Divalent Cation-Dependent Formation of Electrostatic PIP₂ Clusters in Lipid Monolayers

Abstract

Polyphosphoinositides are among the most highly charged molecules in the cell membrane, and the most common polyphosphoinositide, phosphatidylinositol-4,5-bisphosphate (PIP₂), is involved in many mechanical and biochemical processes in the cell membrane. Divalent cations such as calcium can cause clustering of the polyanionic PIP₂, but the origin and strength of the effective attractions leading to clustering has been unclear. In addition, the question of whether the ion-mediated attractions could be strong enough to alter the mechanical properties of the membrane, to our knowledge, has not been addressed. We study phase separation in mixed monolayers of neutral and highly negatively charged lipids, induced by the addition of divalent positively charged counterions, both experimentally and numerically. We find good agreement between experiments on mixtures of PIP₂ and 1-stearoyl-2-oleoyl phosphatidylcholine and simulations of a simplified model in which only the essential electrostatic interactions are retained. In addition, we find numerically that under certain conditions the effective attractions can rigidify the resulting clusters. Our results support an interpretation of PIP₂ clustering as governed primarily by electrostatic interactions. At physiological pH, the simulations suggest that the effective attractions are strong enough to give nearly pure clusters of PIP₂ even at small overall concentrations of PIP₂.

Introduction

The concentration of the lipid phosphatidylinositol-4,5-bisphosphate (PIP₂) in the cell membrane is only of ∼1%, yet it plays an outsized role in many critical processes, including cell division (1), endocytosis and exocytosis (2), and cell motility (3). Evidence exists that PIP₂ forms clusters (4) at the submicron scale in vitro, and it has been speculated that similar domains might form under roughly physiological conditions. It has been conjectured that this clustering is crucial to its function at such low concentration (5,6).

Various mechanisms for the clustering have been proposed, including PIP₂-protein interactions (7,8), exclusion from cholesterol-enriched ordered domains (4,9), and hydrogen bonds (10,11). However, recent experiments showed that PIP₂ clusters can also be induced simply by adding calcium or other divalent ions (4,12). This raises the question of whether a purely electrostatic, ion-mediated mechanism could cause PIP₂ clustering.

A counterion-mediated mechanism would seem unlikely because such attractions are typically quite weak. Biomolecules such as DNA (13) and actin (14) aggregate into large bundles in the presence of multivalent ions, but they each carry a net charge of (∼−10²–10³e) while PIP₂ lipids carry a much smaller net charge (∼3e). Moreover, divalent cations are not sufficient to induce aggregation in bulk aqueous DNA or actin solutions, and the estimated attraction mediated by trivalent or tetravalent species is at most of ∼0.1 k_BT per basepair (15). This small magnitude is not surprising because counterion-mediated attractions vanish in the mean-field approximation (16) and are the collective result of a near-cancellation of repulsive and attractive interactions between like and unlike charges, respectively. We note that the near-cancellation implies that the geometry of the charge configuration is likely to be important so that attractions mediated by small ions such as calcium can behave very differently from those mediated by extended cationic molecules such as spermidine (17).

In this article, we show that ion-mediated attractions in low-charged objects such as lipids are surprisingly strong, so that phase separation not only occurs but can be nearly complete at physiological values of the PIP₂ charge. We conduct simulations on a model designed to retain only the most critical features of the electrostatics and compare the results to experiments on Langmuir monolayers of a mixture of PIP₂ with neutral lipids with added divalent salts. We find semiquantitative agreement between simulations and experiments, suggesting that divalent-ion-mediated attractions are responsible for the observed clustering. The strength of these interactions depends strongly on the net charge of the lipid, which in turn has been shown to depend sensitively on ionic strength and on pH within a physiological range (18).

In addition, the simulations provide, to our knowledge, new insight into the mechanical properties of ion-mediated clusters: at moderate PIP₂ charge, they are like two-dimensional liquids in which lipids can diffuse around as usual, but at sufficiently high PIP₂ charge they form rigid, gel-like clusters upon exposure to divalent ions.

Materials and Methods

Experiments

We look for phase separation using visual analysis of both epifluorescence micrographs and atomic force micrographs of mixed lipid monolayers prepared in a Langmuir trough (Kibron, Helsinki, Finland). L-α-phosphatidylinositol-4,5-bisphosphate (PIP₂) and 1-stearoyl-2-oleoyl phosphatidylcholine (SOPC) were purchased from Avanti Polar Lipids (Alabaster, AL). In the epifluorescence studies, part of the PIP₂ (equal to 0.5 mol % of the total lipid content) is replaced by a fluorescently labeled analog (BODIPY FL-PIP₂), purchased from Echelon (Salt Lake City, UT).

