Alteration of the Lipid Bilayer Structure by Mg²⁺

Abstract

Developing molecular mechanics force fields to model interactions of biological membranes with Mg²⁺ cations is challenging. There are no direct estimates of the binding modes of Mg²⁺ ions with lipid headgroups or other phosphates in the condensed phase. Experimental data on lipid bilayers in Mg²⁺ solution are sparse and limited to biologically relevant but very low ion concentrations. At these concentrations, no statistically discernible effects on bilayer properties are observed. Simulations at these concentrations are difficult due to system size and the extensive conformational sampling required for force field development. Considering these issues, we previously calibrated Mg²⁺–lipid Lennard-Jones cross-terms using benchmarked quantum mechanical target data on small clusters of ions and ligands representative of common cation binding sites on 1-palmitoyl-2- oleoyl-sn-glycero-phosphatidylcholine (POPC). Our simulations with these new Mg²⁺ parameters yielded bilayer structures very similar to those without salt, in agreement with the available experimental data. We adopted this strategy because it worked well for modeling membrane interactions with monovalent cations, for which additional experimental data are available. However, newer studies from our group show that for Mg²⁺ ions, the choice of target Mg²⁺-lipid mimetic clusters is nontrivial. Inclusion of fully coordinated (6-fold) Mg²⁺ ions, which better represent potential ion-lipid structures in the condensed phase, may be critical for selecting models that reproduce experimental condensed-phase interactions of Mg²⁺ with nucleotide phosphates. Using this new protocol, we propose an additional set of Mg²⁺-lipid interaction Lennard-Jones cross-terms. With this parameter set, we find that at concentrations between 100 and 200 mM, there is a systematic thickening of the lipid bilayer, not observed with our previous Mg²⁺-lipid model. Additionally, compared to the earlier model, we observe more Mg²⁺ adsorbed on the bilayer and a larger fraction directly coordinating the lipid headgroups. However, the new model does not alter our previous observation that structural changes in the bilayer correlate with the amount of ionic charge directly coordinating lipid molecules.

Graphical Abstract

INTRODUCTION

Salts have a well-characterized behavior at interfaces in the condensed phase–ions form a classic double layer, where one charge accumulates near the substrate’s surface and the second charge then accumulates to compensate for that charge.¹ This can be explained by using a mean-field approximation. However, the mean-field approximation does not provide details of specific interactions between ionic species and interface moieties. These details are nontrivial, especially in the case of phospholipid membranes, where the substrate itself is liquid and can adopt new conformations in response to ion adsorption.

Molecular dynamics (MD) simulations can, in principle, provide such details. However, the development of MD force fields for Mg²⁺, and modeling their interaction with lipid bilayers, poses significant challenges. First, experimental data needed for force field development and validation is scarce. To the best of our knowledge, there are no direct estimates on the binding modes of Mg²⁺ ions with lipid headgroups or any other phosphates in the condensed phase. Second, the effects of Mg²⁺ on lipid bilayer structure are only known for small concentrations of salt.^2,3 Simulations with these low salt concentrations push the limits of the hardware requirements for conformational sampling and force field testing. For example, in our previous simulations with Na⁺,⁴ we observed between 75 and 90 Na⁺ ions adsorbed to an equilibrated lipid bilayer of 100 POPC molecules per leaflet. If we assume similar numbers of Mg²⁺ to be adsorbed, simulating at a biologically relevant concentration of 0.5 mM⁵ will require more than 11 million waters. Additionally, since the residence time of waters in the first shell of Mg²⁺ is of the order of a microsecond,^6–8 capturing statistics on water-lipid exchanges in the first shell of Mg²⁺ requires prohibitively long MD simulations.

