, characterized by their mole fractions of acidic lipid and surface potentials. The phase with the higher mole fraction of acidic lipid is defined as the domain phase; the phase with the lower mole fraction of acidic lipid is defined as the nondomain phase. We apply the Gouy-Chapman-Stern theory of the diffuse double layer and ligand binding to each phase, as described briefly below. Domain formation results from a decrease in the Gibbs free energy of the system, which our model treats as the sum of two contributions: the electrostatic free energy and the free energy of mixing of the acidic and zwitterionic lipids.

Although the domain and nondomain phases have different surface potentials and surface charge densities, PS and PC both must be at electrochemical equilibrium. In our model (Appendix B), the sum of three generalized forces produces the equilibrium between the acidic lipids in the two phases (Fig. 2): the generalized force resulting from a decrease in the electrostatic free energy of the system that occurs when more peptide binds to the membrane upon domain formation drives PS from the nondomain to the domain phase (µ); the generalized diffusional force moves PS down its concentration (or, more correctly, mole fraction) gradient from the domain to the nondomain phase (µ_f); and the force due to a difference between the surface pressure of the phases moves lipids out of the domain (µ). The sum of two generalized forces produces the equilibrium between the PC in the two phases: the generalized diffusional force (µ_1f) directs PC from the nondomain to the domain phase, and the force due to a difference in surface pressure (µ) acts in the opposite direction.

View larger version (18K): [in this window] [in a new window]   FIGURE 2   Sketch of the generalized forces that maintain equilibrium between lipids in the domain and nondomain phase. µ is the generalized electrostatic force that arises because the electrostatic free energy of the system decreases when PS moves from the nondomain to the domain phase, and pentalysine binds more strongly to the membrane; µf and µ1f are the generalized diffusional forces on PS and PC, respectively; and µ is the generalized force due to the surface pressure difference between the phases. See Appendix B for details.

Gouy-Chapman-Stern model for ligand binding

We use the standard assumptions inherent in the Gouy-Chapman-Stern theory: 1) The homogeneous (h), domain (d), and nondomain (n) phases of the membrane are slabs of uniformly smeared surface charge, which arises from both the acidic lipids and bound peptides. For simplicity, we ignore the binding of monovalent cations to acidic lipids (McLaughlin, 1989), which does not affect the qualitative features of how pentalysine is predicted to form domains (calculations not shown). 2) The solution contains a univalent electrolyte (concentration C_e) and multivalent ions (the peptide, present at trace concentration C_p  C_e; valence z > 1) that are treated by using a mean field theory. 3) The electrostatic potential at the membrane surface, _(i), is described by the Gouy equation (McLaughlin, 1989):

(1)

where the subscript i designates the phase (i = h, d, or n), F is the Faraday constant, R is the gas constant, T is the temperature, _(i) is the surface charge density, ₀ is the permittivity of free space, and _r is the relative permittivity or dielectric constant of the solution. 4) The peptide concentration in the aqueous phase immediately adjacent to the membrane surface, C_p⁰, is linked to its bulk concentration C_p through a Boltzmann-like relationship:

(2)

where the effective valence z_eff  z. The use of an effective valence, which partially compensates for the discreteness of charge effects (Mosior and McLaughlin, 1992, and references therein; Heimburg and Marsh, 1995), is not required to account qualitatively for domain formation.

In addition, we assume that ligand binding to the membrane obeys either the Langmuir isotherm,

(3)

which describes 1:1 binding to localized binding sites (acidic lipids), or the Volmer isotherm, which describes nonlocalized binding of the ligand to the surface (see Appendix A); in Eq. 3 K_p is the intrinsic binding constant and _(i) is the fraction of occupied binding sites on the surface, e.g., the fraction of PS that has formed 1:1 complexes with penta-lysine. The predictions of our model are qualitatively similar with either isotherm; for simplicity, we consider only the more familiar Langmuir isotherm in the body of this paper. The Volmer isotherm probably is more appropriate for pentalysine, however, because the available evidence suggests that this peptide does not bind specifically to acidic lipids (Ben Tal et al., 1996).

