Modeling the Interaction Between Silver(I) Ion and Proteins with 12-6 Lennard-Jones Potential: A Bottom-Up Parameterization Approach

Abstract

Silver(I) ions and organometallic complexes thereof are well-established antimicrobial agents. They have been employed in medical applications for centuries. It is also known that some bacteria can resist silver(I) treatments through an efflux mechanism. However, the exact mechanism of action remains unclear. All-atom force-field simulations can provide valuable structural and thermodynamic insights into the molecular processes of the underlying mechanism. Lennard-Jones parameters of silver(I) have been available for quite some time; their applicability to properly describing the binding properties (affinity, binding distance) between silver(I) and peptide-based binding motifs is, however, still an open question. Here, we demonstrate that the standard 12-6 Lennard-Jones parameters (previously developed to describe the hydration free energy with the TIP3P water model) significantly underestimate the interaction strength between silver(I) and both methionine and histidine. These are two key amino-acid residues in silver(I)-binding motifs of proteins involved in the efflux process. Using free-energy calculations, we calibrated non-bonded fix (NBFIX) parameters for the CHARMM36m force field to reproduce the experimental binding constant between amino acid sidechain fragments and silver(I) ions. We then successfully validated the new parameters on a set of small silver-binding peptides with experimentally known binding constants. In addition, we monitored how silver(I) ions increased the α-helical content of the LP1 oligopeptide, in agreement with previously reported Circular Dichroism (CD) experiments. Future improvements are outlined. The implementation of these new parameters is straightforward in all simulation packages that can use the CHARMM36m force field. It sets the stage for the modeling community to study more complex silver(I)-binding processes such as the interaction with silver(I)-binding-transporter proteins.

1. Introduction

The antimicrobial properties of silver(I) ions are well known and applied in various medical solutions [1,2,3]. However, some bacteria are known to resist silver(I) cytotoxicity through an efficient efflux pump that expels the metal ion out of the cell [4]. The efflux mechanism is based on the interplay between the small periplasmic silver(I)-transporter protein SilF and the tripartite efflux complex SilCBA; the latter functions as a chemiosmotic metal ion/proton antiporter. In addition, the disordered protein SilE acts as a molecular sponge [5] to absorb silver(I) ions in the periplasm, probably to regulate the metal ion concentration [6]. However, the precise role of SilE remains unclear.

Particularly important for the binding of silver(I) ions to SilE and other proteins of the efflux machinery are the amino acids histidine (H) and methionine (M); the motifs HXXM and MXXH are privileged binding motifs for silver(I) ions [7,8]. Their impact, however, on the dynamic structure of the peptide and the binding affinity is not fully understood yet. An interesting observation is that silver(I) binding to SilE and non-structured peptides induces the formation of structured, α-helical motifs. The actual molecular mechanism remains unclear [4,8,9].

All-atom molecular dynamics simulations conducted on the nanosecond to microsecond timescale could provide valuable insights into these unresolved questions. Force-field parameters for silver(I) ions have been developed previously: Won parameterized mono-, di- and tri-valent ions, including silver(I), to reproduce the hydration free energy using Jorgensen’s TIP3P [10] water model [11]. To our understanding, these parameters were unfortunately not correctly integrated into the official distribution of the CHARMM force field. The epsilon values lacked the proper conversion from kilojoules to kilocalories. This issue is currently being reviewed by the developers of the CHARMM force field (Alex MacKerell; personal communication, 5 December 2024). Merz and coworkers determined alternative 12-6 LJ silver(I) parameters. They aimed to reproduce either the hydration free energy (HFE) or the ion–oxygen distance (IOD) for multiple water models [12]. A 12-6-4 LJ model was also proposed to account for polarizability. The Merz group later proposed specific 12-6-4 LJ parameters for the interaction of silver(I) (among other metal ions) with imidazole and acetate [13,14]. While the 12-6-4 LJ potential is certainly a valuable extension, it is not available in most simulation packages by default. Thus, we limited our focus in this work to the standard 12-6 Lennard-Jones potential.

