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. 2023 Nov 10;63(22):7124–7132. doi: 10.1021/acs.jcim.3c01363

Physical Chemistry of Chloroquine Permeation through the Cell Membrane with Atomistic Detail

Mirko Paulikat †, GiovanniMaria Piccini ‡, Emiliano Ippoliti †, Giulia Rossetti †,¶,§, Fabio Arnesano ∥, Paolo Carloni †,⊥,*
PMCID: PMC10685453  PMID: 37947485

Abstract

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We provide a molecular-level description of the thermodynamics and mechanistic aspects of drug permeation through the cell membrane. As a case study, we considered the antimalaria FDA approved drug chloroquine. Molecular dynamics simulations of the molecule (in its neutral and protonated form) were performed in the presence of different lipid bilayers, with the aim of uncovering key aspects of the permeation process, a fundamental step for the drug’s action. Free energy values obtained by well-tempered metadynamics simulations suggest that the neutral form is the only permeating protomer, consistent with experimental data. H-bond interactions of the drug with water molecules and membrane headgroups play a crucial role for permeation. The presence of the transmembrane potential, investigated here for the first time in a drug permeation study, does not qualitatively affect these conclusions.

Introduction

The interaction of drugs with biological membranes impact dramatically on their mechanism of action. A typical example is the FDA-approved antimalarial drug chloroquine (CQ).1,2 This drug also possesses antiviral,3−5 antirheumatic,6−8 and anti-inflammatory properties.9,10 In fact, its beneficial effect stems from the drug’s ability to reach the food vacuole, an acidic compartment of the parasite, so that the drug has to permeate several biological membranes.11 The drug can feature three different protonation species at the extracellular pH (Chart 1), from the neutral one (CQ0), to the mono- (CQ+) and diprotonated (CQ2+) species (pKa1 and pKa2 are 8.1 and 10.4 at 310 K).12

Chart 1. Protomers of Chloroquine (CQ)a.

Chart 1

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a The ring and tail moieties are colored in orange and blue, respectively.

CQ penetrates malaria-infected human erythrocytes by passive diffusion of the free base, which may become protonated and trapped inside the acidic vacuole with a pH value in the range of 4.5–4.9.13,14 However, a detailed study of CQ binding to intact and lysed erythrocytes indicated that the mechanism of CQ accumulation in intact cells is actually a combination of ion trapping at acidic pH (a consequence of the basic nature of the drug and the pH gradient across the membrane) and binding to cell components.15

The analysis of CQ uptake into erythrocytes infected with drug-sensitive and resistant strains of the human malaria parasite Plasmodium falciparum revealed that uptake can be resolved into a nonsaturable and a saturable component.16,17,75 Nonsaturable uptake in the submicromolar range18 is nonspecific and is attributed to low-affinity binding of CQ to plentiful cytosolic proteins.19 Conversely, saturable uptake at nanomolar drug concentrations is important for antimalarial activity18 and attributed to intracellular binding of CQ to ferriprotoporphyrin IX (FPIX), a product of parasite hemoglobin digestion.16,20 FPIX is polymerized into an inert crystalline substance called hemozoin, but CQ inhibits this process causing a buildup of free FPIX and/or CQ–FPIX complex that will ultimately kill the parasite.21−23 Thus, the intracellular uptake of CQ in malaria-infected cells is primarily due to passive diffusion followed by saturable binding of CQ to FPIX rather than active import by membrane transporters.16,24

The drugs’ uptake requires about 1 h.25,26,76 Permeation occurs by fast passive diffusion with a permeability coefficient of 7.2 cm s–1 for CQ0 at 310 K.11,15,27 Only CQ0 permeates the membrane in spite of being extremely scarce in physiological conditions (about one part for 10,000).15,27,77 While one can provide simple electrostatic arguments to explain this—charged molecules are not thermodynamically stable inside the hydrophobic part of the membrane—a molecular view of drug permeation, and in particular of the role of water for drug permeation, is still missing.