The lipid mixture, consisting of SOPC with a total molar PIP₂ fraction of ϕ_PIP is dissolved in a 2:1 chloroform/methanol mixture. A lipid monolayer is formed on a buffered subphase (10 mM HEPES, 100 μM EDTA, 5 mM DTT) by addition of the lipid solution to the air-water interface. The surface pressure is kept at 20 mN/m, corresponding to an initial area per lipid of ∼90 Å².

In the fluorescence studies the monolayer is imaged on an inverted epifluorescence microscope, using the 10× objective. We verify that there are at most two bright spots, likely due to nonspecific insoluble aggregates or contaminants, in a field of view at this stage. The divalent salts CaCl₂ or MgCl₂ are then added at 1 mM to the subphase, followed by gentle mixing to avoid disrupting the monolayer. We allow up to 2 h for domains to coarsen before imaging again.

For the AFM studies, sample preparation is identical with the exception that the buffer in this case contains only 1 μM EDTA. Monolayer samples are transferred from the trough onto a glass coverslip, both before and after addition of divalent salt. These films are imaged on a NanoScope III atomic force microscope (Digital Instruments, Tonawanda, NY) in tapping mode.

We perform these procedures for a range of ϕ_PIP-values and several pH values: 3, 4.5, 6, 7.4, and 9. At these values of the pH, q_PIP is roughly −1.5, −2.7, −3.2, −4.2, and −5.0, respectively, based on acid dissociation constants from Levental et al. (18). However, the ionization state of PIP₂ may be influenced by various geometric and chemical factors (18,19), so we do not assume that these q_PIP values are exact. We collect the results in a phase diagram for each experiment: The fluorescence measurements are the most direct visualization of domains, but might miss the smallest domains because of limited resolution, while the AFM images provide a more detailed picture at smaller length scales.

Simulations

We retain only the competition between electrostatic interactions and excluded volume repulsions by adopting a model in which both lipids and small ions are represented as charged spheres (radius R_i) with an excluded volume interaction given by the purely repulsive (truncated at its minimum and shifted) Lennard-Jones potential (the WCA potential (20)). Parameterized by an energy scale ε = k_BT ≡ 1 (our unit of energy) and length scale σ_ij = R_i + R_j, this potential is given by

$$V_{\text{WCA},ij}\left(r_{ij}\right)=4ϵ\left[{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^6+\frac{1}{4}\right],$$

for r_ij < 2^1/6 σ_ij, and V(r_ij) = 0 otherwise, where r_ij is the center-to-center distance. Note that σ_ij is the distance at which the potential equals k_BT. N = 1600 lipid particles are confined to the z = 0 plane, to mimic the effect of the hydrophobic interaction that keeps them at the air-water interface. We use R_i = R_L = 3 Å for the lipids and R_i = R_CI = 2 Å for the small cations that can explore the entire simulation box. In a study of the dependence of the clustering on cation size, we vary it between 0.5 Å ≤ R_CI ≤ 2.5 Å. The box is periodic in x- and y-directions (size L_x = 320 Å × L_y = 320 Å and has hard walls at z = 0 and z = L_z = 200 Å. The typical distance between lipids in the monolayer at z = 0 is therefore 8 Å.

In addition, the charged spheres interact via the Coulomb interaction, V_C,ij = q_iq_jl_B/r_ij, where we measure charges q in units of the proton charge. In room temperature water the Bjerrum length l_B ≈ 7 Å.

We run molecular-dynamics simulations using LAMMPS (21), with a Nosé-Hoover thermostat (22) and PPPM for the long-range Coulomb interactions (23).

The strong Coulomb attraction between the anionic lipids and the small cations allows them to bind at a distance of roughly σ_ij. The essence of ion-mediated attractions is that these bonds are strong and long-lived enough so that one or two counterions can draw together two lipids and be bound to both simultaneously (24,25). Due to its coarse-grained nature, our model underestimates the binding energy of such bonds. The main source of this effect is that the distance between the lipid particle and the Ca²⁺ in our model is much larger than the distance between a real phosphate group and a Ca²⁺ ion in real PIP₂. This common side-effect of coarse-graining is typically compensated by adjusting the dielectric constant (see, e.g., Marrink et al. (26)). To find the required correction, we compare the PIP₂ charge required for clustering as calculated from the numerical model and as measured in our experiments, at PIP₂ fraction ϕ_PIP = 0.25. Experimentally we find the threshold pH at this PIP₂ fraction to be between 3 and 4.5, which corresponds to a charge of roughly q_PIP ≈ −2 (18). The dielectric constant required in our model to match this threshold is ∼27 (a factor-three lower than that of water). We then use this value of the dielectric constant to obtain the rest of the phase diagram.

