Parameterization of the CHARMM Force Field for Divalent Cations (Ca²⁺/Be²⁺) binding to Anionic Lipids with Isothermal Titration Calorimetry

Abstract

Beryllium toxicity manifests as a rare lung disease, berylliosis, characterized by persistent granulomas. Studies indicate that, in the presence of ${\text{Be}}^{2+}$, macrophage phagocytosis is markedly reduced, potentially hindering the removal of apoptotic cells. Although the exact mechanism by which ${\text{Be}}^{2+}$ ions reduce phagocytosis is unclear, one hypothesis suggests that these small ions outcompete ${\text{Ca}}^{2+}$ in critical ion-lipid and lipid-protein interactions mediating lipid recognition. To explore these interactions at the atomic level using molecular dynamics (MD), we aim to improve existing MD force fields for ${\text{Be}}^{2+}$-lipid interactions. Based on thermodynamic binding data from isothermal titration calorimetry, we have updated the CHARMM36 force field to describe interactions of ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ with palmitoyl-oleyl phosphatidic acid (POPA), palmitoyl-oleyl phosphatidyl glycerol (POPG), and small-molecule mimics of their headgroups. Our results show that the original force field overestimated the binding affinity of ${\text{Be}}^{2+}$ for POPA and POPG by a factor of 4–6. The revised parameters differentiate how ions bind to phosphate groups in monoester and diester forms. We describe the interrelationships among L-J parameters, ion coordination, and binding energies, highlighting the significant role of water in ${\text{Be}}^{2+}$-ion interactions. This work provides updated CHARMM36 force-field parameters for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$, improving the accuracy of their interactions with potent signaling lipids, POPA and POPG, and better reflecting physiological behavior. ${\text{Be}}^{2+}$ exhibits a stronger binding tendency, which can displace ${\text{Ca}}^{2+}$ from its sites and hinder lipid recognition and phagocytosis.

I. INTRODUCTION

Beryllium $\left({\text{Be}}^{2+}\right)$ is the smallest divalent cation in the periodic table. Its ionic radius is smaller than both ${\text{Mg}}^{2+}$ and ${\text{Ca}}^{2+}$, due to which it has a higher ionic charge to radius ratio (ionic potential), $\text{z}/r_{Be}=5.7$, compared to other similarly small, monovalent and divalent cations $\left({\text{Li}}^{+}=\right.1.31,{\text{Mg}}^{2+}=2.78,{\text{Ca}}^{2+}=2.02)$. This makes it a highly polarizing cation, capable of substituting ${\text{H}}^{+}$ in water, forming stable ${\left[\text{Be}{\left({\text{H}}_2\text{O}\right)}_4\right]}^{2+}$ complexes, and creating stronger non-covalent bonds than H-bonds^1,2,3. Although rare in natural environments, beryllium is actively mined and subsequently used in industries that manufacture aircraft, automotive parts, and refrigeration systems. Workers in these industries are exposed to beryllium as oxide or metallic alloy dust⁴. Prolonged exposure through skin contact and inhalation can induce Beryllium Sensitivity (BeS) in certain individuals⁵, which may lead to Chronic Beryllium Disease (CBD) or Berylliosis. In CBD, both innate and adaptive immune responses (including MHC-II allele variants) are activated, leading to unresolving granulomas in the lungs^6,7. Previous work from Ermakov et al.⁸ demonstrated that phagocytosis of lipid-coated beads and senescent erythrocytes by macrophages is reduced by half in the presence of ${\text{Be}}^{2+}$. Therefore, ${\text{Be}}^{2+}$ can inhibit normal cell clearance, possibly by suppressing recognition of apoptotic cells by phosphatidylserine receptors on macrophages, which results from replacing ${\text{Ca}}^{2+}$, which is normally required for lipid recognition. Mediating receptor-lipid complexes, ${\text{Ca}}^{2+}$ is typically coordinated by carboxyls on the protein side and by phosphates and carboxyls on the lipid side. ${\text{Be}}^{2+}$ may not functionally replace ${\text{Ca}}^{2+}$ in such complexes because it has a maximum coordination number of 4, compared to 6–7 for ${\text{Ca}}^{2+}$. Thus, unlike ${\text{Ca}}^{2+}$ it has a much stronger preference to bind and cross-link phosphates rather than mediating between carboxyls and protein phosphates.

Molecular dynamics (MD) is a physics-based simulation method that is used to study cellular interactions at the molecular level with atomistic or coarse grained resolution. It is a deterministic time evolution method and has been used to study various ion and lipid systems^9,10. One of the main challenges of MD simulation is parameterizing accurate force fields (FF)¹¹, that define the bonded (bond, angle, dihedral) and non-bonded (electrostatic, van der Waals) interactions between two atoms. We use the CHARMM36 FF^12,13, as it is the most well-parameterized FF for lipids at the atomistic scale¹⁴; however, it has not been fully parameterized for ${\text{Be}}^{2+}$. Previously, Leonard et al.¹⁵ parameterized the interaction between ${\text{Be}}^{2+}$ and dioleoyl-glycero-3-phosphoserine (DOPS) lipids using experimentally obtained data by isothermal titration calorimetry (ITC), such as the dissociation constant $K_d$. The binding affinity of ${\text{Be}}^{2+}$ and its effects on lipid monolayer compression isotherms¹⁵ were also used for FF parametrization. In this work, we expand the range of lipids to include two anionic lipids, i.e., 1-palmitoyl- 2-oleoyl-sn-glycero-3-phosphate (POPA), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG). These lipids have general biological importance: phosphatidic acid (PA) is a signaling molecule that modulates cytokine responses in the lung, and is also a phospholipid precursor crucial for the production of pulmonary surfactant¹⁶. On the other hand, POPG has been shown to be part of pulmonary surfactant and to have potent anti-inflammatory action¹⁷. We collect experimental ITC data on small-molecule mimics of their headgroups and on liposomes composed of POPA and POPG lipids, with both ${\text{Ca}}^{2+}$ and ${\text{Be}}^{2+}$. The experimental data enabled us to introduce necessary corrections in FF parameters, specifically for ${\text{Be}}^{2+}$.