Considering these issues, we previously chose to calibrate Mg²⁺–lipid Lennard-Jones (LJ) terms using benchmarked quantum mechanical (QM) target data clusters of small molecules representative of the ion binding sites on 1-palmitoyl-2-oleoyl-sn-glycero-phosphatidylcholine (POPC).⁴ Methyl acetate (MeAc) and diethyl phosphate (DEPh) were taken as small-molecule representatives for lipid headgroups, and we targeted the changes in energy and structure associated with replacing water molecules in Mg²⁺–water clusters with these smaller molecules. Using this model, we found that at about 100 mM concentration, Mg²⁺ adsorbed into the headgroup region of the POPC bilayer but without losing its inner-shell waters (steric binding mode). We also observed formation of the ion double layer at the headgroup–water interface. However, Mg²⁺ adsorption had a negligible effect on the POPC bilayer structure. We posited that since our model at high salt did not affect bilayer structure, our model at low experimental salt concentration will also not affect the POPC bilayer structure, making the result consistent with experiment. We adopted this strategy because we showed that it worked well for modeling interactions of lipid bilayers with monovalent cations.⁴ Prior to our development, all simulations, irrespective of the employed force field, reported that monovalent salts thickened POPC bilayers.^9–12 In contrast, experiments reported insignificant changes in POPC lipid bilayer structure.^13,14 The use of our new Na⁺-lipid LJ terms resolved this discrepancy to a large extent.⁴

Recent developments in our laboratory, however, motivate us to explore a modified strategy for developing Mg²⁺–lipid LJ terms. Our recent work of polarizable force fields for describing Mg²⁺–protein/nucleotide interactions¹⁵ suggests that perhaps within the classical framework, a single set of force field parameters for Mg²⁺ do not perform well at simultaneously reproducing energies of both fully coordinated (6-fold) and partially coordinated Mg²⁺ structures. Furthermore, force field developed using 6-fold coordinated structures performed excellently at reproducing not only local interactions of Mg²⁺ ions in clusters containing nucleotide phosphates but also condensed phase binding free energies of Mg²⁺ ions with nucleotides.¹⁵ We have shown that this strategy also works for other cations.¹⁶ Fully coordinated 6-fold clusters of Mg²⁺ were not considered in the development of our previous Mg²⁺ model,¹⁷ in which target data consisted of only partially coordinated structures of Mg²⁺.

Here, we apply this new protocol to the development of a new set of Mg²⁺–lipid LJ terms. Our target data consists exclusively of full 6-fold coordinated Mg²⁺ clusters with different combinations of waters and MeAc/DEPh ligands representative of the common binding sites on POPC. This allows us to focus our model parametrization on clusters that are more representative of the dense, bulk phase systems that we are interested in studying. As before, target data are obtained from benchmarked QM vdW-inclusive density functional theory (DFT).

Using these new parameters, we perform MD simulations of POPC in a MgCl₂ solution with the aim of comparing these results with those of our previous interaction model parameters. We also characterize their behavior using two different ion–water interaction parameter sets, parameters from Grotz et al.^18,19 that are developed to improve the first shell water residence times in comparison to experiments, and parameters from Li et al.²⁰ which target experimental hydration free energies.

In this way, we aim to test how changes to the Mg²⁺–water and Mg²⁺–lipid interaction models affect the adsorption behavior and the resulting perturbations to the bilayer structure. Our goal is not to validate a specific force field parametrization scheme but to identify which structural metrics are most sensitive to these parameter choices and to provide a framework for future comparisons with experimental results. Essentially, in the absence of appropriate experimental data, we have two competing models for describing Mg²⁺–lipid interactions in MD simulations that point to different adsorption behaviors.

METHODS

Mg²⁺ Model Parameters

We perform a parameter search for the 7 pairs of Lennard-Jones (LJ) σ_ij and ϵ_ij interaction cross-terms of Mg²⁺ with lipid headgroup oxygens, carbon, and phosphorus atoms (see Table 1). This search is performed by using target Mg²⁺ clusters containing water molecules and ligands that represent the major cation binding sites in phospholipid headgroups. The clusters contain exactly 6 Mg²⁺ coordinators, representing a full first-shell coordination shell of Mg²⁺.

Table 1.