For the past decade, a variety of state-of-the-art enhanced sampling methods have successfully described the structure, dynamics and energetics of small molecule permeation.32−38 Here we use well-tempered metadynamics (WTMetaD), an exact method to calculate the free energies of a process as a function of appropriate collective variables,39,40 to describe the process. Our calculations are carried out for the two species CQ0 and CQ+, in model membranes with different compositions or in the presence of a transmembrane potential. CQ0 (and not CQ+) passes the membrane, consistent with experimental evidence. The process is not qualitatively changed in the presence of the membrane potential.

Methods

All calculations and most of the analyses were carried out with the GROMACS 2019.4 package interfaced with the PLUMED-2.5.3 plugin.41−43

Lipid Bilayer Preparation

A 2 × 37 pure POPC78 bilayer (M1) and a 2 × 40 POPC/POPS79 (M2) bilayer with 7:3 stoichiometry were generated using the CHARMM GUI web server44 and inserted in a box of sizes 50 Å × 50 Å × 100 Å. A 30 Å thick water slabs were located on top of each leaflet. Eleven (35) Na+ and 11 (11) Cl– ions were added to M1 (M2) so as to ensure electroneutrality and to keep the salt concentration of 150 mM, a value not too dissimilar from the extracellular fluid.45 Overlapping water molecules were removed. M1 and M2 contained 23,423 and 24,752 atoms, respectively.

Molecular Dynamics Parameters

The AMBER Lipid 17,46 TIP3P,47 and Joung–Cheatham48 force fields were used for the membranes, water molecules, and Na+/Cl– ions, respectively. As for the drugs, the GAFF2 force field was employed for bonded and van der Waals parameters of the drugs,49 while the atomic partial charges were calculated using the RESP fit method at the HF/6-31G*//B3LYP/6-31G* level of theory.50−52 Periodic boundary conditions were applied. Electrostatic interactions were calculated using the particle-mesh Ewald summation method with a real space cutoff of 10 Å.53 Lennard-Jones interactions were truncated at the same cutoff value. An analytical correction for the potential energy and for the overall pressure taking into account the truncation of the Lennard-Jones interactions (implemented in GROMACS41) has been applied. All bonds involving hydrogen atoms were constrained using the LINCS algorithm.54 An integration time step of 2 fs was used. The center of mass motion was removed separately for the lipids and aqueous phase every 100 steps. Unless differently stated, (i) constant temperature simulations were achieved by coupling the systems with a Nosé–Hoover thermostat, using a time constant of 0.5 ps;55,56 (ii) constant pressure simulations were obtained using semi isotropic Parrinello–Rahman barostat at 1 bar, using a time constant of 1.0 ps and compressibility of 4.5 × 10–5 bar–1.57

Molecular Dynamics Simulation of M1 and M2

The systems were first energy-minimized by 10,000 steepest descent steps. Then, they were heated up by 100 ps from 0 to 310 K by molecular dynamics with velocity rescale methods with a time constant of 0.1 ps.58 Here, the lipid atoms were restrained to their position by harmonic restraints of 50 kJ mol–1 Å–2. The systems were then unconstrained. Next, M1 and M2 underwent 60 and 110 ns NPT MD simulations, respectively. Some features of these simulations are reported in the Supporting Information.

Insertion of the Drugs

The drugs were placed into the aqueous phase at 35 Å along the membrane normal (z-axis in Figure 1) from the center of the membrane. We used the GROMACS insert-molecule module.41 Also in this case, overlapping water molecules were removed. The resulting systems underwent 10 ns-long NPT simulations. The final configurations were used for subsequent calculations of the free energy. Selected configurations in which the ligand was located at around −40 Å from the center of the membrane along the z-axis (z = 0) were used for subsequent calculations of the diffusion coefficient. For the calculation of the diffusion coefficient, also a total of 1.275 μs NVE trajectories were collected (see Section S7 in the Supporting Information).

Figure 1.

Figure 1

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Permeation coordinate. Left: Snapshot of chloroquine in the presence of a lipid bilayer, schematically indicating the permeation coordinate with the black arrow. Right: The two collective variables, CVring and CVtail, measure the distances of the ring/tail moieties of chloroquine with respect to the membrane center along the normal z-axis.