II. METHODS

A. Small Molecule Proxy for Lipid Headgroups

Our focus is on two phospholipids with different phosphate group configurations, POPA and POPG, which are structurally shown in Fig. S1. Glycerol-3-phosphate (G3P) was used as a small molecule proxy to represent the functional headgroup of POPA and POPG lipids, as well as the ${\text{PO}}_4$ group on phosphorylated proteins. 1 mM HCl was titrated into 2 mM solution of G3P in 10 mM Tris-KCl buffer. Our titration results show that G3P has two pKas $\left(p{K}_{a1}=2.87,p{K}_{a2}=\right.6.65)$, as seen in Fig. S2, and therefore at pH 7 it can exist in two charged states, −1 and −2. In its −2 charged form, G3P’s free phosphate closely mimics the PA headgroup, while in its −1 form, it can serve as a proxy for the PG headgroup. It also provides a better representation of lipid phosphate groups than the previously used small-molecule proxy, dimethyl phosphate (DMP). We created two G3P models for our simulations: G3P1 (−1 charge) and G3P2 (−2 charge), as shown in Fig. S3.

B. Solution and Liposome Preparation

Powdered sn-Glycerol 3-phosphate (G3P) was purchased from Millipore Sigma and used to prepare a 25 mM solution (pH ~ 6) in 10 mM KCl and 10 mM Tris-HCl buffer. For the ITC experiments, ${\text{BeSO}}_4$ and ${\text{CaCl}}_2$ solutions were prepared in the same Tris buffer (pH 7.0). Except for the ${\text{Be}}^{2+}$-G3P ITC experiments, all solutions contained 10 mM KCl. POPA and POPG liposomes were prepared in the same 10 mM KCl and 10 mM Tris-HCl buffer. Since pure POPA and POPG liposomes are not stable, we added 25 mole % of POPC as a bilayer-stabilizing component, resulting in 3:1 POPA:POPC and 3:1 POPG:POPC liposomes. Anhydrous POPC (molecular weight = 770.989 g/mol), POPA (molecular weight = 696.91 g/mol), and POPG (molecular weight = 760.076 g/mol) powders in glass ampoules were purchased from Avanti Polar Lipids. 25 mg of the powdered lipids were dissolved in 2.5 mL of chloroform and used to prepare 3:1 POPA:POPC and POPG:POPC lipid solutions. The chloroform was evaporated using directed airflow, after which the lipid powders were left to dry in a vacuum-sealed desiccator overnight (at least 12 hours). The lipid residue was rehydrated in 10 mM KCl and 10 mM Tris-HCl, then sonicated in a bath sonicator and vortexed to prepare liposome solutions at $500\mu \text{M}$. The sonication and vortex steps were repeated until all visible lipid residue was fully suspended. Soluble products of lipid degradation were removed by dialysis in buffer (10 mM KCl, 10 mM Tris-HCl). The buffer from dialysis was used to prepare the ${\text{BeSO}}_4$ and ${\text{CaCl}}_2$ solutions to maintain the same composition for the liposome ITC experiments.

C. Isothermal Titration Calorimetry (ITC) Protocol

The ${\text{BeSO}}_4$ and ${\text{CaCl}}_2$ solutions were placed in the ITC chamber while the G3P and liposome solutions were titrated in from the syringe. This was done to avoid the high heat of dilution of the divalent cation solutions as done previously by Leonard et al.¹⁵. Titrations were carried out in MicroCal VP-ITC calorimeter by Malvern at 25°C. Each injection, except for the first (2 uL) was 10uL and spaced for 10s duration spaced by 300s interval for a total of 28–30 injections. Each ITC experiment had a control run with only the buffer solution without G3P/liposome titrated into the metal ion solution. The single-site binding model was used to fit the data with 100 Monte Carlo trials to obtain the $K_d$ values and standard deviation for each replicate.

D. Molecular Dynamics

Two topologies for G3P were constructed as mentioned in Section II A. The phosphate group in G3P1 and G3P2 models of glycerophosphate has oxygen atoms of type O2L. Thus the CHARMM36 FF parameter for the BE-O2L $\epsilon$ and $r_{\mathit{\text{min}}}$ NBFIX was modified (Code 1, Code 2).

$$U_{r_{ij}}=\sum _{ij}{\epsilon }_{ij}\left[{\left(\frac{r_{{min}_{ij}}}{r_{ij}}\right)}^{12}-{\left(\frac{r_{{min}_{ij}}}{r_{ij}}\right)}^6\right]$$ (1)

The NBFIX introduced by Leonard et al. was used for ${\text{Be}}^{2+}-{\text{H}}_2\text{O}$ interactions. Packmol¹⁸ and CHARMM-GUI^19,20 was used to build the ion-ligand system in water. Two systems were built for the binding simulations- (i) 20 ${\text{Be}}^{2+}$ ions and 60 G3P molecules, (ii) 20 ${\text{Ca}}^{2+}$ ions and 60 G3P molecules – in 10mM KCl buffer (Table S1). The TIP3P²¹ water model was used for the solvent.

1. System Setup and Simulation: ${\text{X}}^{2+}$ Ion Systems with G3P1/G3P2

Packmol¹⁸ was used to build the ligand in water systems with and without the ion $\left({\text{X}}^{2+}\right)$. All simulations were run using OpenMM 8.0.0²² with CHARMM36¹³ forcefield. The systems were equilibrated using the standard protocol: 5,000 steps of energy minimization, 125,000 equilibration steps in NVT with a timesteps of 1fs, followed by NPT equilibration with a 2fs timestep. OpenMM’s LangevinIntegrator, with a friction coefficient of 1ps⁻¹, served as the thermostat, and the MonteCarloBarostat²³ maintained pressure at 1bar with pressure coupling every 100 steps. Hydrogen bonds to heavy atoms were constrained using OpenMM’s HBonds, which employs the SHAKE algorithm²⁴, while SETTLE and CCMA algorithms^25,26 constrained water hydrogens. Long-range electrostatic interactions were evaluated using Particle Mesh Ewald (PME)²⁷ method. The 10–12 Å force-switch cutoff was used for the Lennard-Jones interactions. All simulations were done at 298K for 40ns as listed in Table S1 (Fig. S4B, Fig. S5B).

