Biophysical Journal 86:1969-1986 (2004)
© 2004 The Biophysical Society
A Computational Model for the Electrostatic Sequestration of PI(4,5)P2 by Membrane-Adsorbed Basic Peptides
Jiyao Wang *,
Alok Gambhir 
,
Stuart McLaughlin and
Diana Murray *
* Department of Microbiology and Immunology, Weill Medical College of Cornell University, New York, New York 10021; Department of Physiology and Biophysics, Health Sciences Center, and Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794
Correspondence: Address reprint requests to Diana Murray, Dept. of Microbiology and Immunology, Weill Medical College of Cornell University, 1300 York Ave., Box 62, New York, NY 10021. Tel.: 212-746-1184; Fax: 212-746-8587; E-mail: dim2007{at}med.cornell.edu.
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ABSTRACT
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The multivalent acidic phospholipid phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) plays a key role in many biological processes. Recent studies show that unstructured clusters of basic residues from a number of peripheral proteins can laterally sequester PI(4,5)P2 in membranes. Specifically, experiments suggest that the basic effector domain of the myristoylated alanine-rich C kinase substrate (MARCKS), or a peptide corresponding to this domain, MARCKS(151–175), sequesters several PI(4,5)P2 and that this sequestration is due to nonspecific electrostatic interactions. Here, we use the finite difference Poisson-Boltzmann method to test this hypothesis by calculating the electrostatic free energy of lateral sequestration of PI(4,5)P2 by membrane-adsorbed basic peptides: Lys-7, Lys-13, and FA-MARCKS(151–175), a peptide based on MARCKS(151–175). In agreement with experiments, we find that the electrostatic free energy becomes more favorable when: 1), Lys-13 and FA-MARCKS(151–175) sequester several PI(4,5)P2; 2), the linear charge density of the basic peptide increases; 3), the mol percent monovalent acidic lipid in the membrane decreases; and 4), the ionic strength of the solution decreases. In addition, the electrostatic sequestration free energy is in excess of the entropic penalty associated with localizing PI(4,5)P2. Our calculations, thus, provide a structural and quantitative description of the observed interaction of PI(4,5)P2 with membrane-adsorbed basic sequences.
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INTRODUCTION
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Phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2 or PIP2) is the major poly-phosphoinositide in mammalian cells and exhibits a wide variety of functions related to its ability to interact with many different proteins: it plays key roles in the attachment of the cytoskeleton to the plasma membrane, membrane trafficking, and the activation of a diverse set of enzymes (De Camilli et al., 1996
; Toker, 1998; Raucher et al., 2000; Cockcroft, 2000; Irvine, 2002; Martin, 2001; Payrastre et al., 2001; McLaughlin et al., 2002; Cantley, 2002; Yin and Janmey, 2003). It has been hypothesized that peripheral proteins that bind PIP2 at the surface of the plasma membrane may contribute to the regulation of PIP2 function by controlling its accessibility to other proteins (Laux et al., 2000; McLaughlin et al., 2002). Among the proteins that have been shown to interact with PIP2 is the myristoylated alanine-rich C kinase substrate (MARCKS), which uses a dramatic cluster of basic residues, termed its effector domain, to interact electrostatically with both monovalent acidic phospholipids and polyvalent phosphoinositides in the plasma membrane (Kim et al., 1994; McLaughlin and Aderem, 1995; Swierczynski and Blackshear, 1995; Laux et al., 2000; Wang et al., 2002). There are a number of other peripheral proteins that contain similar basic sequences that may be adsorbed to the plasma membrane surface (Wang et al., 2002); e.g., MacMARCKS (Blackshear, 1993), GAP43 (Laux et al., 2000), DAKAP200 (Rossi et al., 1999), and adducin (Matsuoka et al., 2000). All may be present in cells at high concentrations and could, therefore, potentially bind most of the cellular PIP2 (McLaughlin et al., 2002). Furthermore, all are protein kinase C (PKC) substrates, and PKC phosphorylation of serines within the basic regions of these proteins would result in the desorption of the basic clusters from the membrane surface and the subsequent release of PIP2. Indeed, recent studies show that MARCKS and peptides based on the basic effector domain of MARCKS, MARCKS(151–175), laterally sequester PIP2 and that the sequestration inhibits the hydrolysis of PIP2 by phospholipase C (PLC). Phosphorylation by PKC or binding of Ca2+/calmodulin displaces the effector domain from the membrane and releases the inhibition of PLC (Kim et al., 1994; Glaser et al., 1996; Arbuzova et al., 1998; Ohmori et al., 2000; Wang et al., 2001). Because PIP2 is a multivalent anionic lipid, its association with the membrane-adsorbed basic effector domain may be driven by electrostatic interactions (McLaughlin et al., 2002; Wang et al., 2002; Gambhir et al., 2004).
Recent experiments with a peptide based on the MARCKS effector domain, MARCKS(151–175), provide evidence that this may well be the case. Binding assays show that this peptide binds with high affinity to phospholipid vesicles containing PIP2 as the only acidic lipid (i.e., vesicles composed of PIP2 and phosphatidylcholine (PC); Wang et al., 2001, 2002; Rauch et al., 2002). In contrast to the PH domain of PLC-
1, the peptide does not require PIP2 for membrane binding: it also binds with high affinity to membranes containing physiological concentrations of monovalent acidic lipids such as phosphatidylserine (PS) (i.e., to PC/PS vesicles). Spectroscopic techniques show that once the peptide is adsorbed to a PC/PS/PIP2 membrane, it laterally sequesters PIP2, even when the PS is present in excess of PIP2 (Gambhir et al., 2004). These experimental studies indicate that both the binding of peptides to PIP2-containing vesicles (i.e., PC/PIP2 vesicles) and the sequestration of PIP2 by membrane adsorbed basic peptides (i.e., on PC/PS/PIP2 vesicles) are driven by nonspecific electrostatic interactions: 1), increasing the ionic strength of the solution decreases the binding of basic peptides to PIP2-containing vesicles and abolishes sequestration; 2), PI(4,5)P2 and PI(3,4)P2 interact with basic peptides with the same affinity, indicating that the interactions are independent of the chemical nature of the phosphoinositide; 3), peptides comprised of the same number of Lys or Arg residues bind PIP2-containing membranes with the same affinity, indicating that the interactions are independent of the chemical nature of the basic residue as well; 4), peptides with high local positive charge density are able to sequester PIP2; and 5), a single peptide may laterally sequester several PIP2 simultaneously.