Free energy of domain formation

Domain formation at constant pressure and temperature is driven by the decrease in the Gibbs free energy of the system, G:

(4)

We consider only two contributions to G: G_m, the increase in free energy of mixing resulting from the decrease in entropy of mixing when acidic and neutral lipids separate, and G_e, the change in electrostatic free energy of the membrane when the two phases form.

As shown schematically in Fig. 2, one of the generalized forces that maintains the equilibrium between the domain and nondomain phases is the difference in the surface pressure between the phases. This means that Eq. 4 should include a pressure term resulting from nonelectrostatic interactions between the lipids. However, we consider the membrane as an incompressible two-dimensional fluid (i.e., the area per lipid remains constant), so no free energy will be stored because of these nonelectrostatic forces. Equation 4 should also contain other nonelectrostatic contributions to the free energy that have been discussed in the literature; see, e.g., Träuble (1977) and Raudino (1995). At low ionic strength, however, the electrostatic contribution should dominate the other terms.

We consider a membrane consisting of 1 mole of lipids having an area A_(h) = N_AA_L, where N_A is Avogadro's number and A_L is the cross-sectional area of one lipid. The fraction of acidic lipids in the membrane is f_(h) (0 < f_(h) < 1). Upon binding of peptide, the membrane separates into two phases: the domain phase (d) has an area A_(d) and a mole fraction of acidic lipids f_(d) > f_(h); the nondomain phase (n) has an area A_(n) and a fraction of acidic lipids f_(n) < f_(h) (Fig. 1). We ignore edge effects, so the shapes of the phases are not important. Our analysis also assumes that the domains are much larger than 1/, the Debye length.

It follows from the definitions (and the assumptions that the area per lipid, A_L, is both the same for PC and PS and constant in the h, d, and n phases) that

(5)

or, combining Eq. 5,

(6)

Note that f_(n) = f_(h) corresponds to A_(d) = 0 and A_(n) = A_(h), that is, to the absence of domains.

The first term in the right-hand side of Eq. 4 is given by

(7)

where

(8)

are the free energies of lipid mixing in each of the phases (Träuble, 1977; Hiemenz, 1986). For simplicity, we assume in Eq. 8 that only two species are present in the membrane: the zwitterionic lipid PC and the acidic lipid PS; specifically, we do not distinguish between free PS and PS bound in a 1:1 complex with a ligand. Equation 8 also assumes that PC and PS are randomly distributed in the homogeneous membrane, the domain, and the nondomain phase.

The second term in Eq. 4 can be represented in a similar form:

(9)

where the electrostatic free energy of each phase is calculated within the framework of Gouy-Chapman theory for a univalent electrolyte (Jähnig, 1976; Träuble et al., 1976; Cevc and Marsh, 1987):

(10)

where _(i) and _(i) are the surface charge density and surface potential of the ith phase, and the parameter B is defined in Eq. 1; _(i) and _(i) can be calculated for each phase from Eqs. 1, 2, and either A2 or A3 in Appendix A.

Note that in the limit of low surface potential _(i), F_(i)/2RT  1, Eq. 10 reduces to the well-known formula for the electrical energy of a capacitor with surface charge A_(i)(i), capacitance/area C, voltage _(i), and distance between the plates equal to the thickness of the diffuse double layer, 1/:

(11)

Because the lipid vesicles used in our experiments can be regarded as macroscopic, closed, and nonisolated systems, their Gibbs free energy assumes its minimum value at equilibrium (Hill, 1960). Thus we minimized the energy G calculated from Eq. 4 as a function of lipid compositions, f_(d) and f_(n), to obtain the theoretical results illustrated in Figs. 6 and 8.