2. System Setup and Simulation: ${\text{X}}^{2+}$ Ion Systems with POPA/POPG membranes

All POPA(-1)/POPG membrane systems were built using CHARMM-GUI Membrane Builder²⁰. The systems were equilibrated using the CHARMM-GUI protocol for membranes for 5,000 energy minimization steps followed by five sequential 125,000 equilibration steps in NVT with restraints on the lipid positions and dihedrals which are gradually removed. This was followed by 250,000 NPT equilibration steps with a timesteps of 2fs. OpenMM’s LangevinIntegrator with a friction coefficient of 1ps⁻¹ was used as thermostat and the MonteCarloMembraneBarostat was used to maintain X-Y isotropic pressure at 1bar with a pressure coupling every 100 steps. The hydrogen bond constraints, L-J cutoff and electrostatic interaction treatment were same as the ligand systems. All simulations were run on OpenMM 8.0.0 at 298K for 200–500ns (Table S2).

E. Clustering Protocol for Bound Configurations

The last 20 ns of the equilibrated ion-ligand simulations were used for clustering. A contact matrix was generated for each ${\text{Be}}^{2+}/{\text{Ca}}^{2+}\left({\text{X}}^{2+}\right)$ ion, recording distances to its four closest neighbors with a P atom (G3P2) and an O atom (TIP3), within a 5 Å cutoff. If fewer than four neighbors were found within the cutoff for any type, the matrix was padded with a very high constant. Consequently, 8 distances were measured and stored for each ${\text{X}}^{2+}$ ion in every frame. The distance measurements were performed in parallel using the job processing package joblib²⁸. K-means clustering was conducted over a range of cluster sizes from 2 to 11, and the KneeLocator module from the package kneed²⁹ was used to identify the optimal k. The radial distribution function (RDF) of the ${\text{X}}^{2+}$ ion from the medoid configuration was calculated, and the position of the minima following the first maximum/peak was determined. A structure cutoff was set at 3 Å beyond the minima distance. All residues with at least one atom within this structure cutoff from the ${\text{X}}^{2+}$ ion were considered part of the bound configuration. The bound configuration from the medoid of each cluster was then used to perform Free Energy Perturbation (FEP)³⁰ calculations.

F. Free Energy Perturbation Protocol

The medoid configurations from each cluster were used to construct the two legs of the FEP thermodynamic cycle - a bound G3P configuration with ${\text{X}}^{2+}$ ion and a G3P configuration with the ion removed to mimic the unbound state. The yank³¹ program was used with the CHARMM36 FF to perform Free Energy Perturbation (FEP)³² calculations on the two states. A second FEP cycle was designed to assess the effect of bound water from the simulations. In this the waters from the medoid configurations were removed in both bound-unbound states and then resolvated. The FEP simulations were run at 298K and 1 atm with a 2 fs time step. Hamiltonian-Replica Exchange^33,34 was attempted 500 times, with exchanges attempted every 1 ps. PME was employed for electrostatic interactions, and a 10–12 Å force-switch cutoff was used for Lennard-Jones interactions, along with a soft-core potential. Harmonic restraints were applied to the initial coordinates of the ${\text{X}}^{2+}$ ion and the phosphorus (P) and oxygen (O) atoms of the ligand. The electrostatic potential was first scaled down with l, followed by the Lennard-Jones potential, both with a $\lambda$ step size of 0.1 (Code 3).

G. Boltzmann Reweighting

The $\Delta G$ from each medoid configuration of bound ${\text{X}}^{2+}$ ion to G3P1/G3P2 was Boltzmann averaged to get the final $\Delta G$-

$$⟨\Delta G⟩=\sum _i\frac{e^{\left(\frac{-\Delta G_i}{RT}\right)}}{Z}*\Delta G_i$$ (2)

Where, $Z=\sum _i{e}^{-\Delta G_i/RT}$ where $i$ is in the set of all medoids.

H. Umbrella Sampling

The ${\text{X}}^{2+}$-membrane simulations were clustered using the method described in Section II E. The method was used to find bound configurations of the ${\text{X}}^{2+}$ ion with POPA/POPC or POPG/POPC phosphate oxygen atoms and cluster them to obtain representative structures. One cluster was selected for further Umbrella Sampling (US)³⁵ analysis. To increase the pulling distance of the ion from the membrane, GROMACS³⁶ module gmx editconf was used to increase the box-dimension along z by 2nm on each side and gmx solvate to add extra water. The bound ${\text{X}}^{2+}$ ion was steered away from its bound position along the z-direction using Steered MD with GROMACS patched with PLUMED³⁷. The same was repeated to steer the ion towards the membrane using a force constant of $k=1000\text{kJ}{\text{mol}}^{-1}{\text{nm}}^{-2}$. Frames from the steered MD were selected for the US windows with a distance separation of 2Å between the ion positions in the frames. Each window was simulated for a total of 40 ns with a restraint of $k=500\text{kJ}{\text{mol}}^{-1}{\text{nm}}^{-2}$ on the ion and on the lipid phosphorus atom to prevent membrane deformation due to the ${\text{X}}^{2+}$ ion. Trajectories were analyzed using the gmx wham module for Weighted Histogram Analysis Method (WHAM)³⁸ to generate the Potential of Mean Force (PMF) profiles. Bootstrapping with 100 trials was performed to determine the standard deviation for the PMFs.

I. Analyses

1. Coordination number

The coordination number of oxygen atoms (O2L-G3P2 or OH2-water) around the ${\text{X}}^{2+}$ ion was calculated along the trajectory to monitor the system’s equilibration. The trajectories were divided into 1 ns blocks. The radial distribution function (RDF) was computed for each block using the MDAnalysis³⁹ module InterRDF with a distance range of 0–10 Å. The RDF was integrated to identify the location of the first minimum following the first peak, yielding the coordination number for each block as shown in Fig. S4B and Fig. S5B. The RDFs of water and G3P2 oxygen atoms relative to the ${\text{X}}^{2+}$ ion were combined to obtain the total oxygen RDF. The positions of the first peak and minima were used to determine the coordination numbers of the first and second shells for water and G3P. The RDF was integrated up to the first minimum for the first shell and beyond it for the second shell to obtain the respective coordination numbers. Multiple coordination number calculations were parallelized using the joblib Python package.

2. Angular distribution

MDAnalysis was used to calculate the angular distribution of the oxygens around the ${\text{X}}^{2+}$ ion (O-X-O). All the oxygen atoms within a distance cutoff of 5 Å from the ${\text{X}}^{2+}$ ion were selected. The unit vector from the ${\text{X}}^{2+}$ ion to every oxygen atom was measured, and the dot product between each pair of vectors was calculated, giving us the cosine angles O-X-O.

$$\theta ={\mathit{\text{cos}}}^{-1}\left({\hat{n}}_i\cdot {\hat{n}}_j\right)$$ (3)

Where, ${\hat{n}}_i$ and ${\hat{n}}_j$ are unit vectors from ${\text{X}}^{2+}$ to the $i$-th and $j$-th oxygen atom.