Thus, we have a coarse-grained model in which lipids are replaced by spheres of the appropriate charge and simulated with explicit counterions using an adjusted dielectric constant. This simplification enables us to explore a large parameter space with modest computations. Of course, this coarse-graining approach is not quantitatively precise, but neither are calculations using typical approximations such as a uniform dielectric constant of 80 for water surrounding highly charged objects. We note that despite the simplicity of our model, it gives surface pressures of ∼20–50 mN/m, which is of the same order as in the experiments. Both in the experiments and in the simulations, the surface pressure drops by a few percent at low ϕ_PIP, and between 10% and 30% at ϕ_PIP = 0.25, upon addition of Ca²⁺.

These simulations were performed for a range of PIP₂ charges q_PIP and PIP₂ fractions ϕ_PIP. To study the mobility of lipids within clusters and the cluster rigidity, we performed additional simulations at ϕ_PIP = 1.

Results

Phase behavior: experiments and simulation

Fig. 1 shows our experimental results: phase diagrams and snapshots of AFM (Fig. 1 a) and fluorescence (Fig. 1 b) studies of calcium-induced domain formation. At high PIP₂ charge, cluster formation is readily observed, for example at pH 7.4 in either experiment, where q_PIP ≈ −4.2 (Fig. 1, a 2, a 3, and b). Fig. 1 b shows epifluorescence micrographs, taken both before (left) and after (right) transferring the sample to a glass coverslip, at 25% PIP₂ and pH 7.4. In these images, bright spots mark regions where PIP₂ is concentrated. In the phase diagram, conditions for which these bright spots are seen are marked with solid disks. Cases that did not show signs of clustering are marked with open circles.

Figure 1.

Phase diagrams (pH versus PIP₂ fraction) and snapshots of experiments on mixed lipid monolayers (containing SOPC and PIP₂) exposed to divalent salt. (a) Phase diagram. (Shaded coexistence region) Where clustering was observed, obtained from AFM studies. (Open disks) Parameter values where no clustering was observed. (Shaded disks are too close to the boundary to determine their behavior with certainty.) The AFM snapshots 1, 2, and 3 represent the conditions indicated by the corresponding points in the diagram: At ϕ_PIP = 0.02, there is no cluster formation at pH 6 but clusters are clearly present at pH 7.4. Larger domains are obtained for ϕ_PIP = 0.25. Domains persist when the surface pressure Π is increased to 35 or 40 mN/m (panels 4 and 4^∗). (b) A very similar cluster formation phase diagram is obtained using epifluorescence with labeled PIP₂. Snapshots are shown for ϕ_PIP = 0.25. (Left snapshot) Taken directly in the Langmuir trough. (Right snapshot) Taken after transferring the sample to a glass coverslip. We note that the apparent area fraction in the image is <0.25 because many of the PIP₂ domains are too small to detect optically.

We note that domains usually appear within minutes, but we allow coarsening for up to 2 h before concluding there is no clustering. Thus we obtain the boundaries of the parameter region that lead to domain formation (shaded in the phase diagram). Fig. 1 a shows AFM images of the transferred samples. These images show a clear distinction between conditions that lead to domain formation (panels a 2 and a 3) and conditions in which the AFM image is flat (panel a 1). Control AFM images of samples without divalent salt did not show any sign of domain formation either. Domains persist when the surface pressure is increased to 35 or 40 mN/m (panels a 4 and a 4^∗, respectively).

Although the two experimental approaches probe the system on different length scales, both of them give the same phase diagram. The exception is one data point, at pH 4.5 and q_PIP = 0.5, which showed clustering in the fluorescence experiments, but which were not as clearly clustered as the other data points in the AFM experiments (marked with a shaded dot in the phase diagram). We note that, in general, the AFM images are less noisy and therefore lead to a more clear-cut distinction between clustering and nonclustering conditions.

