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Effects of Concentration and Ionization Degree of Anchoring Cationic Polymers on the Lateral Heterogeneity of Anionic Lipid Monolayers Xiaozheng Duan,† Yang Zhang,‡ Liangyi Li,† Ran Zhang,† Mingming Ding,*,† Qingrong Huang,§ Wen-Sheng Xu,*,∥,⊥ Tongfei Shi,*,† and Lijia An† †

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China ‡ Northeast Normal University, Changchun 130024, P. R. China § Department of Food Science, Rutgers University, 65 Dudley Road, New Brunswick, New Jersey 08901, United States ∥ James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States S Supporting Information *

ABSTRACT: We employed coarse-grained Monte Carlo simulations to investigate a system composed of cationic polymers and a phosphatidyl-choline membrane monolayer, doped with univalent anionic phosphatidylserine (PS) and tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP2) lipid molecules. For this system, we consider the conditions under which multiple cationic polymers can anchor onto the monolayer and explore how the concentration and ionization degree of the polymers affect the lateral rearrangement and fluidity of the negatively charged lipids. Our work shows that the anchoring cationic polymers predominantly bind the tetravalent anionic PIP2 lipids and drag the PIP2 clusters to migrate on the monolayer. The polymer/PIP2 binding is found to be drastically enhanced by increasing the polymer ionization fraction, which causes the PIP2 lipids to form into larger clusters and reduces the mobility of the polymer/PIP2 complexes. As expected, stronger competition effects between anchoring polymers occur at higher polymer concentrations, for which each anchoring polymer partially dissociates from the monolayer and hence sequesters a smaller PIP2 cluster. The desorbed segments of the anchored polymers exhibit a faster mobility on the membrane, whereas the PIP2 clusters are closely restrained by the limited adhering cationic segments of anchoring polymers. We further demonstrate that the PIP2 molecules display a hierarchical mobility in the PIP2 clusters, which is regulated by the synergistic effect between the cationic segments of the polymers. The PS lipids sequester in the vicinity of the polymer/PIP2 complexes if the tetravalent PIP2 lipids cannot sufficiently neutralize the cationic polymers. Finally, we illustrate that the increase in the ionic concentration of the solution weakens the lateral clustering and the mobility heterogeneity of the charged lipids. Our work thus provides a better understanding of the fundamental biophysical mechanism of the concentration gradients and the hierarchical mobility of the anionic lipids in the membrane caused by the cationic polymer anchoring on length and time scales that are generally inaccessible by atomistic models. It also offers insight into the development and design of novel biological applications on the basis of the modulation of signaling lipids. for the field of medicine, as the anchoring procedure is a key issue in the development of drug delivery.4,5 However, a deep molecular-scale understanding of the anchoring of cationic polymers onto lipid monolayers remains a challenge. The past decades have witnessed the development of some important experimental techniques for understanding molecular arrangements in polymer/lipid complexes, including

1. INTRODUCTION Anchoring of peripheral cationic polymers, such as “natively unfolded” proteins or polypeptides onto phosphatidyl-choline (PC) lipid membranes doped with multivalent phosphatidylinositol 4,5-bisphosphate (PIP2) and univalent phosphatidylserine (PS) anionic lipids, has been the subject of intense studies because of its significance in many biological activities. Investigating the spatial reorganization of anionic lipids on the membrane caused by polymer anchoring is critically important in many distinct physiological processes.1−3 A complete understanding of this phenomenon is also relevant © XXXX American Chemical Society

Received: December 8, 2016 Revised: January 22, 2017 Published: January 23, 2017 A

DOI: 10.1021/acs.jpcb.6b12386 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B fluorescence resonance energy transfer, self-quenching and phospholipase C enzyme-activity measurements, transmission electron microscopy, electron paramagnetic resonance, nuclear magnetic resonance, neutron reflectivity, and so forth.1,2,5−9 These experimental techniques probe the system via different observables to provide complementary views of the properties of the complexes. For example, it was revealed that the anchoring polymers on the membrane interface can extensively sequester the anionic lipids and thereby restrain their mobility.6,7 In addition, the large electrostatic energy gain and the small demixing entropy penalty of the tetravalent PIP2 (constituting about 1% of all lipids) enable it to preferentially cluster underneath the anchoring polymers, while the sequestering of univalent PS (constituting about 10−20% of all lipids) is much less significant, indicating that the interactions between anionic lipids and polymers are modulated by the charges of the lipid headgroups.8 However, probing the polymer/membrane complexes directly in experiments becomes quite challenging because of the quick turnover/ hydrolysis natures of the charged lipids in the membrane.1 Access to high-performance computers and the development of new algorithms also allow for more accurate simulations of polymer/membrane interactions, shedding new light on these interfacial processes. For example, atomistic molecular dynamics simulations have been performed to explore the interactions between positively charged polyelectrolytes and model membranes consisting of zwitterionic and negatively charged phospholipids.10 The all-atom simulations can provide detailed information; however, these simulations introduce more parameters and thus much higher criteria are required for the justification of the models. Moreover, sampling also remains significantly challenging because of the limited time and length scales of these simulations.4 To overcome these limitations, novel coarse-grained models were also developed to elucidate the physicochemical natures of the polymer/membrane interactions.4,11−26 These simulations serve as a universal and robust strategy to explore the system on length and time scales beyond the range of chemically detailed models. In previous work, we designed a simple Monte Carlo (MC) model for the complex of a single polyelectrolyte and a mixed monolayer, by which we extensively analyzed the effects of polymerization degree and the rigidity of the polyelectrolyte as well as the influence of the saline solution on the polyelectrolyte/ membrane interactions.27−32 Our predictions for some key phenomena associated with these interactions, such as the sequestering and fluidity heterogeneity of the charged lipids as well as the polyelectrolyte anchoring, have been shown to be consistent with recent extensive experimental studies.6,9 The anchoring of charged polymers effectively alters the structural and dynamic properties of the oppositely charged lipids, which affects the normal functions of the membrane and further enables the relevant technological applications involving the delivery of natural or synthetic polymers on the membrane. Concerning the associations between cationic polymers and anionic lipid membrane, the effects of two important factors on the properties of the complexes remain unclear. The first factor is the ionization fraction of the cationic polymers. In fact, it is ubiquitous that the peripheral biopolymers have different fractions of (positively charged) basic residues.1 For example, the ionization fractions for MARCKS (154−171), MARCKS (151−175), GAP43 (30−56), and EGFR (645−660) are 7/17, 13/24, 11/26, and 8/15, respectively.1 The second factor concerns the concentration of the cationic polymers. In general,