III. RESULTS

A. Deprotonated G3P interacts with ${\text{X}}^{2+}$ ion

The ITC data for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ binding to the small molecule proxy G3P (glycerol-3-phopshate) were measured. Traditionally, DMP (dimethyl phosphate) has been used as a proxy for phosphate groups in the CHARMM forcefield. However, unlike DMP where the phosphate is capped by two methyl groups, in G3P we have the full phosphoglycerol backbone (modelled especially by the −1 protonation state) improving the forcefield fit to experimental ITC data and making it transferable to other phospholipids as well. Both ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ bind to the phosphate oxygen(s) on G3P. From our pH titrations of G3P we know that the two $p{K}_a\text{s}$ are 2.87 and 6.65 (see Section II A). Using the Henderson-Hasselbach equation we can calculate the proportion of single- (G3P1) and double- deprotonated G3Ps (G3P2) in the solution(Fig. S2).

$$pH=p{K}_a+\text{log}\frac{\left[G3P2\right]}{\left[G3P1\right]}$$ (4)

where, $p{K}_{a1}=2.87,p{K}_{a2}=6.65$ and $\text{pH}=7.00$ gives a ratio [G3P2]/[G2P1] = 2.24, thus we have twice as many G3P2 than G3P1 in our solutions. It is also known that ${\text{Be}}^{2+}$ can substitute water in hydrogen bonds, hence it is highly likely that ${\text{Be}}^{2+}$ deprotonates G3P1 to G3P2 to form stronger non-covalent bonds. Also, from our simulations, we found ${\text{Be}}^{2+}$ does not form bound clusters with G3P1, unlike with G3P2. Thus, going forward, we are primarily concerned with the double deprotonated state of G3P (G3P2) in the case of ${\text{Be}}^{2+}$. The ITC data was collected as described in II C and was integrated into the one-site binding model to obtain the enthalpy $\left(\Delta \text{H}\right)$ and $K_d$.

B. Calorimetric data reveal ${\text{Be}}^{2+}$ to be a stronger binder than ${\text{Ca}}^{2+}$

${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ bind to the phosphate oxygens in G3P/POPA/POPG through electrostatic interactions. The strength of this interaction is determined through the ion’s coordination, distance and screening by water. ${\text{Be}}^{2+}$-G3P binding is an exothermic event unlike for ${\text{Ca}}^{2+}$, which is endothermic as shown in Fig. 1. Our results indicate that the dissociation constant $\left(K_d\right)$ of ${\text{Be}}^{2+}-\text{G}3\text{P}$ is $55.98\mu \text{M}(\Delta G-5.81\text{kcal}/\text{mol})$, while for ${\text{Ca}}^{2+}-\text{G}3\text{P}$ is $418.91\mu \text{M}(\Delta G-4.59\text{kcal}/\text{mol})$, suggesting that ${\text{Be}}^{2+}$ binds to G3P roughly ten times stronger than ${\text{Ca}}^{2+}$. Similarly, the $K_d$ of ${\text{Be}}^{2+}-\text{POPA}/\text{POPG}$ liposome is lower (indicating stronger binding) than for ${\text{Ca}}^{2+}-\text{POPA}/\text{POPG}$ liposome (Fig. 2, Table I). Overall, ${\text{Ca}}^{2+}$ is a weaker binder than ${\text{Be}}^{2+}$ to both the small molecule G3P and the liposomes. This is most likely due to ${\text{Ca}}^{2+}$’s lower ionic potential $\left(\text{z}/r_a\right)$ and higher water coordination compared to ${\text{Be}}^{2+}$, resulting in weaker electrostatic interaction with the phosphate oxygens.

FIG. 1.

ITC thermogram and integrated heat data for G3P binding to (A) ${\text{Be}}^{2+}$ and (B) ${\text{Ca}}^{2+}$. The ITC replicates are shown in three different colors in both upper and lower graphs. Monte Carlo trials are shown in lighter shades.

FIG. 2.

ITC thermogram and integrated heat data for POPA liposome binding to (A) ${\text{Be}}^{2+}$, (B) ${\text{Ca}}^{2+}$ and POPG liposome binding to (C) ${\text{Be}}^{2+}$, (D) ${\text{Ca}}^{2+}$.

TABLE I.

Average Binding Free Energies $\left(\Delta G\right)$ determined by ITC for G3P and Phospholipids with Divalent Cations. The $K_d$ and $\Delta G$ values and errors reported are from the mean and standard deviation of three replicates.

S	C	$K_d\left(\mu \text{M}\right)$	$⟨\Delta G⟩(\text{kcal}/\text{mol})$
G3P	${\text{Be}}^{2+}$	56 ± 15	−5.77 ± 0.15
POPA	${\text{Be}}^{2+}$	8.83 ± 0.3	−6.87 ± 0.02
POPG	${\text{Be}}^{2+}$	61.16 ± 7.05	−5.72 ± 0.07
G3P	${\text{Ca}}^{2+}$	403 ± 25	−4.61 ± 0.04
POPA	${\text{Ca}}^{2+}$	33 ± 20	−6.1 ± 1.94
POPG	${\text{Ca}}^{2+}$	463 ± 162	−4.53 ± 0.29

S = Syringe, C = Chamber. All measurements performed at 298.15 K.

Notably, both ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ bind most strongly to POPA, followed by G3P and POPG, which have similar $K_d$ values. The dissociation constant of ${\text{Be}}^{2+}$ binding to POPA $\left(K_d=8.69\mu \text{M}\right)$ is an order of magnitude lower than that of ${\text{Ca}}^{2+}-\text{POPA}$ $\left(K_d=83\mu \text{M}\right)$. In fact, the $K_d$ of ${\text{Be}}^{2+}-\text{POPG}\left(K_d=63.1\mu \text{M}\right)$ is lower than that of ${\text{Ca}}^{2+}-\text{POPA}$. Therefore, the binding strength order for the two ions is ${\text{Be}}^{2+}-\text{POPA}>{\text{Be}}^{2+}-\text{G}3\text{P}>~{\text{Be}}^{2+}-\text{POPG}>{\text{Ca}}^{2+}-\text{POPA}>{\text{Ca}}^{2+}-\text{G}3\text{P}>\sim {\text{Ca}}^{2+}-\text{POPG}$.