	MATERIALS AND METHODS

Top Abstract Glossary Introduction Materials & Methods Results Discussion Appendix A Appendix B References

Vesicle preparation and fluorescence digital imaging microscopy

Dioleoyl-sn-glycero-3-phosphocholine (DOPC), dioleoyl-sn-glycero-3-phosphoserine (DOPS), and NBD-PS were obtained from Avanti Polar Lipids (Alabaster, AL). The triammonium salt of bovine brain phosphatidylinositol 4,5-bisphosphate (PIP₂) was from Calbiochem (San Diego, CA). NBD-PIP₂, synthesized as described by Chen et al. (1996), was a generous gift of Glenn Prestwich. Large unilamellar vesicles for microscopy were prepared according to the procedure of Haverstick and Glaser (1987). Each sample for microscopy contained 0.1 mM lipid vesicles, either pentalysine or spermine, and 0.5% agarose to immobilize the vesicles. Instrumentation and image processing are described by Yang and Glaser (1995).

Binding measurements

The centrifugation technique for measuring the binding of peptides, such as pentalysine to sucrose-loaded large unilamellar vesicles, was described by Ben Tal et al. (1996). Buser and McLaughlin (1997) provide additional experimental details. Pentalysine was synthesized by Multiple Peptides Systems (San Diego, CA) and was >95% pure, as determined by mass spectrographic analysis and analytical high-performance liquid chromatography. Spermine, 98% pure, was from Aldrich Chemical Co. (Milwaukee, WI).

	EXPERIMENTAL RESULTS AND THEORETICAL CALCULATIONS

Top Abstract Glossary Introduction Materials & Methods Results Discussion Appendix A Appendix B References

Fig. 3 shows how the binding of pentalysine to large unilamellar vesicles depends on the mole fraction of acidic lipid in the membrane. (In this experiment, we used phosphatidylglycerol (PG) instead of PS for technical reasons discussed by Ben Tal et al. (1996). As shown in figure 1 of Kim et al. (1991), zeta potential measurements on multilamellar vesicles show that Lys₅ has no specificity for PS versus PG.) Fig. 3 A plots the percentage peptide bound (at a constant total peptide concentration) as a function of the concentration of accessible lipid for vesicles of four different mole fractions of acidic lipid. Note that the affinity of the peptide for the vesicles increases markedly as the mole fraction of acidic lipid in the vesicles increases. Fig. 3 B plots the percentage of the bound pentalysine as a function of the mole fraction of acidic lipids in the membrane at one accessible lipid concentration (10³ M). The filled circles illustrate that there is a steep (sigmoidal) dependence of the binding on the mole fraction of acidic lipid. We showed elsewhere that the fraction of spermine bound to a membrane is also a steep sigmoidal function of the mole fraction of acidic lipid in the membrane (Chung et al., 1985). The pentalysine data can be described satisfactorily by the Gouy-Chapman-Stern theory, as illustrated by the two curves in Fig. 3 B. These curves show two sets of the parameters z_eff and K_p that describe the data adequately. Note that when the peptide concentration is low, which it is in these experiments, the fit does not depend on the use of the Langmuir or Volmer isotherm, because at low _(h), both isotherms reduce to Henry's law. We found that using either isotherm (with any parameter set that describes the data in Fig. 3 B) leads to qualitatively similar predictions regarding domain formation. We use a Langmuir isotherm and assume that z_eff = 2.5 and K_p = 20 M¹ in most calculations shown here.