the concentration of the peripheral biomacromolecules that can anchor on the anionic lipid membrane in cells ranges from 1 to 10 × 10−6 [mol/dm3],1 which is apparently different at various positions in vivo. For instance, the GAP43 presents a higher concentration in some regions (such as the axonal growth cones of neurons) in the cell than other peripheral cationic biopolymers.1,33 In principle, any cationic polymer with a cluster of positively charged groups can be electrostatically anchored by the tetravalent anionic lipids on the membrane. Hence, in addition to the natively unfolded proteins, synthetic cationic polymers are very useful for exploring the fundamental mechanism of anionic lipid heterogeneity in both experiments and simulations.6,34−37 Evidently, both the polymer ionization degree and polymer concentration can change the entropy− energy balance of the system; hence, important properties, such as the sequestering extent and fluidity restriction of the negatively charged lipids in the membrane, are expected to be strongly affected by these factors. While experimental studies1,33 have generated some important results for the influence of polymer ionization degree and polymer concentration on the properties of polymer/membrane complexes, it is generally difficult to fine-tune these molecular parameters in experiment, leaving their effects on sequestering and dynamical heterogeneity of the anionic lipids largely unexplored. This lack of understanding hampers the progress in the design and development of more effective charged polymer materials for biological applications. In this article, we address the above issues by performing coarse-grained MC simulations. We consider a system of positively charged polymers and a monolayer membrane composed of PIP2, PS, and PC lipids. By simplifying the detailed molecular structures of the lipids and polymers, our coarse-grained simulations can explore the system on time and length scales relevant to the interactions between multiple polymers and the mixed lipid membrane. This allows us to extensively explore the effects of the cooperation between the cationic segments of each polymer with different ionization degrees and the effects of the competitions between the anchoring polymers on the lateral sequestering and corresponding mobility of the charged lipids, thereby providing a better understanding of the biophysical mechanism and offering insight into the innovation of novel biotechnologies for signaling-lipid modulation.36,38−42 In Section 2, we briefly depict our MC model and the detailed parameters in the simulation. In Section 3, we analyze the effects of the concentration and ionization degree of the anchoring cationic polymers on the sequestering of different anionic lipids. Further, we explore how these factors affect the mobility of the lipid clusters and elucidate the hierarchical mobility of single lipids in the clusters. In Section 4, we summarize our results and provide the conclusions.

2. MODEL AND SIMULATION DETAILS Polymer/membrane interactions can be studied with the aid of atomistic molecular dynamics simulations to complement the experiments because of the limitations in experimental techniques for lipid membranes. These atomistic simulations provide a detailed description of the system under study; however, they require strict justifications for modeling parameters and greatly increased the computational costs. Consequently, the systematic study for the effects of different molecular factors on the system properties remains challenging. Recently, the progress in simulating polymer/membrane B


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The Journal of Physical Chemistry B complexes has been extensively reviewed by Rossi et al.,4,43 where the strengths and shortages of atomistic simulations and simple coarse-grained simulations are discussed in detail. Because of our current interest in elucidating the fundamental mechanism of the polymer/membrane interactions, we employ a very simple coarse-grained model to investigate the system, which can access length and time scales beyond the range of detailed models. Our model includes positively charged polymers and a mobile lipid membrane composed of charge-neutral and negatively charged lipids. We design this MC model on the basis of our previous works27−32 and other references,15,18 which is described below, along with an introduction to the simulation method. Because we focus on the interactions between the lipid membrane and cationic polymers rather than specific proteins, we model each cationic polymer as a freely jointed chain.44 Despite its very simplified nature, this model is expected to capture the basic characteristics of real polymers. The polymerization of the chain is N = 20, with each polymer segment coarse-grained as a hard sphere. The diameter (d) of each segment is set to 8.66 Å, and the bond length of the polymer is also equal to d. The fraction of the cationic segments in each polymer is set to be f, and each cationic segment has a positive charge at its center. Given the fact that our model is clearly rather idealized, it is difficult to make a quantitative comparison between the polymer and any specific protein; therefore, each polymer may represent a polypeptide with basic residues in our model. We consider the lipid membrane as a monolayer containing 2500 phospholipid headgroups, which are coarse-grained as 50 × 50 disks hexagonal closely packed on an impenetrable planar surface that resides at z = 0. In the monolayer, the phospholipids include electronically neutral PC (ZPC = 0), tetravalent PIP2 (ZPIP2 = −4), and univalent PS (=−1) molecules as mentioned in Section 1, where ZPC, ZPIP2, and ZPS are the valences of the lipid headgroups. The charges of the headgroups are placed at the center of the disks. We set the diameter (d) of each lipid headgroup to 8.66 Å and hence the area of each disk is 65 Å2. We cast the potential energy functional of the system into the general form U = UA + UB + UNB

and the anionic lipids on the monolayer) via the Debye− Hückel approximation uel(rij) = ZiZjlB

rij

(3)

where rij denotes the separation distance between charged particles i and j, Zi represents the valence of the particle i, and lB = 7.14 Å is the Bjerrum length for water at room temperature. In eq 3, the Debye screening length (κ−1) is expressed as κ −1 =