Free Energy Calculations

The free energy as a function of a specific collective variable was calculated by well-tempered metadynamics.39 Our collective variables (CVs) are the distances between the drug’s center of masses (COMs) and the COM of 40 selected membrane atoms, representing the center of the membrane. They correspond to the z-component of its direction vector (see Figure 1 which shows the z-axis). The center of the membrane is set to have z = 0. This CV has been used also in previous drug permeation studies:32−38 Gaussians with 1.2 kJ mol–1 initial height and 0.5 Å sigma values were deposited every 2 ps, similarly to refs (36 and 59). The bias factor for CQ+ (25) is larger than that for CQ0 (20), because a higher free energy barrier of the charged species is expected. The bias potential was evaluated on a grid of spacing of 0.01 Å. The reweighting factor c(t) was calculated on the fly. Free energy profiles were constructed through the reweighting scheme of ref (60).

Here, 4.5 μs were simulated for each system. The first 500 ns were not included in the analysis as in ref (60). Errors of the free energy profiles were estimated by block averaging with three blocks of the processed data (see Supporting Information). The free energy profiles were then symmetrized and checked for their asymmetry (see Supporting Information). The minimum free energy paths on the 2D free energy surface were determined by the string method.61

The calculations with the electric field were carried out using the GROMACS routine41 to mimic the presence of a transmembrane potential. A potential of 10 mV Å–1 was set. Not too dissimilar potentials have been used in other setups, such as the computational electrophysiology simulations.62−65 Here, 3 μs were simulated with and without the electric field, using a simpler one-dimensional CV space (see Figure S14a in Supporting Information).

Calculated Properties

(i) The diffusion and the permeability coefficient were calculated as described in Section S7 of Supporting Information.66,67 (ii) Radial distribution functions of the water-drug H-bonds were calculated from the well-tempered metadynamics runs for M1. All snapshots in which the drug was located in the aqueous phase with a distance larger than 30 Å from the membrane center (10,403 and 14,440 structures for CQ0 and CQ+, respectively) were used. (iii) The free energy differences between CQ0 and CQ+ were calculated as in refs (35 and 68). The free energy of CQ0 is first shifted to account for its acid–base equilibrium in the aqueous phase, considering pKa2 (10.4) at the conditions of the simulation (neutral pH and temperature of 310 K).80 The CQ0⇌CQ+ free energy surface is then determined by weighting the individual free energy surfaces with respect to the calculated population of protomers as a function of CVs (see Supporting Information, Section S4 for details). (iv) The dipole moment of CQ0 was calculated at the B3LYP/6-31G* level of theory using the Gaussian09 code.69

Results and Discussion

As a first step, the free energy associated with the permeation of the CQ molecule is calculated using well-tempered metadynamics, which is an exact method to calculate the free energy landscapes as a function of apt CVs.40 Previous studies have used either one or two CVs.36,38,59 Choosing an additional CV has been shown to significantly improve the results.36 Here, we choose the following CVs: the distances between the center of the membrane and the ring/tail moieties of CQ (Figure 1).

Permeation of CQ0

MD simulations of CQ0 (Chart 1) in explicit solvent and in the presence of the POPC membrane (Figures 1 and 2) show that all H-bond functional groups of CQ0 interact with the solvent (Figure S3). After leaving the bulk solvent, the ring and tail moieties of CQ0 interact with POPC headgroups, while the rest is still fully solvated (Figure 2a). Then, the ring moiety dives into the membrane (Figure 2b) and the tail interacts, in turn, with the POPC headgroups (Figure 2b). In this step, the free energy decreases by 20 kJ mol–1 (Figure 2, left). Subsequently, CQ0 forms H-bonds with POPC headgroups and water molecules, while the remainder interacts with the hydrophobic core of the membrane (Figure 2c). This is the global free energy minimum (−40 kJ mol–1 lower than in the solvated state), located inside the membrane. Then, the free energy increases by 11 kJ mol–1: CQ0 is entirely inside the membrane, interacting exclusively with the hydrophobic core (Figures 2d and 2e). The second part of the translocation is, as expected, completely symmetrical with respect to the first part (Figure 2f). We conclude that CQ0 is located at the water/membrane interfaces, so as to form H-bond interactions with its polar moiety and hydrophobic with the rest. It can permeate from side to side in the submillisecond time scale, taking into account the barrier of about 10 kJ mol–1. The experimental evidence also shows that the neutral molecule can permeate through the erythrocyte cell membrane. Thus, our results are consistent with these experiments, with the caveat that the latter were performed in a different environment than the one used here.