The weaker binding to POPG liposomes can be explained by steric hindrance from the PG lipid headgroup, which differs from the PA headgroup. The phosphate oxygens on POPG are less accessible due to the glycerol group, leading to weaker binding of both ions. Conversely, POPA liposomes are the strongest binders for both ions, likely because lipids in liposomes are confined to a plane in high density, making phosphate oxygens more accessible and allowing for multiple interactions. G3P molecules are not spatially restricted, so their ion-binding is balanced by their diffusional distribution in surrounding water. Our results show that ${\text{Be}}^{2+}$ binds much more strongly than ${\text{Ca}}^{2+}$ for G3P, POPA and POPG liposomes. Both ions follow the same trend of binding strengths - POPA > G3P > POPG, as described above.

C. LJ Parametrization Recreates Inner Shell Hydration

In previous versions of the CHARMM36 forcefield, the NBFIX $r_{\mathit{\text{min}}}$ for O2L to ${\text{Be}}^{2+}$ was set at 2.92Å (from Leonard et al.¹⁵), yielding a Boltzmann-averaged free energy of −25 kcal/mol which is 4.3 times the experimental $\Delta G(-5.82\text{kcal}/\text{mol})$. For ${\text{Ca}}^{2+}$ simulations, the initial $r_{\mathit{\text{min}}}$ was 3.256 Å and had a Boltzmann averaged $\Delta G$ of −12 kcal/mol, which is 2.6 times the experimental $\Delta G$ (−4.59 kcal/mol). This shows that the initial CHARMM36 lipid forcefield L-J parameters overestimated binding for both ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$.

To remedy this, ${\text{Be}}^{2+}/{\text{Ca}}^{2+}$ and G3P binding simulations were conducted at different L-J $r_{\mathit{\text{min}}}$ values (See Table II) and clustered as described in Methods (Section II E). The last 20 ns were used for further analysis. We observe a clear difference between G3P1 and G3P2 oxygen atoms (O2L) that coordinate ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$. Based on the $p{K}_a$ values of G3P, we expect only G3P2 (-2) to interact with the ions, especially ${\text{Be}}^{2+}$. This is confirmed by our simulations, where the coordination number (CN) of G3P1, from the equilibration plots in Fig. S4B and Fig. S5B for both ions, is never greater than 1 across all $r_{\mathit{\text{min}}}$ values tested. In contrast, G3P2 shows an increase in the CN of the O2L atoms to ${\text{Be}}^{2+}$ as the $r_{\mathit{\text{min}}}$ increases, rising from $1.4\left(r_{\mathit{\text{min}}}=2.92\AA \right)$ to $4.9\left(r_{\mathit{\text{min}}}=4.50\AA \right)$. The $r_{\mathit{\text{min}}}=3.50\AA$ appears to be an outlier relative to the linear increase in CN. We will later see that this is a transition point in the G3P2 oxygen density around ${\text{Be}}^{2+}$. The ${\text{Ca}}^{2+}$ and G3P2-O2L CN change little, slightly decreasing from $5.9\left(r_{\mathit{\text{min}}}=3.256\AA \right)$ to $4.8\left(r_{\mathit{\text{min}}}=3.80\AA \right)$ as $r_{\mathit{\text{min}}}$ increases.

TABLE II.

${\text{X}}^{2+}-\text{O}2\text{L}$ NBFIX $r_{\mathit{\text{min}}}$ values tested for force field optimization.

$\text{Ion}({\text{X}}^{2+}$)	$r_{\mathit{\text{min}}}(\AA )$
${\text{Be}}^{2+}$	2.92*, 3.00, 3.50, 3.75, 3.80, 3.90, 4.00, 4.25, 4.37, 4.50
${\text{Ca}}^{2+}$	3.256*, 3.40, 3.60, 3.80

^*indicates the original CHARMM36 parameters.

The radial distribution function (RDF) and the coordination number (CN) of the oxygen atoms around the ions ${\text{X}}^{2+}$ give us insight into the structure of the configurations. The inner and outer CN were obtained by fitting the CN timeseries to a Poisson distribution. The density profile for ${\text{Be}}^{2+}-\text{O}2\text{L}$ at the initial $r_{\mathit{\text{min}}}2.92\AA$ as seen in Fig. 3A shows a sharp first shell peak at $r=1.8\AA$ followed by a smaller second shell bump at 3.8Å. As the $r_{\mathit{\text{min}}}$ increases, the first peak density drastically reduces by nearly half at $r_{\mathit{\text{min}}}3.00\AA$. The density profile at $r_{\mathit{\text{min}}}3.50\AA$ is a transition point, as it still retains a first-shell peak but has shifted from the original distance to $r~2.2\AA$. By increasing the ${\text{Be}}^{2+}-\text{O}2\text{L}{r}_{\mathit{\text{min}}}$, we have shifted the first shell O2L to merge with the second shell, and $r_{\mathit{\text{min}}}=3.50\AA$ is the transition point. We can see this in the inner vs. outer shell coordination numbers in Fig. 3C. The inner CN of O2L reduces to less than 1 as the $r_{\mathit{\text{min}}}$ increases for ${\text{Be}}^{2+}$. At the same time the inner shell CN of water increases to 4 which indicates that as the $r_{\mathit{\text{min}}}$ increases ${\text{Be}}^{2+}$ becomes fully hydrated with a CN of 4 water this pushes out the G3P into the outer shell. The outer shell CNs of G3P and water do not change much after the initial shift, as evidenced by the stable CN in Fig. 3C. We see a similar shift in the first-shell peak for ${\text{Ca}}^{2+}$, where the transition occurs at $r_{\mathit{\text{min}}}=3.40\AA$, with the water inner CN increasing from 4 to 6 and the G3P inner CN reducing to close to zero. These observations are supported by the angular distribution of water around ${\text{Be}}^{2+}$ which shifts into a tight tetrahedron as observed by the O-Be-O $\left(\theta \right)$ angular distribution in Fig. 3E and Fig. 3F whereas the water around ${\text{Ca}}^{2+}$ forms an octahedral geometry.

FIG. 3.