1 1000e 2NA ∑i

Zi2C i ε0εrkBT

(4)

where e denotes the elementary charge, NA represents Avogadro’s constant, Zi = 1 denotes the valence of the univalent ions, and εr represents the relative dielectric constant (εr = 78.5 for the solution and εr = 2 for the monolayer).16,17 We report the length and energy in units of d and kBT, respectively. In the simulation, we implement the periodic boundary conditions in the x and y directions parallel to the monolayer and consider the z direction to be infinite. We put the polymers on the monolayer and randomly generate charged lipids on the lattice, where the empty sites are occupied by neutral PC lipids. To mimic the dynamic properties of the complex, we model the motion of an anionic lipid in the monolayer with respect to the Kawasaki algorithm18,45,46 by swapping it with a randomly selected neighboring lipid, which has proven to be effective to simulate the lipid movement. Hence, the distance for the trial position update of each anionic lipid is d. In addition, we simulate the motion of the polymers through kink-jump, crankshaft, and translation for partial chain,47 which is compatible to that for an anionic lipid. In every MC step, we perform the trial position updates for all polymer segments and all negatively charged lipids in accordance with the Metropolis algorithm.48 These trial movements allow us to avoid dynamic trapping of the complex, which otherwise would result in a reliable mobility for both the lipid and the polymers.28,29,31,32 We first employ 106 MC steps (MCs) athermal relaxation to wipe off the artifact caused by the initial configuration, within which we confine the polymers to move above the monolayer interface. We then employ 2 × 106 MCs for the system relaxation, within which the polymers interact with the lipid membrane through UNB in eq 2. This procedure is tested to be sufficiently long for system equilibration and energy minimization. Further, we perform another 2 × 106 MCs athermal relaxation for ensemble average. For each parameter set, we perform 20 parallel simulations to improve the statistics. Because the polymer represents the polypeptide with positively charged residues, it is natural to distribute charge on a freely jointed chain to account for the ionization fraction of the polypeptide. We thus vary the segmental ionization fraction ( f) of the polymers in the range of 0.33, 0.5, 0.7, 0.75 to 1.0. Furthermore, we change the number of polymer chains (Nc) from 2, 4, 8 to 16 and calculate the polymer concentration (Cp) according to Cp = Nc/Am, where Am denotes the area of the monolayer; therefore, the polymer concentration (Cp) ranges from 0.00092, 0.00185, 0.0037 to 0.0074 [d−2]. These polymer concentrations can also be converted into 2.05 × 10−11, 4.09 × 10−11, 8.18 × 10−11, and 1.64 × 10−11 [mol/dm2], respectively. We consider several compositions of the monolayers, including PC/PS/PIP2 = 98:1:1 (YPC = 2450,

(1)

where UA and UB denote the energy terms for the bond angle variation and the bond fluctuation of the polymers, respectively. In the current work, we consider the polymers as flexible chains with fixed bond length of d; therefore, both UA and UB are equal to zero. UNB designates the nonbonding energy, which includes the hard-sphere potential (UHS) and electrostatic potential (UE) UNB = UHS + UE

exp( −κrij)

(2)

We employ the hard-sphere potential to account for the impenetrability of the membrane and the excluded volume of the polymer segments. In addition, we immerse the complex in a 1:1 univalent salt solution with the ionic concentration of Ci. The solvent and the ions are treated implicitly in the model. To account for the overall screening effect from the saline solution, we calculate the electrostatic potential between charged particles (including the cationic segments of the polymers C


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with the segmental fractions ( f) of 0.5 and 1.0 in Figure 1a,b, respectively. The polymer concentration (Cp) is fixed at

YPS = 25, and YPIP2 = 25), PC/PIP2 = 99:1 (YPC = 2475 and YPIP2 = 25), and PC/PS/PIP2 = 89:10:1 (YPC = 2225, YPS = 250, and YPIP2 = 25), where YPC, YPS, and YPIP2 denote the number of PC, PS, and PIP2 lipids in the monolayer, respectively. As the investigations on the monolayer with PC/PIP2 = 99:1 allow us to explore the effects of anchored polymers on the sequestering and mobility of the PIP2 molecules, we can further compare PS and PIP2 by detecting polymer anchoring on the membrane with PC/PS/PIP2 = 98:1:1. In addition, the monolayer of PC/ PS/PIP2 = 89:10:1 can represent the case with realistic lipid ratios.15,17 Because of the similar general trends of the static and dynamic properties examined in our study for these different lipid compositions, we mainly focus on the system with PC/ PS/PIP2 = 98:1:1. We are interested in the lateral sequestering and mobility of the monolayer caused by polymer anchoring in this study; therefore, we focus on the systems with ionic concentration (C i ) set at 0.01 M. Under this ionic concentration, polymers with different ionization degrees can adsorb onto the monolayer. In Section 3, we also discuss the effects of the saline solution on the structural and dynamic properties of the polymers/monolayer complex. This dynamic model allows us to calculate the mean square displacement (MSD) of the polymers and the anionic lipids, by which we can determine whether the anionic lipids are sequestered. In the previous studies,28,29 we showed that the cationic polymer can cause different sequestrations for multivalent and univalent anionic lipid species and thus reduce their translational mobility, which is confirmed by recent experimental studies.6,9 We have also found that a highly charged flexible polyelectrolyte anchoring on the mixed lipid membrane exhibits a mobility of mpc ∝ N−1 (N is the chain length of the polyelectrolyte), which is also observed experimentally.49 These results demonstrate the validity of our model for elucidating the fundamental physical mechanisms of the polymer/monolayer interaction. For this simple coarsegrained model, it is also important to point out its limitations. First, we neglect the detailed molecular structures of the lipid molecules and the anchoring polymers. Second, we calculate the MSD of the polymers and the anionic lipids to determine lipid sequestration. Although it has proven to be an effective strategy for exploring the dynamic properties of the polymer/ membrane complex in equilibrium state,28,29,31,32 the MC steps cannot be considered for real-time measurements. Third, we employ the Debye−Hückel approximation to account for in the electrostatic interaction. Although this method is widely accepted,12,15,17,27,30 it ignores the effects of ionic correlations of the saline solution.50−52 Given that our model can successfully explore polymer/membrane interactions in the equilibrium state on larger length and time scales compared to those of the atomic models, we expect that the above simplifications in our model can be justified and do not qualitatively alter the following results and conclusions.