Because of the importance of membrane organization to many biological processes, it is of interest to understand how the membrane adsorption of basic sequences affects the electrostatic properties of membrane surfaces, which may consequently lead to lateral reorganization of PIP2 through an electrostatic mechanism. In this work, we provide a computational model for the sequestration of PIP2 by membrane-adsorbed basic peptides that is experimentally characterized in a companion paper (Gambhir et al., 2004). Our model, based on solutions to the Poisson-Boltzmann equation, explicitly tests the hypothesis that nonspecific electrostatic interactions are sufficient to drive the lateral accumulation of PIP2 by membrane-adsorbed basic sequences. Specifically, we use the finite difference Poisson-Boltzmann (FDPB) method (Davis and McCammon, 1990; Sharp and Honig, 1990b; Honig and Nicholls, 1995; Baker et al., 2001) with atomic models of PIP2, membranes and peptides (Fig. 1) to calculate the electrostatic free energy of laterally sequestering a PIP2 lipid from a region of "bulk" membrane (Fig. 1, A and B) to a region in the vicinity of a membrane-adsorbed basic peptide (Fig. 1, C and D). There are many examples of protein domains, e.g., PH, PX, FYVE, and ENTH domains, that contain basic regions that bind poly-phosphoinositides in a specific, 1:1 fashion (Lemmon, 2003). Here, we examine a different mode of PIP2 binding that is based on nonspecific interactions, which do not depend on structural detail and need not be 1:1. Rather, in this case, there may be a "many-to-one" interaction between several PIP2 lipids and one of many possible basic sequences (Wang et al., 2002; Rauch et al., 2002; Gambhir et al., 2004). Hence, establishing that nonspecific electrostatic interactions can provide enough energy to account for the experimentally observed partitioning supports the existence of a fundamentally different type of interaction between peripheral proteins and these important signaling lipids.
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FIGURE 1 The FDPB calculations of the electrostatic free energy of PIP2 sequestration,  Gel(PIP2), are based on atomic-level models of the peptide/membrane system. The view is from above, looking down on an example of the peptide/membrane models used in our calculations. In the example illustrated here, the composition of the "bulk" membrane is 5:1 PC/PS. The peptide, Lys-13, is colored cyan, and the headgroups of PC, PS, and PIP2 are colored white, red, and yellow, respectively. Initially, membrane-adsorbed Lys-13 and PIP2 are infinitely far apart (A and B), and PIP2 is considered to be located in the bulk membrane phase, which contains  1 mol% PIP2. The arrow denotes the position to which the PIP2 will be sequestered. In the final state (C and D), PIP2 has moved, as suggested by the arrow in panels A and B, to a position adjacent to the membrane-adsorbed Lys-13 peptide. It is assumed that the presence of PIP2 does not affect the orientation of Lys-13 with respect to the membrane, i.e., in A and C, Lys-13 remains in its minimum electrostatic free-energy orientation as determined in the absence of PIP2. Panels A and B represent the initial state, and panels C and D represent the final state used in the calculation of Gel(PIP2) in Eq. 2.
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Traditionally, the electrostatic properties of membrane systems have been described by smeared charge models based on Gouy-Chapman theory, which assumes that the charges due to both the acidic lipids and bound peptide are smeared uniformly over a planar membrane surface (McLaughlin, 1989). Previous experimental and theoretical work shows that "smeared charge" models have utility in providing quantitative descriptions when the shape and charge distribution of the molecules can be neglected (Kim et al., 1991; Heimburg and Marsh, 1996). However, simple smeared charge models are unable to describe the electrostatic properties of membrane surfaces that depend on localized effects produced by multivalent species, such as poly-phosphoinositides and clusters of basic residues on peptides and electrostatically polarized proteins. For example, our previous FDPB calculations on phospholipid bilayers with a high surface concentration of adsorbed basic peptides demonstrate that to describe the observed electrostatic properties of these systems, it is crucial to account for the molecular detail of the peptides (Murray et al., 1999). The FDPB method, through describing lipids and proteins in atomic detail, realistically depicts the complex electrostatic potential patterns that protein/membrane systems often produce as well as the desolvation effects that occur upon association of the interacting species. However, it makes a number of simplifying assumptions: 1), the solvent is represented as a dielectric continuum, i.e., a structureless aqueous phase; 2), the finite size of the salt ions as well as ion-ion correlation effects are ignored; and 3), the membrane and peptide are assumed to be static structures. A number of experimental approaches suggest that water molecules at the membrane surface may be treated in the continuum limit (reviewed in McLaughlin, 1989), and theoretical work has justified the assumptions related to salt ions for physiological conditions (Carnie and Torrie, 1984). By neglecting the dynamics of the systems we are studying, our models are not able to account for hydrogen bonding and other interactions that rely on structural detail. Hence, in terms of structural representation, it is intermediate between smeared charge models on the one hand, and molecular dynamics and Monte Carlo simulations on the other. Dynamical simulations are extremely valuable in depicting the short-time (< µs), detailed motions of lipids in a membrane environment (Pastor and Feller, 1996; Forrest and Sansom, 2000), but have been limited in their capacity to describe the electrostatic properties of membranes and protein/membrane systems (Tobias, 2001). The FDPB method has proved to be a reliable theoretical methodology for depicting the electrostatic free energies of interaction that occur in large, highly charged multicomponent systems, especially those involving high ionic strengths (Honig and Nicholls, 1995). Recently, an adaptive Poisson-Boltzmann (PB) solver has been developed (Baker et al., 2001) that allows for the calculation of the electrostatic properties of extremely large molecular assemblages (Elcock, 2002).
Several groups have modified smeared charge models to more realistically depict the charge distributions of membrane-adsorbing molecules and membrane surfaces (May et al., 2000, 2002; Haleva et al., 2004). These thermodynamic models predict that there is significant lateral redistribution of both monovalent and multivalent charged lipids in response to the membrane association of oppositely charged proteins. However, in this study, we assume, in agreement with the available experimental results, that monovalent acidic lipids are not appreciably sequestered by membrane-adsorbed basic peptides (Kleinschmidt and Marsh, 1997; Murray et al., 2002). As shown in Fig. 1, monovalent acidic lipids (red) remain distributed uniformly in the membrane, and only the redistribution of the biologically important PIP2 (yellow) is considered. Our computational models of the interactions of PIP2 and membrane-adsorbed basic peptides presented here, thus, provide insight into the lateral organization of these molecules by quantifying the role of electrostatics and by providing molecular models of the membrane-associated complexes.
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METHODS
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Finite difference Poisson-Boltzmann calculations: overview
Electrostatic potentials and free energies are obtained from a modified version of the DelPhi program (Gallagher and Sharp, 1998) that solves the nonlinear Poisson-Boltzmann equation for protein/membrane systems (Ben-Tal et al., 1996). DelPhi produces finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) for a system where the solvent (plus 1:1 electrolyte, i.e., KCl) is described in terms of a bulk dielectric constant and mean concentrations of mobile ions, whereas large solutes (here, basic peptides) and lipids comprising the bilayer (e.g., PIP2) are described in terms of the coordinates of the individual atoms as well as their atomic radii and partial charges. The FDPB method has previously been shown to yield satisfactory agreement with experimental measurements of the binding of peptides and proteins to charged membranes (Ben-Tal et al., 1996, 1997; Murray et al., 1998, 2002; Arbuzova et al., 2000; Murray and Honig, 2002; Diraviyam et al., 2003).