The simulation snapshot in Fig. 2 c, obtained after simulating for 3.5 ns using 25% PIP₂ with charge q_PIP = −4, shows still-growing clusters at a scale of ∼10 nm. As expected, the positions of the condensed calcium ions (red disks in Fig. 2 c) clearly indicate their role in binding the charged lipids (green disks) together. To map out the phase diagram in the simulations, we follow the coarsening dynamics by keeping track of the static structure factor of the charged lipids,

$$S\left(\mathbf{k}\right)=\frac{1}{N}\sum _{i,j}^N\text{exp}\left[i\mathbf{k}\cdot \left({\mathbf{r}}_i-{\mathbf{r}}_j\right)\right],$$

where N is the number of PIP₂ particles. As a function of k ≡ |k|, a maximum in this function at k = k_peak indicates that the PIP₂ positions are developing structure at a length scale 2π/k_peak. For the more pronounced cases of cluster formation (deep in the phase-separated regime), we followed this peak as a function of time and verified that it scales with time as k_peak ∼ t^−1/3, consistent with the general theory of coarsening of a binary fluid mixture (27). Thus, even though the counterion-mediated origin of phase separation yields irregularly shaped clusters instead of circular ones, this does not seem to affect the kinetics of coarsening. In the phase diagram in Fig. 2 a, all parameter values (ϕ_PIP, q_PIP) for which an appreciable peak appears that approaches k_peak = 0 in S(k) for long times were marked as cluster-forming (within the coexistence region). Both in the experiment and simulation, we found that divalent cations cause phase separation when the lipid charge is high enough (pH 4.5 or higher in experiment, q_PIP ≤ −2 in simulation). Monovalent cations were never seen to induce clusters.

Figure 2.

Phase diagram (charge versus PIP₂-fraction) and snapshots from simulation of charged-neutral mixed lipid monolayers exposed to divalent salt. (a) Phase diagram obtained using a divalent ion radius R_CI = 2 Å. (Solid disks in the shaded coexistence region) Where clustering was observed. (Open circles) Mixed samples. (Gray disks are too close to the boundary to determine their behavior with certainty.) (b) Larger divalent ions require a higher lipid charge to induce clustering (shown for ϕ_PIP = 0.05). (c) The simulation (PIP₂ charge q_PIP = −4, PIP₂ fraction ϕ_PIP = 0.25, and divalent ion radius R_CI = 2 Å) after 3.5 ns of coarsening. Charged and neutral lipids are dark green and light gray discs, respectively, and divalent ions that are close to the lipid monolayer are indicated with smaller dark red dots. (d) Strength (shaded contours) and direction (streamlines) of the electric field around a stringlike domain taken from the simulation, illustrating that further growth of the domain is likely to occur at the end.

Larger divalent ions than Ca²⁺ should mediate weaker attractions, because larger binding distances imply lower Coulomb energies. This effect should manifest itself in a higher charge on the PIP₂ needed to obtain cluster formation with larger ions. We verified this in experiments at q_PIP = 0.25 using Mg²⁺, which has a larger hydrated radius than Ca²⁺, although the precise values are uncertain (note that the reported hydrated radii vary, mainly due to different methods to determine them, but Mg²⁺ is consistently larger (3–7 Å) than Ca²⁺ (2.6–6.3 Å) (28–30)). We find that Mg²⁺ only induces clusters if $\text{pH}\ge 6$ while Ca²⁺ already does it at pH 4.5. In agreement with this observation, the ability of divalent cations to drive cluster formation in our simulations also decreases with increasing ion size (Fig. 2 b).

Cluster morphology

The morphology observed in the early stages of coarsening in the simulations illustrates some particular features of ion-mediated attractions. The PIP₂-rich clusters (see Fig. 2 c) are often irregularly shaped, and even stringlike. This occurs because the attraction, of the order of a few k_BT, is the net result of strong attractions (PIP₂-Ca²⁺) and strong repulsions (PIP₂-PIP₂ and Ca²⁺-Ca²⁺) that can each be several tens of k_BT.

In the earliest stages of coarsening, most domains are stringlike, because for very small clusters such linear arrangements have the lowest Coulomb energy. As the domains grow, compact shapes become energetically favorable but are difficult to reach for two kinetic reasons: First, once there is a stringlike cluster, the electric field in its neighborhood is focused toward the end of the string (see Fig. 2 d), making it more likely for the next lipid to bind at the end, thus extending the string. Second, any rearrangement of the lipids requires the nearby counterions to move aside, which involves energy barriers of the order of the bare (tens of k_BT) interactions. As a result, the evolution toward more compact shapes is severely hindered kinetically, and irregularly shaped domains, which have also been seen experimentally (4,7), can persist even in the later stages of coarsening (Fig. 2 c). This observation also strongly suggests that irregularly shaped clusters are gel-like because diffusion of lipids within the cluster should be hindered by the same energy barriers.