View larger version (20K): [in this window] [in a new window]   FIGURE 3   (A) Binding of pentalysine to large (100 nm) unilamellar sucrose-loaded PC:PG vesicles of different compositions under conditions where domains do not form. The external solution contains 0.1 M KCl buffered to pH 7.0 with 1 mM 3-(N-morpholino)propanesulfonic acid. Peptide (typical concentration 106 M, much lower than the lipid concentration) was equilibrated with the vesicles for 15 min, then the vesicle-bound peptide was separated by centrifugation (T = 25°C). The concentration of peptide in the supernatant was measured by fluorescamine assay, as described by Buser et al. (1994), Ben Tal et al. (1996), and Buser and McLaughlin (1997). Part A plots the percentage pentalysine bound versus the concentration of accessible lipid, the concentration of lipid in the outer leaflet of the membrane ([L]access = 1/2[L]tot). The mole fraction of acidic lipid in the membranes is 10% (triangles), 20% (squares), 33% (hexagons), and 50% (circles). The curves represent the fit of the data to the equation: percentage of peptide bound = 100K[L]access/(1 + K[L]access), where K is the molar partition coefficient (e.g., Peitzsch and McLaughlin, 1993). (B) The percentage of pentalysine bound is plotted as a function of the mole fraction of acidic lipid in the vesicle at an accessible lipid concentration of 103 M. The filled circles are experimental values from the curves in A for [Lipid]access = 103 M; they illustrate the steep (sigmoidal) dependence of binding on mole fraction of acidic lipid in the membrane. The data are described by our model (Gouy-Chapman-Stern theory), assuming a 1:1 binding of pentalysine to acidic lipids (Langmuir isotherm) with either the parameter set Kp = 0.1 M1 and zeff = 5 (squares, dashed curve), or the set Kp = 20 M1 and zeff = 2.5 (triangles, solid curve).

We now consider how pentalysine decreases the free energy of the system upon domain formation, G. To illustrate the essential features of the model, we first assume a membrane containing 10% acidic lipid (i.e., f_(h) = 0.1) separates into domain and nondomain phases with constant fractions of PS: f_(d) = 0.5 and f_(n) = 0.09. (Equation 6 shows that the domain occupies ~2% of the membrane area.) We explore how G depends on the concentrations of peptide, C_p, and univalent electrolyte, C_e. If the calculated G is negative, domains will form. If the calculated G is positive, however, domains may still form, because the chosen f_(d) and f_(n) may not correspond to the minimum of G; we then minimize G more correctly as a function of f_(d) and f_(n).

Fig. 4 illustrates the key feature of our model of domain formation. Fig. 4 A plots the calculated surface potentials of a membrane as a function of the pentalysine concentration: the filled circles illustrate the predicted potentials if domains do not form; the triangles and squares illustrate the predicted potentials of the nondomain and domain phases, respectively, if domains do form. At a very low C_p (< 10¹⁰ M), peptide does not bind significantly to the membrane, so the surface potential of the domain phase is much more negative (~ 150 mV) than the surface potential of the nondomain phase (~ 70 mV). As the peptide concentration increases from 10⁹ to 10⁶ M, the surface potential of the domain, _(d), decreases rapidly in magnitude and approaches the values for the (h) and (n) phases, whereas _(h) and _(n) remain essentially constant; the peptide binds preferentially to the domain phase because of the Boltzmann factor in Eq. 2. At high peptide concentrations (>10⁵ M), the surface potentials of all of the phases tend to the same value.

View larger version (17K): [in this window] [in a new window]   FIGURE 4   The theoretically predicted effect of pentalysine on (A) the surface potentials of the homogeneous membrane (h), and the domain (d) or the nondomain (n) part of the membrane; and (B) the change in free energy of the system upon domain formation. Calculations in A were carried out by inserting Eqs. 2, 3, and B2 into Eq. 1, then solving with respect to the surface potential as a function of peptide concentration, assuming localized 1:1 binding of a peptide to an acidic lipid. Calculations in B were carried out using Eqs. 1 and 4-10, with the surface potentials shown in A. Parameter values: f(m) = 0.1, f(d) = 0.5, f(n) = 0.09, Ce = 0.01 M, Kp = 20 M1, and zeff = 2.5.