Structural analysis of ion-G3P interactions: (A) ${\text{Be}}^{2+}$ and (B) ${\text{Ca}}^{2+}$ RDFs at different $r_{\mathit{\text{min}}}$ values; Probability densities of the inner shell coordination number P(CN) of G3P (reds) and water (blues) for (C) ${\text{Be}}^{2+}$ and (D) ${\text{Ca}}^{2+}$ ion. The color intensity displays the shift in P(CN) from low (light blues/reds) to high (dark blues/reds) $r_{\mathit{\text{rmin}}}$; Angular distribution functions for (E) O-Be-O and (F) O-Ca-O) as a function of the $r_{\mathit{\text{min}}}$. The colorbar goes from red (lowest $r_{\mathit{\text{min}}}$) to blue (highest $r_{\mathit{\text{min}}}$).

When we look at the raw (total) CN timeseries (Fig. S6B, Fig. S5B), we find that the ${\text{Be}}^{2+}-\text{O}2\text{L}$ CN increased with the increase in the $r_{\mathit{\text{min}}}$ when the first shell peak shifted from the inner to the outer shell. This implies that at low $r_{\mathit{\text{min}}}$ the O2L-O2L electrostatic repulsion takes precedence over the ${\text{Be}}^{2+}-\text{O}2\text{L}$ attractive term, thus reducing the number of O2L atoms that the ion can coordinate at low $r_{\mathit{\text{min}}}$. The ion ${\text{X}}^{2+}$ can now accommodate more G3P2 molecules at a larger distance r since the O2L-O2L electrostatic repulsion decreases as $1/r$. But these G3P2 molecules must be accommodated in the outer shell as observed by the inner vs. outer shell CN in Fig. S8A and Fig. S8B. As the $r_{\mathit{\text{min}}}$ increases, we implicitly change the ${\text{X}}^{2+}-\text{O}2\text{L}$ (G3P2) configuration into ${\text{X}}^{2+}-\text{H}2\text{O}-\text{O}2\text{L}$ (G3P2), where the ${\text{X}}^{2+}$ electrostatically interacts with the water oxygen, while the water forms hydrogen bonds with the G3P oxygen (O2L). The water thus forms the inner interaction shell while the G3P2 is in the outer shell. This is similar to what has been previously observed for ${\text{Mg}}^{2+}$ and ${\text{Ca}}^{2+}$ interacting with RNA phosphates^40,41, where ${\text{Mg}}^{2+}$, with its higher ionic potential, mainly interacts with the inner shell of the phosphate oxygen, whereas ${\text{Ca}}^{2+}$ interacts through the outer shell (with water in the inner shell). We expect that ${\text{Be}}^{2+}$, with its higher polarizing ability than ${\text{Ca}}^{2+}$, will induce the surrounding water and G3P2 dipoles, which cannot be adequately represented in an all-atom additive (non-polarizable) framework. But we attempt to achieve a close approximation by adopting the configuration that best matches the experimental binding enthalpy data for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ to G3P.

D. Updated Lennard-Jones Parameter Corrects Overbinding

We ran simulations of the ${\text{X}}^{2+}$ ions with G3P2 at various $r_{\mathit{\text{min}}}$ values (Table II) and clustered the bound ${\text{X}}^{2+}$-G3P2 configurations to obtain the structure representative of the cluster medoid Fig. 4. These final structures were used to calculate the binding $\Delta G$ using Free Energy Perturbation (FEP) as mentioned in Section II F, results listed in Table III. The final $r_{\mathit{\text{min}}}$ obtained for ${\text{Be}}^{2+}$ is $3.80\AA$ and for ${\text{Ca}}^{2+}$ is 3.60 Å (Fig. 5).

FIG. 4.

Representative configurations of hydrated ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ bound to G3P2. (A) ${\text{Be}}^{2+}$ medoid and (B) ${\text{Ca}}^{2+}$ medoid. The ions are shown in van der Waals representation with ${\text{Be}}^{2+}$ in pink and ${\text{Ca}}^{2+}$ in cyan. Waters are represented in triangle licorice.

TABLE III.

Free energy of binding $\left(\Delta G\right)$ calculated from FEP simulations at various $r_{\mathit{\text{min}}}$ values for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ with G3P. The free energy values and errors were calculated using Multistate Bennet Acceptance Ratio (MBAR) in PymBAR⁴².

$\text{Ion}\left({\text{X}}^{2+}\right)$	$r_{\mathit{\text{min}}}(\AA )$	$\Delta G(\text{kcal}/\text{mol})$
${\text{Be}}^{2+}$	2.92	−25.27 ± 1.38
	3.00	−29.62 ± 1.43
	3.50	−14.89 ± 1.37
	3.75	−6.59 ± 1.62
	3.80	−5.43 ± 0.92
	3.90	−6.22 ± 0.78
${\text{Ca}}^{2+}$	3.256	−12.18 ± 0.93
	3.400	−5.46 ± 1.02
	3.600	−3.38 ± 1.14
	3.800	−1.08 ± 0.91

Final optimized $r_{\mathit{\text{min}}}$ parameters: ${\text{Be}}^{2+}=3.8\AA$ and ${\text{Ca}}^{2+}=3.6\AA$.

FIG. 5.

Binding $\Delta G$ from FEP at different $r_{\mathit{\text{min}}}$ for (A) ${\text{Be}}^{2+}$ with G3P2 and (B) ${\text{Ca}}^{2+}$ with G3P. The blue line indicates FEP performed with bound water, while the black line indicates FEP with resolvated waters. The dashed red line represents the experimental $\Delta G$ from ITC.

The potential energy $\left(V\right)$ of ion binding can be attributed to the following terms-

$$V=V_{X^{2+}-O2L}+V_{X^{2+}-{\text{H}}_2\text{O}}+V_{{\text{H}}_2\text{O}-O2L}$$ (5)

where, $V_{X^{2+}-O2L}$ is the electrostatic term between ${\text{X}}^{2+}$ and O2L, $V_{X^{2+}-{\text{H}}_2\text{O}}$ is the electrostatic term between the ${\text{X}}^{2+}$ and the water oxygen and $V_{{\text{H}}_2\text{O}-O2L}$ is the hydrogen bond term between O2L and the water hydrogen (Fig. S3). We observe that the binding free energy $\left(\Delta \text{G}\right)$ becomes less favorable (less negative) as the $r_{\mathit{\text{min}}O2L-X^{2+}}$ increases. This trend is consistent across the entire $r_{\mathit{\text{min}}}$ range in ${\text{Ca}}^{2+}$, but interestingly, the $\Delta G$ of ${\text{Be}}^{2+}$ binding to G3P shows a nonlinear trend Fig. S9. At small $r_{\mathit{\text{min}}}$ the $\Delta G_{B{e}^{2+}}$ is highly negative, indicating strong binding between ${\text{Be}}^{2+}-\text{O}2\text{L}$ and O2L, as the distance $r$ is small. The $\Delta G$ becomes less favorable as $r_{\mathit{\text{min}}}$ increases because the $V_{{\text{Be}}^{2+}}-O2L$ term decreases inversely with distance until $\Delta G$ peaks at $r_{\mathit{\text{min}}}=3.80\AA (-5.43\text{kcal}/\text{mol})$.