In the calculations described in this work, each atom of a peptide/membrane system is assigned a radius and partial charge that is located at its nucleus. The molecular model is then mapped onto a three-dimensional cubic grid of l3 points, each of which represents a small region of the peptide, membrane, or solvent. The charges and radii used for the amino acids were taken from a CHARMM22 parameter set (Brooks et al., 1983); those used for the lipids are the ones described in Peitzsch et al. (1995) and were used in previous studies (Ben-Tal et al., 1996, 1997; Murray et al., 1998). The partial charges for PI(4,5)P2 were taken from similar functional groups from the CHARMM22 parameter set so that the net charge on the lipid headgroup is -4; it was assumed, in agreement with experimental evidence, that one of the oxygens in the phosphate group at position 5 of the inositol ring was protonated at physiological pH (McLaughlin et al., 2002). The molecular surfaces of the molecules are defined as the locus of points traced out by the inward facing surface of a spherical probe or radius 1.4 Å (the radius of a water molecule). Regions inside the molecular surfaces of the peptide and membrane are assigned a dielectric constant of 2 to account for electronic polarizability and those outside are assigned a dielectric constant of 80 (Sharp and Honig, 1990b). An ion exclusion layer is added to the solutes and extends 2 Å beyond the molecular surfaces (see, e.g., Fig. 3 of Ben-Tal et al., 1996). The nonlinear Poisson-Boltzmann equation is solved in the finite difference approximation, and the numerical calculation of the potential is iterated to convergence, which is defined as the point at which the electrostatic potential changes <10-4 kT/e between successive iterations. Electrostatic free energies are obtained from the calculated potentials (Sharp and Honig, 1990a).
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FIGURE 3 FDPB calculations suggest that the nonspecific electrostatic component of the sequestration of PIP2 from bulk membrane to positions within and around the imprint of a membrane-adsorbed basic peptide is significant. For each of the three peptides denoted, the black and gray bars represent the results for 2:1 and 5:1 PC/PS, respectively. The values plotted for  Gel(PIP2) and GS correspond to the mean of the Boltzmann factor-weighted averages calculated with the Gel(PIP2) values depicted in Fig. 2, and the error bars correspond to one standard deviation from the mean (see Methods for details). (A) The black and gray bars represent the average electrostatic free energy of sequestration, Gel(PIP2), and the white bars, above, represent the average free energy of PIP2 demixing, GS, for the corresponding membrane containing 1 mol% PIP2. (B) The black and gray bars represent the average net energy, Gel(PIP2) + GS.
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Calculation of the electrostatic free energy of interaction of basic peptides with phospholipid membranes
The electrostatic free energy of interaction of a basic peptide associating with a phospholipid bilayer, Gel, is determined as the difference between the electrostatic free energy of the peptide docked at the surface of the membrane, Gel(P·M), and the electrostatic free energies of the peptide, Gel(P), and membrane, Gel(M), infinitely far apart, i.e., taken separately:
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The electrostatic free energies in Eq. 1 are dependent on the size of the finite difference grid and the resolution or scale of the calculation through a grid-dependent electrostatic self-energy term due to the distribution of each partial charge onto the grid. To remove the self-energy contribution, it is necessary to ensure that the molecules and, thus, the fixed charges, have the same location on the grid in the initial and final states; this is true of the calculations with PIP2 described below. Gel was calculated as a function of the distance, R, of closest approach between the van der Waals surfaces of the peptide and membrane. These calculations defined the orientation of minimum electrostatic free energy for each of the basic peptides examined in this study.
Phosphatidylcholine (net charge of 0) and phosphatidylserine (net charge of -1) bilayers were built as described previously (Ben-Tal et al., 1996). The lipids were distributed uniformly in an hexagonal array and each lipid headgroup occupies an area of 68 Å2 in the plane of the membrane. Each leaflet of the bilayer contains 192 lipids so that the bilayers have lateral dimensions of 130 Å x 120 Å. The headgroup regions from the two opposing leaflets encompass 1/2 the thickness of the bilayer, which is 62 Å; in between resides the acyl chain portion of the lipids. It was assumed that the lipids change neither structure nor position upon interaction with a peptide. Previous work has shown that the membrane partitioning of a basic peptide that resides outside the polar envelope of the membrane, i.e., pentalysine, is independent of whether the membrane is in the liquid crystalline or gel phase, suggesting that the use of static bilayer models is appropriate for calculating the electrostatic free energy of their membrane interaction (Ben-Tal et al., 1996). Two types of PC/PS membranes were used in determining the electrostatic free energy of interaction of basic peptides with membranes: 5:1 and 2:1 PC/PS.
Three basic peptides were considered in this study: acetyl-Lys-7-amide, acetyl-Lys-13-amide, and acetyl-FA-MARCKS(151–175)-amide. FA-MARCKS(151–175) is a peptide based on the effector domain of MARCKS in which the five phenylalanines are replaced by alanine. It has the amino acid sequence: acetyl-KKKKKRASAKKSAKLSGASAKKNKK-amide. Experiments suggest that MARCKS(151–175) has an extended conformation both in solution and when associated with a membrane surface (Qin and Cafiso, 1996; Zhang et al., 2003). Due to electrostatic repulsions among the basic residues, Lys-13 and Lys-7 are expected to adopt extended conformations as well. The peptides were, therefore, built in extended form using the Insight/Biopolymer molecular modeling package (INSIGHT-II, Accelrys, San Diego, CA). To reduce atomic overlaps and to relax torsional and dihedral constraints, each peptide model was energy minimized using the Insight/Discover molecular modeling package (INSIGHT-II, Accelrys). The minimization consisted of 100 iterations with a conjugate gradient method in gas phase using the CVFF force field and neglecting electrostatic interactions. The minimization did not significantly alter the extended structure of the peptides. The Lys-7, Lys-13, and FA-MARCKS(151–175) peptide models have dimensions of 31 Å x 17 Å x 7 Å, 53 Å x 17 Å x 7 Å, and 97 Å x 18 Å x 7.5 Å and net charges of +7, +13, and +13, respectively. In the FDPB calculations, the plane of each peptide was kept parallel to the membrane surface and the vertical distance between the van der Waals surfaces of the peptide and membrane was varied. For the purpose of mapping the molecules onto the finite difference grid, the peptide was rotated about an axis perpendicular to the membrane surface such that the peptide has a diagonal orientation with respect to the grid to reduce the overall size of the system that needed to be considered. For example, by placing the peptide on a diagonal, the minimal size of a square that could accommodate a Lys-13 peptide was reduced from 53 to 42 Å2. The calculations were designed to determine the peptide orientation that produces close to the minimum free energy of electrostatic interaction with the membrane; this is the orientation considered throughout this study. Previous work has established that, for peripheral association, the electrostatic contribution to binding free energies is well described by consideration of the minimum free energy orientation alone (Ben-Tal et al., 1996, 1997; Murray et al., 1998; Arbuzova et al., 2000).