Fig. 4 B shows the corresponding change in the free energy of the system, G, upon domain formation. The contribution due to the entropy of mixing, G_m  0.008 kcal · mol¹, does not vary with C_p because it depends only on the fractions f_(d) and f_(n), which we assume are constant in these calculations; thus the change in G as C_p increases is due to the change in the electrostatic contribution, G_e. At low peptide concentrations, C_p < 10¹⁰ M, when the electrostatic potential of the domain is high (Fig. 4 A), the electrostatic free energy of the partitioned membrane exceeds the electrostatic energy of the homogeneous membrane, G_e > 0. In other words, bringing the negatively charged lipids together requires additional work. Under these conditions, the electrostatic free energy term, 0.01 kcal · mol¹, and the mixing term, 0.008 kcal · mol¹, contribute about equally to preventing domains like those illustrated in Fig. 1 B from forming in the absence of peptide. In the intermediate range of peptide concentrations, 10⁹ to 10⁶ M, there is significant peptide binding to the domain phase, but not to the nondomain phase. This neutralizes the charge of the domain substantially, reducing the electrostatic free energy of the partitioned membrane relative to that of the homogeneous membrane. Fig. 4 B predicts that domain formation becomes energetically favorable for 10⁷ M < C_p < 10⁶ M. At higher peptide concentrations (>10⁵ M), the homogeneous membrane, as well as the domain and nondomain phases, have significantly reduced surface potentials (Fig. 4 A). In this case, lateral reorganization of the membrane into domains does not produce a significant change in the electrostatic free energy, G_e  0, and domains do not form, because the change in mixing free energy is unfavorable (G  G_m > 0 in Fig. 4 B for C_p > 10⁵ M).

Thus a simple electrostatic model predicts that domains first form, then break up as the peptide concentration increases. As discussed in Appendix A, this is true not only for the model assuming localized 1:1 binding of the peptide to acidic lipids (Langmuir isotherm, Eq. 3), but also for the model assuming nonlocalized binding (Volmer isotherm).

Experimental data obtained with pentalysine (Fig. 5, upper row) agree qualitatively with this prediction. Before the addition of pentalysine, phosphatidylserine is not found in domains, but appears to be distributed randomly in the vesicles (left vesicle denoted control in upper row of Fig. 5). As the concentration of the basic peptide increases, domains form that are enriched in acidic lipid. At higher peptide concentrations (>2 mM), however, the acidic lipids are again distributed randomly in the membrane. Although the predictions illustrated in Fig. 4 agree qualitatively with the experimental data, the concentration of peptide required to form domains is higher than predicted. We obtained similar data with spermine, a basic ligand with valence +4 (Fig. 5, lower row): domains form, then break up as the concentration of spermine increases.

View larger version (79K): [in this window] [in a new window]   FIGURE 5   Formation of membrane domains by pentalysine and spermine in large unilamellar vesicles visualized using fluorescence microscopy. (A) Seven different vesicles containing 90 mol% DOPC, 9.5% mol% DOPS, and 0.5 mol% NBD-PS in 10 mM Tris buffer (pH 7.4), after the addition of the indicated concentrations of pentalysine. (B) Seven different vesicles of the same composition after the addition of the indicated concentrations of spermine. Vesicles were visualized for NBD fluorescence. Domains containing PS form as the concentrations of pentalysine (A) or spermine (B) increase. At higher concentrations (>2 mM), the domains break up and PS is distributed randomly. The images were normalized to a mean radiance value of 100 ± 5, and the corresponding intensity values are displayed according to the pseudocolor scheme at the bottom of the figure. The white bar equals 4 µm.

Fig. 6 shows how the model predicts the change in free energy of the system on domain formation will vary as the ionic strength of the solution increases; the curves were calculated from the Langmuir model, assuming that the peptide concentration in solution remains fixed. Note that G becomes positive as the ionic strength increases. The physical interpretation of this prediction is straightforward: when the salt concentration increases, the thickness of the diffuse double layer, 1/, decreases, and less electrical energy is stored in the diffuse double layer (see Eq. 11). Less electrical energy, G_e, is available to overcome the (positive) mixing term G_m, and domains cannot form.

View larger version (14K): [in this window] [in a new window]   FIGURE 6   Change in free energy of the system on domain formation versus electrolyte concentration, as calculated from the model with localized 1:1 binding of pentalysine to acidic lipids. Parameter values: Kp = 0.1 M1, zeff = 5, Cp = 108 M (), and Kp = 20 M1, zeff = 2.5, and Cp = 106 M (). The values of f(d) and f(n) are calculated as those giving the most negative value to the free energy. These values change with salt concentration. The model predicts that domains will form at low (0.01 M) but not high (0.1 M) concentrations of salt.