Figure 2.

Figure 2

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Permeation of CQ0 through a POPC membrane. Left: the free energy of the process, calculated as a function of CVring and CVtail (see Figure 1). The minimum free energy path is plotted as black line (top) and is shown in its one-dimensional representation below. (a–f) Representative snapshots of the CQ0 permeation process across the POPC membrane. The associated free energies are indicated in the minimum free energy profile.

Protonated Species

The molecular mechanism of permeation of CQ+ is similar to that of CQ0. However, in this case the global minimum is far more solvated than in the case of the neutral molecule, most likely because the solvent stabilizes the charged molecule (Figure 3b). Here, the ring moiety interacts with the hydrophobic core of the membrane, while the charged tail of CQ+ interacts with water molecules and POPC headgroups at the lipid/water interface. More importantly, the maximum free energy inside the membrane now shifts by as much as 35 kJ mol–1 with respect to the solvent state. This is caused by the destabilization of the charged molecule within the membrane along with membrane deformation and water defects (Figure 3c–f). The total energy barrier for membrane translocation is 60 kJ mol–1. Thus, we conclude that, consistent with experiment, the protonated CQ+ does not cross the membrane, within the limitations that different membranes have been used.

Figure 3.

Figure 3

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Permeation of CQ+ through a POPC membrane. Left: the free energy of the process, calculated as a function of CVring and CVtail (see Figure 1). The minimum free energy path is plotted as black line (top) and is shown in its one-dimensional representation below. (a–f) Representative snapshots of the CQ+ permeation process across the POPC membrane. The associated free energies are indicated in the minimum free energy profile.

The calculated free energy difference between CQ0 and CQ+ suggests that the protonated species is not stable within the membrane (Figure 4a). The reversal point is located at the lipid/water interface, when the charged tail of CQ+ enters the hydrophobic core of the membrane (CVtail ≈ ± 10 Å). The permeation mechanism can be described as follows: the protonated CQ+ dives into the membrane with its ring moiety, while the tail moiety is still sufficiently solvated at the lipid/water interface (Figures 3b and 4). As discussed above, this corresponds to the global minimum of CQ+. When the tail moiety enters the hydrophobic core of the membrane, the proton is expected to be transferred to the solution phase. Both water molecules and POPC headgroups interact with the tail moiety and could act as proton acceptors (Figure 3b). The neutral CQ0 is then located inside the membrane (Figure 2c) and is able to pass the membrane center. The total barrier for membrane translocation is 16 kJ mol–1, consistent with the experimental evidence that CQ0 can pass the membrane. Upon leaving the membrane, the amine nitrogen gets reprotonated so that the tail moiety exits the hydrophobic core of the membrane first, followed by the ring moiety to complete the permeation process.

Figure 4.

Figure 4

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Protonation-dependent permeation of CQ through a POPC membrane. (a) The free energy difference of CQ+ and CQ0, as a function of CVring and CVtail (see Figure 1). The calculated profile of CQ0 is shifted with respect to the aqueous state, considering a solution pH of 7 and a pKa value of 10.4 at 310 K. Red indicates a preferred protonated state (CQ+), while blue indicates a preferred neutral state (CQ0). (b) Free energy surface for the permeation of CQ0⇌CQ+, as a function of the two CVs, weighted according to the calculated population of the corresponding protonation state. The minimum free energy path is shown as black line. (c) 1D minimum free energy path of the CQ0⇌CQ+ free energy surface. Suggested positions for proton transfer are indicated as red arrows.

In a recent study, the permeation process of a weak base, propranolol, was investigated by MD simulations at constant pH, allowing for dynamic protonation of the molecule in the inhomogeneous environments.70 Similar to our findings, the change in protonation state was observed at the lipid/water interface and the free energy profile proceeds along the energetically favorable protomer in the different phases.70 We conclude that the protonation states of CQ (or similar drug-like molecules) can have a significant impact on the permeation mechanism and energetics even if only the neutral molecule is able to cross the membrane center.

Impact of Membrane Composition on Permeation

Next, the permeation process of CQ0 was investigated across a POPC/POPS mixed bilayer. We used a deliberately high concentration of POPS (30%) in order to study the effect of negatively charged membranes. However, we do not propose this as an universal model of cell membranes, which present great variability in their composition.