A sequence of focusing runs (Gilson et al., 1987) of increasing resolution was employed to calculate the electrostatic potentials. In the initial calculation, the peptide/membrane model encompassed a small percentage of the grid (10%) and the potentials at the boundary points of the grid are approximately zero; this procedure ensures that the system is electroneutral. The calculation of Gel for Lys-13 on a 2:1 PC/PS membrane in 0.1 M KCl employed focusing resolutions of 0.375, 0.75, 1.5, and 3.0 grid/A, each with a grid size of l3 = 2573. The precision in Gel is determined as the difference between the results obtained at the two highest resolution scales. This difference is much less than the value of the calculated free energy of interaction (<0.3 kcal/mol) for R > 1.5 Å and is 1–2 kcal/mol for R < 1.5 Å. Because the distance corresponding to the minimum electrostatic free energy is 2–2.5 Å, the orientations of minimum electrostatic free energy of interaction for the three peptides are well defined and reliable. The calculation of a full electrostatic free energy curve for Lys-13 on a 2:1 PC/PS membrane in 0.1 M KCl required 3 Gb of main memory and 80 h of CPU time on a Silicon Graphics Origin3400 (Mountain View, CA) with 500-MHz R14K processors. A tutorial on how to perform these calculations is available at our website: http://maat.med.cornell.edu/qnifft.html.
Basic peptides are placed in their minimum free-energy orientations at the surfaces of PC/PS membranes
Throughout this paper, we examine the electrostatic sequestration of PIP2 by three membrane-adsorbed basic peptides: Lys-7, Lys-13, and FA-MARCKS(151–175). We make the assumption that these peptides interact similarly with both PC/PS membranes and PC/PS membranes that contain PIP2, which is present at small concentrations (1%). In other words, it is assumed that the sequestration of PIP2 from "bulk" membrane to the vicinity of a membrane-adsorbed basic peptide does not change the membrane-associated state that the peptides are predicted to have in the absence of PIP2. In addition, in most of our calculations, we consider a single orientation of each peptide at the membrane surface, the orientation of minimum electrostatic free energy of interaction with pure PC/PS membranes as determined by the calculations described above. In all cases, the minimum electrostatic free energy of interaction occurred at distances, R, between the van der Waals surfaces of the peptide and membrane of 2.0–2.5 Å; throughout, we use R = 2.5 Å to depict the minimum free-energy orientation.
As shown in previous work on similar systems (Ben-Tal et al., 1996; Murray et al., 1998), a basic peptide experiences an increasing electrostatic attraction as it approaches the membrane surface from large distances. When the peptide is close to the membrane surface, the desolvation repulsion experienced by charged and polar groups on both the peptide and membrane dominates the electrostatic attraction. The balance of these two effects predicts that there is a minimum in the electrostatic interaction when the van der Waals surfaces of the peptide and membrane are separated by about the thickness of a layer of water (R 2.5 Å), i.e., when both molecules are essentially solvated. The exact location of these basic peptides has not been determined experimentally, but surface pressure measurements on monolayers show they do not penetrate the polar headgroup region, in contrast to peptides that contain both basic and aromatic residues. In all cases the minimum electrostatic free energy of interaction is predicted to be quite strong and ranges from -4 kcal/mol for Lys-7 and 5:1 PC/PS to -12 kcal/mol for Lys-13 and 2:1 PC/PS. In agreement with experiments (Ben-Tal et al., 1996), the electrostatic free energy of interaction becomes more favorable as the mol percent acidic lipid in the membrane increases and as both the number and density of basic residues in the peptide increases. An example of the minimum free-energy orientation of a peptide is depicted in Fig. 1 A where Lys-13 is docked parallel to and 2.5 Å above the surface of a 5:1 PC/PS membrane.
Calculation of the electrostatic free energy of the sequestration of a single PIP2 lipid by a membrane-adsorbed basic peptide
An example of the scheme followed for determining the electrostatic free energy of laterally sequestering a PIP2 from a region of bulk membrane to a region adjacent to or beneath a membrane-adsorbed basic peptide, Gel(PIP2), is illustrated in Fig. 1. The initial state of the system is composed of two equal-sized regions of membrane containing the same mol percent monovalent acidic lipid: one with a basic peptide (e.g., Lys-13) adsorbed to its surface (Gel(P·M); Fig. 1 A), and one with a single PIP2 lipid (Gel(PIP2·M); Fig. 1 B). Fig. 1, A and B, represent the situation in which PIP2 is "infinitely" far away from the membrane-adsorbed peptide. The final state of the system is also composed of two equal-sized regions of membrane containing the same mol percent monovalent acidic lipid: one with PIP2 in the vicinity of the membrane-adsorbed peptide (Gel(PIP2·P·M); Fig. 1 C), and one in the absence of PIP2 (Gel(M); Fig. 1 D). Fig. 1, C and D, represent the situation in which PIP2 is sequestered by the membrane-adsorbed basic peptide, leaving behind a region of bulk membrane. Gel(PIP2) is the difference between the electrostatic free energies of the models for the final state (Fig. 1, C and D) and the electrostatic free energies of the models for the initial state (Fig. 1, A and B) as determined by the FDPB method:
 | (2) |
As described above for Eq. 1, it is necessary to ensure that the molecules remain in the same location on the finite difference grid in both the initial and final states to subtract out the grid-dependent electrostatic self-energy. Gel(PIP2) was calculated for many different locations of PIP2 with respect to the membrane-adsorbed peptides as illustrated in Fig. 2. The dependence of Gel(PIP2) on both the mol percent monovalent acidic lipid in the membrane (either 5:1 PC/PS or 2:1 PC/PS) and the ionic strength of the solution was calculated.
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FIGURE 2 FDPB calculations suggest that PIP2 can associate with a membrane-adsorbed basic peptide through nonspecific electrostatic interactions in many different ways. The view is from above, looking down on the membrane. The peptides, FA-MARCKS(151–175) (A and B), Lys-13 (C and D), and Lys-7 (E and F), are colored cyan. The ovals represent the positions of lipids in the membranes with respect to the peptides. Each number is the calculated electrostatic free energy, Gel(PIP2), in kcal/mol, for sequestering a PIP2 lipid from bulk membrane, either 2:1 PC/PS (A, C, and E) or 5:1 PC/PS (B, D, and F), to a given position, either adjacent to or beneath the peptide, as shown. The peptides are located in their minimum free-energy orientations determined in the absence of PIP2 (see Methods). The positions highlighted in bold are further investigated in subsequent figures.