This prediction agrees well with the experimental results we have obtained with spermine (Fig. 7) and pentalysine (data not shown). Pentalysine and spermine form stable domains enriched in PS in a solution containing 10 mM salt, but not in a solution containing 100 mM NaCl. Yang and Glaser (1995) observed that domain formation induced by MARCKS(151-175) is favored when the ionic strength of the solution is low, although domains also form in solutions containing 100 mM salt. The different results obtained with pentalysine and MARCKS(151-175) suggest that additional factors stabilize the domains formed by MARCKS(151-175) at physiological salt concentrations.

View larger version (122K): [in this window] [in a new window]   FIGURE 7   Effect of ionic strength on domain formation in large unilamellar vesicles by spermine. The upper row in A shows five different vesicles (90 mol% DOPC, 9.5 mol% DOPS, and 0.5 mol % NBD-PS) in 10 mM Tris buffer (pH 7.4), in the presence of 100 µM spermine. The lower row in A shows five different vesicles of the same composition in 10 mM Tris buffer (pH 7.4), in the presence of 100 µM spermine plus 100 mM NaCl. (B) Five different vesicles in either low ionic strength (upper row) or high ionic strength (lower row), as in A, except that the spermine concentration was increased to 200 µM. The figures show that domains formed in the presence of the spermine at low ionic strength break up when the ionic strength increases. The images were normalized to a mean radiance value of 100 ± 5, and the intensity values are displayed according to the pseudo-color scheme at the bottom of the figure. The white bar equals 4 µm.

For the theoretical calculations presented in Fig. 4, we assumed that the domain and nondomain phases contained fixed fractions of acidic lipid. Fig. 8 illustrates predictions obtained for more realistic conditions, where we calculate the fractions f_(d) and f_(n) that yield the most negative value of G. The curves in Fig. 8 have deeper minima than the curve in Fig. 4 B and tend to zero at very low and very high peptide concentrations, where domains do not form. Our model predicts that the fraction of acidic lipid in the domain, f_(d), increases steeply to ~0.5 when the domain begins to form at C_p = 10⁷ M, then decreases gradually to 0.1 as C_p increases to 10⁵ M and the domain breaks up (not shown). The size (Eq. 6) of the domain phase also is predicted to change as the peptide concentration increases (not shown).

View larger version (18K): [in this window] [in a new window]   FIGURE 8   Change in the free energy of the system on domain formation versus peptide concentration calculated from the model with localized 1:1 binding of pentalysine to acidic lipids. Parameter values: Kp = 0.1 M1 and zeff = 5 (), and Kp = 20 M1 and zeff = 2.5 (). The fraction of acidic lipids in the nonseparated, or homogeneous, membrane is f(h) = 0.1, and the values of f(d) and f(n) are chosen as those giving the most negative value to the free energy. Ce = 0.01 M.

We then used the model to estimate the fraction of PIP₂ that partitions into domains formed by pentalysine. In these calculations, PIP₂ was regarded as a trivalent acidic lipid (Toner et al., 1988) that binds pentalysine with the same binding constant K_p as PS. Two direct binding measurements (not shown) support the assumption that PIP₂ does not form high-affinity complexes with pentalysine. First, PC/PG/PIP₂ vesicles containing 18% PG and 0.5% PIP₂ bind pentalysine with the same affinity as PC:PG vesicles containing 20% PG (squares in Fig. 3 A). This result can be contrasted with the results obtained with the PH domain of PLC- (Garcia et al., 1995; Lemmon et al., 1996), which forms high (µM) affinity 1:1 complexes of known structure with PIP₂ and inositol trisphosphate (Ferguson et al., 1995). Second, PC/PIP₂ vesicles containing 5% PIP₂, which have about the same electrostatic surface potential as PC/PG vesicles containing 20%PG, bind pentalysine with only ~10-fold higher affinity than the PC/PG vesicles: the data are shifted ~10-fold to the left of the squares in Fig. 3 A. Thus pentalysine interacts somewhat more strongly with PIP₂ than with monovalent acidic lipids such as PS and PG, but less strongly with PIP₂ than does the PH domain of PLC-. We assumed that the mole fraction of PIP₂ in the vesicles was small compared to the fractions of PC and PS and that it did not form a third membrane phase. The areas of the two phases were calculated from Eq. 6. However, the energy G was minimized as a function of three parameters: f_(d), f_(n), and the fraction of PIP₂ in one of the phases. Our calculations predict that when domains form, PIP₂ should partition strongly into the domain phase.