Lennard-Jones Parameters for Magnesium Interactions: Well Depth ϵ_ij (kJ/mol) and Distance Parameter σ_ij (nm), Comparing the 2025 Optimized Model, the 2024 Model, and the Original LB-Rules

	2025		2024		LB-rules
parameter	ε	σ	ε	σ	ε	σ
MG-CH3	0.60498	0.22161	0.68709	0.14257	0.19239	0.30856
MG-CH2	1.36553	0.41404	0.63126	0.20617	0.13238	0.32468
MG-OA	25.25725	0.30372	5.05190	0.26223	0.19044	0.26890
MG-P	29.74732	0.23348	3.89200	0.27811	0.32318	0.29044
MG-OM*	22.04699	0.20018	3.22262	0.17691	0.20771	0.26469
MG-CO*	0.57040	0.42212	0.56152	0.37127	0.06152	0.34796
MG-O*	2.06827	0.24468	2.43058	0.13069	0.20771	0.26469

These target clusters are geometry optimized at the DFT level using PBE0,²¹ with the Tkatchenko–Scheffler dispersion corrections²² as implemented in FHI-aims.²³ Geometry optimizations are first performed with the “light” basis set as provided in the FHI-aims software package and then with the “really-tight” basis. Both geometry optimizations are performed with a force convergence threshold of 0.005 eV/Å. Energies of these optimized clusters are used to compute substitution energies, and geometries are computed as an array of distances between all particles in the cluster and the cation. As before,⁴ we do not target the interaction energies of Mg²⁺ in clusters. Instead, we target substitution energy, that is, the energy associated with replacing water molecules with ligands (X) representing the POPC headgroup:

$${\left({\text{MgW}}_6\right)}^{2+}+nX\iff {\left({\text{MgW}}_{6-n}{\text{X}}_n\right)}^{2+}+n\text{W}$$ (1)

The substitution energy associated with this reaction is

$$\Delta E_{\mathrm{sub}}=E_{\mathrm{MgWX}}+n{E}_{\text{W}}-E_{\mathrm{MgW}}-n{E}_{\text{X}}$$ (2)

where E_MgW is the energy of the optimized geometry of Mg²⁺ cluster with 6 waters and E_MgWX is the energy of optimized geometry, the mixed cluster of Mg²⁺ consisting of n X ligands and 6 – n waters. We use two different ligands, methyl acetate that represents the ester-fragment connecting the lipid acyl chains to the glycerol backbone and diethyl phosphate that represents the phosphate fragment in the lipid headgroups. E_W and E_X are, respectively, the energies of the optimized geometries of isolated water and isolated ligands.

Parameter optimizations were performed using the ParOpt software package developed by our group.²⁴ We used the Nelder–Mead optimizer to simultaneously optimize the 14 LJ cross terms for each atom type in our target clusters. Constraints are detailed in Table S1 of the Supporting Information.

We first perform parameter searches using a full-random simplex initialization to obtain 400 converged simplexes, regarding a simplex as converged if the RMSD collapses to 10 × 10⁻³. The best parameters from this search are then used to perform another search using a around-point initialized simplex, with an RMSD cutoff of 10 × 10⁻⁵, again for 400 converged simplexes. From this search, we select the parameters that balance the error in substitution energies and geometries simultaneously. These optimized parameters are listed in Table 1. We denote these parameters as the Mg²⁺ 2025 model and compare them with our parameters from Saunders et al. 2024,¹⁷ which we will refer to as the Mg²⁺ 2024 model. There are substantial differences between the Mg²⁺ 2024 and Mg²⁺ 2025 models, with the greatest changes in the size of the well depth ϵ_ij for MG-OA, MG-P, and MG-OM*.

The substitution energies before and after optimization are compared to the target QM values in Table 2. The geometries before and after optimization are compared to QM geometries in figure S1 in the Supporting Information. We note substantial improvements in both substitution energies with a minimal loss of accuracy in geometries, with parameter optimization reducing the mean absolute error in ΔE_sub from 0.26 to 0.01.

Table 2.

Energies (kJ/mol) Associated with Substituting n Water Molecules in 6-Fold Mg-Water Clusters with n Methyl Acetates (MeAcs) or n Diethyl Phosphates (DEPhs)^a

	n	QM	LB rule	optimized
MeAc	1	−71.29	−59.18	−71.28
	2	−127.20	−112.47	−122.88
	3	−166.16	−155.99	−167.84
	4	−192.53	−187.59	−192.28
DEPh	1	−775.55	−312.57	−754.82
	2	−1333.69	−553.24	−1333.65
	MAPE		0.26	0.01

^aSubstitution energies are defined in eq 2.