Figure 1. Equilibrated configurations of the polymer/monolayer complexes for the case of Cp = 0.0037 and PC/PS/PIP2 = 98:1:1. Green and violet spheres denote the cationic and charge-neutral segments of the polymers, respectively; red, blue, and yellow spheres denote the headgroups of PIP2, PS, and PC lipids, respectively. The segmental ionizations ( f) of the polymers are set to be (a) 0.5 and (b) 1.0, respectively.

0.00185, and the composition of the monolayer is PC/PS/ PIP2 = 98:1:1. These results are simply used to show the lipid heterogeneity caused by the interfacial anchoring of cationic polymers. Next, we provide a detailed analysis of the effects of these molecular factors on the lateral rearrangement and dynamics of the anionic lipid species. 3.1. Lateral Sequestering of Anionic Lipids. In contrast to the charged polymer binding onto uniformly charged interfaces, the positively charged polymers anchored on the membrane monolayer can attract the mobile negatively charged lipids, thereby resulting in the spatial sequestering and fluidity restriction of the charged lipids. In previous studies, it has never been assessed systematically how the competitions between the polymers with different synergistic effects of connected cationic segments contribute to the lipid sequestering. To characterize the lipid heterogeneity, we distinguish the “sequestered” charged lipid from the “freely diffusing” one underneath an anchoring polymer using the method described in our previous works.28,29,31,32 For each polymer/lipid complex, we define

3. RESULTS AND DISCUSSION Lipid membranes are essential for biological functions, such as the communications between the cells and the organism, which depend on the structural and dynamic heterogeneity of the lipid species. In this section, we explore the effects of concentration and ionization fraction of the anchoring polymers on the lateral redistribution and mobility restriction of the negatively charged lipids. As an illustration, we display the equilibrated configurations of the monolayer anchored by cationic polymers D


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Figure 2. Ratio (φs) of the sequestered PIP2 to PS lipids in the interaction zones of the anchoring polymers and the amount (Ms) of these anionic lipids in the zones of each anchoring polymer. The segmental ionization fraction (f) varies from 0.3 to 1.0. The polymer concentration ranges from (a) Cp = 0.00092, (b) Cp = 0.00185, (c) Cp = 0.0037 to (d) Cp = 0.0074.

eight interaction zones, with the kth zone indicating the area on the monolayer at a distance of k × d (8.66 Å) from the center of each segment of the polymer, which has proven to be an effective means to detect the properties of the oppositely charged particles bound to a charged polymer.53 In each MC step, these interaction zones may change their shapes and sizes in accordance with the new conformation of the diffusing anchored polymer. In the ensemble average, we examine the system in all 50 MCs and define a lipid as being sequestered in the kth zone if it continuously remains within a zone for the 50 MCs. We further define all anionic lipids sequestered in each zone for the 50 MCs as a lipid cluster. Therefore, a lipid cluster sequestered by an anchoring polymer includes eight domains (in eight interaction zones), with the larger domain containing the smaller one. We calculate the amount of anionic lipids sequestered in these domains to characterize the size and concentration gradient of the lipid cluster. In Figure 2, we display the ratio (φs) of the total sequestered PIP2 to PS lipids in each zone underneath the anchoring polymers and the number (Ms) of PIP2 and PS sequestered in each zone underneath a single anchoring polymer. At low polymer concentrations (e.g., Figure 2a), we observe an increase in the amount (Ms) of PIP2 lipids sequestered by each anchoring polymer when the segmental ionization fraction (f) increases. The simulation results are consistent with the trends observed in experiments, which demonstrates that increasing the ionization fraction of the linear biopolymer can enhance the sequestering of the multivalent lipids.7 Our results further illustrate the significant concentration gradient of these tetravalent lipid molecules around the anchoring polymers. The tetravalent lipids rarely sequester in the first interaction zone,

whereas the amount of sequestered PIP2 lipids increases in larger zones, especially for highly charged polymers. In comparison, no PS lipid sequestering is observed in small zones. The Ms of PS exhibits only a slight increase from the sixth to eighth zones. By increasing the Cp from 0.00185 to 0.0074 (Figure 2b−d), we find that the ratio (φs) for PIP2 sequestered by the anchoring cationic polymers increases significantly, whereas Ms exhibits a decrease, which demonstrates that the competitions between the increased number of anchored cationic polymers cause the formation of much smaller PIP2 clusters under each anchored polymer. We also note that at high concentrations, the cationic polymers with high segmental ionization fractions almost confine all PIP2 in the third zones, as shown in Figure 2c,d. In these cases, a considerable amount of PS lipids is restrained in the fourth to eighth zones, which indicates the accumulation of univalent lipids around the polymer/PIP2 complexes. Our results illustrate that the positively charged polymers preferentially attract the multivalent anionic lipids to achieve the local charge-neutrality. Hence, the amount (Ms‑PIP2) of sequestered PIP2 underneath each anchoring polymer and the ratio (φs) of total sequestered PIP2 can be roughly estimated by Ms‑PIP2 ≈ |Zs| × N × f/|ZPIP2| and φs ≈ |Zs| × N × f × Cp × Am/(| ZPIP2| × YPIP2), respectively, when the local PIP2 lipids can sufficiently neutralize the anchoring cationic polymers, that is, | ZPIP2| × YPIP2 ≤ |Zs| × N × f × Cp × Am. This finding demonstrates that the difference in the charge of the lipid headgroups of the PIP2 and PS lipids results in their selective sequestering by the positively charged polymers, which is E