Cluster rigidity

For those PIP₂ charges at which cluster formation was observed, additional simulations at q_PIP = 1 provide information on cluster rigidity or gelation. As shown in Fig. 3 a, we find from the mean-square displacement that at q_PIP ≤ −3.5, the PIP₂ do not diffuse over the course of the simulation (corresponding to 3.5 ns), indicating that clusters are mechanically rigid on that timescale. At q_PIP ≥ −2.5, on the other hand, the lipids diffuse around freely, indicating that the clusters are fluid. These curves are averaged over five runs with identical parameters but different initial random conditions. At q_PIP = 3, the system appears to be marginally rigid on the timescale of our runs; the lipids diffuse in some runs but not in others.

Figure 3.

Diffusion and rigidity of lipids within PIP₂ domains at ϕ_PIP = 1 and R_CI = 1 Å. (a) Mean-square displacement for lipids in a PIP₂-domain as a function of time, for various PIP₂ charges, as shown in the legend. For sufficiently negative PIP₂ charge, the domains are solid. (b) The stiffness of the effective harmonic interaction between neighboring PIP₂ molecules in the PIP₂ domain, obtained by displacement correlation analysis. (Black diamonds) Stiffness corresponding to normal (central) effective interactions. (Red disks) The (negligibly small) effective tangential stiffness.

Within a rigid cluster, each lipid has a well-defined average position about which it fluctuates thermally. What keeps them in place can be described as an effective interaction between nearby PIP₂ molecules, mediated by the divalent counterions. The strength of this effective interaction is obtained from the matrix of displacement correlations U, defined via

$$U_{ij}={\langle u_i\left(t\right)u_j\left(t\right)\rangle }_t,$$ (1)

where u_i(t) is the deviation of coordinate i from its average value at time t. Hence, U is 2N × 2N for our two-dimensional system. When these deviations are small they explore the effective potential energy V_eff around its minimum, so we can describe it by a second-order Taylor expansion. This allows extraction of the dynamical matrix K of the system as the inverse of the correlation matrix,

$$\frac{{\partial }^2{V}_{eff}}{\partial u_i\partial u_j}\equiv K_{ij}=k_{\text{B}}T{\left(U^{-1}\right)}_{ij},$$ (2)

which can be obtained directly from the partition function (31). The elements of the dynamical matrix then provide the stiffness of the effective spring that acts between two neighboring PIP₂. The result is shown in Fig. 3 b: The tangential stiffness of the effective interaction between neighboring PIP₂ is negligible, indicating that the effective interaction does not prevent particles from sliding past each other, while the normal effective stiffness is ∼4 k_BT/Ų when q_PIP ≤ −4.

Discussion

The two experiments yield nearly identical phase diagrams, showing clustering of PIP₂ for pH ≥ 4.5 at PIP₂ fractions at ∼25%, a threshold which approaches pH 7.4 at PIP₂ fractions as low as 2%.

The phase diagram of our numerical model compares surprisingly well with the experiments. The only parameter we introduce is the dielectric correction factor, a usual necessity in coarse-grained simulations. It is fixed by comparing clustering at one packing fraction (ϕ_PIP = 0.25), after which the rest of the phase diagram is reproduced without any free parameters.

It should be noted that, although hydrogen bonds between the PIP₂ molecules exist and may play a role when the charges are small (10), our work strongly suggests that they do not play a dominant role in multivalent ion-induced clustering—if they did, having a higher PIP₂ charge would make it harder to form clusters, rather than easier, as we report in Figs. 1 a and 2 a.

One might ask how relevant our results are to biological membranes. Most of our measurements are taken at a relatively low surface pressure of 20 mN/m to prevent barrier leakage of the lipids. However, the formation of domains persists when surface pressure is increased up to 35 or 40 mN/m (see Fig. 1 a 4), and between 20 and 35 mN/m the typical domain size even grows with surface pressure. This is a characteristic signature of domain formation driven by electrostatic correlations, because a denser aggregate containing charged lipids will attract more divalent ions. We also observed domains by AFM in monolayers containing 1% PIP₂ at 35 mN/m over subphases containing 150 mM KCl, pH 7.4, suggesting that even at roughly physiological conditions, Ca²⁺-induced clustering can be relevant (Y.-H. Wang and P. A. Janmey, unpublished).