Bilayer Construction

Simulation systems are prepared following the procedure in Saunders et al. 2024¹⁷ by creating a bilayer leaflet of 100 POPC lipids along a 10 by 10 grid. This leaflet is reflected along the z-axis to produce the second leaflet. Then, 60,000 waters are added along the box z-dimension. This results in a system with 300 waters per lipid. This is needed to ensure that waters in bulk solvent at the box boundary are isotropic, as can be seen in Figure 1 of the results section. MgCl₂ is added by randomly replacing 216 waters with Mg²⁺ and 432 waters with Cl⁻ for a starting concentration of 200 mM MgCl₂. The resulting simulation box is used in both Mg²⁺ 2025 HFE and microsimulations; energy minimization and annealing were done under the matching parameter set for the simulation. Systems are energy-minimized using the steepest-descents algorithm to remove bad-contacts. Following energy minimization, both systems are allowed to settle in an NPT dynamic run at a temperature of 250 K for 1 ns. Systems are then annealed by heating to 350 K, and cooling in steps of 10 K to the simulation run temperature of 300 K in steps of 155 ps. This process results in a system that is around 7.4 nm long in the x and y dimensions and approximately 36.9 nm in the z dimension.

Figure 1.

Water orientational order parameters P₁ (a) and P₂ (b). In (a), we note increased positive ordering in the systems simulated with Mg²⁺ 2025 parameters, compared to other systems. Dashed lines on (b) denote the positions of the bilayer 2D_C, D_hh, and hydration boundary, respectively, as one moves further from the bilayer center. Here, we note increased ordering overall in the Mg²⁺ 2025 systems compared to all other simulation systems.

Molecular Dynamics

The Mg²⁺ 2025 parameters are used in two 1 μs-long simulations of POPC with MgCl₂, one using the water–Mg²⁺ interaction term computed using the Mg²⁺ HFE model of Li et al.²⁰ and one using the Mg²⁺ micro from Grotz et al.^18,19 Lipid-bonded and nonbonded interactions are described using the gromos 43-a1s3 force field.²⁵ Simulations were performed by using Gromacs version 2024.0²⁶ with an integration time step of 4 fs. Neighbor searching is performed every 2 steps using Verlet neighbor-lists. The PME algorithm is used for electrostatic interactions with a cutoff of 1.6 nm. A reciprocal grid of 52 × 52 × 240 cells is used with fourth-order B-spline interpolation. A single cutoff of 1.6 nm is used for van der Waals interactions. Temperature coupling is done with the Nose–Hoover algorithm holding the system temperature at 300 K.²⁷ Pressure coupling is done with the Parrinello–Rahman algorithm holding the system pressure at 1 atm.²⁸

Trajectories are analyzed using tools provided in the Gromacs software package,²⁶ in-house code developed using the Gromacs API, and using the MDanalysis python package.^29,30

RESULTS AND DISCUSSION

Water Structure and Hydration Boundaries

To differentiate interfacial ions from those in the bulk solvent, we first need to define the interfacial boundary. As before,¹⁷ we do this using the orientational ordering of water molecules. Waters near the lipid bilayer interface are ordered due to the electrostatic and steric interactions with the lipid bilayer as well as interactions with dissolved salts. The orientation of these waters can be probed by computing the orientational order parameters $P_1=\langle \cos \beta \rangle$ and $P_2=\langle \frac{1}{2}(3{\cos }^2\beta -1\rangle$, where β is the angle made between the water oxygen-hydrogen bond vector and the box z-axis. We use this vector instead of the water dipole moment vector because of its relationship with the electric field gradient of D₂O that is related to the quadrupolar splitting value reported in deuterium NMR.³¹ The hydration boundary marks the location where water molecules become orientationally isotropic beyond which they no longer contribute to quadrupolar splitting. We use this boundary to distinguish between adsorbed ions and ions in the bulk solvent. In our previous work,¹⁷ we demonstrated that ion densities outside this boundary follow Poisson–Boltzmann theory, while those inside deviate from it. This breakdown in the mean-field behavior indicates a specific interaction with the membrane.