We first assessed whether the aforementioned 12-6 Lennard-Jones parameters could be directly applied to study the interaction of silver(I) ions with the HXXM binding motif as described by the CHARMM36m [15] force field. We describe the development of improved 12-6 Lennard-Jones parameters for modeling the interaction of silver(I) with histidine, methionine and phenylalanine. We thereby employed a bottom-up strategy: we first developed parameters for the silver(I) interaction with sidechain fragments for which affinity data were available from the literature or that we measured by potentiometric or spectrophotometric titrations. We then validated the derived parameters against binding constants data for HXXM and MXXH motifs, as measured by NMR titrations [7,8]. Finally, as an application of the new parameters, we tested them against structural data for the oligopeptide LP1 (also called B1b [9]), in particular the transition from an intrinsically disordered peptide to an α-helical structure in the presence of silver(I) ions.

2. Methodology

This section provides a general outline of the chosen methodology. Details of the applied computational procedures are given in the Electronic Supplementary Information (ESI).

2.1. Non-Bonded Interaction Potential

In the family of CHARMM force fields, the non-bonded interaction between a pair of atoms is given by the following potential:

(1)$E_{NB}=E_{elec}+E_{LJ}={\displaystyle \frac{Q}{4r\pi D}}+\epsilon \left[{\left({\displaystyle \frac{R^{min}}{r}}\right)}^{12}-2{\left({\displaystyle \frac{R^{min}}{r}}\right)}^6\right]$

where r is the distance between the two atoms, $Q$ is the product of their partial charges and D is the product of the vacuum permittivity and the relative permittivity of the medium (=1 for explicit water simulations). The parameters ε and R^min are in general derived from the Lorentz–Berthelot rule [16,17]:

(2)$R^{min}=\left\{\begin{array}{cc}{R}_i^{min}/2+R_j^{min}/2& \left(\mathrm{Lorentz}\right)\hfill \\ & \mathrm{or}\hfill \\ R^{NBFIX}=l_{ij}(R_i^{min}/2+R_j^{min}/2)& \left(\mathrm{if}\mathrm{specified}\right)\hfill \end{array}\right.$

and

(3)$\epsilon =\left\{\begin{array}{cc}\sqrt{{\epsilon }_i{\epsilon }_j}& \left(\mathrm{Berthelot}\right)\hfill \\ & \mathrm{or}\hfill \\ {\epsilon }^{NBFIX}=k_{ij}\sqrt{{\epsilon }_i{\epsilon }_j}& \left(\mathrm{if}\mathrm{specified}\right)\hfill \end{array}\right.$

where the subscript indicates an atom-type specific parameter of the i-th and j-th atom. Besides this general combination rule, it is also possible with the NBFIX feature of CHARMM to directly specify ε^NBFIX and R^NBFIX for an interaction between two specific atom types (instead of using the Lorentz–Berthelot rules). Alternatively, ε^NBFIX and R^NBFIX can be expressed in terms of pairwise correction coefficients k_ij and l_ij, respectively [18]. This allows one to selectively modify the strength and distance for a particular interaction without affecting the other interactions. In what follows, we refer to the pair ε^NBFIX and R^NBFIX as NBFIX parameters.

2.2. Preliminary Evaluations

As an initial test, Won’s parameter set [11] and Merz’s HFE and IOD parameter sets [12] for silver(I) ions were tested in combination with the CHARMM36m force field [15] using the general Lorentz–Berthelot rule. The strong silver-binding tetrapeptide HEFM was chosen as a test case because it includes four amino acid sidechains that are supposed to bind silver. As shown in the Section 3.1 and Table 1, all three sets drastically underestimated the binding affinity of HEFM and silver(I).