As for the use of monolayers instead of real membranes, we first note that PIP₂ in the cell membrane only resides on the inner leaflet. In addition, the use of monolayers will not significantly affect the electrostatics because distances between opposite charges are much smaller than the thickness of the low-dielectric layer of a membrane. However, an important limitation of monolayers in both experiment and simulation is that membrane curvature is not allowed. There might be changes in the exact concentrations or charges at which domains first form when membrane curvature is allowed, and indeed the cation-driven changes in surface pressure we measure on the PIP₂-containing leaflet might be enough to trigger local curvature in a bilayer.

Because the interactions in our model have been stripped down to the bare minimum of electrostatics and steric repulsion, the only attractive interaction in the simulations is the Coulomb attraction between PIP₂ and Ca²⁺. Therefore, the observed phase separation must be due to counterion-mediated attractions. In both DNA solutions and in PIP₂, the negative charges come from phosphate groups and are typically several Å apart. For PIP₂, however, the net binding energy per lipid in 30-lipid clusters with Ca²⁺ is 6 k_BT for q_PIP ≈ −3, which is much stronger than in DNA (15). (This binding energy is calculated with respect to a reference state of 15 lipid dimers, neutralized with Ca²⁺, so that the cluster is charge-neutral and monopole terms do not dominate the result.) This large difference must originate from rather subtle differences in the packing geometry of charges in the two cases. Chain connectivity of DNA prevents the charges from organizing in the low-energy configurations that our lipids take (see Fig. 2 c), but instead forces both negative and positive charges into roughly linear arrangements (33), increasing repulsive contributions to the electrostatic energy and thereby weakening the effective attraction.

Although the binding energy between lipids in a cluster is a collective effect and can only be estimated with respect to a chosen reference state, the linearized effective interaction between neighboring PIP₂ is always well defined. One can think of this as the potential of mean force between PIP₂ that is left after integrating out the positions of the calcium ions, expanded around the average distance between the PIP₂ molecules involved. We determined the stiffness of the effective calcium-mediated bond between PIP₂ molecules to be ∼4 k_BT/Ų for the case of gel-like clusters of highly charged PIP₂ (q_PIP ≤ −4). This is approximately an order-of-magnitude lower than the stiffness with which a single Ca²⁺ is bound to a PIP₂ in our simulations, consistent with the notion that ion-mediated attractions are the result of near-cancellation of much stronger attractive and repulsive interactions. Yet at q_PIP ≤ −4 the ion-mediated attractions are still strong enough to lead not only to phase separation, but also to mechanical rigidity in PIP₂-rich domains.

Whether or not this rigidifying effect could be noticeable in living cells is questionable. First, we note that the timescale of our simulations is of the order of nanoseconds; more highly negative values of q_PIP would be needed to achieve rigidity at longer timescales relevant to experiments and to biological processes. Second, other effects that were not included in our simulations—such as active processes (e.g., from molecular motors) and increased disorder (because real lipids are not spheres in a plane)—also act to drive the threshold value of q_PIP for rigidity beyond the physiological value of q_PIP ≈ −4. We note that a similar calcium-induced gelation effect has been observed experimentally in polymer amphiphile systems (34). In that context, gelation is less surprising because the total charge per molecule is much higher for the polymer amphiphiles than for PIP₂.

In summary, we have presented experiments and coarse-grained simulations on lipid monolayers that demonstrate the clustering of PIP₂ in mixed monolayers via calcium-mediated electrostatic attractions. Furthermore, we detected a transition from fluid to gel domains as the charge on the PIP₂ increased, and obtained the conditions for cluster rigidity from the simulations. Between PIP₂ charges of −2 and −4, the strength of ion-mediated attractions is highly sensitive to the PIP₂ charge; they become strong enough to make long-lived cross-links between lipids when q_PIP ≈ −4, as illustrated by the interaction stiffnesses in Fig. 3.

In all, our results suggest that at physiological pH the effective calcium-mediated attraction can drive the formation of fluid clusters of PIP₂ even at PIP₂ mole fractions of 2% or lower. In the cell, other factors such as the presence of other polycationic ligands, i.e., polyamines and protein domains, can also affect PIP₂ distribution; however, the clustering effect of Ca²⁺ is likely to remain a significant influence on PIP₂ distribution.