The first-order parameter P₁ represents an in–out ordering with respect to the bilayer center. The second-order parameter P₂ is a nematic ordering, which is related to the organization of water quadrupole moments. If P₂ is zero, this indicates an isotropic distribution with no preferred alignment. To compute P₁ and P₂, we divide the simulation unit cell into 2000 slices along the membrane transverse (z-) axis. The average values over the last 150 ns of the simulation are plotted in Figure 1, with points shown for every 200 slices. The first-order parameter indicates a significant increase in the positive ordering induced by the Mg²⁺ 2025 parameters compared to the no-salt and Mg²⁺ 2024 simulations. The second-order parameter indicates increased ordering as one approaches the bilayer starting from the hydration boundary, indicated by the set of dashed lines furthest from the bilayer center point. The hydration boundary is calculated using the histogram of P₂. The outermost region of negative ordering is fit to an exponential function, and the length scale of the exponential is used to find the location where P₂ is considered to be effectively zero. Lines to delimit these values are drawn in the plot in Figure 1, and these positions are noted for each bilayer in Table 3. Ordering increases as we approach bilayer D_hh, indicated by the second set of dashed lines. There is also a steeper decline as one follows the plot into the acyl chain region denoted by the bilayer 2D_C—denoted by the innermost dotted lines—in the Mg²⁺ 2025 Micro system. We note that the hydration boundary of both of the 2025 simulations is further from the bilayer center compared to the 2024 simulations, resulting in a larger region of biological water at the bilayer surface. This alone can result in a greater number of ions adsorbed in at least the steric adsorption mode.

Table 3.

Bilayer Structural Parameters^a

	without salt	Mg2+ HFE 2024	Mg2+ Micro 2024	Mg2+ HFE 2025	Mg2+ Micro 2025
hydration boundary (Å)	N/A	34.5	33.3	34.8	35.9
perfectly adsorbed charges	0	1.90	0.00	0.00	0.00
imperfectly adsorbed charges	0	3.68	6.23	28.43	96.93
sterically adsorbed charges	0	37.11	31.45	106.00	20.11
DHH (Å)	37.57 ± 1.27	38.15 ± 1.20	37.75 ± 1.19	40.75 ± 0.92	40.26 ± 0.96
DP–P (Å)	38.69 ± 4.866	39.56 ± 5.76	39.12 ± 5.94	42.35 ± 4.01	41.71 ± 2.94
2DC (Å)	26.98 ± 0.35	28.99 ± 0.31	28.08 ± 0.40	31.45 ± 0.29	30.84 ± 0.29
VCH1/CH2 (Å3)	26.33 ± 0.05	26.21 ± 0.05	26.33 ± 0.05	26.22 ± 0.04	26.12 ± 0.04
VCH3 (Å3)	54.97 ± 0.39	54.77 ± 0.39	54.98 ± 0.40	54.74 ± 0.24	55.19 ± 0.26
VC (Å3)	899.72 ± 1.01	895.85 ± 1.05	899.83 ± 1.06	895.94 ± 0.95	894.00 ± 1.11
$A_L=\frac{V_C}{D_C}$	66.71 ± 0.89	61.80 ± 0.66	64.10 ± 0.92	56.97 ± 0.54	57.98 ± 0.57

^aThe bilayer hydration boundary is defined as the position away from the bilayer center beyond which the solvent is isotropic and denotes bulk solvent from the bound solvent. The number of adsorbed charges in each adsorption mode are within the hydration boundary of the system and are further classified by the degree of loss of hydration water–steric adsorbed have lost no water, imperfect have lost at least one, and perfect have replaced all water oxygens for lipid oxygens. The bilayer thickness D_hh is defined as the distance between the peaks in the electron density of the system, roughly localizing the phosphate groups. D_P–P is measured as the peak-to-peak distance from the number density of the phosphate group, serving as an additional measure of the distance between the headgroups on either leaflet of the bilayer. 2D_C is the thickness of the acyl-chain region of the bilayer and is measured as the distance between the Gibb’s surfaces of the acyl-chain probability density. Lipid component volumes V_CH3 and V_CH1/CH2 are computed using the method of Petrache et al.³² V_C is computed from the component volumes by multiplying by the number of these components in each acyl chain. $A_L=\frac{V_C}{D_C}$ is the two-dimensional area occupied per lipid on the bilayer surface.^25,33–36 We note a correlation between simulations with larger numbers of adsorbed charges and perturbation of the bilayer structure from that of the simulation without salt, especially in the bilayer 2D_C.