An intuitive strategy to analyze and eventually correct the underestimated affinity is to adopt a bottom-up approach by studying the interaction of each amino acid sidechain with silver(I) separately [19]. We therefore represented each amino acid as a sidechain fragment by removing the backbone and converting the C^β and H^β atoms into a methyl group (Figure 1); for example, ethylmethylsulfide was chosen as sidechain analog for methionine. For histidine, we converted the C^α and H^α atoms due to technical reasons (see ESI) and therefore used 4-ethylimidazole as a sidechain fragment. By applying the HFE parameter set of Merz [12], the binding constant was then determined for each fragment with the following procedure:

1. We performed MD-based Umbrella Sampling (US) simulations in explicit water to sample along the reaction coordinate of binding, i.e., the distance between silver(I) ions and the coordinated atom [20].

2. The Potential of Mean Force (PMF) was determined along the binding reaction coordinate through WHAM [21].

3. From the PMF, the binding constant log₁₀(K_bind,_calc) was calculated (and, consequently, the binding free energy ∆G_bind,calc) [22].

4. We then compared the calculated binding constant with the experimental one from the NIST database [23] or from measured values by potentiometric and spectrophotometric titrations (see ESI) and performed a calibration if necessary.

Our initial test calculations for HEFM were carried out with CHARMM’s modified TIP3P [24] (named cTIP3P hereafter) since it is the recommended water model for the CHARMM36m force field. The parameterizations of Merz and Won, however, were carried out with Jorgensen’s original TIP3P model (sTIP3P). To probe the influence of the two TIP3P solvation models, we calculated the PMFs and binding constants of the fragments for both water models.

2.3. Calibration of NBFIX Parameters

The main goal of this work was to derive NBFIX parameters for the CHARMM36m force field to better model the silver(I)–methionine and silver(I)–histidine interactions in particular. The modeling of histidine sidechains presented a unique challenge. Depending on the pH, the histidine sidechain could exchange between four different protonation states (Figure 2): one positively charged state with both N atoms of the imidazole ring protonated (named Hsp in CHARMM), two neutral tautomers with either the proton on the N^δ (Hsd) or on the N^ε (Hse), and one negatively charged state with no protons on the N atoms (imidazolate-like form). The latter is very rare in biological contexts (see PDB entry 7WAA for an example) as it requires very basic conditions (pK_a = 12–14) [25,26]. The Hse tautomer was observed by NMR experiments and in crystal structures of small silver(I)-binding peptides and analogs thereof [9,27,28]. In addition, quantum mechanical calculations showed that 4-methylimidazole (Hse tautomer) features a higher binding affinity than 5-methylimidazole (Hsd tautomer) [29]. Thus, in this work, we only parameterized the Hse tautomer (and thus 4-ethylimidazole as a sidechain representative molecule), where silver(I) binds to the nitrogen N^δ. Note, however, that under certain conditions, the silver(I) ion can bind to the N^ε nitrogen, for example, in SilF, where the histidine is buried inside the protein and the Hsd tautomer is stabilized through specific interactions [6]. The possibility of including the biologically relevant tautomers through constant-pH computer simulations is discussed in the Section 4.

As a starting point for our optimization, we selected the 12-6 LJ HFE parameters of Merz [12] and determined the initial NBFIX parameters for the interaction of silver(I) ions with three specific atom types of the CHARMM36m force field: NR2 (for the N^δ atom of histidine), S (for the sulfur atom of methionine) and CA (for the six aromatic atoms of phenylalanine). No NBFIX correction was necessary for the glutamic acid sidechain fragment. Then, a calibration procedure was performed to determine the optimal NBFIX parameters that were able to correctly reproduce the experimental binding constant and binding distance of the corresponding sidechain fragments. The procedure was the following:

1. Target equilibrium distances (d_eq,target, Table 2) between silver(I) and coordinated atoms of each fragment were taken either from the literature or determined by DFT calculations; target binding constants (log₁₀(K_bind,_exp), Table 2) corresponded to those of the experiments (see ESI and cited references in Table 2).