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The Journal of Physical Chemistry B qualitatively consistent with the experiments.6 Our coarsegrained simulations also illustrate that an increase in the segmental ionization fraction of the polymer causes the formation of a sharper concentration gradient in the sequestered PIP2 cluster around the anchored polymer chain. Once the amount of charge of the anchoring polymers surpasses that of the tetravalent lipids, the polymers tend to sequester all tetravalent lipids, that is, φs ≈ 1 and Ms‑PIP2 ≈ YPIP2/(Cp × Am), when |ZPIP2| × YPIP2 > |Zs| × N × f × Cp × Am. Positively charged polymer/PIP2 complexes attract the univalent anionic PS lipids to form into a layered, onion-skin distribution around the sequestered tetravalent lipid clouds on a larger length scale. This result can help design new biotechnologies on the basis of anionic lipid regulation. To further characterize the spatial redistribution of the anionic lipids, we calculate the radial distribution functions (RDFs) for different lipid species. We denote the RDF between PIP2 lipids and the RDF between PS lipids as gPIP2(r) and gPS(r), respectively, and display their values for the naked monolayer (dash−dot lines) without polymer anchoring in Figure 3a,c. As expected, both gPIP2(r) and gPS(r) increase with r

competitions between the anchoring polymers result in more intriguing redistributions of the anionic lipids. For f = 0.5, gPIP2(r) exhibits higher values at r < 10 (×8.66 Å) than those for the naked monolayer, indicating that more PIP2 lipids are sequestered by the larger amount of anchoring polymers. Our results also show that in this case gPS(r) exhibits the same result as the naked monolayer, indicating that the tetravalent PIP2 lipids play the dominant role in the anchoring of polymers, whereas the PS does not cluster in the presence of PIP2. For large segmental ionization fractions (f ≥ 0.5), the gPIP2(r) results show a decrease at r < 10 (×8.66 Å) with increasing polymer concentration. The enhanced competition between highly charged polymers greatly reduces the electrostatic energy gain in the anchoring of each polymer chain and increases the loss in the demixing entropy of the confined anionic lipids; therefore, the PIP2 lipids tend to form smaller clusters underneath each partially dissociated polymer on the monolayer. In addition, if the 1% PIP2 lipids cannot neutralize the cations on the anchoring polymers sufficiently, the PS lipids cluster in the vicinity of the polymer/PIP2 complexes (shown, for example, as the solid line in Figure 3c), resulting in a slight increase in the gPS(r) values at r < 4 (×8.66 Å). For comparison, we show the corresponding equilibrated configurations for the system with PC/PIP2 = 99:1 and PC/ PS/PIP2 = 89:10:1 in Figure S1 and display the results of φs, gPIP2(r), and gPS(r) for these systems in Figures S2−S4. For both systems, the sequestrations of the PIP2 lipids exhibit similar dependences on the polymer concentration (Cp) and the segmental ionization fraction ( f). For the monolayer with PC/PS/PIP2 = 89:10:1, when the total amount of cations of the anchoring polymers exceeds that of the local anions taken by the PIP2 lipids, the PS lipids display significant clustering around the polymer/PIP2 complexes. Our results for the cluster sizes and concentration gradients of the sequestering anionic lipids on a length scale that can account for the effects of polymer competitions provide valuable information and insights for understanding the membrane heterogeneity. 3.2. Segmental Distribution of Anchoring Polymers. The segmental distribution of the anchoring polymers can serve as another important evidence for the lipid sequestering. In Figure 4, we display the segmental distribution of the anchoring

Figure 3. RDFs for the PIP2 and PS lipids in monolayer with PC/PS/ PIP2 = 98:1:1. The segmental ionization fraction ( f) varies from 0.5 to 1.0, and the polymer concentration (Cp) is set to be 0.00185 and 0.0074.

and gradually reach unity due to the electrostatic repulsions between charged lipids. When the polymer concentration (Cp) is 0.00185 and segmental ionization fraction (f) is 0.5, gPIP2(r) at r < 8(×8.66 Å) presents a slight increase compared to the result for the naked monolayer (see Figure 3a), indicating the sequestering of the tetravalent lipids caused by the anchoring of the weakly charged polymers. By increasing f from 0.5 to 1.0, the peak values of gPIP2 at r < 8 (×8.66 Å) increase significantly, indicating that the sequestered PIP2 lipids display a sharper concentration gradient under the anchoring polymers. Figure 3b shows that as the Cp further increases to 0.0074, the

Figure 4. Distribution of the anchoring polymer segments on the monolayer with PC/PS/PIP2 = 98:1:1. The polymer concentration (Cp) is set to be (a) 0.00185 and (b) 0.0074. F


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The Journal of Physical Chemistry B polymers, denoted as gp(r), at positions r above the monolayer surface. For Cp = 0.00185, the gp(r) results exhibit a significant shoulder peak contributed by the tails and loops of the anchoring cationic polymers (see Figure 4a). This finding accords well with the earlier experiments and simulations for electric double layers of polyelectrolyte adsorption on charged interfaces,54,55 which illustrates that these studies on polyelectrolyte adsorption could also be applied to qualitatively predict the conformational variations of the anchored cationic polymers on an anionic lipid membrane. By increasing the segmental ionization fraction from 0.3 to 1.0, we observe a significant enhancement in gp(r) at small r, which demonstrates that the increase in the polymer segmental ionization fraction can significantly strengthen the anchoring. The enhanced synergistic effects of the anchoring positively charged segments weaken the electrostatic repulsions between the sequestered charged lipids. By increasing Cp to 0.0074, we observe a significant decay in the contact value of gp(r) and a large tail of gp(r) at 2 < r < 4 (×8.66 Å) (see Figure 4b). An increased amount of polymers competitively anchor on the membrane surface and contend for the charged lipids; therefore, these polymers cannot adsorb on the monolayer firmly, and they partially dissociate from the monolayer, exhibiting the brushlike conformations. This finding also provides the evidence that the sequestered anionic lipids form a smaller cluster underneath each partially adsorbed polymer for the anchoring of the concentrated polymers. 3.3. Mobility of Polymer/Lipid Complexes. The mobility of anionic lipids is another important aspect in the cellular signaling activities. On the naked monolayer, anionic lipids exhibit fast mobility. The anchoring cationic polymers sequester and restrain the anionic lipids; and accordingly, the lipid clusters confine the mobility of the anchoring polymers.8,16 Experiments probing the interaction between cationic polymers and anionic membranes raised a number of questions on the effect of polymer size, shape, and charge density on the properties of the system.1,2,4−9 Besides, the dynamic properties of the lipid membrane also depend on the competition effects between the anchoring cationic polymers and the synergistic effects of the connected cationic segments, which further affect membrane functioning. We now discuss the effects of polymer concentration and segmental ionization fraction on the mobility of the complex. 3.3.1. Mobility of the Anchoring Polymers. We first investigate the mobility of the anchoring polymers by calculating the MSD of the mass-center (denoted as mpc) and the ends (denoted as mpe) of the anchoring polymers for each of the 50 MCs28,29,31,32 in Figure 5a,b, respectively. At a low polymer concentration (Cp = 0.00092), the electrostatic attractions between adsorbing polymers and the charged lipids are significantly strengthened by the increase in the segmental ionization fraction. As a result, each polymer sequesters more anionic lipids, which accordingly enhances the confinement of the polymer; and therefore, both mpc and mpe exhibit a decrease, indicating a significant decrease in the polymer mobility. By increasing Cp, each polymer partially disassociates from the membrane surface; and hence, we observe an apparent enhancement in both mpc and mpe. We also note that the mpc results present a slight decrease for high polymer concentrations (Cp ≥ 0.0037) when the polymer ionization fraction (f) is increased from 0.75 to 1.0, whereas the mpe results exhibit a significant increase. The concentrated anchoring polymers bring a larger amount of cations onto the monolayer than the