MG²⁺ ADSORPTION BEHAVIOR

We classify any ion within the hydration boundary as at least sterically adsorbed, with further distinction, steric, imperfect, or perfect, based on how much dehydration the ion undergoes when approaching the bilayer center. Perfectly adsorbed ions have no coordinating waters remaining in their first hydration shell. An imperfectly adsorbed ion has at least one coordinating water but not a full coordination shell of waters. And finally, sterically adsorbed ions have their first coordination shell of waters intact, but they are spatially located within the hydration boundary of the lipid bilayer. To evaluate this, we define a cutoff to the first hydration shell computed from radial distribution functions. The cutoff used for Mg²⁺ in all systems is 3.3 Å, which captures the first peak for Mg²⁺ and lipid oxygens, water, and Cl⁻. We compute the nearest oxygens (lipid phosphate, glycerol, ester fragment, Cl⁻, or water) within these cutoffs of cations across the simulation system and generate a histogram averaged over slices and then over the last 150 ns of simulation time. This histogram is shown in Figure 2.

Figure 2.

Coordination partners of Mg²⁺. We note that while the Micro water with the 2024 parameters (b) do result in some dehydration of the Mg²⁺ in the headgroup region of the bilayer, both 2024 parameters (a,b) yield nearly no dehydration of Mg²⁺ at any location in the simulation box. The 2025 HFE parameters (c) still largely do not dehydrate, but the 2025 Micro parameters (d) do result in loss of 1–2 waters from the Mg²⁺ coordination shell within the headgroup region. We see substantial interaction with the headgroup phosphate oxygens, and no significant interaction with the glycerol or ester linkage oxygens. We also note the increased interaction with Cl⁻ in the simulations using the 2025 (c,d) parameters compared to both simulations with the 2024 parameters (a,b). The number of first shell Cl⁻ remains below one per ion in any simulation.

We note that the Mg²⁺ 2024 parameters result in very little dehydration of ions throughout the simulation box. The 2025 parameters result in loss of 1–2 waters as the ion approaches the bilayer center, with the Mg²⁺ 2025 Micro parameters resulting in the greatest degree of dehydration among parameter sets. The Mg²⁺ 2025 HFE parameters result in some loss of first shell water but no replacement in the first shell with lipid oxygens. There are a significant number of Mg²⁺–Cl⁻ pairs, where a single Cl⁻ replaces water in the first shell of Mg²⁺ as the ion moves into the lipid-occupied region of the bilayer. If these ions do not otherwise lose water for lipid parts, then they are counted as sterically adsorbed.

The Mg²⁺ 2025 Micro parameters appear to have a preference for direct interaction with the phosphate group oxygens when dehydrated, and none of the Mg²⁺ parameters studied result in significant direct interaction with the ester fragment and glycerol oxygens. There are also far fewer pairs with Cl⁻ under this parameter set. Fractions of ions in each adsorption mode have been computed by counting the number of ions in each frame within the hydration boundary and the number of those that have lost one water or all of their waters. We compute the averages over the last 150 ns and then fractions of the total adsorbed ions present in each mode. These values are shown in Figure 3, alongside the fraction of ions adsorbed vs the fraction remaining in the bulk solvent.

Figure 3.

(a) Distribution of Mg²⁺ ions in different membrane adsorption modes. Mg²⁺ are first classified into those in bulk and those adsorbed in membranes. Among those adsorbed in the membrane, Mg²⁺ are further classified into those that are perfectly, imperfectly, and sterically adsorbed. We note that compared to the 2024 models, the 2025 models result in increased membrane adsorption, and among the adsorbed Mg²⁺, the 2025 models result in increased direct coordination with lipid headgroups. Next to the plot, we show examples of Mg²⁺ in the steric (b) and imperfect (c) adsorption modes from our simulations. The perfect adsorption mode is rare in our simulations; thus, an example is not included. We note that in this example of the steric adsorption mode, (b) there is a Cl− (green) included in the hydration shell of the Mg²⁺ ion (magenta). This is an example of a partial–ion pair, which while having lost a water from the first—shell, it is not coordinating with lipid components directly_these are counted as sterically adsorbed.