2. Using the procedure given in Section 2.2, the PMF and binding constant were calculated.

3. If the minimum of the PMF matched the target distance, we moved to the next step; otherwise, R^NBFIX was adjusted and step 2 was repeated.

4. If the calculated binding free energy was within a given error threshold of 0.5 kcal/mol, the NBFIX parameters were accepted; otherwise, ε^NBFIX was adjusted and steps 2–3 were repeated.

While the chosen procedure to adjust R^NBFIX (step 3) and ε^NBFIX (step 4) should not have changed the outcome of the fitting process, it could, however, impact the efficiency. As a general and solid recipe, we propose the following adjustment series:

(4)$\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}3:R_{i+1}^{NBFIX}=R_i^{NBFIX}+{\gamma }_d\left(d_{eq,target}-d_{eq,calc,i}\right)$

(5)${\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}4:\epsilon }_{i+1}^{NBFIX}={\epsilon }_i^{NBFIX}+{{\gamma }_{K}k}_{B}T\mathrm{l}\mathrm{n}\left({\displaystyle \frac{K_{bind,exp}}{K_{bind,calc,i}}}\right)$

where the index i indicates the iteration number, k_B is the Boltzmann constant and T is the temperature. The factors γ_d and γ_K determine the step size; we typically used values between 0.5 and 1.5. The convergence could be improved by employing other root-finding techniques such as the bisection method. Even more efficient optimization strategies could make use of free-energy methods by, for example, applying multi-state acceptance ratio estimators [30].

2.4. Validation on HXXM and MXXH Silver-Binding Motifs and LP1 Oligopeptide

The goal of this step was to check the efficacy of the NBFIX parameters when transferred to a larger system. The validation involved calculating two different properties:

• The binding constant of four silver-binding tetrapeptides (HEFM, MNEH, HAAM and MAAH);

• The α-helical content in a longer peptide, LP1 (sequence: AHQKMVESHQRMMG), which was observed to form an α-helical structure upon the addition of silver(I) ions [9].

In both cases, potential-scaled molecular dynamics was employed by scaling down ε to speed up the kinetics of the dissociation process (and adjusting R^NBFIX to have the same equilibrium distance). Hamiltonian reweighting was then used to retrieve the unbiased binding constant (ESI).

To evaluate the ability of silver(I) to favor the formation of α-helixes in LP1, three simulations were performed in parallel. In one, the LP1 peptide was simulated alone in solution, whereas, in the other two, it was simulated in the presence of one silver(I) ion and five silver(I) ions, respectively. After that, the α-helical content was monitored (see ESI) and compared for the three cases.

3. Results and Discussion

3.1. Testing of Existing Silver(I) Parameters on HEFM Tetrapeptide

The silver(I) binding constants obtained for the HEFM tetrapeptide prior to the calibration procedure are reported in Table 1. The values are given for different cases, combining box size (30 and 50 Å to verify potential size effects) and parameter sets (Won, HFE and IOD). In all cases, we noticed that the binding constants were lower than or equal to 10 (log₁₀(K_bind,calc) ≤ 1), indicating a drastic underestimation of the interaction strength between silver(I) ions and the HEFM peptide (experiment: log₁₀(K_bind,exp) = 6.6) [8]. This was not really surprising because those parameters were developed to model silver(I)–water interactions only, without any intended correction for interactions with organic solutes.

Table 1

Results for the initial MD simulations of the HEFM tetrapeptide. Three blocks of simulations of 100 ns each were performed for two box sizes and each parameter set. Values are given with standard error of the mean from block analysis.