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Models for the Lys-7, Lys-13, and FA-MARCKS(151–175) peptides were built as described above. The peptides were docked at the surfaces of the PC/PS membranes in their minimum free-energy orientations determined in the absence of PIP2; i.e., it was assumed that the presence of PIP2 does not affect the membrane-associated states of the basic peptides. This assumption is reasonable because the minimum free-energy orientations of the peptides are similar for different mol percentages of PS and because we are modeling the experimental situation in which the basic peptides are bound to PC/PS vesicles that contain only a trace amount (e.g., 1 mol%) of PIP2. In addition, a search for the minimum electrostatic free energy of the peptide/PIP2/membrane system that accounts for the effect of PIP2 on the minimum free-energy orientation of the peptides for each of the conditions we examined would be computationally intractable due to technical considerations of the grid-dependent, electrostatic self-energy contribution (see discussions after Eqs. 1 and 2) and the computational expense of numerically solving the nonlinear PB equation (see below). Hence, except where noted, the basic peptides were parallel to and located at a distance R = 2.5 Å from the membrane surface.
Phospholipid membranes were constructed as described above except that a single PIP2 replaced a single PC or PS lipid to construct the membranes containing PIP2 (e.g., Fig. 1, B and C). We calculated Gel(PIP2) for most of the positions denoted schematically by ovals in Fig. 2, which, as illustrated, extend several lipid layers in the plane of the membrane beyond the imprint of the peptide on the membrane surface. To accurately calculate Gel(PIP2) and to fully account for the electrostatic interactions arising not only from the peptide but the surrounding lipid milieu, the membranes used in the calculations had to be large enough to extend several Debye lengths beyond the outermost lipid layers considered. This allowed each position denoted in Fig. 2 to be examined with sufficient bulk membrane surrounding the site of sequestration. For example, in the calculations of Gel(PIP2) with Lys-13, which is depicted in Fig. 1, we used membranes that contained 1400 lipids per leaflet. The smallest membrane required for our calculations should extend several Debye lengths (one Debye length is 10 Å in 0.1 M KCl) beyond the region of membrane encompassing all of the positions at which we calculate Gel(PIP2). In addition, we further increased the size of the membrane (by more than double) so that the computational grid would focus into the membrane at the two highest resolution scales to obtain good estimates for the electrostatic potential at the grid boundary. For Lys-13, this meant constructing membranes of 40 x 35 lipids per leaflet.
The coordinates for the PIP2 headgroup, Ins(1,4,5)P3 were taken from the experimentally determined structure of the Ins(1,4,5)P3-bound PH domain from PLC-1 (Ferguson et al., 1996; Protein Data Bank identifier 1mai). As stated above, the radii and partial charges for the headgroup were taken from similar functional groups from the CHARMM22 parameter set. To construct a full model for PIP2, Ins(1,4,5)P3 was docked onto the glycerol backbone and acyl chain region of a PC lipid. Because we are interested in the electrostatic properties of the membrane surface, structural details of the acyl chains of the lipids in our static membranes can be ignored. The net charge of PIP2 is -4. PIP2 was placed in a membrane at a particular position using the same procedure for building PC/PS membranes, as described above, so that the acyl chain region of the PIP2 lipid was aligned with the acyl chain region of the surrounding lipids. As the orientation of the PIP2 headgroup has not been determined experimentally, the PIP2 headgroup in our membrane models (yellow in Fig. 1) was placed on the lipid backbone in two limiting orientations. In the first orientation, the long dimension of the inositol ring was perpendicular to the membrane surface so that the PIP2 headgroup extends 4 Å beyond the van der Waals envelope of the PC/PS membrane. In the second orientation, the long dimension of the inositol ring was parallel to the membrane surface so that the PIP2 headgroup is within the van der Waals envelope of the PC/PS membrane. The latter orientation was used for calculations of Gel(PIP2) for positions beneath the membrane adsorbed peptides; PIP2 with the former orientation were sterically excluded from this region. The values of Gel(PIP2) calculated for a position adjacent to membrane-adsorbed Lys-13, illustrated in Fig. 1, are independent of the orientation, parallel or perpendicular to the membrane surface, of the PIP2 headgroup. In addition, we performed calculations in which the charge distribution on a PC lipid was adjusted so that the lipid had a net charge of -4. Calculations of the sequestration of this lipid, Gel(PC(z = -4)), to a position either adjacent to or beneath a membrane-adsorbed peptide differ from Gel(PIP2) by <-0.3 kcal/mol. These "control calculations" suggest that the calculated Gel(PIP2) is relatively insensitive to both the charge distribution and shape of the headgroup of PIP2, in agreement with the experimental evidence mentioned in the Introduction that suggests the sequestration is due to nonspecific electrostatic interactions.
As in the calculation of Gel (Eq. 1), a sequence of focusing runs was used to determine the electrostatic potentials on the finite difference grid from which the electrostatic free energies are derived. All values of Gel(PIP2) are precise to within 0.1 kcal/mol. The calculation of Gel(PIP2) for a single position in the vicinity of Lys-13, required a grid size of l3 = 2253, focusing resolutions of 0.3, 0.6, 1.2, and 2.4 grid/Å, and 2.2 h of CPU time on the SGI Origin3400. The calculation of Gel(PIP2) for a single position adjacent to FA-MARCKS(151–175), required a grid size of l3 = 2893, focusing resolutions of 0.3, 0.6, 1.2, and 2.4 grid/Å, and 6.3 h of CPU time on the Pittsburgh Supercomputing Center terascale computing system (PSC TCS), which contains 1-GHz Compaq Alphaserver ES45 (Palo Alto, CA) processors. The calculation of Gel(PIP2) for a single position beneath FA-MARCKS(151–175), required a grid size of l3 = 3373, focusing resolutions of 0.35, 0.7, 1.4, and 2.8 grid/Å, and 10.3 h of CPU time on the PSC TCS. Altogether, the production runs that produced the results in Fig. 2 alone required 1690 h or 70 days of CPU time.