The 2025 parameters result in significantly more adsorbed ions and, as a result, more adsorbed charges in both cases, with the most increased in the Mg²⁺ 2025 HFE simulation. We count the number of adsorbed charges in each adsorption mode by multiplying the number of ions in each mode by their charge; this would be 2 charges per Mg²⁺, and a Mg²⁺ paired with a Cl⁻ counts as a single charge. These numbers can be seen in Table 3 rows 2–4. We also note an increase in the number of imperfectly adsorbed ions in the Mg²⁺ 2025 HFE simulation. However, the Mg²⁺ 2025 Micro parameters result in ions shifting to the majority in the imperfect adsorption mode from the steric mode seen in both 2024 simulations. The Mg²⁺ 2025 HFE parameters still remain, with the largest fraction of ions in the steric adsorption mode. These differences in the distribution of adsorbed Mg²⁺ ions—particularly the rise in imperfect adsorption for Mg²⁺ 2025 Micro—raises the question of how such interactions reshape the membrane itself. We therefore turn to a structural analysis of the lipid bilayer to evaluate the consequences of these adsorption patterns.

Bilayer Structure

The effect of changes in ion adsorption on the bilayer structure was assessed through several structural parameters. Electron densities were computed using the gmx density tool included in the GROMACS software suite. Histograms were calculated in 1 ns chunks along the bilayer normal (z-axis) and centered at zero using the position of the minimum density, corresponding approximately to the bilayer midplane. These histograms were then symmetrized about the center and averaged over the final 150 ns of each trajectory.

From the resulting profiles, we calculated the small-angle X-ray scattering (SAXS) form factor by subtracting the average water electron density and applying a cosine transform. Electron density profiles and corresponding simulated SAXS form factors are listed in Figure 4.

Figure 4.

SAXS form-factors and associated electron densities for Mg²⁺ simulations. (a) Mg²⁺ 2024 under both Micro and HFE has little effect in changing the bilayer form-factor compared to that of the no-salt simulation, consistent with the available experimental results at lower ion concentrations. Conversely, both of the simulations with 2025 parameters result in significant thickening of the bilayer. This is also seen in the associated electron densities (b), where we see much taller peaks that are further apart in the Mg²⁺ 2025 simulations than that obtained from the 2024 simulations.

We note significant broadening of the bilayer peak-to-peak distance in the electron densities of the 2025 systems compared to the 2024 systems. Additional structural parameters are computed from the various number density histograms of our simulations. Similarly to the electron densities, we use the Gromacs GMX density tool to compute the number density histogram over 1 ns chunks of our simulation. We then center these histograms using the centerpoint found from the electron density at each 1 ns chunk. These histograms are then symmetrized and averaged over the last 150 ns of simulation time. These can be seen for solvent and lipid headgroup components of in Figure 5. We note greater accumulation of Mg²⁺ in the Mg²⁺ 2025 simulations, with greater peak densities of cations in the headgroup regions, with the largest peak in the Mg²⁺ 2025 HFE system.

Figure 5.

Number density histograms of lipid headgroup components. Vertical lines denote the bilayer tructural features such as the hydration boundary in purple, the D_hh in orange, and the 2D_C in red. We note that within the hydration boundary of each system, there is accumulation of ions–anions near the trimethylammonium nitrogen and cations accumulate near the phosphate group. The Mg²⁺ 2025 parameters (b,d) have a much larger accumulation of both ions in the headgroup region of the bilayer compared to the Mg²⁺ 2024 systems (a,c).