Figure 5. MSD of (a) the mass-centers (mpc) and (b) the ends (mpe) of the anchoring polymers for each of the 50 MCs. The segmental ionization fraction (f) varies from 0.3 to 1.0, and the polymer concentration (Cp) ranges from 0.00092 to 0.0074.

total anions taken by the tetravalent and univalent lipids and thereby the anchoring polymers locally overcharge the monolayer. In addition, the sequestered univalent PS lipids cannot adsorb the polymers firmly. Therefore, at high polymer concentrations (Cp ≥ 0.0037), the highly charged polymers form larger tails protruding into the solution, resulting in a slight decrease in mpc but a dramatic increase in mpe. 3.3.2. Mobility of Anionic Lipid Clusters. We then consider the mobility of the anionic lipid clusters confined by anchoring polymers and display the MSD of the mass-centers of the PIP2 domains (denoted as md‑PIP2) and PS domains (denoted as md‑PS) in the interaction zones for all 50 MC steps in Figure 6. As a comparison, we display MSD of the mass-centers of the anchoring polymers (mpc) in this figures. For Cp = 0.00092, the electrostatic attractions between the anchoring polymers and the PIP2 lipids are strengthened by increasing the polymer segmental ionization fraction ( f) from 0.3 to 1; and therefore, the md‑PIP2 results exhibit a significant decrease (see Figure 6a), implying that the PIP2 clusters exhibit a slower mobility, corresponding to the variations of the mobility of the anchoring polymers (mpc). Recent experiments by Shi et al. have illustrated the restriction of the tetravalent anionic lipids by positively charged polymers and elucidated the dynamic coupling between the anchored polymers and the sequestered tetravalent lipids.6,8 Our simulations for the mobility of the anchored polymer and the sequestered PIP2 clusters are in good agreement with these experimental results. In comparison, even if a few PS remain in the sixth to eighth zones, these univalent lipids do not interact with the anchoring cationic polymers in the presence of the PIP2 lipids and still present a much faster mobility (see Figure 6a,b). By increasing the Cp from 0.00185 to 0.0074 (Figure 6b−d), we find that the mobility of the sequestered tetravalent anionic lipids exhibits a G


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Figure 6. MSD of the mass-center of the sequestered PIP2 domains (md‑PIP2) and PS domains (md‑PS), and MSD of the mass-center of the anchoring polymers (mpc) for each of the 50 MCs. The segmental ionization fraction (f) varies from 0.3 to 1.0, and the polymer concentration (Cp) is set to be (a) 0.00092, (b) 0.00185, (c) 0.0037, and (d) 0.0074.

present faster mobility (the solid diamond symbols) than those confined to the first zone of the weakly charged polymers (the solid square symbols). More intriguingly, the enhanced synergistic effects among the cationic segments of the highly charged polymers decelerate the average mobility of the single PIP2 in the interaction zones. Therefore, the PIP2 lipids sequestered by the weakly charged polymers (e.g., the solid square symbols) exhibit a faster mobility than those sequestered by the highly charged polymers (e.g., the solid diamond symbols) in the larger zones, for example, the seventh or eighth interaction zone. The electrostatic repulsion from the tetravalent anionic PIP2 prevents the PS aggregation in the smaller zones; therefore, the mobility of the PS lipids is independent of the variation in the segmental ionization fraction. With the increase in the polymer concentration (Cp) from 0.00185 to 0.0074 (Figure 7b−d), the polymers form the brush-like structures. The PIP2 lipids exhibit a more confined mobility underneath the partially adsorbed polymers, which results in the decrease in ml‑PIP2. For Cp ≥ 0.0037 and f = 1.0, the anchoring cationic polymers sequester all of the PIP2 lipids in the third zone and hence the ml‑PIP2 shows a plateau (see Figure 7c,d). Accordingly, when the PIP2 lipids in the monolayer cannot fully neutralize the cations on the anchoring polymers, the PS lipids accumulate in the vicinity of each polymer/PIP2 cluster, resulting in a decrease in ml‑PS. We display the corresponding results of mpc, mpe, md, and ml for the cases of PC/PIP2 = 99:1 and PC/PS/PIP2 = 89:10:1 in