The mechanism of permeation across the POPC/POPS mixed bilayer is similar to that of the pure POPC membrane. However, quantitatively, the energetics of the permeation process differs slightly in the headgroup regions (Figure 5). After leaving the bulk solvent, both the ring and tail moieties of CQ0 interact with the POPC/POPS headgroups, while the remaining part of the molecule is still fully solvated (Figures S12a and S13a). The free energy increases slightly by 7 kJ mol–1. The increase in free energy is more pronounced than for the pure POPC membrane, possibly due to the disruption of the rather strong interactions between the POPS headgroups (which are negatively charged) and water molecules. Then, the ring moiety dives into the membrane and the other moiety interacts, in turn, with POPC/POPS headgroups (Figures S12b and S13b). The free energy decreases by 20 kJ mol–1. Next, the drug is inside the membrane: the molecule forms H-bonds with POPC/POPS headgroups and water molecules, while the rest interacts with the hydrophobic core of the membrane (Figures S12c and S13c). This is the global free energy minimum (−42 kJ mol–1 lower than in the solvated state). Then, the free energy increases by 12 kJ mol–1 when the molecule is completely inside the membrane, interacting only with the hydrophobic core (Figures S12d and S13d). The second part of the translocation is, as expected, symmetrical with respect to the first part. Thus, our simulations suggest that the drug is located at the water/membrane interfaces, so as to form H-bond interactions with its polar moiety and hydrophobic with the rest.

Figure 5.

Figure 5

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Effect of the membrane composition on the permeation of CQ0. Left: Free energy surface for the permeation of CQ0 through a POPC/POPS membrane, as a function of the CVring and CVtail. The minimum free energy path is shown as black line. Right: 1D minimum free energy path of the free energy surface for CQ0 permeating POPC (blue) and mixed POPC/POPS (red).

Impact of External Potential on Permeation

The effect of the membrane potential on permeation has not been investigated so far, to the best of our knowledge. Here, we compare the energetics of the permeation of CQ0 with and without an external electric field (E) of 10 mV Å–1 along the POPC membrane. Our field value is not too dissimilar to that widely used in computational electrophysiology setups.62−65 To a first approximation, we expect changes in the potential energy of the process of the order of the 2E·μ (≈ 2–3 kJ mol–1), where μ = 5.8 D is used for the dipole moment of CQ0. Therefore, even fields much larger than the physiological ones (≈0.5–3 mV Å–1)45 are unlikely to drastically affect permeation. The free energy calculations of CQ0 permeation using CVCQ81 show that this is indeed the case (Figure 6). The first free energy minimum is −43 kJ mol–1 lower than the value in the solvated state, and 3 kJ mol–1 lower than the value without the external electric field. Thus, CQ0 slightly prefers the lipid phase when an E-field is taken into account. The free energy increases by 7 kJ mol–1 when the molecule is completely inside the membrane. The second free energy minimum is even lower (−46 kJ mol–1). This asymmetry arises from the preferred orientation of CQ0 along the direction of E (Figure S14). We conclude that the effect of the external electric field is of minor importance for CQ0 permeation under physiological conditions. As a perspective of our work, one could extend the investigations in the presence of the external membrane potential to a comprehensive set of ionizable drugs (such as those reported in ref (71)). These would lead to a more robust conclusion.

Figure 6.

Figure 6

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Effect of the external potential on permeation. Top: Ball-and-stick representation of CQ0 showing its dipole moment as an arrow from negative (red) to positive (blue) charge distribution. Bottom: Comparison of free energies with and without an external field for CQ0 permeation through the POPC membrane. The direction of the external field is shown as an arrow.