Boltzmann-weighted averages of the electrostatic and entropic components to the sequestration of PIP2
We used the following relations to calculate the average electrostatic free energy of sequestration and the average entropic cost of PIP2 demixing:
 | (3) |
 | (4) |
where Q = 
(exp(-Gi/kBT) is the partition function, kB is the Boltzmann constant, T is the absolute temperature, Gj is the electrostatic free energy associated with PIP2 moving to position j in the membrane, and the sum is over all positions, j. Our standard state corresponds to a region of membrane which, on average, is occupied by one PIP2 in the absence of peptide. Therefore, when the membrane contains 1 mol% PIP2, we sum over 100 positions, and when the membrane contains 0.1 mol% PIP2, we sum over 1000 positions. The energetic and entropic costs for PIP2 sequestration by a membrane-adsorbed basic peptide are given by Gel = Gel(PIP2)2-Gel(PIP2)1, and GS = -T (S2 - S1), where Gel(PIP2)1 and S1 are the average electrostatic free energy and entropy of PIP2 in the initial state, i.e., in the absence of peptide (Fig. 1 B), and Gel(PIP2)2 and S2 are the average electrostatic free energy and entropy of PIP2 sequestration in the final state, i.e., in the presence of peptide (Fig. 1 C). In our model, we assume PC and PS are not redistributed, and hence there are no energy and entropy changes associated with these lipids. In the initial state, it is assumed for simplicity that Gj, the change in electrostatic free energy of PIP2 when it moves from one position in the bulk membrane to another, is 0, i.e., that all positions in the bulk membrane in the absence of peptide are of equal electrostatic free energy. In this case, Eq. 3 gives Gel(PIP2)1 = 0 and Eq. 4 reduces to S1 = -kB ln(1/N), where N = 100 for 1% PIP2 and GS1 = -2.73 kcal/mol, and where N = 1000 for 0.1% PIP2 and GS1 = -4.09 kcal/mol. For the calculation of Gel(PIP2)2 and S2 for the final state, the summations in Eqs. 3 and 4 are over the electrostatic free-energy values depicted in Fig. 2. However, the number of positions surrounding each peptide for which we calculate significant electrostatic free energy changes is less than the number of positions in our standard states, i.e., N = 100 and 1000. We assume that Gj = 0 for the required remaining positions and that PIP2 is essentially experiencing bulk membrane in the absence of peptide at these positions. The Boltzmann-weighted averages for the electrostatic free energy and entropic cost of PIP2 sequestration for the Gel(PIP2) values depicted in Fig. 2 are listed in Tables 1 and 2 for standard states corresponding to both 1% PIP2 and 0.1% PIP2.
Determination of the statistical significance of Gel(PIP2)
The free-energy values plotted in Fig. 3 and listed in Tables 1 and 2 are calculated from Boltzmann-weighted averages of the free-energy values determined from the calculations depicted in Fig. 2. We used the "bootstrap" method to determine the statistical significance of these values (Efron and Tibshirani, 1993). Simply put, the bootstrap is a method that uses data resampling to determine the trustworthiness of a statistic, in our case the Boltzmann-weighted average. The advantage of the bootstrap is that it leverages a limited data set to approximate the variability of a statistic about its unknown "true" value without making assumptions about the underlying distribution. The bootstrap calculates the statistic with M different subsamples. Each subsample is randomly drawn from the original data set with replacement, i.e., once a particular value is chosen, it is still included for selection in future draws. The result is then the mean and standard deviation of the M values for the statistic obtained from the M subsamples. For example, if 
is our original data set, with each xi corresponding to a different Gel(PIP2) value, then 
is a bootstrap sample obtained by sampling x randomly with replacement. We, thus, generate a large number (M = 1000) of bootstrap samples 
, each consisting of n Gel(PIP2) values. For each subsample, we calculate the Boltzmann-weighted averages as given in Eqs. 3 and 4. The mean and standard deviation of the M = 1000 values are plotted in Fig. 3.
Calculation of the electrostatic free energy of the sequestration of multiple PIP2 lipids by a membrane-adsorbed basic peptide
Fig. 6 illustrates schematically the sequential sequestration of several PIP2 lipids by a membrane-adsorbed basic peptide. For example, as depicted in Fig. 6 B, the first PIP2 lipid is sequestered to position 1, a second PIP2 is then sequestered to position 2, and so on. The calculated electrostatic free energy of sequestering a PIP2 to position 1 from bulk membrane is given by Gel(PIP2) in Eq. 2. The presence of the first PIP2 is expected to affect (i.e., increase) the electrostatic sequestration energy of the second PIP2 relative to its sequestration in the absence of other PIP2. Hence, each subsequent PIP2 is considered in succession, and its electrostatic free energy of lateral sequestration is calculated in the presence of the PIP2 lipids that were previously sequestered to their corresponding positions. The electrostatic free energy of placing a second PIP2 at position 2 in the presence of a PIP2 already at position 1 (Gel(2(PIP2)) is determined from the electrostatic free energies of initial and final states that are correspondingly different from those depicted in Fig. 1 and used in Eq. 2. In this case, although the initial state of the system is still composed of two equal-sized regions of membrane containing the same mol percent monovalent acidic lipid, one region contains a basic peptide adsorbed to its surface with a PIP2 already sequestered at position 1 (Gel(PIP2·P·M)), and the other contains a single PIP2 lipid (Gel(PIP2·M)) in position 2. This represents the situation in which the second PIP2 is in bulk membrane, far away from the first PIP2 and the membrane-adsorbed peptide. The final state of the system is also composed of two equal-sized regions of membrane containing the same mol percent monovalent acidic lipid, however, one region has a PIP2 at position 2 in the vicinity of the membrane-adsorbed peptide with the first PIP2 already at position 1 (Gel(2(PIP2)·P·M)), and the other region contains no PIP2 (Gel(M)), as in Eq. 2. This represents the situation in which the second PIP2 is sequestered by the membrane-adsorbed basic peptide in the presence of the first PIP2, leaving behind a region of bulk membrane. Gel(2(PIP2) is the difference between the electrostatic free energies of the models for the final state and the electrostatic free energies of the models for the initial state as determined by the FDPB method:
 | (5) |
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FIGURE 6 Representative configurations used in the calculation of the sequestration of multiple PIP2 lipids by membrane-adsorbed basic peptides: FA-MARCKS(151–175) (A), Lys-13 (B), and Lys-7 (C). The view is from above, looking down on the membrane. The scheme reflects the sequential partitioning of PIP2 lipids from bulk membrane to the positions labeled in the order given by the numbering. Illustrations representing the other configurations examined in this work are included with the supplementary material.
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More generally, to calculate the electrostatic free energy of sequestration of the nth lipid to the vicinity of a membrane-adsorbed peptide when (n - 1) PIP2 are already sequestered, we use FDPB calculations and a scheme based on the following relationship:
 | (6) |
Gel(n(PIP2)) was calculated for many different configurations of PIP2 lipids with respect to the membrane-adsorbed peptides as illustrated in Fig. 6 and the supplementary material. Membranes with two surface concentrations of monovalent acidic phospholipid were considered (5:1 PC/PS and 2:1 PC/PS). We make the assumption that there is an infinite reservoir of PIP2, present at 1 or 0.1 mol%, so that when one or more PIP2 are bound, the number of PIP2 per area of membrane in the bulk does not change. Therefore, we estimate that the increase in the free-energy penalty associated with the entropy of lipid demixing in the presence of other PIP2 is small, and, hence, we approximate the change in free energy due to lipid demixing when n PIP2 are sequestered as n·GS(PIP2) (see Tables 1–3).