significant decrease. The increase in the polymer concentration strengthens the competitions between the adhering polymers, which causes the sequestered PIP2 lipids to form into smaller clusters underneath the polymers. These smaller sequestered PIP2 lipid clusters are confined within the smaller interaction zones underneath the adhering polymer, resulting in a decrease in md‑PIP2. When the anchoring polymers overcharge the local PIP2 lipids (i.e., Cp = 0.0037 and f ≥ 0.7), the PS lipids are also restricted in the vicinity of the polymer/PIP2 complexes; therefore, we find a dramatic decrease in the mobility of the PS lipid domains (md‑PS) (e.g., vacant inverse-triangle, sphere, and diamond symbols and solid lines in Figure 6c,d). 3.3.3. Mobility of Single Anionic Lipids. We now consider the mobility of single anionic lipids in the vicinity of the anchoring polymers by comparing the MSD of the single PIP2 (denoted as ml‑ PIP2) and PS (denoted as ml‑PS) sequestered underneath the anchoring polymers, for each of the 50 MCs. Our results show that the single anionic lipids still exhibit much faster mobility than the anchoring polymers even when they are sequestered. The mobility of the single lipids is determined by the occluded area formed by the adsorbed cationic segments of the anchoring polymers. When Cp = 0.00092 (Figure 7a), the highly charged polymers flatten onto the monolayer and form a larger two-dimensional interaction network because of the enhanced synergistic effects among the more adhering cationic segments. Therefore, the single PIP2 can freely move in the larger first interaction zone of the highly charged polymers and H


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Figure 7. MSD of single PIP2 (ml‑PIP2) and single PS (ml‑PS) sequestered in each interaction zone for each of the 50 MCs. The segmental ionization fraction (f) varies from 0.3 to 1.0, and the polymer concentration (Cp) is set to be (a) 0.00092, (b) 0.00185, (c) 0.0037, and (d) 0.0074.

4. CONCLUSIONS In this article, we employed coarse-grained MC simulations to explore the effects of concentration and ionization degree of the anchoring cationic polymers on the lateral redistribution and mobility restriction of different anionic lipid species in a membrane monolayer. We find that the tetravalent PIP2 lipids predominantly aggregate underneath the anchoring polymers and the confined PIP2 domains exhibit synchronized movements with the polymers. The freely diffusing univalent PS lipids cannot electrostatically interact with the polymers if the local PIP2 lipids sufficiently neutralize the anchoring cationic polymers. Increasing the polymer ionization fraction drastically strengthens the polymer/PIP2 binding; accordingly, a larger amount of PIP2 lipids with a sharper concentration gradient sequester underneath each anchoring polymer and the polymer/PIP2 complexes exhibit a slower mobility. By increasing the polymer concentration, the competition between the polymers hinders their complete adsorption onto the membrane and results in the formation of a smaller sequestered PIP2 cluster underneath each partially adhering polymer. The desorbed segments of the anchored polymer exhibit a faster mobility, whereas the PIP2 domains are closely restrained by the limited adhering cationic segments of the anchoring polymers. In each PIP2 domain, the synergistic effects of the adhering cationic segments in each anchoring polymer result in the hierarchical mobility of each sequestered PIP2 domain. The enhancement of the synergistic effects among the cationic segments elevates the mobility of the PIP2 closely sequestered underneath the polymer but slows the average mobility of the single PIP2 in the clusters. If the PIP2 lipids cannot sufficiently neutralize the concentrated anchoring cationic polymers, the PS

Figures S5−S9, which exhibit similar dependences on the effects of the polymer concentration and the segmental ionization fraction. This illustrates that our work confers a possible rationale for explaining the properties of the realistic membrane. We also explore how the salt effect of the solution affects the properties of the polymer/monolayer complex. Our results illustrate that, as the salt concentration increases, the enhanced screening effect of the solution can sufficiently weaken the attraction between the charged lipids and the polymers. Therefore, the extents of the polymer association and lipid sequestering are weakened and hence the adhering polymers, the lipid domains, and the single segregated lipids display a quicker motility. These findings are consistent with previous experimental conclusions, which show that increasing the ionic concentration of the solution can drastically weaken the electrostatic interaction between the cationic polymers and an anionic membrane.7 In summary, our analysis for the MSD of the anchoring polymers and the sequestered anionic lipids suggests that the polymer/lipid complexes exhibit complicated dynamic behaviors. The anchoring polymers display a significantly restricted mobility on the monolayer, which is sensitively dependent on the concentration and the segmental ionization fraction. The synergistic effects among the anchoring cationic polymer segments can make the sequestered anionic lipids exhibit hierarchical mobility in the lipid domains. Our coarse-grained simulations provide the insight for elucidating the fundamental mechanisms for the dynamic heterogeneity of the lipid membrane on a large space and length scale that cannot be assessed by the all-atom models. These findings can help innovate novel biotechnologies for signaling-lipid modulation. I