Box Size (Å)	Number of Peptides	Number ofAg+ Ions	ParameterSet	Affinitylog10(Kbind,calc)
30	1	1	Won a	0.8 ± 0.1
			HFE b	1.0 ± 0.1
			IOD c	0.5 ±0.1
50	1	1	HFE b	0.8 ± 0.2
			IOD c	0.6 ± 0.1

^a Obtained from interpolation of hydration free energy maps [11]. ^b Optimized to reproduce the hydration free energy [12]. ^c Optimized to reproduce the metal ion–water oxygen distance [12].

3.2. Testing of Existing Parameters on Sidechain Fragments and Calibration of NBFIX Parameters

When the HFE parameters of Merz [12] were tested on the interaction of silver(I) with the sidechain fragments (Table 2, column “HFE”), we noted that the interaction strength was underestimated for all sidechain fragments except for propanoate. For the latter, the calculated binding constants were reasonably close to the experimental values (0.89 and 1.25 versus 0.73, respectively, for cTIP3P and sTIP3P); the same held for the equilibrium distance (see also ESI for the PMF profile).

Table 2

Optimized ε^NBFIX (kcal/mol) and R^NBFIX (Å) as well as pairwise correction coefficients k_ij and l_ij (see Equation (1)) for the interaction between silver (I) ions and specific atom types of the sidechain fragments. Results are reported for the two water models cTIP3P and sTIP3P. Calculated association constants for the corresponding sidechain fragments are reported together with the standard error of the mean from block analysis. Calculated and experimental target equilibrium distances d_eq,calc (corresponding to the minimum of the PMF profile) and d_eq,target are also reported.

CHARMM Atom Type(Sidechain Fragment)	Water Model	εNBFIX(kij)	RNBFIX(lij)	deq,calc a	deq,target b	HFE Parameters c log10(Kbind,calc)	NBFIX d log10(Kbind,calc)	Experimentlog10(Kbind,exp)
NR2(4-ethylimidazole)	cTIP3P	−4.7 (116)	2.25(0.71)	2.08	2.05–2.2 e	−1.50 ± 0.02	3.82 ± 0.02	3.75 f–3.85 g
	sTIP3P	−4.4 (109)	2.25(0.71)	2.11		−0.15 ± 0.01	3.86 ± 0.03
S(ethylmethylsulfide)	cTIP3P	−11.9 (196)	2.50(0.67)	2.55	2.3–2.5 h	−1.89 ± 0.02	3.70 ± 0.02	3.6 i–3.7 j
	sTIP3P	−11.85(195)	2.50(0.67)	2.54		−0.29 ± 0.01	3.71 ± 0.03
CA(toluene)	cTIP3P	−1.77(74)	2.65(0.79)	2.29 k	2.3 k,l	−2.43 ± 0.03	0.43 ± 0.06	0.44 m
	sTIP3P	−1.715(72)	2.65(0.79)	2.29 k		−2.42 ± 0.01	0.43± 0.03
N/A. n(propanoate)	cTIP3P	N/A n	N/A n	2.05(2.43) o	2.1–2.4 p	0.89 ± 0.03	0.89 ± 0.03	0.73 m,q
	sTIP3P	N/A n	N/A n	2.05(2.43) o		1.25 ± 0.02	1.25 ± 0.02

^a From the minimum of the PMF profile. ^b Target equilibrium distance (see text and references below). ^c Ref. [12]. ^d Ref. [12] with NBFIX corrections; this work. ^e Literature values [27,28].^f Measured for 4(5)-methylimidazole; this work (see ESI). ^g Measured for 4(5)-ethylimidazole; this work (see ESI). ^h Literature values [28,31]. ⁱ Measured for ethylmethylsulfide; this work (see ESI). ^j Measured for dimethylsulfide [32]. ^k Refers to the distance from the center of the aromatic ring. ^l From DFT calculations (see ESI). ^m NIST database [23]. ⁿ Not applicable because no NBFIX corrections were necessary (i.e., Lorentz–Berthelot rule applied). ^o The value in parenthesis refers to the distance between the silver(I) ion and the carboxyl C atom for which the PMF was actually calculated (see ESI). ^p Literature value [33]. ^q Measured for acetate.