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RESULTS
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Nonspecific electrostatic interactions provide a driving force for the lateral sequestration of PIP2 by membrane-adsorbed basic peptides
We used the FDPB method to calculate the electrostatic free energy associated with moving a PIP2 to the vicinity of a membrane-adsorbed basic peptide, Gel(PIP2) (see Fig. 1). Through the use of atomic models, the calculations account for the shape and charge distribution of the interacting species and, consequently, the effect that PIP2 and the peptide have on each other's electrostatic potentials as well as the desolvation repulsion that may occur upon association. Fig. 1 illustrates a representative example of the peptide/membrane models used in the calculation of Gel(PIP2). Panels A and B depict the initial state of the system in which a basic peptide (Lys-13, cyan) that is docked at the surface of a 5:1 PC/PS membrane (PC, white; PS, red) in its minimum free-energy orientation (see Methods) and a PIP2 lipid (yellow) are infinitely far apart. Panels C and D depict the final state of the system in which the PIP2 is moved from "bulk" membrane to a position in the vicinity of the peptide, i.e., PIP2 is "sequestered" by the membrane-adsorbed basic peptide (denoted by the arrow in panels A and B). Gel(PIP2) is the difference of the electrostatic free energies of these final and initial states. Fig. 2 summarizes the results of many calculations, each of which corresponds to the sequestration of PIP2 to a different position in the membrane with respect to the peptide. The peptides (cyan) are located in their minimum free-energy orientations as determined for the corresponding PC/PS membrane (2:1 or 5:1). Lipid positions in the plane of the membrane are denoted schematically as ovals. Values for Gel(PIP2) are reported in kcal/mol at the locations to which a single PIP2 lipid is sequestered. Each value is precise to within 0.1 kcal/mol as judged by the difference in Gel(PIP2) for the two highest resolution scales from the focusing calculations (see Methods). As described in the sections below, our calculations support the hypothesis that nonspecific electrostatic interactions are a significant driving force for PIP2/peptide colocalization (McLaughlin et al., 2002; Wang et al., 2002; Haleva et al., 2004; Gambhir et al., 2004).
No effort was made to optimize Gel(PIP2) for the many calculations we performed (see Methods). Specifically, we assumed that both the orientation of the peptide with respect to the membrane and the distribution of PS are unaffected by the presence of PIP2. In the several cases we tested, it was possible to decrease Gel(PIP2) by up to 0.5 kcal/mol through optimizing the lateral distance between the membrane-adsorbed peptide and PIP2 by moving the peptide in a plane parallel to the membrane surface with respect to a specific position of PIP2, denoted schematically by an oval in Fig. 2. The vertical distance of the peptide from the membrane surface also affects Gel(PIP2); see Fig. 5, below.
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FIGURE 5 The electrostatic free energy of sequestration of PIP2 decreases as the distance between FA-MARCKS(151–175) and the membrane decreases. The position to which PIP2 is sequestered is shown as a bold black oval in panels A and B of Fig. 2. The calculations represented on the left were performed for the peptide FA-MARCKS(151–175) in its minimum electrostatic free-energy orientation for which the distance between the van der Waals surfaces of the peptide and membrane (R) is 2.5 Å. The calculations represented on the right were performed for R = 0 Å. The calculations examined three different lipid compositions in 0.1 M KCl: 2:1 PC/PS (black bars), 5:1 PC/PS (gray bars), and 1:0 PC/PS (white bars).
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There are many energetically equivalent sites for PIP2 in the vicinity of a membrane-adsorbed basic peptide
As depicted in Fig. 2, Gel(PIP2) for many different positions with respect to a membrane-adsorbed peptide is significant, i.e., more favorable than thermal energy, which is 0.6 kcal/mol at T = 298 K. For example, in Fig. 2 D, which contains the results of calculations with Lys-13 on 5:1 PC/PS, Gel(PIP2) < -0.6 kcal/mol for at least 40 positions and <-2.0 kcal/mol for at least 20 positions. In this case, Gel(PIP2) is most negative for positions directly beneath the peptide (e.g., -4.4 kcal/mol), but is also significant (e.g., -0.9 kcal/mol) for positions even two lipid layers away from the imprint of the peptide on the membrane surface. This suggests that PIP2 can sample over 3000 Å2 of the surface of a 5:1 PC/PS membrane in the vicinity of an adsorbed Lys-13 peptide and experience a significant electrostatic attraction to the peptide. For all cases depicted in Fig. 2, the calculations suggest that nonspecific electrostatic interactions contribute to the recruitment of PIP2 to regions that contain a membrane-adsorbed peptide.
The electrostatic free energy of PIP2 sequestration is in excess of the entropic penalty for PIP2 localization
Because the electrostatic association of a PIP2 with a membrane-adsorbed peptide is not specific, i.e., there are many energetically equivalent ways in which PIP2 may interact with the peptide, the free energy loss due to lipid demixing upon the sequestration of a PIP2 from bulk membrane to a localized region, GS, is expected to be relatively small. The Boltzmann-weighted averages of the electrostatic free energy of PIP2 sequestration and the free energy of PIP2 demixing for the six conditions illustrated in Fig. 2 are depicted in Tables 1 and 2 for membranes containing 1 mol% PIP2 (Table 1) and 0.1 mol% PIP2 (Table 2). As suggested by the values for Gel(PIP2) in Fig. 2, the entropic cost is greatest in those cases for which the electrostatic sequestration is most favorable. For example, for membranes containing 1 mol% PIP2, Gel(PIP2) = -3.8 kcal/mol and GS = +1.2 kcal/mol for Lys-13 on 5:1 PC/PS, whereas Gel(PIP2) = -0.7 kcal/mol and GS = +0.2 kcal/mol for FA-MARCKS(151–175) on 2:1 PC/PS. As depicted by the bar graph in Fig. 3 A, Gel(PIP2) (gray and black bars) is in significant excess of GS (white bars) leading to a favorable net free energy (Fig. 3 B) for most conditions when the membrane contains 1 mol% PIP2. However, as depicted in Table 2 the entropic cost is a much greater proportion of the magnitude of the electrostatic sequestration free energy for membranes containing 0.1 mol% PIP2, and in this case, our calculations predict that PIP2 would be, at best, only weakly sequestered.
The electrostatic free energy of PIP2 sequestration depends on both the net charge and linear charge density of the peptide
Fig. 3 summarizes the data presented in Fig. 2. The Boltzmann factor-weighted averages of the free energies, i.e., Gel(PIP2) in Fig. 3 A and Gel(PIP2) + GS in Fig. 3 B, were calculated for each of the conditions examined: three basic peptides and two membrane compositions. The mean values and errors depicted in Fig. 3 were determined statistically as described in Methods. Overall, considering either electrostatic interactions alone (Fig. 3 A) or both electrostatic and entropic contributions (Fig. 3 B), the PIP2 sequestration free energy is predicted to be most favorable for Lys-13 and similar in the cases of FA-MARCKS(151–175) and Lys-7. That Lys-13 is predicted to sequester PIP2 more strongly than FA-MARCKS(151–175) agrees with what is observed experimentally and suggests that the linear charge density of the peptide is an important determinant because both peptides have a net charge of +13 (Gambhir et al., 2004). Our calculations also predict that PIP2 is sequestered significantly more strongly by Lys-13 than Lys-7 and, hence, that the net charge of the peptide is also an important determinant. The experiments, however, indicate that PIP2 interacts strongly with both Lys-7 and Lys-13 (Gambhir et al., 2004). Possible reasons for this discrepancy are considered in the Discussion section.