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(2) Yeung, T.; Gilbert, G. E.; Shi, J.; Silvius, J.; Kapus, A.; Grinstein, S. Membrane Phosphatidylserine Regulates Surface Charge and Protein Localization. Science 2008, 319, 210−213. (3) Vance, J. E.; Steenbergen, R. Metabolism and Functions of Phosphatidylserine. Prog. Lipid Res. 2005, 44, 207−234. (4) Rossi, G.; Monticelli, L. Simulating the Interaction of Lipid Membranes with Polymer and Ligand-coated Nanoparticles. Adv. Phys. X 2016, 1, 276−296. (5) Di Paolo, G.; De Camilli, P. Phosphoinositides in Cell Regulation and Membrane Dynamics. Nature 2006, 443, 651−657. (6) Shi, X. J.; Li, X. S.; Kaliszewski, M. J.; Zhuang, X. D.; Smith, A. W. Tuning the Mobility Coupling of Quaternized Polyvinylpyridine and Anionic Phospholipids in Supported Lipid Bilayers. Langmuir 2015, 31, 1784−1791. (7) Gambhir, A.; Hangyas-Mihalyne, G.; Zaitseva, I.; Cafiso, D. S.; Wang, J. Y.; Murray, D.; Pentyala, S. N.; Smith, S. O.; McLaughlin, S. Electrostatic Sequestration of PIP2 on Phospholipid Membranes by Basic/aromatic Regions of Proteins. Biophys. J. 2004, 86, 2188−2207. (8) Golebiewska, U.; Gambhir, A.; Hangyas-Mihalyne, G.; Zaitseva, I.; Radler, J.; McLaughlin, S. Membrane-bound Basic Peptides Sequester Multivalent (PIP2), but not Monovalent (PS), Acidic Lipids. Biophys. J. 2006, 91, 588−599. (9) Shi, X. J.; Kohram, M.; Zhuang, X. D.; Smith, A. W. Interactions and Translational Dynamics of Phosphatidylinositol Bisphosphate (PIP2) Lipids in Asymmetric Lipid Bilayers. Langmuir 2016, 32, 1732−1741. (10) Hill, E. H.; Stratton, K.; Whitten, D. G.; Evans, D. G. Molecular Dynamics Simulation Study of the Interaction of Cationic Biocides with Lipid Bilayers: Aggregation Effects and Bilayer Damage. Langmuir 2012, 28, 14849−14854. (11) Haleva, E.; Ben-Tal, N.; Diamant, H. Increased Concentration of Polyvalent Phospholipids in the Adsorption Domain of a Charged Protein. Biophys. J. 2004, 86, 2165−2178. (12) Mbamala, E. C.; Ben-Shaul, A.; May, S. Domain Formation Induced by the Adsorption of Charged Proteins on Mixed Lipid Membranes. Biophys. J. 2005, 88, 1702−1714. (13) Dias, R. S.; Pais, A.; Linse, P.; Miguel, M. G.; Lindman, B. Polyion Adsorption onto Catanionic Surfaces. A Monte Carlo Study. J. Phys. Chem. B 2005, 109, 11781−11788. (14) Loew, S.; Hinderliter, A.; May, S. Stability of Protein-decorated Mixed Lipid Membranes: The Interplay of Lipid-lipid, Lipid-protein, and Protein-protein Interactions. J. Chem. Phys. 2009, 130, No. 045102. (15) Tzlil, S.; Ben-Shaul, A. Flexible Charged Macromolecules on Mixed Fluid Lipid Membranes: Theory and Monte Carlo Simulations. Biophys. J. 2005, 89, 2972−2987. (16) Khelashvili, G.; Weinstein, H.; Harries, D. Protein Diffusion on Charged Membranes: A Dynamic Mean-field Model Describes Time Evolution and Lipid Reorganization. Biophys. J. 2008, 94, 2580−2597. (17) Tzlil, S.; Murray, D.; Ben-Shaul, A. The “Electrostatic-Switch” Mechanism: Monte Carlo Study of MARCKS-membrane Interaction. Biophys. J. 2008, 95, 1745−1757. (18) Kiselev, V. Y.; Marenduzzo, D.; Goryachev, A. B. Lateral Dynamics of Proteins with Polybasic Domain on Anionic Membranes: A Dynamic Monte-Carlo Study. Biophys. J. 2011, 100, 1261−1270. (19) Tian, W. D.; Ma, Y. Q. Theoretical and Computational Studies of Dendrimers as Delivery Vectors. Chem. Soc. Rev. 2013, 42, 705− 727. (20) Tu, C. K.; Chen, K.; Tian, W. D.; Ma, Y. Q. Computational Investigations of a Peptide-Modified Dendrimer Interacting with Lipid Membranes. Macromol. Rapid Commun. 2013, 34, 1237−1242. (21) Barnoud, J.; Rossi, G.; Monticelli, L. Lipid Membranes as Solvents for Carbon Nanoparticles. Phys. Rev. Lett. 2014, 112, No. 068102. (22) Barnoud, J.; Rossi, G.; Marrink, S. J.; Monticelli, L. Hydrophobic Compounds Reshape Membrane Domains. PLoS Comput. Biol. 2014, 10, No. e1003873. (23) Rossi, G.; Barnoud, J.; Monticelli, L. Polystyrene Nanoparticles Perturb Lipid Membranes. J. Phys. Chem. Lett. 2014, 5, 241−246.

lipids cluster around to further neutralize the polymer/PIP2 complexes and exhibit a restricted mobility. We also illustrate that increasing the ionic concentration of the salt solution can weaken the interaction between the monolayer and the anchoring polymers and hence enfeeble the lateral sequestering and dynamic restrictions of the negatively charged lipids. In the past decades, the role of simulations in designing novel materials for biomedicine has become more prominently significant. Although the alternations of the concentration and ionization degree of the anchored cationic polymers are experimentally accessible, yet the direct probing of the polymer/membrane complexes remains quite challenging because of the unstable physiological natures of the charged lipids. By investigating the effects of these two factors on the sequestering and dynamical heterogeneity of the charged lipids, our work thus can help improve the relevant experimental approaches in the sense that it may inspire experimentalists to design systems. Our systematic coarse-grained simulations on length and time scales beyond the range of chemically detailed models provide useful results for elucidating the fundamental mechanism of the polymer/membrane interaction and serve as an essential input for experimental studies on the regulation of signaling lipids.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b12386. Lateral sequestering of the anionic lipids and the restricted mobility of the polymer/lipid complexes for the system with membrane compositions of PC/PIP2 = 99:1 and PC/PS/PIP2 = 89:10:1, respectively (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.D.). *E-mail: [email protected] (W.-S.X.). *E-mail: [email protected] (T.S.). ORCID

Qingrong Huang: 0000-0001-8637-0229 Wen-Sheng Xu: 0000-0002-5442-8569 Tongfei Shi: 0000-0002-6763-2200 Present Address ⊥

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States (W.S.X.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was funded by the National Natural Science Foundation of China (Nos. 21404103, 21234007, 21604086, and 51473168). The authors acknowledge the Special Program for Applied Research on Super Computation of the NSFCGuangdong Joint Fund (the second phase) and the Computing Center of Jilin Province for their computational support.

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REFERENCES

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