This prediction agrees qualitatively with two different types of experimental data. First, direct fluoresence measurements show that PIP₂ is sequestered in domains formed by pentalysine. Fig. 9 B shows that NBD-PIP₂ is distributed randomly in a PC/PS/PIP₂ vesicle when the concentration of pentalysine is low (<100 µM), and that the addition of 100 µM, 500 µM, 1 mM, or 2 mM Lys₅ produces domains enriched in NBD-PIP₂ (Fig. 9 B) as well as NBD-PS (Fig. 9 A). Pentalysine concentrations greater than 4 mM cause the domains enriched in PIP₂ and PS to break up. The MARCKS(151-175) peptide also produces domains enriched in PIP₂ as well as PS (Glaser et al., 1996). Second, millimolar concentrations of pentalysine and spermine inhibit the phosphoinositide specific-PLC-catalyzed hydrolysis of PIP₂ ~10-fold (data not shown). The results we observed with millimolar concentrations of spermine and pentalysine are very similar to those reported by Glaser et al. (1996) for micromolar concentrations of MARCKS(151-175). These observations with pentalysine and spermine support our previous suggestion that the ability of MARCKS(151-175) to sequester the biologically important multivalent lipid PIP₂ in lateral domains is a nonspecific electrostatic phenomenon.

View larger version (67K): [in this window] [in a new window]   FIGURE 9   The domains produced by pentalysine contain high concentrations of PIP2 as well as PS. (A) Images of seven different vesicles with the same composition (89 mol% DOPC, 9.5 mol% DOPS, 1 mol% PIP2, and 0.5 mol% NBD-PS) formed in a solution containing 10 mM Tris (pH 7.4). Addition of the indicated concentration of pentalysine produces domains enriched in NBD-PS, which break up at high concentrations of pentalysine (>4 mM). (B) Images of seven different vesicles with the same composition (89 mol% DOPC, 10 mol% DOPS, 0.5 mol% PIP2, and 0.5 mol% NBD-PIP2) formed in a solution containing 10 mM Tris (pH 7.4). Addition of the indicated concentration of pentalysine produces domains enriched in NBD-PIP2, which break up at high concentrations of pentalysine (>4 mM). The images were normalized to a mean radiance value of 100 ± 5, and the intensity values are displayed according to the pseudo-color scheme at the bottom of the figure. The white bar equals 4 µm.

	DISCUSSION

Top Abstract Glossary Introduction Materials & Methods Results Discussion Appendix A Appendix B References