The NBFIX parameters optimized to reproduce the experimental binding constant of the sidechains fragments are reported in Table 2, together with the calculated and experimental binding constants. The fragments 4-ethylimidazole and ethylmethylsulfide possessed the highest experimental binding constants of 3.85 and 3.6, respectively (in the logarithmic scale). This explained the high binding constants of the peptides containing such residues (log₁₀(K_bind,exp) = 5–6.7). In the CHARMM36m force field, the sulfur of methionine was basically charge-neutral (−0.09 e), which means that there was no electrostatic stabilization for the interaction with silver(I). Thus, a very strong NBFIX correction (high ε^NBFIX in absolute terms) needed to be applied to the sulfur atom of ethylmethylsulfide in order to correct its affinity. This result can be better appreciated by observing Figure 3, which contains the PMF profiles of three sidechain fragments before and after the calibration (in black and red lines, respectively). As a general observation, the HFE parameter set yielded less attractive PMFs. In particular, in the case of ethylmethylsulfide and toluene, the interaction passed from purely repulsive to attractive after the calibration procedure, which explains why the binding constant of the HEFM peptide was drastically underestimated during the preliminary evaluations.

3.3. Validation of Four Silver-Binding Tetrapeptides

To validate the fragment-optimized NBFIX parameters, we calculated the binding constants for the silver-binding tetrapeptides HEFM, MNEH, HAAM and MAAH (Table 3). Overall, the calculated binding constants were on the same order of magnitude as the experimental values. In terms of Gibb’s free energy, they were within 1 kcal/mol of the experimental reference values. Moreover, no significant difference was found when comparing cTIP3P and sTIP3P.

While the experiments measured subtle differences between these peptides in terms of affinity, the calculations predicted basically the same binding constant for all peptides. A potential reason for this leveling/flattening is the neglect of the protonation/tautomerism of histidine in the calculations above. Here, we would like to remind the reader that the calculated binding constants in Table 2 basically corresponded to microscopic binding constants for specific peptides where histidine can only exist in its tautomer Hse; Hse is the preferred silver(I)-binding tautomer for small peptides (see above). According to constant-pH simulations of the apo form, the MAAH peptide displayed a significantly decreased population of the preferred Hse tautomer (36%) with respect to HAAM (60%). Thus, there was a larger tautomeric penalty to overcome for MAAH than for HAAM; see the companion article for more details on this tautomeric correction [7]. As a result, the calculated binding constant with tautomeric correction, log₁₀(K_bind,corr), was 0.22 lower for MAAH (5.47) than for HAAM (5.69), in excellent agreement with the experiment (5.4 ± 0.1 and 5.7 ± 0.1 for MAAH and HAAM, respectively).

3.4. Application to Oligopeptide LP1

As a further validation of the parameters, we tested the ability to reproduce structural features of silver-bound peptides, i.e., the increase in the α-helical content of the 14-residue peptide LP1 in the presence of silver(I) ions [9]. Figure 4 reports the average α-helical content of the LP1 peptide (in percentage) as a function of simulation time; at the beginning of the simulation, the peptide was completely extended (linear backbone). A single silver(I) ion in the simulation box was sufficient to increase the α-helical content to about 17–18% within 5 μs in the case of Jorgensen’s water model (sTIP3P; Figure 4b). By contrast, in the absence of the ion, the α-helical content remained around 5–6%. With the CHARMM TIP3P water model, no such increase was seen for a single silver(I) ion. When the number of silver(I) ions was, however, augmented to five, the helical content increased too with respect to the simulation without silver(I) ions, in agreement with the experiment. It seems that the sTIP3P water model could more easily induce α-helical motifs, in agreement with previous observations [34].