Simultaneously, as the O2L oxygen density $g\left(r\right)$ shifts away from ${\text{Be}}^{2+}$, the water density around ${\text{Be}}^{2+}$ increases to fill the space and maintain a tight tetrahedral geometry. The water in the first shell does not change once this geometry is achieved at $r_{\mathit{\text{min}}}=3.50\AA$, so the attractive $V_{X^{2+}-{\text{H}}_2\text{O}}$ also does not change. Beyond the transition, the O2L density in the second shell increases, allowing ${\text{Be}}^{2+}$ to accommodate more G3P2 oxygen, leading to a more attractive (more negative) $V_{{\text{H}}_2\text{O}-O2L}$ term, which appears as the dip in $\Delta G_{B{e}^{2+}}$ after $r_{\mathit{\text{min}}}=3.80\AA$. However we do not observe this trend in the case of ${\text{Ca}}^{2+}$ where the $\Delta G_{C{a}^{2+}}$ linearly becomes less negative as $r_{\mathit{\text{min}}}$ increases which implies that the second and third terms in Eq. (5) do not change significantly for ${\text{Ca}}^{2+}$ within the range of $r_{\mathit{\text{min}}}$ we tested.

We wanted to measure the effect of the bound water molecules in the ${\text{X}}^{2+}-\text{G}3\text{P}2$ structures. Thus, we calculated the $\Delta G$ when the bound waters from the configurations are removed and resolvated before the FEP step. From Fig. 5A and Fig. 5B we can see that the water removal did not impact $\Delta G_{{\text{Ca}}^{2+}}$ much. This implies that the bound water do not have strong interactions with ${\text{Ca}}^{2+}$. We observe a similar trend for ${\text{Be}}^{2+}$, except for in the region beyond $r_{\mathit{\text{min}}}3.8\AA$ where we see the $\Delta G\text{s}$ differ significantly for the configuration with bound-water vs. resolvated water. This suggests that the $\Delta G$ beyond $r_{\mathit{\text{min}}}$ of $3.8\AA$ is a function of bound water, but not so much at lower $r_{\mathit{\text{min}}}\text{s}$. This water-dependence indicates that ${\text{Be}}^{2+}$ coordination shifts from a inner-shell (direct ${\text{Be}}^{2+}-\text{O}2\text{L}$) to outer-shell coordination (indirect bridging through ${\text{Be}}^{2+}-{\text{H}}_2\text{O}-\text{O}2\text{L}$) at $r_{\mathit{\text{min}}}3.8\AA$. Whereas, for ${\text{Ca}}^{2+}$ this is not as stark as the ${\text{Ca}}^{2+}-\text{O}2\text{L}$ interaction remains more diffuse between inner and outer shell. Thus, the final $r_{\mathit{\text{min}}}(3.8\AA )$ for ${\text{Be}}^{2+}$ that matches the experimental heat data, recreates the outer shell interaction between ${\text{Be}}^{2+}-\text{O}2\text{L}$ bridged by water.

E. Liposome Data Validates ${\text{X}}^{2+}$-Membrane Interaction

To validate our L-J $r_{\mathit{\text{min}}}$ adjustments, we ran simulations of ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ in POPA and POPG membrane systems Table S2. As in the previous simulations, we used our clustering method to obtain tightly bound ${\text{X}}^{2+}$-lipid configurations and found representative configurations. The configuration of the first (best) cluster was used to run umbrella sampling (US) simulations as described in Section II H. We know from our experimental ITC data that ${\text{Be}}^{2+}-\text{POPA}$ has the highest affinity with a $K_d$ of $8.69\mu \text{M}$, while ${\text{Be}}^{2+}-\text{POPG}$ has $K_d$ of $63.1\mu \text{M}$ giving us a binding $\Delta G$ of −6.88 kcal/mol and −5.71 kcal/mol, respectively. The binding $\Delta G\text{s}$ of ${\text{Ca}}^{2+}-\text{POPA},\text{POPG}$ also lie in the same range (−6.92 kcal/mol, −4.62 kcal/mol) Fig. 6. Our umbrella sampling simulations reveal a similar magnitude of binding affinities especially for $\text{POPA}-\Delta G_{\mathit{\text{Be}}-\mathit{\text{POPA}}}=-5.05\pm 0.38\text{kcal}/\text{mol},\Delta G_{\mathit{\text{Be}}-\mathit{\text{POPG}}}=-1.64\pm 0.4\text{kcal}/\text{mol},\Delta G_{\mathit{\text{Ca}}-\mathit{\text{POPA}}}=-2.59\pm 0.6\text{kcal}/\text{mol}$ and $\Delta G_{\mathit{\text{Ca}}-\mathit{\text{POPG}}}=-1.98\pm 0.65\text{kcal}/\text{mol}$, thus validating our parametrization. These binding free energies are however dependent on several factors in addition to the reaction coordinate (distance from membrane COM) such as ion-solvation, lipid coordination and conformation, hence they cannot be directly used for comparison but provide the relative order of the free energies.

FIG. 6.

Potential of mean force (PMF) profiles for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ binding to (A) POPA (red) and (B) POPG (blue) bilayers, obtained from umbrella sampling simulations. Shaded regions denote bootstrapping errors and the standard deviations are listed. The reaction coordinate represents the distance between the cation and the membrane center of mass. Pnels (C-G) show the ${\text{Be}}^{2+}$ ion along being pulled along the RC (distance from membrane COM). ${\text{Be}}^{2+}$ ion is shown in pink with its radius doubled for visibility and the membrane hedgroup phosphates are shown in yellow. (C) Umbrella Sampling windows shown with the ion $\left({\text{Be}}^{2+}/{\text{Ca}}^{2+}\right)$ pulled from the membrane center of mass. The ion is shown in pink with its radius doubled and only the membrane lipid phosphorus atoms are shown in yellow for ease of visualization. The RC, distance from the membrane COM, is shown as an arrow with dotted lines.