Permeability Coefficients

As a final step, we calculated the permeability coefficient from the inhomogeneous solubility-diffusion model. The position-dependent diffusion coefficients are given in the Supporting Information. The permeability coefficients of CQ0 are 38.2 ± 7.8 cm s–1 and 44 ± 12 cm s–1 for the permeation through the POPC and the POPC/POPS model membranes, respectively. Considering the protonation-dependent permeation process (CQ0⇌CQ+), the permeability coefficient amounts to 26.0 ± 6.0 cm s–1. The use of more than one CVs for a proper description of the permeation path free energy (and thus the permeability coefficient) might be crucial for conformationally flexible drugs. In this study, two CVs were required for CQ+, possibly because the charged tail and ring moieties prefer an aqueous and a hydrophobic environment, respectively (see Figure 3). Instead, in CQ0, where the tail is neutral, one CV was sufficient (see Table S2 in the Supporting Information). The difference between the experimental value (7.2 cm s–1 at 310 K for the human erythrocyte membrane)11,15 can be ascribed, at least in part, to the different chemical environments: the real cell membrane differs from our model membranes in several aspects. Most importantly, it features a high content of cholesterol that can significantly affect membrane permeability, usually lowering its value.72,73 In addition, our models also lack sphingolipids that are charged groups and that usually increase the permeability.74 So, in the end the membrane permeability will be modified by these chemicals in a highly nontrivial manner.

Conclusions

In conclusion, we present a study of chloroquine permeability along permeation through model membranes. The calculated permeability of the drug is about three to six times higher than experimentally found in biological membranes. Previous drug permeation studies predicted permeabilities with errors similar to that found here.32,33,36,38 The difference might be ascribed, at least in part, by the highly diverse environments and by possible changes due to dynamic protonation of the drug, here not included.70 In addition, we show that both the neutral (CQ0) and the protonated (CQ+) species are partially solvated in their global free energy minima at the membrane/water interface. However, while CQ0 can cross the hydrophobic core of the membrane in the absence of any H-bond interactions, CQ+ requires these interactions at its charged moiety in the permeation process. Consequently, CQ0 is the only species able to cross the membrane in a time scale compatible with experiments. The impact of cell membrane potential is negligible.

Acknowledgments

The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) and the Jülich Supercomputer Center for providing the computing time for this project. We also thank the University of Bari and the Italian Ministero dell’Università e della Ricerca (PRIN 2017WBZFHL to F.A.) for support. G.R. and P.C. acknowledge the Helmholtz European Partnering fundings for the project “Innovative high-performance computing approaches for molecular neuromedicine:, as well as the Joint Lab “Supercomputing and Modeling for the Human Brain” of the Helmholtz Association, Germany. G.R. also acknowledges the Federal Ministry of Education and Research (BMBF) and the state of North Rhine-Westphalia as part of the NHR Program. Open access publication fee funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), No. 491111487.

Data Availability Statement

The free energy calculations were carried out with the GROMACS 2019.4 package (https://www.gromacs.org/) interfaced with the PLUMED-2.5.3 plugin (https://www.plumed.org/). Parameter and topology files, starting configurations, and input files for the free energy calculations are provided in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.3c01363.

  • Some features of the classical MD simulations of the membrane models M1 and M2; hydrogen bond analysis of CQ in the aqueous phase; detailed analysis of free energy surfaces; representative snapshots showing the permeation across the membrane models; description of the calculation of the CQ0⇌CQ+ free energy surface; computational details on the calculation of the diffusion coefficients and permeability coefficients (PDF)

  • Parameter and topology files, starting configurations, and input files for the free energy calculations (ZIP)

The authors declare no competing financial interest.

Supplementary Material

ci3c01363_si_001.pdf (7.4MB, pdf)
ci3c01363_si_002.zip (2.3MB, zip)

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  78. 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine.
  79. 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine.
  80. We assume that the doubly charged CQ2+ is not stable in the membrane, so that CQ2+ is expected to be deprotonated in the aqueous phase to form the CQ+ before entering the membrane. Under this assumption, the free energy surface would only be slightly shifted without an impact on the permeation mechanism.
  81. In these simulations, we used a simplified one-dimensional CV space, representing the distance of the center of mass of the entire CQ0 molecule to the center of the membrane (see Figure S14a in Supporting Information).

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ci3c01363_si_001.pdf (7.4MB, pdf)
ci3c01363_si_002.zip (2.3MB, zip)

Data Availability Statement

The free energy calculations were carried out with the GROMACS 2019.4 package (https://www.gromacs.org/) interfaced with the PLUMED-2.5.3 plugin (https://www.plumed.org/). Parameter and topology files, starting configurations, and input files for the free energy calculations are provided in the Supporting Information.

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