Overall, the α-helical content was still relatively modest after 5 μs of MD. It should be noted that the folding of the peptide into a helix was a slow process, and our simulation time could not capture the full dynamics. A part of the problem was that the chosen simulation approach (with a scaled potential) slowed down the folding dynamics since the scaling favored the silver(I) dissociation.

4. Conclusions and Outlook

Our new force field parameters for silver(I) ions are capable of reproducing binding constants for tetrapeptides on the same order of magnitude as experimental values. Also, the increased α-helical content of LP1 in the presence of silver(I) was correctly detected with these new parameters. These results validate the applicability of the simple yet accurate LJ model, which can be tightly tuned by means of the NBFIX feature of the CHARMM force field family to selectively correct atom–atom non-bonded interactions, without affecting the rest of the force field. We anticipate that the methodology proposed in this work can be in principle applied to any metal ion, provided there are reference data for binding constants and distances and valid LJ potential to represent that ion.

We note, however, further improvements for the future simulations of silver(I) interactions with peptides and proteins:

• Histidine tautomerism: The explicit inclusion of the various protonation states of histidine (and in general all titrable amino acids, especially cysteine). In this work, we assumed that a single static protonation state (Hse) with a microscopic binding constant coincided with the experimental macroscopic binding constant of 4-ethylimidazole. A more realistic description would allow for a dynamic change of histidine protonation states by constant-pH simulations [35,36,37] where each state would bind silver(I) with a specific microscopic binding constant.

• Polarization: This effect is particularly pertinent to deal with the coordination of three or more amino acids to the same silver(I) center, as is observed in more complex systems such as silver-binding oligopeptides (e.g., LP1) or proteins (e.g., SilE). The NBFIX LJ potentials are fully additive and therefore may lead to an overestimation of the affinity. Polarization could be included in the context of a polarizable force field such as AMOEBA or CHARMM’s Drude force field [38,39]. Another potential limitation of 12-6 potential due to the lack of polarizability could affect the conformation transitions involving polar secondary structure elements (e.g., α-helices).

• Cationic dummy metal ion model: To account for particular coordination geometries, extension to a model with cationic dummy charges could be beneficial [40].

• Extension of the parameterization to other sidechain fragments (e.g., thiols/thiolates to represent cysteine) and the peptide backbone: The availability of experimental data is the limiting factor here. In this light, we would like to emphasize that a careful determination of the reference parameters (equilibrium distance and binding constant) is crucial for the parameterization procedure and can highly influence the sampling.

• Sampling: Finally, improvements may result through the use of enhanced sampling techniques such as Replica Exchange [41]. This could be crucial for an integrative approach that combines the affinity simulation of silver(I) with the constant-pH feature.

Author Contributions

Conceptualization, M.S.; Methodology, L.M., V.M. and M.S; Investigation, L.M., A.B., V.M. and M.P.; Writing—original draft, L.M., V.M. and M.S.; Writing—review and editing, L.M., K.M.F. and M.S.; Visualization, L.M. and V.M.; Supervision & Project administration & Funding acquisition, K.M.F. and M.S. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Electronic Supplementary Information (ESI) is available online at https://doi.org/10.1101/2024.11.28.625676. It contains experimental methods and computational details and the corresponding references [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75].

Acknowledgments

The authors would like to acknowledge the High Performance Computing Center of the Université de Strasbourg for providing technical assistance. A.B. and K.M.F. thank the University of Fribourg and the Fribourg Center for Nanomaterials (FriMat).