The electrostatic free energy of PIP2 sequestration decreases as the net charge of the lipid becomes more negative
PIP2, in its fully unprotonated state, has a net charge of -5. Experiments indicate that, at pH 7.0, at least one proton is bound to the phosphate at either the 4 or 5 position of the inositiol ring (van Paridon et al., 1986). Hence, under physiological conditions, PIP2 may have a net charge between -3 and -5 (Toner et al., 1988; McLaughlin et al., 2002). For most of the calculations presented in this report, we assume that z = -4. However, our calculations predict that the electrostatic sequestration is sensitive to the net charge of PIP2. For example, for sequestration to the position demarcated by the bold blue oval in Fig. 2 D, PIP2 lipids with a valence of -3, -4, and -5 are predicted to have electrostatic sequestration free energies of -2.3, -3.5, and -4.4 kcal/mol, respectively. Thus, phosphoinositides with a higher negative charge, e.g., phosphatidylinositol 3,4,5-trisphosphate (PIP3), should be sequestered even more strongly than PIP2. On the other hand, the dependence on net charge is weaker for more peripheral positions: For the position demarcated by the bold black oval in Fig. 2 D, Gel(PIP2) decreases by only 0.8 kcal/mol when the net charge is decreased from -3 to -5. Importantly, PIP2 with z = -4 is sequestered to this same position significantly more strongly than PS (z = -1); Gel(PIP2) is -2.9 kcal/mol whereas Gel(PS) is only -1.0 kcal/mol.
The electrostatic free energy of PIP2 sequestration increases as the mol percent PS in the membrane increases
Fig. 2 presents Gel(PIP2) for each of the three peptides on both a 5:1 and 2:1 PC/PS membrane. Comparisons of panels A, C, and E with panels B, D, and F, respectively, show that Gel(PIP2) is consistently more favorable when the bulk membrane contains 5:1 PC/PS. This prediction agrees with experimental observations (see Figs. 7 B and 11 from Gambhir et al., 2004). Fig. 3 plots Gel(PIP2) and Gel(PIP2) + GS for the calculations depicted in Fig. 2. The free energy of PIP2 sequestration decreases by 1 kcal/mol for all peptides when the mol percent PS in the membrane decreases from 33 (black bars) to 17 (gray bars). The basis for the difference in Gel(PIP2) as a function of membrane composition is considered in more detail in the Discussion section.
The electrostatic free energy of PIP2 sequestration increases as ionic strength of the aqueous phase increases
Fig. 4 depicts the ionic strength dependence of Gel(PIP2) for sequestration to the two positions in the vicinity of Lys-13 denoted by bold ovals in Fig. 2, C and D. As expected for an electrostatic interaction and in agreement with experiments (see Fig. 9 from Gambhir et al., 2004), Gel(PIP2) increases as the ionic strength increases. When [KCl] = 0.3 or 0.5 M, Gel(PIP2) is significantly less favorable than the values at [KCl] = 0.1 M.
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FIGURE 4 The electrostatic free energy of sequestration of PIP2 from bulk membrane to a position either adjacent to (circles) or beneath (squares) a membrane-adsorbed Lys-13 peptide increases as the ionic strength increases. The open and filled symbols represent calculations of Gel(PIP2) for 5:1 and 2:1 PC/PS, respectively. The two positions to which PIP2 was sequestered are represented by bold ovals in panels C and D of Fig. 2.
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The electrostatic free energy of PIP2 sequestration decreases as the distance between peptide and membrane decreases
Recent spectroscopic studies reveal that the phenylalanine residues in a peptide based on the MARCKS effector domain, MARCKS(151–175), penetrate into the acyl chain region of phospholipid vesicles (Qin and Cafiso, 1996; Rauch et al., 2002; Zhang et al., 2003; Ellena et al., 2003). (The peptide we consider here, FA-MARCKS(151–175), has alanines in place of the phenylalanines and is not expected to appreciably penetrate the membrane interface.) We are unable to satisfactorily model the membrane interaction of MARCKS(151–175) with our static peptide and membrane models. However, we can roughly approximate the effect that MARCKS(151–175) has on the electrostatic properties of membranes by docking the FA-MARCKS(151–175) peptide at the surface of our bilayer models so that the van der Waals surfaces of peptide and membrane are just touching (R = 0 Å). Fig. 5 shows how Gel(PIP2) decreases as the distance between the peptide and membrane decreases. Specifically, the electrostatic free energy of sequestering PIP2 to a position adjacent to FA-MARCKS(151–175) (bold ovals in Fig. 2, A and B) decreases by 0.5–1.0 kcal/mol for 2:1, 5:1, and 1:0 PC/PS membranes when the distance between peptide and membrane decreases from 2.5 Å (the distance corresponding to the minimum electrostatic free-energy orientation of FA-MARCKS(151–175)) to 0 Å. This is consistent with the stronger sequestration of PIP2 by MARCKS(151–175) versus FA-MARCKS(151–175) observed experimentally (Gambhir et al., 2004). Localizing basic residues more closely to the membrane interface increases their positive potential profile due to a combination of image charge effects and a perturbation of the diffuse double layer, as explained in our companion paper (Gambhir et al., 2004), and, thus, provides a stronger electrostatic driving force for PIP2 sequestration.
The electrostatic free energy of PIP2 sequestration is strongly dependent on the solution of the nonlinear versus linear Poisson-Boltzmann equation
The linearized version of the Poisson-Boltzmann equation is applicable only when the electrostatic potentials are small compared to 1 kBT/e, i.e., for low fixed charge densities (McLaughlin, 1989; Sharp and Honig, 1990b; Misra and Honig, 1995). This is not the case for the systems we are examining here. As illustrated below in Fig. 8, the -1 kBT/e or -25 mV equipotential profiles of 2:1 PC/PS and 5:1 PC/PS in 0.1 M KCl extend appreciably into the aqueous phase. Furthermore, the basic peptides produce regions of strong positive potential. Hence, the concentration of monovalent ions is quite high in the vicinity of the peptide and membrane, which constitutes another regime, i.e., high ionic strength, in which the linear PB equation breaks down. When inappropriately applied, the linear theory predicts erroneously large electrostatic potentials. Previous work showed that solution of the full nonlinear PB equation is required to accurately reproduce the electrostatic equipotential profiles of membranes containing acidic phospholipids (Peitzsch et al., 1995). In addition, other computational work showed that the salt-dependent terms obtained from solutions to the nonlinear PB equation constitute 30% of the electrostatic free energy of interaction of a Lys-5 peptide with 2:1 PC/PS in 0.1 M KCl (Ben-Tal et al., 1996). Here, we find an even more dramatic effect: Gel(PIP2) is 5 kcal/mol more positive when the nonlinear versus the linear PB equation is solved, i.e., the linear PB treatment p
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ABSTRACT
INTRODUCTION