Our simple theoretical model predicts that small basic peptides use electrostatic interactions to form lateral membrane domains enriched in acidic lipids. The model assumes that more peptides bind to the membrane when domains form; this decreases the electrostatic free energy stored in the diffuse double layer adjacent to the membrane. To a first approximation, the double layer may be represented as a parallel plate capacitor (see Eq. 10). The charged lipids and adsorbed peptides represent one plate; the counterions located a distance 1/ from the surface represent the oppositely charged capacitor plate. At low ionic strength, when the Debye length (1/) is large, this decrease in electrostatic energy due to peptide binding can overcome the change in free energy due to the entropy of mixing of the lipids, which always increases upon domain formation. Our experiments provide qualitative support for the four salient predictions of the model. First, we showed that the small multivalent basic ligands Lys₅ and spermine do form lateral domains enriched in acidic lipids (Fig. 5). When these ligands are present at very low concentrations, their binding to vesicles exhibits a steep sigmoidal dependence on the mole fraction of acidic lipid in the membrane (Fig. 3 B and Chung et al., 1985), which is consistent with the fundamental assumption of the model. Second, the domains break up as the concentration of ligand increases to high values (Fig. 5). This observation strongly supports our assumption that domain formation is not due to attractive interactions between the peptides; in the latter case, domains should be more stable at high peptide concentrations. Third, decreasing the ionic strength of the solution favors domain formation (Fig. 7), which supports our assumption that electrostatic interactions drive domain formation. Fourth, when the membrane contains trace concentrations of the multivalent acidic lipid PIP₂, this lipid partitions strongly into the domains formed by basic peptides (Fig. 9); this inhibits hydrolysis of PIP₂ catalyzed by phospholipase C (see above). We stress that this partitioning, which is seen with the MARCKS(151-175) peptide as well as with Lys₅, does not require the formation of a high-affinity specific 1:1 complex between PIP₂ and either peptide. Direct measurements show these peptides, in contrast to the PH domain of PLC-, do not bind PIP₂ with high affinity (see above).

The results from fluorescence digital imaging microscopy reported here agree very well with results obtained recently with a different technique (G. Gröbner and A. Watts, personal communication), monitored lateral domain formation induced by pentalysine in PC/PG membranes by means of solid-state static and magic angle spinning (MAS) ³¹P NMR.

The qualitative agreement we observed between the experimental results and the predictions of the model suggests that electrostatics plays an essential role in domain formation under our conditions. Not surprisingly, however, this oversimplified model fails to describe the data quantitatively. Specifically, the calculated pentalysine concentration required to form domains (10⁷ to 10⁶ M in a 0.01 M salt solution; circles in Fig. 8) is three orders of magnitude lower than the experimentally observed value (10⁴ to 10³ M; see Fig. 6). Calculations of the electrostatic contribution to domain formation based on realistic molecular models of phospholipid membranes and pentalysine (Ben Tal et al., 1996) are in progress; these calculations consider the highly nonuniform nature of the potential adjacent to a membrane with adsorbed basic peptides, and should provide a more realistic description of how electrostatic interactions contribute to domain formation. Specifically, the calculations show that PIP₂ can be sequestered in domains formed from basic peptides like pentalysine by a discreteness-of-charge mechanism (D. Murray and S. McLaughlin, unpublished observations).

In contrast to the domains formed by pentalysine and spermine, the domains formed by MARCKS(151-175) do not break up at high peptide concentration and are stable in physiological (0.1 M) salt solutions (Yang and Glaser, 1995; Glaser et al., 1996). This MARCKS peptide contains five Phe that penetrate the polar headgroup region of the bilayer (Qin and Cafiso, 1996; Glaser et al., 1996), is much longer than pentalysine, and has more basic residues (13 versus 5). Experiments are in progress to assess the importance of these three factors in domain formation.

An interesting biological implication of this work relates to the ability of basic peptides to sequester the biologically important lipid PIP₂ in lateral domains. The evidence reported here and in Glaser et al. (1996) suggests that the partitioning of PIP₂ into the lateral domains formed by pentalysine or MARCKS(151-175) is due to a nonspecific electrostatic effect. Clusters of basic residues on proteins such as MARCKS and caveolin, which are found in lateral domains in biological membranes, also should be able to sequester PIP₂. Thus we expect that PIP₂ will be found at high concentrations in the nascent phagosomes of macrophages, which contain high concentrations of MARCKS (Allen and Aderem, 1995), and within caveolae, which contain high concentrations of caveolin (Simons and Ikonen, 1997). Two recent reports show that PIP₂ is localized at high concentrations within caveolae (Hope and Pike, 1996; Liu et al., 1997).