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations and Symbols

B1b	oligopeptide Ac-AHQKMVESHQRMMG-NH2
CA	CHARMM36m atom type for aromatic carbon of amino acids
CD	circular dichroism
CHARMM	Chemistry at Harvard Macromolecular Mechanics
cTIP3P	CHARMM’s TIP3P water model
D	product of the vacuum permittivity and the relative permittivity
∆Gbind,calc	calculated binding free energy
DFT	density functional theory
ε	Well depth of the Lennard-Jones potential
Eelec & ELJ	electrostatic and Lennard-Jones interaction energies
ENB J	non-bonded interaction energy
deq,calc & deq,target	calculated and target equilibrium distance
γd, γK	pairwise correction coefficients
Glu	glutamic acid
HAAM	tetrapeptide Ac-HisAlaAlaMet-NH2
HEFM	tetrapeptide Ac-HisGluPheMet-NH2
HFE	hydration free energy
His	histidine
Hsd	δN-tautomer of histidine
Hse	εN-tautomer of histidine
Hsp	protonated histidine
IOD	ion–oxygen distance
kB	Boltzmann constant
Kbind,calc and Kbind,exp	calculated and experimental binding constant
Kbind,corr	calculated binding constant with tautomeric correction
kij	binary interaction coefficient for ε
lij	binary interaction coefficient for Rmin
LJ	Lennard-Jones
LP1	see B1b
MAAH	tetrapeptide Ac-HisAlaAlaMet-NH2
MD	molecular dynamics
Met	methionine
MNEH	tetrapeptide Ac-MetAsnGluHis-NH2
NB	non-bonded
NBFIX	non-bonded fix
NMR	nuclear magnetic resonance
NR2	CHARMM36m atom type for non-protonated imidazole nitrogen of histidine
Phe	phenylalanine
PMF	potential of mean force
Q	product of partial charges of two interaction atoms
r	interatomic distance
Rmin	distance where the Lennard-Jones potential takes a minimum
S	CHARMM36m atom type for methionine sulfur
sTIP3P	Jorgensen’s TIP3P water model
T	temperature
TIP3P	transferable intermolecular potential with three points
US	umbrella sampling
WHAM	weighted histogram analysis method

Footnotes

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Figures and Tables

Figure 1. Sidechain fragments to represent histidine, methionine, phenylalanine and glutamic acid.

Figure 2. Protonation states of the histidine sidechain as defined in CHARMM force field family: Hsp (left, positive), Hse (center, neutral) and Hsd (right, neutral).

Figure 3. PMF profiles and structures of (a) 4-ethylimidazole, (b) ethylmethylsulfide and (c) toluene with HFE-only parameters (black line) and NBFIX parameters (red line) in cTIP3P (left) and sTIP3P (right) water models. PMF curves are plotted together with the standard error of the mean obtained from an average over four blocks (lighter colors—barely visible due to the small magnitude). For propanoate, the distance refers to the one from the carboxylic C atom. For toluene, the distance refers to the one from the center of the aromatic ring. Structures are reported for the cTIP3P water model.

Figure 4. Percentage of α-helical content of LP1 over time (µs) for simulations in cTIP3P (a) and sTIP3P (b) in the absence (apo, blue) and presence of 1 (red) or 5 (green) silver(I) ions.

Table 3

Calculated binding constants for the studied tetrapeptides (HEFM, MNEH, HAAM and MAAH) with the optimized NBFIX parameters. For each peptide, eight potential-scaled MD simulations of about 800 ns each were performed (see ESI for more details). The results are shown for both cTIP3P and sTIP3P. Calculated association constants are reported together with the standard error of the mean from block analysis.

PeptideSequence	WaterModel	HFE with NBFIXlog10(Kbind,calc)	Experimentlog10(Kbind,exp)
HEFM	cTIP3P	6.0 ± 0.1	6.6 ± 0.1
	sTIP3P	6.0 ± 0.2
MNEH	cTIP3P	5.8 ± 0.1	5.4 ± 0.1
	sTIP3P	5.8 ± 0.1
HAAM	cTIP3P	5.9 ± 0.1	5.7 ± 0.1
	sTIP3P	6.1 ± 0.1
MAAH	cTIP3P	5.9 ± 0.1	5.4 ± 0.1
	sTIP3P	5.9 ± 0.1

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