The bilayer thickness D_B and the acyl-chain region thickness 2D_C are computed as the distance between the Gibb’s surfaces of the probability densities of solvent and the lipid acyl-chain carbons, respectively.³⁷ These are computed from the number densities of these species for each 1 ns chunk of the simulation and then averaged over the last 150 ns of the simulation time. The values for these are listed in Table 3. We also compute the lipid component volumes using the method of Petrache et al.³² To do this, we partition the lipid number densities into headgroup and chains, with the headgroup consisting of any particles above the acyl chain ester fragment and the chains as just the acyl chain carbons. We partition the chains into groups of CH2 + CH1 and the terminal CH3 atoms. We optimize the following objective function to partition the volume in each histogram slice z_j from the number densities to these groups:

$$\Omega \left(v_i\right)=\sum _{z_j}^{{\rho }_s}\left(1-\sum _{i=1}^{N_{groups}}\left({\rho }_i\left(z_j\right){\left(v_i\right)}^2\right)\right)$$ (3)

From this, we obtain partial volumes for the groups v_CH1&CH2, v_CH3, and v_Headgroup. We equate the V_CH2 = v_CH1&CH2 as these densities have significant overlap, and thus, the volumes cannot be separated. This, along with V_CH3 = v_CH3, can be seen in Table 3. These volumes multiplied by the number of each moiety in a lipid are used to compute V_C. Finally, we compute the A_L as the ratio 2 × V_c/2D_C.^25,33–36

We note that in the systems with the smallest number of adsorbed charges in nonsteric modes (perfect and imperfect), in this case, the 2024-Mg²⁺ parameters show the smallest increase in 2D_C. The Mg²⁺ 2025 systems have the greatest number of adsorbed charges in nonsteric modes and have the largest increase in 2D_C over the system simulated without salt. We note that this trend is not followed necessarily in the D_hh, which is not a reliable measure of bilayer thickness due to the effect of headgroup tilt angle and overlapping number densities of water and salt in the headgroup region. In addition to these measures, we also compute a bilayer thickness from the distance between the peaks in the number density of the lipid headgroup phosphate. We note that this measure of bilayer thickness correlates more with what is seen in 2D_C for each bilayer system than the trend in the bilayer D_hh. Together, we note that the systems with the greatest number of charges in the Langmuir-type (nonsteric) modes correlate with an increase in the bilayer thickness (Figure 6).

Figure 6.

Adsorbed charge per adsorption modality per lipid as a function of the lipid bilayer hydrocarbon thickness 2D_C. We compare both our results from this work and our previous work with monovalent ions.¹⁷ There is a clear trend in the total number of adsorbed charges (i.e., any charges not in bulk solvent), where more charges result in a greater 2D_C. However, if one examines the sterically adsorbed charges, the trend is not as strong. This seems to indicate that the nonsteric charges are most responsible for the perturbation of the bilayer thickness from that of the no-salt simulation shown as the blue region on the plot.

CONCLUSIONS

We have presented a comparison between two Mg²⁺ parameter sets developed by our group under two different water–ion interaction models. The Mg²⁺ 2024 parameters, optimized using clusters of ions and lipid-component ligands at subfull oxygen coordination of the ion,¹⁷ predict steric adsorption with negligible bilayer thickening. By contrast, the Mg²⁺ 2025 parameters, optimized using fully coordinated clusters by replacing the missing ligand oxygens with waters, similar to sets of target data used to improve parameters for Mg²⁺–nucleotide phosphate interactions,¹⁵ yield significantly more ions in nonsteric adsorption modes, greater direct coordination with lipid phosphates, and a correlated increase in bilayer thickness. Both parameter sets reproduce their respective substitution energy targets, but the choice of partially versus fully coordinated clusters leads to divergent predictions for bilayer behavior. This raises a fundamental question about the nature of Mg²⁺ adsorption and potentially of divalent ions in general. Both water-separated and direct-interaction adsorption modes have been described for Mg²⁺–phosphate interactions in biological molecules,^{18,19,38–44} and simulations with older ion models tend to favor the water-separated modes.^{18,19,38,39,45} With sparse experimental data for lipid bilayers at relevant salt concentrations, it is not yet possible to judge these models. Thus, the two parameter sets serve as complementary hypotheses and experimental targets, highlighting that the critical open question is not only which parameters best reproduce bilayer structure but also which underlying reference chemistry most faithfully represents Mg²⁺–lipid interactions in the condensed phase.

Supplementary Material

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c04665.

Parameter bounds and active constraints for the Lennard-Jones terms used in Mg²⁺–lipid interactions, comparative plots of Mg²⁺–ligand cluster geometries optimized with QM and molecular mechanics methods, and references supporting the computational methodology (PDF)