The higher binding $\Delta G$ for Be-POPA/POPG indicates stronger binding than that of ${\text{Ca}}^{2+}$. Further we found that the original L-J $r_{\mathit{\text{min}}}$ for ${\text{Be}}^{2+}$-lipid interactions led to reduction of the area per lipid (APL) of the POPA membrane due to the over binding of ions to the POPA phosphate. We observe a similar but markedly reduced compaction in the ${\text{Be}}^{2+}$-POPG membrane. With our updated L-J $r_{\mathit{\text{min}}},{\text{Be}}^{2+}$ no longer causes the exaggerated compression in the POPA membrane. It also corrects for the condensation in POPG and instead increases the APL for the POPG membrane Fig. 7. We do not see significant changes to the APL with ${\text{Ca}}^{2+}$ however, we observe an increase in the lipid-ion coordination from the original 0.8 (POPA) and 0.5 (POPG) to the updated 2.4 (POPA) and 2 (POPG).

FIG. 7.

Area per Lipid (APL) of POPA and POPG membranes in the presence of (A) ${\text{Be}}^{2+}$ and (B) ${\text{Ca}}^{2+}$, comparing original and updated L-J parameters. Boxplot of APLs shown for data from quartiles Q1 (bottom), Q3 (top), with the whiskers for Q0 (bottom) and Q4 (top). The median (Q2) is highlighted as a red line in the box center with outliers as circles.

Physiologically, this shows that ${\text{Be}}^{2+}$ can displace ${\text{Ca}}^{2+}$ in membrane-ion binding events since it is thermodynamically more favorable. As reported previously, ${\text{Be}}^{2+}$ binding produces crosslinking of lipid headgroups, membrane rigidification, and a lower area per lipid⁸. Our work accurately models ion-lipid binding interaction using experimental data to achieve reasonable binding thermodynamics based on parameters fit to small molecule ITC.

IV. CONCLUSION

Our research extends the range of lipid targets for toxic ${\text{Be}}^{2+}$ ions to include two minor but important components of lung surfactant, POPA and POPG. Phosphatidic acid (POPA) is a precursor to phospholipids and part of the lysophosphatidic acid signaling pathway that controls inflammatory responses¹⁶. Phosphatidylglycerol (POPG) has shown strong anti-inflammatory effects¹⁷. Our data on the interactions between these lipids and toxic ${\text{Be}}^{2+}$ ions highlight the competitive binding, in which ${\text{Be}}^{2+}$ can replace ${\text{Ca}}^{2+}$ ions normally present at the lipid binding sites. As a result, our work opens a new path for studying the roles of minor lipids in the mechanism of berylliosis. Our experiments allowed us to fine-tune the FF parameters, especially for ${\text{Be}}^{2+}$ interactions with two different phosphate groups.

Ionic competition in living cells and on their surfaces requires a more precise quantitative description. MD simulations should serve as an advanced tool for studying ion binding sites, coordination, and energetics, but the accuracy of MD results depends directly on the quality of force fields. ${\text{Ca}}^{2+}$ is the main intracellular signaling ion in most organisms and also mediates a wide range of extracellular interactions. The presence of ${\text{Be}}^{2+}$, a competitor for ${\text{Ca}}^{2+}$, can disrupt multiple structures and signaling mechanisms, particularly recognition and removal of apoptotic cells. In this work, we sought to adjust the additive FF parameters previously used for ${\text{Ca}}^{2+}$-phosphate interactions and reparametrized the force field for its toxic competitor, ${\text{Be}}^{2+}$.

We demonstrate that ${\text{Be}}^{2+}$ is a stronger binder than ${\text{Ca}}^{2+}$ to glycerophosphate (G3P), a good mimic of phosphorylated groups in macromolecules and lipids. ${\text{Be}}^{2+}$ also binds to POPA and POPG phospholipids significantly more strongly than ${\text{Ca}}^{2+}$. The binding strength order is POPA > G3P > POPG for both ions. The strongest ${\text{Ca}}^{2+}$-POPA binding affinity is still weaker than the weakest ${\text{Be}}^{2+}$-POPG binding. We found that the existing version of the CHARMM36 force field parameters overestimates the binding free energy for ${\text{Be}}^{2+}-\text{G}3\text{P}$ by a factor of 4–6 and for ${\text{Ca}}^{2+}-\text{G}3\text{P}$ by a factor of 3, compared to the actual ITC values of −5.8 kcal/mol and −4.59 kcal/mol, respectively. Experimentally derived $K_d$ and $\Delta G$ values for ion binding were used to correct the Lennard-Jones parameters with NBFIX, reducing over-binding. Our free energy calculations suggest that ${\text{Be}}^{2+}$ can replace ${\text{Ca}}^{2+}$ in key lipid-binding events involving proteins.

Our CHARMM36 parameterization for ${\text{Be}}^{2+}$ and ${\text{Ca}}^{2+}$ was developed for the additive force field and involved extensive multi-faceted analyses of relationships among L-J parameters, ion coordination numbers, and binding energies. We identified a strong water contribution in the structure of the first coordination shell, especially for ${\text{Be}}^{2+}$. Our data support the previous idea that ${\text{Ca}}^{2+}$ can act as an electrostatic “glue” between phospholipids and their receptors because of its optimal 6-coordinated configuration. The smaller ${\text{Be}}^{2+}$, with higher affinity but requiring 4-fold coordination, cannot functionally replace ${\text{Ca}}^{2+}$.

Our adjustments resulted in good agreement with experimental binding energies. Yet, the nature of ionic competition poses the challenge of simultaneously capturing the energetics and structure of the binding for a strongly polarizing metal ion such as ${\text{Be}}^{2+}$. Since we know that ${\text{Be}}^{2+}$ can polarize its surroundings by inducing dipoles, it cannot be fully represented by an additive FF and future work will focus on applying this to the Drude polarizable FF when anionic lipids are fully optimized. However, as an approximation, our parameters now allow physiologically correct binding strength at atomistic resolution and at higher simulation speeds than any polarizable force field^43,44.

Supplementary Material

Supplementary figures, tables, topology files for the molecules and tested and final L-J parameters are provided in the SI document. Code can be found online on the Github repository (https://github.com/jbodosa/beryllium_data).